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RSA Cryptosystem Speed Security Enhancement (Hybrid and Parallel Domain Approach)
: Encryption involves every aspect of working with and learning about codes. Over the last 40 years, it has grown in prominence to become a prominent scholarly discipline. Because most interactions now take place online, people require secure means of transmitting sensitive information. Several modern cryptosystems rely on public keys as a crucial component of their architecture. The major purpose of this research is to improve the speed and security of the RSA algorithm. By employing Linear Congruential Generator (LCG) random standards for randomly generating a list of large primes; and by employing other selected algorithms, such as the Chinese Remainder Theorem (CRT) in decryption, exponent selection conditions, the Fast Exponentiation Algorithm for encryption, and finally, a comparison of the enhanced RSA versus the normal RSA algorithm that shows an improvement will be provided.
Introduction
With the use of cryptography, sensitive information may be concealed from prying eyes. The protection provided by urban touchable and physical devices against data access by unauthorized parties is insufficient. Therefore, specialists and developers need to build and extend safety mechanisms to protect data and prevent attacks from starting at such a crucial point. For this reason, "encryption" was borrowed from elsewhere; it is a crucial component of any adequate safety system and a prerequisite for any practical means of influencing or creating such a system. Skill is required to keep the secret from random people. The importance of data encryption over simple message transport is growing as our collective knowledge base expands. Cryptography is used to protect this information, and it may be broadly classified into two subfields: secret-key and public-key cryptography [1].
Today's cryptography relies significantly on the principles of mathematics and computer science. Due to the computational hardness assumptions used in their creation, cryptographic algorithms are very difficult for an adversary to crack in reality. It is conceivable in theory to crack such a system, but doing so in practice is currently impossible. Therefore, we call these methods "computationally and parallel domain approach, the study contribution increases the speed and security of the RSA algorithm.
Organization
This research study is based on the speed and security of the RSA cryptosystem algorithm in hybrid and parallel domain techniques. The paper is broken into sections. The introduction, problem statement, outcomes, and contributions are all included in Part 1. Section 2 addresses the technical background of cryptography; Section 3 examines the literature review, and Section 4 provides an indepth look at the RSA. Section 5 comprises all of the implemented methods and mathematical methodologies for the improved RSA algorithm. Section 6 contains the improved RSA algorithm. Section 7 delves deeper into the results and debate. Finally, Part 8 will summarize the research with recommendations for future work, and the appendix section provides all of the Python codes used for creating our modified RSA and results on GitHub [5].
Background
Cryptography ensures data integrity in information security, providing assurance that data has not been altered with hash algorithms. One other benefit of using digital signatures is that they may be used for non-repudiation or authentication of the parties involved [6], they are two types of cryptography.
Symmetric key cryptography
Symmetric cryptography Figure 1 shows the simplest type of encryption when both parties use the same secret key to encrypt and decrypt data. They are two distinct categories of symmetric key cryptography designated by the quantity of data they are able to process: block ciphers and stream ciphers. The block cipher organizes the input data into blocks or groups of consistent size (within a few bytes), facilitating efficient encryption and decryption, while the stream cipher converts the data format suitable for encryption and decryption. Examples of symmetric encryption algorithms include Blowfish, AES, RC4, DES, RC5, and RC6. One of the primary advantages of symmetric algorithms is their ability to be used in real-time systems, which asymmetric algorithms cannot because each user needs their own unique key.
Asymmetric key cryptography
The use of two distinct keys is at the heart of asymmetric cryptography, commonly known as public-key cryptography. When encrypting plain text with asymmetric encryption, two keys are used a public one that may be shared openly and a private one that shouldn't be revealed under any circumstances. Asymmetric cryptography provides not just the privacy that encryption does but also using digital signatures it is possible to acquire authentication, non-repudiation, and integrity. The context of a signed message is compared to the input used to generate the signature [7]. To counter the fact that anybody in possession of the secret key may read an encrypted communication, asymmetric encryption makes use of a pair of keys that are mathematically connected to one another RSA, DSA, and Diffie-Hellman are all examples of asymmetric algorithms. Using symmetric cryptography with a straightforward and safe key exchange system enabled by an asymmetric key method makes it possible to have a quick technique that generates compact cipher texts [8].
Related work
Many enhancements were made to the RSA algorithm by many researchers [4]. Some relevant studies are included below: For the hybrid domain, which is the improvement of Classical RSA and one or two additional algorithms. Rebalanced RSA and Multi-Prime RSA were proposed by Boneh and Shacham [9]. A strategy for integrating two previously improved RSA versions was developed by Alison et al. [10]. To increase the security levels and overall execution speed of the method, Gupta and Sharma [11] integrated RSA with the Diffie-Hellman public key cryptographic technique. Based on an additive homomorphic property, Dhakar et al. [12] introduced the MREA (Modified RSA Encryption Algorithm), and they demonstrated that it is far more secure than the regular RSA and extremely resistant to brute force attacks. The RSA and El-Gamal cryptosystems were joined by Ahmed et al. [13] using the Discrete Logarithm Problem (DLP) for El-Gamal and the Integer Factorization Problem (IFP) for RSA. For asymmetric cryptosystems, the pairing of IFP with DLP gave a reasonable processing speed. The El-Gamal and RSA algorithms were less effective than the indicated system computations as a result. In order to secure the upload of data to the cloud, Mahalle and Shahade [14] presented an RSA variation that makes use of the AES method and three keys (a public key, a private key, and a secret key). The authors' conclusion is that this AES-RSA hybrid will effectively give cloud users data security.
In order to make factorization more difficult overall, Arora and Pooja [15] proposed a novel algorithm in 2015. This algorithm uses a hybrid of RSA and the El-Gamal algorithm. AES + RSA and Twofish + RSA, a hybrid implementation of one symmetric algorithm with another asymmetric algorithm, were recently proposed by Jintcharadze and Iavich [16]. They came to the conclusion that RSA + Twofish outperforms the abovementioned hybrid algorithms in terms of speed and memory use. Alamsyah and others [17] to increase the security of two-factor authentication, combined RSA and the one-time pad approach.
For multi-threading or parallel techniques. C. W. Chiou [18] compares a fresh modular exponentiation technique to reduce the time it takes for modular exponentiation to execute in 1993. Because of fewer operations, this method offered a roughly 33% greater throughput. Ayub et al. [19] developed an OpenMP-based parallel CPU-based RSA method implementation that parallelizes the algorithm's exponentiation phase to aid in speedy encryption and decryption. Their analysis concludes that the program's execution time has been improved. Rahat et al. [20] improved efficiency by using a unique parallel data structure termed a Concurrent Indexed List of character blocks in 2019. The essay presented three different simultaneous RSA implementations. With a possible speed-up factor of 4.5.
For the CRT enhancements domain. Wu et al. [21] presented a CRT-RSA in 2001. Their proposal use Montgomery's algorithm rather than CRT, yielding better results for decryption and digital signatures. Blomer et al. [22] presented another CRT-RSA for using CRT to solve fault attack vulnerabilities on RSA-based signature algorithms. According to them, CRT-RSA is widely employed in smart card transactions. Sony et al. [23] proposed using multiple keys and CRT to improve data transmission security by increasing processing time and algorithm security. Quisquater and Couvreur [24] proposed a rapid decryption technique in 1982. Based on previously reported Standard RSA weaknesses, they developed an RSA deciphering method that employs an enhanced modular exponentiation methodology and is based on the CRT, with the goal of increasing overall performance time.
Finally, Aiswarya et al. [25] proposed a novel Binary RSA Encryption Algorithm (BREA) encryption method in 2017. Its security is further increased by converting the encrypted cipher text generated by the Modified RSA Encryption Algorithm (MREA) into binary code format. As a result, the intruder will struggle to decrypt the data. In the same year, Sahu et al. [26] presented a more secure approach than the original by making modulus n private as well.
RSA Algorithm
In 1977, Ron Rivest, Adi Shamir, and Leonard Adleman of the Massachusetts Institute of Technology revealed the public description of the Rivest Shamir Adleman (RSA) algorithm [27]. The system's safety comes from the difficulty of factoring the products of two large prime numbers. This difficulty is the foundation of the one-way RSA core function, which is straightforward to calculate in one direction but prohibitively so in the other. Consequently, RSA is secure since it is mathematically impossible to obtain such numbers or it would take too much time to do so, regardless of the available computing power. In addition, the encryption's safety is directly proportional to the size of the key. An algorithm's effectiveness increases exponentially when its size is doubled. Typical bit lengths for RSA keys are 2048 or 4096.
RSA isn't just used for encryption; it's also the basis for digital signatures, in which only the owner of a private key may "sign" a message, but anybody can check its authenticity using the public key. Several protocols, including SSH, OpenPGP, S/MIME, and SSL/TLS, rely on RSA signature verification [28]. Many firms utilize RSA for personnel verification. Cryptographic techniques are used in chip-based smart cards to ensure security by verifying the PIN code [29]. Pretty Good Privacy (PGP), a freeware that provides encryption and authentication for e-mail and file storage applications, also uses RSA for key transfer.
Furthermore, SSL provides data security by establishing an RSA key exchange during the SSL handshake client-server authentication at the end of the connection between the internet-based communications protocol TCP/IP and application protocols such as HTTP, Telnet, Network News Transfer Protocol (NNTP), or File Transfer Protocol (FTP). The determinism of the original RSA encryption means that the same plain text will always yield the same cipher text when using the same key pair. Due to this feature, the technique is susceptible to a "selected clear text attack," in which an attacker generates cipher texts randomly from a pool of known clear texts and checks whether or not they are equal to previously generated cipher texts. An adversary can learn about the original data without having to decrypt it by making this comparison [3].
Structure of Classical RSA algorithm
Generate Large Prime numbers p and q. Calculate modulus N = P · Q.
Implementation of Algorithms
We used many theories and algorithm techniques to improve the total performance of the RSA cryptosystem using our modified RSA algorithm from prime number creation through key generation, encryption, and decryption. All of the approaches applied for the enhancement are listed here.
Linear Congruential Generator
Pseudo-Random Numbers are created deterministically (meaning that they can be replicated) and must look independent, with no visible patterns in the numbers. We utilized this approach to quickly construct a big list of odd integers for a subsequent primality test. The algorithm function's Python code is on my Github [5].
Where Xn is the random integers generated, P1 is the multiplier, P2 is the increment, and m is the modulus, X0 is the initial seed value of the series. As in [29] Linear congruential generator of Equation (1) has a full period (cycle length of m) if and only if the equation meets the following conditions: gcd(P2, m) = 1; P1 ≡ 1( mod p)); P1 ≡ 1( mod 4); With m = 2 k , P1 = 4b + 1, P2 as an odd number where (b, k > 0) we will get a full period of length m, for our RSA prime generation approach: The modulus m should be a known nearest prime from 2 (n+1) , n being the n-bits key, this value is fixed (constant) in our approach.
Miller Rabin Prime Primality testing
The Miller-Rabin primality test [31] is a probabilistic primality test that determines if a particular number is likely to be prime, which is known to be the simplest and quickest test known; this test employs Fermat's Little Theorem [2]. We need to generate two huge prime numbers during the RSA key generation process, and after that, we need to ensure that they are indeed prime. Let us verify "n" primality ⇐⇒ n is an odd number.
Algorithm 1: Miller-Rabin primality test
Find integer k and m such that: n − 1 = 2 k · m Choose randomly any integer a ε [1, n − 1] Compute b0 = a m mod n Compute bi,"k" times, bi = −1 2 mod n The result must be ±1: If the solution is 1, n is a composite number and if the solution is -1, n is a prime number. Repeat the test "i" times. The probability of a composite n passing "i" tests is 1/4i; for our implementation the probability is 2 −128 . GitHub repository [5] has a Python code of this algorithm.
Extended Euclidean algorithm
Euclid's algorithm if gcd (a, b) = d, then there exist integers x, y such that ax + by = d. The first step in the Euclidean method is to divide the bigger integer, a, by the smaller number, b, to get the quotient, q1, and the remainder, r1(less than b), a = q1b + r1 Next, we'll use b and r1 to go on in the same manner, eventually arriving at the value: b = q2r1 + r2 rn−2 = qnrn−1 + rn Finding the largest common divisor is complete after we have achieved rn|rn−1. This is shown by the evidence below: After solving for rn −2 = qnrn−1 + rn, in the previous step, we arrive at the following equation: rn −2 = qnrn − 1 + rn Now, suppose d is the gcd of a and b. So we get <d|a and d|b>. Hence, we get rn as the Greatest Common Divisor (gcd) of a and b.
Fermat's Little Theorem
Fermat's Little Theorem Let a ∈ N and p be a prime number, then: a p ≡ a mod p (6) a p−1 ≡ 1 mod p (7)
CRT Chinese Remainder Theorem
A system of two or more linear congruencies does not necessarily have a solution, even though each of the individual congruencies does [33]. The Chinese Remainder Theorem CRT describes the solutions for a system of simultaneous linear congruencies.
x ≡ a mod m and x ≡ b mod n have a unique solution if the modules are relatively prime to each other, two to two. Where gcd (m, n) = 1.
Fast Exponentiation Algorithm
The speed with which we can calculate M e (mod N) for integer n of this magnitude is a significant aspect of public-key cryptography. The integers used in modern RSA keys are at least 1024 bits long.
The traditional method for raising to a power, say x 8 is as follows: x ⃗⃗⃗⃗⃗⃗⃗⃗ x 2 ⃗⃗⃗⃗⃗⃗⃗⃗⃗ x 3 ⃗⃗⃗⃗⃗⃗⃗⃗⃗ x 4 ⃗⃗⃗⃗⃗⃗⃗⃗⃗ x 5 ⃗⃗⃗⃗⃗⃗⃗⃗⃗ x 6 ⃗⃗⃗⃗⃗⃗⃗⃗⃗ x 7 ⃗⃗⃗⃗⃗⃗⃗⃗⃗ x 8 Where Sqr means squaring and Mul means multiplying. We squared first, followed by six successive multiplications, a total of seven operations. In RSA, we would have to execute 21024 multiplications for a power of 1024 bits, which is not at all convenient. The square and multiply algorithm is the fastest way to perform this exponentiation.
Consider the same example shown above to calculate x 8 using square and multiply algorithm: x ⃗⃗⃗⃗⃗⃗⃗⃗ x 2 ⃗⃗⃗⃗⃗⃗⃗⃗ x 4 ⃗⃗⃗⃗⃗⃗⃗⃗ x 8 We only need 3 squaring operations, note that the square and multiplication operation has the same time complexity.
To know the number of squaring and multiplying operations required we convert the exponent to its binary equivalent, where we have "1" we square and multiply in that order, and where we have "0" we apply square operation only, This method is called the Fast exponentiation algorithm [34]. See Algorithm [3].
Recommendations to select the value "e"
We recommended using a very small public key value "e" less than√Φ (n). Therefore the trap Φ(n) = (p − 1)(q − 1), p and q being primes of at least 1024 bits, and the size of Φ(n) will be approximately equal to that of n, a little smaller but with the same magnitude(number of bits). Since the public key "e" and the private key "d" are inverses in the field Φ (n), that is, d = inv [e, Φ (n)] then we get the following relation e· d (mod Φ (n)) = 1, for this equality to hold, the product "e· d" must leave the field Φ (n) at least once so that the operation in that module returns the value 1. In other words, it will be true that e· d = k· Φ (n) + 1, with k = 1, 2, 3, 4...
For this product to come out at least once from the body Φ (n), that is with k = 1, given that the public key "e" has for example 17 bits, the value of the private key d should be at least greater than 1007 bits, for the hypothetical case (and with almost null probability) that the equation is fulfilled for k = 1. In practice, that value of k = 1 or a low value of k, will be very unlikely and, therefore, we can expect a private key "d" very close to or equal in bits to the value of n as it happens in the practice. In other words, it will be computationally difficult to guess the value of the private key d, since finding a number within a 1024-bit body means an intractable computation time, with an average of 21023 attempts [35]. Forcing then the public key e to being a small value, less than 20 bits within a body of 1024 bits or greater guarantees that the private key d is a very large value and, therefore very secure since it is computationally intractable to find it by brute force.
In our model, we will choose value "e" from Fermat's numbers less than√Φ (n), and since all Fermat's numbers are prime numbers we won't necessarily need to check if gcd(e, ϕ(n)) = 1 which saves time. This relatively small value of "e" forces the private key "d" to have a size similar to the modulus n and makes a brute force attack impractical. For example the value 65537 a known prime number as Fermat number (F4) was used to create the SSL certificates See Figure 3.
[Fermat's prime] Fn = 2 2 In addition to the advantages mentioned, Fermat primes such as F4 have a significant feature that is worth highlighting. The binary representation of F4 has only two one bits equal to 65, 53710 = 100000000000000012 = 01000116. This fact has great utility in exponentiation computational efficiency.
Paired private and public keys
When an RSA key is generated, Euler's thotient function Φ (N) is used as a trap to calculate the private key "d" knowing the public key "e". Since (e, Φ(N)) = 1, it is guaranteed that the inverse "d" exists and that it is the only inverse of "e" in that field Φ(N). The encryption is done afterward in the public body N so that anyone can use it. And in said body N it is no longer satisfied that the only inverse of the public key "e" is the private key "d". There is at least one other value other than a "d" that allows deciphering what is encrypted with the public key.
These keys are called paired private keys. It has been said that an asymmetric cipher system has a single public key, and therefore also a single private key. For the RSA cryptosystem, this has turned out to be false. An example will better illustrate this. That is, for the ciphered body N = 2109 with public key e = 13, the numbers 349, 853, and 1357 are paired private keys d0 that fulfill my function more than the private key d. Every RSA key will have at least one matching private key. The number of even private keys depends strongly on the primes P and Q.
Unencryptable messages
One of the security vulnerabilities are non-recommended keys that either do not encrypt the information to protect or do so in a predictable way. For example, in the symmetric algorithm DES (Data Encryption Standard), there were weak or semi-weak keys, which did not satisfy the singledigit principle enunciated by Shannon; and gave solutions known as false solutions. Something similar happens in RSA, where there are unencryptable messages, or rather, unencryptable numbers.
0 key mod N = 0 and 1 key mod N = 1 (10) Another value that is transmitted in the clear is (n -1), since: Example: Consider the RSA key with n = 17 · 29 = 493 and e = 11, we have: In addition to these three numbers, in RSA there will always be another 6 numbers that are not encrypted.on our example: To locate these unencryptable numbers requires a brute force encryption attack on the space of the primes p and q, to verify the values of X that yield the following inequalities: X e (mod P) = X and X e (mod Q) = X for 1 < X < Q -1, P-1 Keys of 1024 bits or more make calculations within the primes p and q computationally intractable if each has at least 512 bits. Therefore, for those keys, it will not be possible to find the remaining unencryptable numbers. The equations to calculate the unencryptable numbers are shown below: The number of unencryptable numbers σn within a field n is: The unencryptable numbers will be: N = [q· (inv (q, p)) · Np + p· (inv (p, q)) · Nq] mod n (13) Where: Np are the solutions of N e mod p = N and Nq are the solutions of N e mod q = N As can be seen, the only complicated calculation that occurs is in the last two equations, which means attacking by brute force all values of N candidates to be non-cipherable numbers, with 1 < N < (P − 1) for prime P and 1 < N < (Q − 1) for prime Q
Optimised RSA algorithm
For our modified RSA, we drew the following conclusions concerning the sizes of the operands: Carefully select the prime numbers p and q such that factoring them would be computationally unfeasible. As a rule of thumb, the bit lengths of these primes should be roughly comparable. For example, if the number n is 1024 bits in length, then the appropriate sizes for p and q are approximately 512 bits.
The exponent is typically small in order to maximize the power of the exponentiation.
RSA Modified
Generate Large Prime numbers p and q generate truly unpredictable random numbers list using LCG Section 5.1, then tests for primality we used Rabin-Miller probabilistic test Section 5.2.
Calculate modulus N = P · Q Calculate X to replace N. X = N − (P + Q) The key length, which is commonly stated in bits, determines its size. We recommended the Karatsuba algorithm Section 5.3 for N computation. The Karatsuba approach begins to pay off as ndigits increase, as it can multiply hundreds of digits quicker than the standard technique.
Calculate Euler's totient function, which is defined as: Φ(N) = X + 1 Reduced multiplication of (P-1) ( Decryption Plain-Text message M = C d (mod N) We proposed to use CRT Section 5.6 and Fermat's Little Theorem 5.6 for fast computation and monitoring security.
RSA Modified Example
We begin by walking over on how to generate RSA encryption and decryption keys. After that, we'll go through a basic example to see how encryption and decryption work in practice.
Two prime numbers "P" and "Q" are chosen. At present, such numbers must be of the order of 1024 bits, at least. For our example, Let us use a 16-bits prime for illustration n_digits = 16 log 2 = 5 Using Equation (5) A fermat's value of "e < 39733" is chosen. We will take Fermat number three. e = F3 = 2 2 3 + 1 = 257 < 39733 , since all Fermat's numbers are primes therefore gcd (257, 1578717360) = 1. Calculate d, the multiplicative inverse of module n. Since gcd (e, Φ(n)) = 1, we will apply Extended Euclidian algorithm [1] to express 1 as a linear combination of integer u and v such that: Equation [14] into [15] we Step 1: First compute the binary representation of the exponent "257". 25710 = 1000000012 Step 2: Read the binary representation of the exponent from left to right. 1000000012 = b0b1b2b3b4b5b6b7b8 Step 3: For every subsequent bi = 1 apply square and multiplication while every subsequent bi = 0 we apply the square operation only.
This completes the encryption process See Compute: (6851 · 67699 · 9075) + (55757 · 23321 · 41355) = 57983316650610 mod (23321 · 67699) = 123456 Plain-text message M = 123456 as expected. We also want to look into the temporal complexity of each method. In this situation, we're interested in the algorithm's efficiency, or how long it takes the function to generate at least two prime integers. As shown in Table 2, traditional prime generation always yields a single prime number by randomly selecting an odd number and testing for primality, however, our suggested LCG prime generation method yields a list of primes in a short time. Figure 4 illustrates a graph.
Key Generation
Consider n as the number of bits of P or Q both prime and N as the product of P and Q.
Modulus computation
The time complexity to compute the modulus N product of two big primes P and Q of the same bit size is ( 2 ) 2 using big O-natation that is O (n 2 ). By using the Karatsuba algorithm Section [5.3] the time complexity goes down to O (n 2 3 ) approximately O (n 1.58 ).
Thotient computation
The time complexity to compute Φ (N) product of two large integers (P − 1) and (Q − 1) of the same bit size is ( 2 ) 2 using big O-natation that is O (n 2 ), by substituting X = N − (P + Q), Φ (N) = X + 1 the time complexity goes down to O (n)
Making the exponent smaller vs Classical RSA
In making an algorithm faster, we can actually use a small exponent and still RSA will be secure, In Table 3 changing the public key exponent e to the binary representation we can tell the number of operations that are required for the square multiply algorithm using exponentiation, fast encryption is possible using this small exponent and RSA is still secure for short. The public exponent "e" can be smaller in this case, but "d" must be as big as "N" now, thus we applied the Chinese remainder theorem (CRT) to accelerate decryption. This technique lowers n_bits modular exponentiation into two n/2_bits modular exponentiations plus the CRT steps described above, while P −1 can be precomputed and saved. The Chinese remainder theorem, according to Table 4, is substantially faster at the expense of system parameters and memory, and it does not require any modular inversion implementation, saving development costs and memory. As illustrated in Figure 6, 7 and 8 both the CRT and decreasing the exponent need less processing time than the standard RSA. Because it adds randomness to the cryptography method, RSA's improved performance increases speed and security.
Comparison of Total Time Complexity
The time complexity study of the enhanced RSA method and the traditional RSA algorithm will now be described using big O notation. For time complexity operations, we have the following features, as described by [36] and [37]: Sum (x + y), the sum of two n-bit values has a time complexity of O (n). Subtraction (x -y), is an addition of a negative integer, its asymptotic time complexity is O (n).
Multiplication (x * y), the product of two n-bit values, has a time complexity of O (n 2 ). Division (x / y), is a multiplication of an inverted integer, its asymptotic time complexity is O (n 2 ). Module (A mod N), given an n-bit A, the algorithm's time complexity is O (n 2 ). Exponentiation in modules (A B mod N) has a time complexity of O (n 3 ). The Extended Euclid's Algorithm, Using the gcd (a, b) = gcd (b, a mod b) rule, Euclid's method computes the gcd of two integers a and b and yields the last value of "a" as gcd when b is zero. To examine the Extended Euclid's algorithm, assume a and b of n-bits, and a mod b < a/2 at each iteration. As a result, the algorithm will only make n recursive calls (since each division decreases one bit of n). In addition, a division of complexity O (n 2 ) is done at every recursive step to extract the new argument b for the following iteration. When we add up the whole time, we obtain. O (n) · O (n 2 ) = O (n 3 ) Multiplicative Inverse, Time complexity is O (n 3 ) due to the usage of the Extended Euclid method. Primality Test, the N key is n bits long, while the prime integer p is (n/2) bits long. In practice, the primality test is performed using the probabilistic Miller-Rabin test, Algorithm [5.2]. The most expensive operation in the Miller-Rabbin technique, given a number p of n bits, is modular exponentiation, which has an O (n 3 ) complexity. Furthermore, to ensure a high level of confidence, this test is repeated about ln (p) / 2 [38], resulting in a complexity of O(n). As a result, the final complexity is O (n 3 ) · O (n) = O (n 4 ) We can examine the overall RSA performance in contrast to the suggested RSA from all of the above time complexity properties, as presented in Table 5.
Conclusion
This study proved helpful with a combination of the Chinese Remainder Theorem (CRT) algorithm, Fast exponentiation Algorithm, small exponent, and Linear Congruential Generator (LCG) that has been proposed with the normal RSA algorithm for fast and secure communication for large data. We applied the proposed theorems, multiplication algorithms, and randomness techniques to redesign the execution of the RSA cryptosystem that improves speed on the RSA encryption side while the security of data was maintained and upgraded with the CRT on the decryption side. This research objective includes a detailed overview of the most successful classical cryptographic Technique RSA. The study proposed an RSA with the Chinese Remainder Theorem using a small value of the exponent, which helped enhance the cryptographic algorithm. Another contribution is the discussion on different multiplication algorithms and their pseudo-codes. Future work will discuss the practical implementation of the modified RSA algorithm's security attacks and threats. But unless we encounter a situation that puts our data in danger, we will continue to use what we have. | 7,453.6 | 2023-01-01T00:00:00.000 | [
"Computer Science"
] |
USE OF GREENDRONE UAS SYSTEM FOR MAIZE CROP MONITORING
This research work presents the use of a low-cost Unmanned Aerial System (UAS) – GreenDrone for the monitoring of Maize crop. GreenDrone consist of a long endurance fixed wing air-frame equipped with a modified Canon camera for the calculation of Normalized Difference Vegetation Index (NDVI) and FLIR thermal camera for Water Stress Index (WSI) calculations. Several flights were conducted over the study site in order to acquire data during different phases of the crop growth. By the calculation of NDVI and NGB images we were able to identify areas with potential low yield, spatial variability in the plant counts, and irregularities in nitrogen application and water application related issues. Furthermore, some parameters which are important for the acquisition of good aerial images in order to create quality Orthomosaic image are also discussed.
INTRODUCTION
The use of UAS for civilian applications such as precision agriculture and forestry as remote sensing device is increasing owing to the availability of low-cost sensors and system (Nebiker, S. et al. 2000;S. A. Aziz, et al.2004).ResearchMoz, in a Jan 2014 report, projected that the agricultural robot market size to grow from $817 million in 2013 to $16.3 billion by 2020.The use of farm inputs, particularly of fertilizers, is inadequate and the fertilizer delivery methods are very inefficient.With the increasing cost of agriculture inputs, it is essential for sustainable farming that the agriculture inputs should be efficiently used to increase the crop production.
The qualitative and quantitative report of site-specific farm soil and crop help the farmer to make best use of fertilizers, pesticides and water.Variable rate application based on site-specific field information is the key to reduce input cost and to increase yield.The farm management zones, ground gradient, relative biomass, high resolution color and health map are some of the site-specific field information required by the farmer to control and properly apply the agriculture inputs.
A "management zone" is a sub-region of a field that expresses a relatively homogeneous combination of yield limiting factors for which a single rate of a specific crop input is appropriate.The ground gradient provides information regarding field irrigation plan and ground laser levelling.The high-resolution crop vigor helps to precisely identify unhealthy areas without manual field scouting.Unmanned Aerial Vehicle (UAV) equipped with a Multi-spectral cameras (Khanna R. et al., 2015;D. Anthony et al., 2014) assist in achieving this goal in minimum amount of time and provides much more detailed information about the farm as compared traditional scouting technique.The advantages of using such system are low temporal resolution, independence from weather conditions such as cloud covers and very high resolution maps for site specific advice.
Fertilizers are not cheap and therefore, it is essential that they should be efficiently and effectively used to produce maximum increase in crop yields so that farmers receive the best possible outputs from their expenses.However, the increased in the usage of fertilizer is not delivering optimum yield because of not using standardized practices.The fertilizer consumption (Kg/ha of arable land) for US is 131.9 while for Pakistan is 135.25 (World Bank, 2016).On the contrary US is having three times more cereal production using almost similar amount of fertilizer per hectare.There are several problems which are impeding the balance and efficient use of fertilizers (Juliane et. al., 2015).These are commonly not providing fertilizers at the right time at the right place in the field, improper application methods and time and lack of knowledge among farmers about the need for balanced fertilizer applications (Agüera, F. et al., 2011).It is not a static but a dynamic concept.An Optimum fertilization strategy is the only way to ensure a sustainable agriculture that can provide the world population with high quality food while minimizing the impact on the environment.The scarcity of water and increasing prices of agricultural inputs needs proper study of crops especially for under developing countries such as Pakistan.We monitored winter maize crop using a UAS in order to improve crop production, which is the main source of fodder for dairy farms.
STUDY AREA AND DATA COLLECTION
The study was conducted at Sar-Sabz Nestle-Pakistan Farms Renla-Khurd, Pakistan (30.9167 N,74.7165 E) where the ground elevation varies from 180m to 190m as shown in the figure 1.
Hardware
The aerial survey is conducted using a custom long endurance fixed wing platform developed at LUMS.The system was developed to overcome the limitation to survey large areas using low-cost systems.The use of fixed wing topology is mainly for the long endurance and to decrease vibration, without the use of motorized gimbal, which is an essential consideration for large area mapping mission.The UAV is equipped with a custom modified NDVI camera in order to create a dense 3D point cloud map.The complete system consist of a fixed wing UAV with onboard electronics and NDVI camera, a pilot RC transmitter and a ground control station as shown in figure 5.The ground control station consist of a mission planner software along with a telemetery module for real-time flight management.The wingspan of the UAV is 1.72m and the length of the UAV is 1.18m.The weight of the fully assembled system is 3Kg and the payload capacity is about 1Kg.The maximum cruise speed of the plane is 90 kph and has a flight endurance of 60-90 minutes.
Figure 5. Ground Control Station and GreenDrone UAV
The UAV is equipped with a modified 12.1 mega pixel canon SX260HS camera for image acquisition.The internal IR filter is replaced with a custom NGB (Near-Infrared, Green, Blue) bandpass filter glass to block red light and instead record near-infrared light above 700nm wavelength.Furthermore, the camera is installed with Canon Hacker's Development Kit (CHDK) to automatically capture images every second.The camera has an internal GPS which records the geographic coordinate of the area along with each image.A special UAV camera mounting is designed and fabricated using a 3D printer in order to reduce camera vibration.
The flight height, camera shutter speed and focus do have an effect on results of 3D point cloud generation.During a test flight the images were analysed and it was found out that the image time-stamp was varying between 3-10 second.It was further investigated and found to be caused by the autofocus setting of the camera.During the second test flight autofocus was disabled and the focus was manually set to infinity.This resulted into blurred images but the software was able to stitch the images together.The blur effect was investigated and found to be caused by the auto shutter time.In the third test flight, the shutter time was also fixed to 1/2000 second.
Photogrammetry
It is a science of making measurements from images.Photogrammetry process involves pre-processing of input images followed by the ortho-rectification of the images.Now a days, because of the availability of cheap computational power, many free and commercial software are available which have automated the photogrammetric process.The images acquired during aerial survey have a resolution of 4000x3000 pixels while the camera's CMOS sensor has a width of 6.17mm and height of 4.55mm.The images were captured in camera's nadir position.The image data were later processed independently using two different software namely visualSfM (Wu, C., 2011) and Pix4D (Christoph S, 2017).The visualSfM is a GUI based free tool that automate the SfM (Structure from Motion) process on input images on a multicore system with GPU installed.It is developed by university of Washington and Google Inc.The software uses bundle adjustment with Levenberg-Marquardt algorithm (K.Levenberg, 1944) to determine camera's intrinsic and extrinsic parameters.Pix4D is a commercial tool which is able to make 3D models from input images.The software detects salient features in input images followed by feature matching and thereafter constructing 3D dense point cloud from matched features along with camera poses.Furthermore, the software can generate an ortho-rectified mosaic from the input images.The ortho-rectified image has a Ground Sample Distance (GSD) which is dependent on the UAV flight height.
A quick comparison has revealed that Pix4D creates a denser point cloud compared to VisualSfM.Both of the software are run on an Intel Core i5, 3.3 Ghz, Quad-core PC with 16GB RAM installed and SSD hard disk.
RESULTS
The following table presents the results of flights and post processing details on the acquired imagery.To achieve a higher GSD, the flights must be conducted at a low altitude but this reduces the coverage area and increases the number of images and flight duration.Furthermore, due to smaller field of view, at lower altitude, crop canopy appears to be flat and similar which generated some voids and at some areas misaligned point cloud.These artifacts were manually removed by removing some low quality images.A view of the generated 3D point cloud is shown in the figure below.Out of 17 zones, zone five has the highest relative NDVI index (100%), whereas zone 14 has relatively lowest NDVI index (69.9%).The crop health is represented as a percentage with respect to the most vigorous zone.This relative health map can help the farm management to investigate the problem in low vigour areas by manual analysis using field scouting.Furthermore, by the help of resultant imagery, we have identified the following problems at the study site.
Water-Logging
Zone 2, 13 and 14 in figure 8(c) were identified as weak zones and the information was provided to the farm management team.It was identified that the low crop vigor in these zones were due to rain water logging a few days before the flight was conducted.This also highlighted the fact that the water logging was due to uneven ground level in these zones, therefore, laser land-levelling is required before the next crop cycle.Due to rain water logging some plants were damaged which resulted relatively smaller plant density.The lesser number of plants were observed in the logged region which are highlighted in figure 9.This caused a significant decrease in the yield of zone 2.
Improper ground levelling
Along with water logging, we also observed on the un-cultivated parts of the study-site that the farm needs laser levelling as there was no proper water levelling.Due to not having proper water levelling, some parts did get more water whereas some parts of field remained dry as depicted in figure 10.
Figure 10.Land level problem sites
Non-Uniform Sowing
The maize seeds were sown manually by the farm labor.The areas with non-uniform plant density were also clearly identifiable from the ortho-rectified mosaic image, as shown in the figure 11, which indicates that an aerial survey a few days after sowing is necessary so that plant density can be made uniform by seeding more plants.
Non-uniform application of Nitrogen
The fertilizers were supplied to soil by mixing in water.However, due to flood irrigation there was irregular supply of Nitrogen in the field, as shown in figure 11.The areas nears water inlet showed more nitrogen concentration which implies that nitrogen is not uniformly distributed throughout the field.
DISCUSSION
During the previous winter cycle of the maize crop, the average yield was reported to be 15 ton/acre while the average yield for the studied cycle was reported to be 14 ton/acre.Thus, we attribute the decline in yield due to improper supply of water, fertilizers, improper land levelling, flood irrigation and three crop cycles in a year which decreases soil nutrients.This has also demonstrated the effectiveness for the use of GreenDrone UAS system for better crop management and production.
To validate the accuracy of calculated NDVI images, we have compared the NDVI of our collected data on November 12 th 2016, with the calculated NDVI image of Sentinel-2A Satellite of November 14 th 2016.By qualitative analysis we find them quite similar as shown in the figure 13, though there is noticeable difference in pixel resolution i.e. 3 cm/pixel in UAV data and 10 m/pixel in the satellite data.
In the future, we aim to work on yield estimation from the 3D point cloud and soil analysis and weed detection (Peña et. al., 2013) using GreenDrone.
Figure 2 .
Figure 2. NDVI Orthomosaic of the study-site overlaid on the satellite map The study site is surveyed five times during the winter season, each time at different heights in order to access the quality of orthomosaic image.The first flight was conducted on 12 th November, 2016, at a height of 100m above ground level at 1400 hours.Two weeks after the first flight, on 26 th November, 2016, two more flights were conducted at the height of 100m and 50m at 1330 and 1430 hours, respectively.Four weeks after the second flights, two more flights were conducted at the height of 80m and 60m at 1245 and 1345 hours, respectively.During each flight the UAV cruise speed was set to 10 m/sec.The flight was planned in such a way that there is 80 percentage lateral image overlap.During each flight the UAV took-off autonomously after being thrown in the air, as shown in the figure 3, and followed a series of way-points, as shown in figure 4.
Figure 3 .
Figure 3. Automatic take-off of the GreenDrone UAV The UAV has flown along the planned waypoints taking images at locations scheduled by the mission planner software.Different flight paths were planned which took from 30 minutes to 60 minutes during each flight.
Figure 4 .
Figure 4. Planned and logged trajectory of a flight
Figure 6 .
Figure 6.3D point cloud of the test site
Figure 9 .
Figure 9. Low plants count problem due to water logging
Figure 11 .
Figure 11.Non-Uniform sowing pattern by labor
Figure 12 .
Figure 12.Nitrogen Concentration problem due to flood irrigation
Figure 13 .
Figure 13.NDVI Image comparison (a) UAS image (b) Satellite (Sentinel-2A) image There were five flights conducted during three different days.Flight images were post processed using Pix4D software to create orthomosaic images and 3D point clouds.The software offers different settings (Low, Medium, and High) for images alignment, feature matching, dense point cloud creation, digital surface model and orthomosaic creation.Each flight data was processed using different photogrammetric settings of the software.For each flight data different settings were tested and the optimum settings which resulted in the correct alignment of images are used to create the orthomosaic image.The different settings are presented in table 1. | 3,270.4 | 2017-08-24T00:00:00.000 | [
"Agricultural and Food Sciences",
"Engineering",
"Environmental Science"
] |
Metabolomic Alteration of Oral Keratinocytes and Fibroblasts in Hypoxia
The oxygen concentration in normal human tissue under physiologic conditions is lower than the atmospheric oxygen concentration. The more hypoxic condition has been observed in the cells with wound healing and cancer. Somatic stem cells reside in a hypoxic microenvironment in vivo and prefer hypoxic culture conditions in vitro. Oral mucosa contains tissue-specific stem cells, which is an excellent tissue source for regenerative medicine. For clinical usage, maintaining the stem cell in cultured cells is important. We previously reported that hypoxic culture conditions maintained primary oral keratinocytes in an undifferentiated and quiescent state and enhanced their clonogenicity. However, the metabolic mechanism of these cells is unclear. Stem cell biological and pathological findings have shown that metabolic reprogramming is important in hypoxic culture conditions, but there has been no report on oral mucosal keratinocytes and fibroblasts. Herein, we conducted metabolomic analyses of oral mucosal keratinocytes and fibroblasts under hypoxic conditions. Hypoxic oral keratinocytes and fibroblasts showed a drastic change of metabolite concentrations in urea cycle metabolites and polyamine pathways. The changes of metabolic profiles in glycolysis and the pentose phosphate pathway under hypoxic conditions in the oral keratinocytes were consistent with those of other somatic stem cells. The metabolic profiles in oral fibroblasts showed only little changes in any pathway under hypoxia except for a significant increase in the antioxidant 2-oxoglutaric acid. This report firstly provides the holistic changes of various metabolic pathways of hypoxic cultured oral keratinocytes and fibroblasts.
Introduction
Oxygen plays an important role in energy metabolism and signal transduction in maintaining the homeostasis of the microenvironment of the living body. The response of cultured cells to oxygen concentration has attracted attention as a physiological factor. The partial pressure of oxygen (pO 2 ) varies throughout the body ranging from 9% pO 2 in the lungs to 0.1% pO 2 in the peripheral tissues, depending on blood flow. Mohyeldin et al. [1] reported that the oxygen concentration is >7% pO 2 in the dermis and 0.2-8% pO 2 in the epidermis. Skin appendages show lower oxygen concentrations than the epidermis; hair follicles have 0.1-0.8% pO 2 and sebaceous glands have 0.1-1.3% pO 2 [2,3]. Culturing keratinocytes at 2% oxygen concentration has been reported to suppress stratification, cellular enlargement, and differentiation [4]. In cultured fibroblasts, the production levels of vascular endothelial growth factor (VEGF) and type I collagen, which are related to angiogenesis, collagen production, and tissue remodeling, have been altered in hypoxic conditions, indicating their roles in tissue remodeling during wound healing [5]. Hypoxic conditions increase the induction efficiency of induced pluripotent stem (iPS) cells and promote the undifferentiated cell proliferation of mesenchymal stem cells and neural stem cells [6][7][8]; therefore, hypoxic cultures have been attempted to be applied in regenerative medicine.
Hypoxia-inducible factor 1-alpha (HIF-1a) is the main regulator of cellular hypoxic response and binds to promoters of genes encoding glucose transporters and glycolytic enzymes that are important for metabolic reprogramming from oxidative phosphorylation to glucose metabolism [3]. Decreased oxygen consumption in the mitochondria prevents the production of reactive oxygen species (ROS) by suppressing the electron transport system, resulting in cell survival under hypoxia [9]. In cancer tissues, energy production dominantly depends on the glycolysis pathway (Warburg Effect) [10], and various metabolic shifts, such as glutaminolysis activation, due to insufficient nutrition and oxygen have been observed [10].
Oral mucosa-derived cells are a useful source for regenerative medicine and basic research, including disease model fabrication [11]. The influence of oxygen concentrations on cancer and wound healing in oral mucosa has been examined [12,13]; however, no report on the oxygen concentration in vivo has been published. Since the culture of oral mucosal epithelial cells under hypoxic conditions suppresses differentiation and senescence and promotes colony formation, hypoxic exposure is beneficial for applications in regenerative medicine, similar to other cells [14].
Although metabolic reprogramming plays an important role in stem cell biology and pathological conditions under hypoxia, the effects of hypoxia on oral mucosal keratinocytes and fibroblasts are poorly elucidated. Therefore, the purpose of this study is to demonstrate the characteristics of the metabolic mechanisms of oral mucosal keratinocytes and fibroblasts in hypoxia.
Primary oral fibroblast cultures were established by an explant culture technique using the connected tissue after the epithelial layer was scraped off. Small explants were placed in a 60-mm Petri dish (Corning, New York, NY, USA) and incubated in Dulbecco's modified Eagle medium (DMEM; FUJIFILM Wako Pure Chemical Corporation, Osaka, Japan) supplemented with 10% fetal bovine serum (Thermo Fisher Scientific), gentamicin, and amphotericin B as previously described [16].
Six of the oral mucosa keratinocytes and fibroblasts used in the study were from passages 3 to 5. To culture the cells under hypoxic conditions, culture vessels were placed in a humidified modular incubator chamber (Billups Rothenberg, Inc., Del Mar, CA, USA), flushed for 2 min with a gas mixture of either 2.0% O 2 (5.0% CO 2 -93.0% N 2 ) or 0.5% O 2 (5.0% CO 2 -94.5% N 2 ), and then placed in an incubator at 37 • C. Cells were fed with either a 2% or a 0.5% O 2 tension equilibrating complete media every other day. As a normoxic condition (20% O 2 ), vessels were placed in ambient oxygen in an incubator at 37 • C with a humidified 5.0% CO 2 environment as described previously [17].
Metabolite Extraction
Oral keratinocytes and fibroblasts were plated on 100-mm dishes and cultured under 2% or 0.5% O 2 conditions for 24 h or 72 h. Each experimental condition was performed in duplicate for metabolite extraction and for cell counting after trypsinization to normalize the metabolomics data. For metabolite extraction, cells were washed twice with 5 mL of icecold 5% D-mannitol and then immersed in 1 mL of methanol containing internal standards (25 mM each of methionine sulfone, 2-[N-morpholino]-ethanesulfonic acid, and D-camphor-10-sulfonic acid) for 10 min on ice. The lysate was scraped and collected in 1.5 mL tubes, snap-frozen by liquid nitrogen, and then stored at −80 • C until analysis. To 400 µL of the dissolved samples, 400 µL of chloroform and 200 µL of Milli-Q water were added, and the mixture was centrifuged at 10,000× g for 3 min at 4 • C. The aqueous layer was filtered to remove large molecules by centrifugation through a 5-kDa cut-off filter (Merck Millipore, Burlington, MA, USA) at 9100× g for 2.0 h at 4 • C. Then, 320 µL of the filtrate was concentrated by centrifugation and dissolved in 50 µL of Milli-Q water containing reference compounds (200 µM each of 3-aminopyrrolidine and trimesate) immediately before the capillary electrophoresis time-of-flight mass spectrometry (CE-TOF-MS) analysis.
The instrumentation and measurement conditions used for CE-TOF-MS were described elsewhere [18]. Briefly, cations and anions in the 50-1000 m/z range were analyzed independently. The migration times of each chromatograph were normalized by dynamic programming-based methods, and metabolite identification was conducted by matching the m/z and corrected migration times with our standard library [19]. To calculate the absolute concentration of each metabolite, corresponding standard compounds were prepared. The peak area of each metabolite was divided by those of the internal standard compound (methionine sulfone) to calculate the relative area by eliminating the unexpected bias of MS sensitivity fluctuation. The standard mixture was measured before the sample measurement, and based on the ratio of relative areas of each metabolite in the sample and standard mixture, the concentrations were calculated. The upper and lower quantifications limits were already measured using standard mixtures, and the peaks under lower limits were treated as not detected (N.D.).
The overall metabolomic profiles were assessed by clustering analysis. Statistical analysis was performed by a two-tailed Student's t-test. Differences were considered significant at p < 0.05. The data processing and pathway visualization were conducted by our proprietary software, MasterHands and Pathway Visualization [19][20][21].
The Metabolomic Concentration of Oral Keratinocytes and Oral Fibroblasts
Metabolomic analysis successfully identified and quantified 208 and 203 metabolites in cultured oral keratinocytes and fibroblasts, respectively, under atmospheric oxygen concentration. The log 2 of fold change (F.C.) in the metabolite concentration between these cells and p-values are shown in the scatter plot ( Figure 1). The 33 and 13 metabolites showed higher (log 2 F.C. > 1) and lower (log 2 F.C. < −1) concentration of keratinocytes at a significant level (p < 0.05), respectively.
PCA was performed individually for each cell type to evaluate the effect of oxygen concentrations. The score plots of keratinocyte revealed that the samples with normoxic conditions were located at the right (labeled as K 20%), 2% O 2 conditions were located at the center (K 2% 24 h and 72 h), and 0.5% O 2 conditions were located at the left (K 0.5% 24 h and 72 h) ( Figure 2a). Thus, the first principal component (PC1) reflects the oxygen condition. The loading plots showed the distribution of various metabolites along with PC1.
Alteration of the Pentose Phosphate Pathway (PPP) and Urea Cycle under Hypoxia
Among various metabolic pathways, the PPP and urea cycle with various ambient oxygen cultures showed a distinct difference between oral keratinocytes and fibroblasts (Figures 3 and 4). Among the 13 metabolites in the PPP, 11 and three showed significant differences depending on the O 2 condition in oral keratinocytes and oral fibroblasts, respectively ( Figure 3). In the urea cycles, including 22 metabolites, 11 and two metabolites showed a significant difference in these cells (Figure 4). Time dependency in 2% O 2 showed less difference comparing with that of 0.5%. As commonly observed features in both cells, lactate, an end product of glycolysis, decreased significantly in 0.5% 72 h (Figure 3a,b). 6-phosphogluconate (6PG) showed a significant decrease, whereas ribose 5-phosphate (R5P), the intermediate metabolites in PPP, significantly increased in the hypoxic oral keratinocytes. A decrease of phosphoribosyl pyrophosphate synthetase1 and 2 (PRPS1 and 2), ribose 5-phosphate isomerase A (RPIA), and ribulose-5-phosphate-3-epimerase (RPE) were observed, which may lead to the accumulation of R5P by producing less PRPP and xylose-5P. Oral fibroblasts showed a decrease of glucose 6-phosphate (G6P) in hypoxia, while oral keratinocytes did not. According to our microarray results, glucose 6-phosphate isomerase (GPI), which is needed to convert G6P to F6P, was higher in hypoxic oral fibroblasts (Table S1). In addition, the NADPH/NADP+ ratio regulates the activity of glucose 6-phosphate dehydrogenase (GPD), which converts G6P to D-Glucono-1,5-lactone 6-phosphate; the latter has a lower tendency in hypoxic oral fibroblasts (data not shown [22]), which may also contribute to the low level of G6P [23]. G6P in oral fibroblasts showed the same tendency with 6PG which indicates the constant metabolism kinetics between them.
Interestingly, oral keratinocytes and fibroblasts showed unique balance changes among intermediate metabolites in the urea cycle and polyamines. Reduced Asn in both hypoxic cells may be because of the decrease of glutamic-oxaloacetic transaminase 1 (GOT1) gene expression level, which generates Asn under hypoxia (Table S1) [24]. Increased 2-oxoglutaric acid (α-ketoglutaric acid; α-KG) was observed in hypoxic oral fibroblasts. Glutamine (Glu), Asn, and fumarate are decreased in both hypoxic cells while ornithine increased in hypoxic oral keratinocytes and did not decrease in hypoxic oral fibroblasts. The decrease of argininosuccinate synthase 1 (ASS1) is consistent with the low level of argininosuccinate in both hypoxic cells (Table S1). Ornithine is catabolized by ornithine decarboxylase 1 (ODC1) to putrescine as a substrate for the synthesis of polyamines, such as spermidine and spermine. As a result of the decrease of ODC1, putrescine and other polyamines (i.e., spermidine, spermine, and acetyl-putrescine) may decrease in contrast to ornithine in both hypoxic cells (Figure 4a,b, Table S1). p-values were calculated using Student's t-test (two-tailed, unequal variance). * p < 0.05 was shown for comparison between each data for 20% oxygen.
Discussion
Keratinocytes in the stratified squamous epithelium are the major cellular components of the oral mucosa, which are derived from the ectoderm. Fibroblasts in the fibrous connective tissue layer are derived from the mesoderm. Although they are adjacent tissues to the border of the basement membrane, their cellular characteristics vary because of their origin. Since metabolic conditions under the hypoxic microenvironment of their cells are supposed to be further different from the ambient condition, we conducted metabolomic analyses in various oxygen conditions to characterize their metabolomic features.
Oral keratinocytes and fibroblasts under atmospheric oxygen concentration showed the presence of various metabolites with different concentrations. In oral fibroblasts, lysine and ornithine, which are required for collagen synthesis and crosslinking, were higher [25,26]. In contrast, N-acetylputrescine, one of the polyamine metabolites important for maintaining epithelial homeostasis, was higher in oral keratinocytes [27]. Thus, metabolites of oral keratinocytes are quite distinct from those of oral fibroblasts even under 20% oxygen concentration.
Metabolomic analyses were conducted under two different environmental factors, exposure time and oxygen concentrations. The cells were exposed for either 24 (shortterm) or 72 h (long-term) and then cultured in 2% oxygen, which is the concentration preferred by keratinocyte precursor cells, as well as 0.5% oxygen, which is a severe oxygen concentration, such as in wound healing. Oral keratinocytes showed various metabolic changes in response to hypoxia, especially in glycolysis, the PPP, and the urea cycle. In a temporal metabolomic analysis of the first-line response to oxidative stress, it has been reported that epidermal keratinocytes and dermal fibroblasts showed fluctuation in glycolysis and PPP metabolites within 1 min [28]. Differences in time dependency were little, especially in 2% O 2 , which may be because the time course was excessive in the present study.
In hematopoietic and pluripotent stem cells, PPP was elevated [29,30]. Glycolysis and PPP dominantly produce energy and suppress the generation of ROS, which is an important mediator of cell damage and the cell death process, and it maintains the quiescent state as well. We previously reported that ROS generation was suppressed under hypoxia in oral keratinocytes [14]. Nonetheless, the proliferation of oral keratinocytes increased at 2% and 0.5% oxygen concentrations [14]. A decrease of G6P was seen in hypoxic oral fibroblasts. The upregulation of GPI and downregulation of NADPH/NADP+ that are reported as the hypoxic reaction may retrieve cellular survival and increase proliferation and angiogenesis in hypoxic oral fibroblasts [23,31]. This study revealed that the production of R5P, which is the intermediate metabolite of PPP, increased while 6PG decreased in hypoxic oral keratinocytes. Gene expression changes of 6-phosphogluconate dehydratase (PGD), which produces 6PG from R5P, and transaldolase1 (TALDO1), which produces erythrose 4-phosphate (E4P) and fructose 6-phosphate (F6P) from S7P and glyceraldehyde 3-phosphate (G3P) were inconsistent with their related metabolite changes ( Figure 3, Table S1). The activity of PGD and TALDO increases sharply in alkaline pH [32,33], which may lead to low 6PG synthesis or high S7P, since the intracellular environment of hypoxic cells is acidic [34]. 6-phosphofructo-2-kinase/fructose-2,6-biphosphatase 3 (PFKFB3) is an enzyme that switches glycolysis to PPP, and it was elevated in both hypoxic cells (Table S1). It could maintain oral keratinocytes in an undifferentiated state in conjunction with p63, an undifferentiated marker of keratinocytes, and promote collagen synthesis in oral fibroblasts [35,36].
The various metabolites' concentration in the polyamine pathway and the aspartate to fumarate in the urea cycle were reduced, and the accumulation of ornithine was also found in both hypoxic cell types. The limitation of Asn supports cellular proliferation in hypoxic cancer, which is consistent with our previous study that oral keratinocytes highly proliferate in hypoxia [24,37,38]. Mitochondrial activity is low in hypoxia; as a result, fumarate synthesis decreased following the whole TCA cycle deactivation [39]. A low level of polyamines was observed in both hypoxic cell types. Since polyamines are known to be involved in the keratinocyte cell differentiation process [40], the result in this study was consistent with our previous study that showed that hypoxia maintained an undifferentiated state of oral keratinocytes.
In contrast to oral keratinocytes, oral fibroblasts demonstrated fewer changes in both the PPP and urea cycle. Oral fibroblasts showed the deactivation of overall metabolism, particularly, the metabolites of the TCA cycle, which was lower than those in oral keratinocytes. In addition, both the PPP and the urea cycle in oral fibroblasts are less susceptible to hypoxia than those in oral keratinocytes. In contrast, an increase in α-KG, which is a co-activator of prolyl hydroxylase that is an HIF-1a degrading enzyme, was observed under hypoxia. α-KG, an endogenous intermediate metabolite in the TCA cycle, is a molecule that is involved in multiple metabolic and cellular pathways as well as acting as an antioxidant [41]. Therefore, in oral fibroblasts, α-KG inhibits ROS in hypoxia, which may be involved in cell survival and cellular senescence.
The present study has several limitations. First, we used a limited number of samples because of the usage of primary culture cells. Second, we did not perform any functional assays. By clarifying the molecular response of this metabolic reprogramming, further studies on cellular hypoxic responses are necessary in the future. Focusing on subcellular compartments of glutamine metabolism and its lipogenesis might reveal novel functions [42,43]. Here, we discussed the expression of the metabolic enzymes using only microarray data. Validation of these expressions and activities is required to confirm the reason for metabolomic pathways' change.
In conclusion, we observed the metabolomic concentrations of oral keratinocytes and fibroblasts for the first time and revealed their holistic changes of two major cell types in the oral mucosa. An increase in PPP and a decrease in polyamine production under hypoxia were detected in this study, which would support our previous data showing that hypoxia can maintain oral keratinocytes in an undifferentiated state and prevent them from cellular senescence. In oral fibroblasts, the overall metabolism changes were smaller than those of oral keratinocytes. Although there were only little changes in any pathway under hypoxia, the concentration of α-KG increased. The metabolic reprogramming findings of our study could contribute to providing insights into stem cell biology, wound healing, and cancer biology.
Author Contributions: H.K. contributed to the conception, design, data acquisition, analysis, and interpretation drafted; M.S. contributed to the conception, data analysis, and interpretation, drafted; A.E. and M.K. contributed to data acquisition and analysis; Y.H., N.S. and A.S. contributed to data acquisition; H.O. contributed to interpretation; K.I. contributed to the conception, design, and interpretation. All authors have read and agreed to the published version of the manuscript.
Institutional Review Board Statement:
All procedures performed in studies involving human participants were following the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. The protocol for obtaining human keratinized oral mucosa tissue samples was approved by the Niigata University Hospital Internal Review Board (2015-5018).
Informed Consent Statement:
Patients undergoing minor dentoalveolar surgery were provided sufficient information regarding this study, and all participating individuals signed an informed consent form.
Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available.
Conflicts of Interest:
Authors declare that they have no conflict of interest. | 4,405.8 | 2021-03-01T00:00:00.000 | [
"Biology",
"Medicine"
] |
Regularized degenerate multi-solitons
We report complex PT-symmetric multi-soliton solutions to the Korteweg de-Vries equation that asymptotically contain one-soliton solutions, with each of them possessing the same amount of finite real energy. We demonstrate how these solutions originate from degenerate energy solutions of the Schroedinger equation. Technically this is achieved by the application of Darboux-Crum transformations involving Jordan states with suitable regularizing shifts. Alternatively they may be constructed from a limiting process within the context Hirota's direct method or on a nonlinear superposition obtained from multiple Baecklund transformations. The proposed procedure is completely generic and also applicable to other types of nonlinear integrable systems.
Introduction
Soliton solutions to nonlinear integrable wave equations play an important role in nonlinear optics [1]. The first successful experiments to detect them have been carried out more than forty years ago [2]. A particularly important and structurally rich class of solutions are multi-soliton solution which asymptotically behave as individual one-soliton waves. This feature allows to view N -soliton solutions as the scattering of N single one-solitons with different energies.
In analogy to von Neumann's avoided level crossing mechanism in quantum mechanics [3], it is in general not possible to construct multi-soliton solutions possessing asymptotically several one-solitons at the same energy. The simple direct limit that equates two energies in the expressions for the multi-solitons diverges in general. Some attempts have been made in the past to overcome this problem. One may for instance construct slightly modified multi-soliton solutions that allow for the execution of a limiting process towards the same energy of some of the multi-particle constituents [4,5]. However, even though the solutions found are mathematically permissible, they always possess undesired singularities at certain points in space-time and have infinite amounts of energy. These features make them non-physical objects.
Inspired by the success of PT -symmetric quantum mechanics [6,7,8], many experiments have been carried out in optical settings, exploiting the formal analogy between the Schrödinger and the Helmholtz equation. In particular, the existence of complex soliton solutions in such a framework has recently been experimentally [9,10,11] verified and it was shown [12] that such type of solutions may posses real energies and lead to regular solutions despite being complex. Here we will employ a similar idea and demonstrate that they can be used to overcome the above mentioned infinite energy problem related to degenerate multi-soliton solutions. Starting from a quantum mechanical setting we show that the degeneracy is naturally implemented by so-called Jordan states [13] when Darboux-Crum (DC) transforming [14,15,16,17] degenerate states of the Schrödinger equation. Finiteness in the energy is achieved by carefully selected complex PT -symmetric shifts in the dispersion terms.
Subsequently we show how such type of solutions are also obtainable from other standard techniques of integrable systems. For Hirota's direct method [18] this can be achieved by reparameterizing known solutions such that they will become suitable for a direct limiting process that leads to degeneracy together with a fitting complexification that achieves the regularization. For the other prominent scheme, the Bäcklund transformations we also demonstrate how the limit can be carried out on a superposition of three solutions in a convergent manner.
Here we consider in detail one of the prototype nonlinear wave equations, the Kortewegde Vries (KdV) equation [19], for the complex field u(x, t) depending on time t and space x. This equation is known to arise from standard functional variation from the Hamiltonian density In general, for PT -symmetric models the energy remains real despite the fact that the Hamiltonian density is complex [20]. The PTsymmetry is realized as PT : x → −x, t → −t, i → −i, u → u, leaving (1.1) invariant. As we will demonstrate below it is essential to have complex contributions to u in order to render the energy finite. Our manuscript is organized as follows: In section 2 we discuss the general mechanism that allows to implement degeneracies into Darboux-Crum transformations. We show that degenerate states in the Schrödinger equation need to be replaced by Jordan states in order to obtain nonvanishing and finite, up to singularities, solutions. Subsequently we elaborate in detail on the novel features of degenerate two and three soliton solutions and explain how the regularizing shifts need to be implemented. In section 3 and 4 we explain how Hirota's direct method and nonlinear superpositions obtained from four Bäcklund transformations need to be altered in order to allow for the construction of degenerate complex multi-soliton solutions with finite energy. We state our conclusions in section 5.
Darboux-Crum transformations, generalities
The Darboux-Crum transformations [14,15,16,17] are well-known to generate covariantly an entire hierarchy of Schrödinger equations to the same eigenvalue E = −λ 2 in a recurrence procedure. Following [17] we recall here that in case of degeneracy one has to replace the eigenstates of the Schrödinger equation by so-called Jordan states Ξ (k) λ defined as solutions of the iterated Schrödinger equation with potential V and eigenvalue E(λ) depending on the spectral parameter λ. Thus for k = 0 the corresponding Jordan state simply becomes the eigenfunction of the Schrödinger equation, that is Ξ from the first solution ψ λ . The general solution to (2.1) is easily seen to be with χ (k) λ := ∂ k ψ λ /∂E k and Ω (k) λ := ∂ k φ λ /∂E k . Some identities that will be useful below immediately arise from this. Differentiating the Schrödinger equation with respect to E yieldsĤ χ which can be employed to derive Let us see how these states emerge naturally in degenerate DC-transformations. With E(λ) = −λ 2 , the first iterative step in this procedure is simply to note that the equation with same eigenvalue as in (2.1) for k = 0, but new potential 1 Here and in what follows we always understand (ln f ) x as a short hand notation for fx/f . is solved by where D ψ (φ) := φ x − (ψ x /ψ)φ is the Darboux operator. The hierarchy of Schrödinger equations is then obtained by repeated application of these transformations. It is clear that a subsequent iteration of the degenerate solution in (2.7) will simply produce again the potential V and hence nothing novel. However, using the second fundamental solution ds to the level one equation yields something novel. In this case the new potential becomes where we used identity (2.4) through which the Jordan states enter the iteration procedure. The corresponding wave function to this potential is Proceeding in this way, the solutions to the hierarchy of equation with potentials and wave functions Evidently we may also chose to have a partial degeneracy keeping some of the λ i s different from each other, in which case we simply have to replace consecutive ψ λ i by Jordan states. For instance, taking λ 1 = λ 2 and λ 3 = λ 4 = λ 5 = λ we obtain the potential with either λ = λ 1 or λ = λ 2 . Notice from (2.8) the sequence of Jordan states always has to accompanied by a χ (0) λ = ψ λ . Let us now see how this procedure can be employed in finding degenerate multi-soliton solutions by means of inverse scattering.
Degenerate complex KdV multi-soliton solutions
The different methods in integrable systems take various equivalent forms of the KdV equation as their starting point. The Darboux-Crum transformation exploits the fact that the central operator equation underlying all integrable systems, the Lax equation L t = [M, L], may be written as a compatibility equation between the two linear equations (2.14) For the KdV equation (1.1) the operators are well-known to take on the form Thus L becomes a Sturm-Liouville operator, such that the first equation in (2.14) may be viewed as the Schrödinger equation (2.10) with L ≡ H being interpreted as a Hamiltonian operator. Considering now the free theory with u = 0 and taking the wave function in the form ψ(kx + ωt), the second equation in (2.14) is solved by assuming the nonlinear dispersion relation 4k 2 + ω = 0. For λ = −α 2 /4 the two linear independent solutions to (2.14) are simply We allowed here for a constant µ ∈ C in the argument and normalized the Wronskian as Suitably normalized, i.e. dropping overall factors, the first Jordan states resulting from (2.16) are computed to ) Using these explicit expressions the crucial identities (2.4) in the above argument are easily confirmed. We also verifŷ 22) which yield the defining relations for the Jordan states upon a subsequent application of the energy shifted HamiltonianĤ as defined in (2.1).
Degenerate two-solitons
To compute the degenerated two-soliton solution we use the above expressions to evaluate the Wronskian W (ψ µ,α , χ (1) µ,α ) involving one Jordan state. As indicated in (2.2) we may take the constants c l , d l different from zero, which we exploit here to generate suitable regularizing shifts. First we compute where we used the identity (2.17) and the property of the Wronskian W (f, gh) = W (f, g)h+ f gh x . We note that one of the dispersion terms already includes a shift µ. Next we demand that also the dispersion term αx−3α 3 t is shifted by a constant ν, which is uniquely obtained from The degenerate two-soliton solution u = 2(ln W ) xx resulting from (2.11) and (2.24) reads (2.25) This solution becomes singular when the Wronskian vanishes, which is always the case for some specific x and t when ν, µ ∈ R. However, for the PT -symmetric choice ν = iν, µ = iμ,ν,μ ∈ R this solution becomes regularized for a large range of choices forν andμ. From we observe that wheneverν/ sinμ > −1 the imaginary part of W can not vanish and therefore u µ,ν;α,α will be regular in that regime of the shift parameters. Furthermore, we observe that u µ,ν;α,α involves two different dispersion term αx − α 3 t + µ and αx − 3α 3 t + ν, each with a separate shift. In the numerator the latter becomes negligible in the asymptotic regimes where the degenerate two-soliton behaves as two single solitons traveling at the same speed with one slightly decreasing and the other with slightly increasing amplitude due to the time-dependent pre-factor. In the intermediate regime, when the linear term αx − 3α 3 t term in the numerator contributes, it produces a scattering between the two one-solitons with the same energy. We depict this behaviour in figure 1. In addition to the regularization, this entire qualitative behaviour is due to the fact that our solutions are complex.
We observe that the larger and smaller amplitudes have exchanged their relative position in the two asymptotic regimes with their mutual distance kept constant. This is of course different from the standard nondegenerate case where the solitons continuously approach each other before the scattering event and separate afterwards. Again this is Im [uµ,ν;α,α(x, t)] x Figure 1: Degenerated KdV two-soliton compound solution with α = β = 2, µ = iπ3/5 and ν = iπ/5 at different times.
achieved through the complexification of our solution. Here the scattering is governed by some internal breatherlike structure as in confined to a certain region. As demonstrated in figure 2 this internal structure can be manipulated by varying the shift ν.
Im [uµ,ν;α,α(x, t)] x For a fixed instance in time we can employ ν to increase or decrease the distance between the single soliton amplitudes and even find a value such that the distance becomes zero. However, this value is in the intermediate regime and as time evolves the two solitons will separate again to some finite distance in the asymptotic regime.
Our interpretation is supported by the computation of the energies resulting from (1.3) with Hamiltonian density (1.2) for the solution u µ,ν;α,α . Numerically we find the finite real energies i.e. precisely twice the energy of the one-soliton u µ;α , reported for instance in [12].
In order to compare with various other methods it is useful to note that the degenerate Wronskians may be obtained in several alternative ways. We conclude this subsection by reporting how the expression for the Wronskian (2.24) can be derived by mean of a limiting process directly from the two-soliton solution. This is seen from by starting from the defining relation for the Jordan state χ (1) W ψ µ,α , χ (1) µ,α = 2 lim β→α ∂ ∂β W ψ µ,α , ψ µ,β (2.28) where in the last step we chose h = β−α. The shift can now be implemented by determining λ from the limit of the expression W ψ µ+λν,α , ψ µ−λν,β = W ψ µ,α , ψ µ,β cosh 2 λν 2 − W φ µ,α , φ µ,β sinh 2 λν 2 (2.33) It it is obvious that for the limit (2.32) of the shifted expression to be finite we require λ ∼ (α − β) with constant of proportionality chosen in such a way that it yields 1/2α in the limit. Hence we obtain (2.35) These identities will be useful below when we relate this approach to Hirota's direct method.
Degenerate three-solitons
To find the degenerate three-soliton solution we may once again compute the Wronskian, albeit now involving two Jordan states. As discussed in the previous section, the expression for W (ψ µ,α , χ µ,α , χ µ,α ) will inevitably lead to solutions with infinite energy. Thus we will again exploit (2.2) with nonvanishing constants c l , d l to generate the regularizing PTsymmetric shifts. A suitable unique choice is ρ;α and η (9) ν;α , where the first governs the asymptotic behaviour and the remaining ones the additional structure in the intermediate regime. The solution u µ,ν,ρ;α,α,α = 2(ln W ) xx is depicted in figure 3.
We observe that asymptotically we have three single one-solitons moving at the same speed. They exchange their positions in the intermediate region near the origin, when the linear terms in (2.37) contribute.
For the general three-soliton solution we have also additional options available, namely to produce the degeneracy only in two of the one-solitons while keeping the remaining one at a different velocity. A suitable choice that produces the desired shifts is We depict the corresponding KdV solution u µ,ν,ρ;α,α,γ = 2(ln W ) xx in figure 4. We clearly observe that asymptotically we have a degenerated two-soliton and a onesoliton solution with the faster two-soliton overtaking the slower one-soliton.
where we introduced the shift function f (x, y, z) := 4 9 It will be important below to note that the sum of all shifts adds up to zero, f (α, β, γ) + f (β, γ, α) + f (γ, α, β) = 0. Once again our interpretation is supported by the computation of the corresponding energies. Numerically we find which are again finite and real energies irrespective of whether the shifts are taken to be complex or real.
Degenerate complex multi-soliton solutions from Hirota's direct method
Hirota's direct method [18] takes a different equivalent form for nonlinear wave equations as starting point. The system at hand, the KdV equation (1.1), can be converted into Hirota's bilinear form by means of the variable transformation u = 2(ln τ ) xx . The required combination of Hirota derivatives in terms of ordinary derivatives are 3) The τ -function can be identified with the Wronskian in the previous section, up to the ambiguity of an overall factor exp [c 1 x + c 2 + f (t)] with arbitrary constants c 1 , c 2 and function f (t). Remarkably equation (3.1) can be solved with a perturbative Ansatz τ = ∞ k=0 ε k τ k in an exact manner, meaning that this series terminates at N -th order in ε for the corresponding N -soliton solution. Order by order one needs to solve the following set of linear equations Let us first see how the Hirota equations are solved using Wronskians involving Jordan states. We start with the two-soliton solution and take τ 1 = W x ψ, χ (1) . Using identity (2.4) in the form W x ψ, χ (1) = cψ 2 , the first order Hirota equation (3.4) reads This equation is solved using the above mentioned nonlinear dispersion relation, i.e. by taking ψ(x, t) = ψ(x − α 2 t).
Degenerate complex multi-soliton solutions from superposition
It is well-known that the combination of four Bäcklund transformations combined in a Bianchi-Lamb [21,22] commutative fashion gives rise to a "nonlinear superposition principle", e.g. [12]. Introducing the quantity u = w x , it takes on the form for the KdV equation where w 0 , w 1 , w 2 and w 12 correspond to different solutions. Relating w 1 and w 2 to the standard one-soliton solution and setting w 0 to the trivial solution w 0 = 0, the general formula (4.1) becomes with w µ;α (x, t) = α tanh 1 2 (αx − α 3 t + µ) , κ 1 = α 2 /2 and κ 2 = β 2 /2, see [12]. Remarkably in this form the limit lim β→α w µ,μ;α,β can be performed directly The corresponding solution the KdV equation will still be singular, but when implementing the same shifts as in (2.34) we compute and thus recover precisely the solution (2.25). The relation to the treatment in section 2 involving DC-transformations is achieved by considering (2.11) for n = 0 with V (0) = 0. Then we read off the identification w µ;α = 2 ln ψ µ,α x , which is confirmed by the explicit expression (2.16).
Conclusions
We have constructed a novel type of compound soliton solution composed of a fixed number degenerate one-soliton constituents with the same energy. Asymptotically, that is for large and small time, the individual one-solitons travel at the same velocity with almost constant amplitudes. In the intermediate regime they scatter and exchange their relative position. Thus the entire collection of one solitons may be viewed as a single compound object with an internal structure only visible in a certain regime of time. As we have shown, one may construct solutions in which these compounds scatter with other (degenerate) multi-solitons at different velocities.
Technically these compound structures arose from carefully designed limiting processes of multi-soliton solutions. We have demonstrated how these limits can be performed within the context of standard techniques of integrable systems, employing Darboux-Crum transformations involving Jordan states, Hirota's direct method with specially selected coefficients and on the nonlinear superposition obtained from Bäcklund transformations. While the limits led to mathematically admissible nonlinear wave solutions, they always possess singularities such that their energy becomes infinite. In order to convert them into physical objects it was crucial to implement in addition some complex regularizing shifts.
When comparing the different methods, the DC-transformations require the most substantial modification by the introduction of Jordan states. This approach is very systematic and the modified transformations always constitute degenerate soliton solutions. To carry out the limit within the context of Hirota's direct method requires some guesswork in regards to the appropriate choice of coefficients, which we overcame here by relying on the information from the DC-transformations. The nonlinear superposition of three solutions appears to be the most conductive form for taking the limit directly. The disadvantage in this approach is that expressions for higher multi-soliton solutions are rather cumbersome when expressed iteratively. So far in all approaches the regularizing shift were introduced in a somewhat ad hoc fashion.
There are various open issues left to be resolved and not reported here. Evidently the suggested procedure is entirely generic and not limited to the KdV equations or the particular type of solutions and boundary conditions considered here [23]. It would be interesting to apply them to other types of integrable systems as that might help to unravel some further universal features. For instance, one expects that the regularizing shifts can be cast into a more universal form that might be valid for any arbitrary number of degeneracies when exploiting further their ambiguities. Furthermore it is desirable to complete the argument on why the energies of these complex solutions are real. This follows immediately when they and the corresponding Hamiltonians are PT -symmetric. As demonstrated in [12], this can be achieved with suitable real shifts in time or space, but in addition one also requires the model to be integrable. We report on these issues in more detail elsewhere [24]. | 4,800.6 | 2016-05-20T00:00:00.000 | [
"Mathematics"
] |
Double ring bending tests on heat pretreated soda–lime silicate glass
The strength of glass plays an important role in the dimensioning of glass components in the building industry. Here, not only parameters such as support conditions, loading rate, relative humidity etc. play an important role, but the damage by means of scratches also determines the fracture strength of glass. A heat treatment after damaging may have an influence on the resulting glass strength. The correlation between heat treatment temperature, and in particular elevated temperatures up to the glass transition temperature, and fracture stress has been studied by different researchers with several approaches of pre-treatment of specimens and test setups. This paper methodically presents various preliminary investigations which were carried out within the framework of the pre-treatment of the samples in order to investigate the influence of heat treatment of the pre-damaged samples on the fracture stress. For this purpose, double ring bending tests were performed at room temperature on pre-damaged, heat-treated soda–lime silicate glass specimens. The aim of the investigations is to obtain estimates of the extent to which a heat treatment prior to the strength test influences the fracture strength of soda–lime silicate glass. Parameters like the heat treatment temperature, the dwell time of the samples inside the furnace and the furnace design were considered. The results show that the heat treatment can increase the fracture stress of soda–lime silicate glass as float glass significant due to an assumed healing of the pre-damage during heat treatment.
Introduction and previous research
A major factor determining float glass strength is damage such as scratches or cracks due to the brittle material behavior of glass. Scratches and cracks can be caused by the float glass process itself, the cutting after the float process or also maybe by transport afterwards. With regard to the later dimensioning of glass constructions made of float glass in the building industry, the influence of these damages on the computationally usable material strength is reflected. Due to the fact that the usable bending strength of float glass is low compared to thermally toughened glass, the use of thermally toughened glass sheets is advantageous. However, the toughening process of the glass also increases its price, which causes the material costs of glazing to rise. If the strength of float glass could be increased by another treatment at lower temperatures, more float glass could possibly be used for glazing. Another application in building industry is fused deposition modelling of glass (Seel et al. 2018a), or simply speaking 3-D printing of glass. Due to the printing process, defects and voids can occur (Seel et al. 2018b) within the additive manufactured component. These flaws represent notches or cracks in the brittle material, which can lead to stress peaks and a comparatively less resistance of the glass. Based on the current state of research, the question has been raised whether the strength of pre-damaged soda-lime silicate glass as float glass can be increased by means of heat treatment, which does not correspond to thermal toughening.
Heat treatments of soda-lime silicate glass as float glass have so far been largely carried out at elevated temperatures (550 to 725 • C) by Shinkai et al. (1981), Manns and Brückner (1983), Hrma et al. (1988), Holden and Frechette (1989), Girard et al. (2011), Doquet et al. (2014) and Zaccaria and Overend (2016), although lower temperatures (300 • C) have also been used (Wiederhorn 1969). In some investigations, the humidity during heat treatment was regulated within the furnace chamber (Holden and Frechette 1989;Girard et al. 2011). Furthermore, the dwell time of the samples at the temperature varied also in the different publications. The heat treatment Wiederhorn (1969) used, was 1 h at 300 • C to dry the specimens and relieve residual stresses within the glass. The procedure of drying the samples was carried out in order to be able to perform tests in an inert environment (with regard to stress corrosion cracking of glass due to water). Girard et al. (2011) varied the moisture content of the ambient air during heat treatment up to a maximum of 75% RH. Dry ambient conditions were achieved with the aid of noble gas (argon). The heat treatments for crack healing investigations were carried out at temperatures between 550 • C (glass transition temperature) and 620 • C (softening point of the investigated soda-lime silicate glass). The dwell time of the samples within the furnace and the ambient environment varied between 1 and 28 h in order to be able to investigate the influence of time on crack healing. Manns and Brückner (1983) used 4 h and 600 • C with ambient humid conditions as heat treatment before testing the samples via double ring bending test. They observed that the bending strength of the investigated soda-lime silicate glass as float glass increased. Hrma et al. (1988) also observed crack healing due to the strength test after heat treatment. In their studies they could observe that even a short heat treat-ment (15 min to 1 h) can influence the resulting fracture strength of soda-lime silicate glass. Holden and Frechette (1989) used a temperature of 550 • C with different dwell times and different time spans for the presence of humidity for their heat treatment experiments. They concluded that a combination of humidity which also has to be present before the heat treatment in combination with an elevated temperature (550 • C) may heal cracks as pre-damage in soda-lime silicate glass as float glass. The studies of Holden and Frechette (1989) and Girard et al. (2011) showed, that crack healing occurs at elevated temperatures (550 • C). Holden and Frechette (1989) and Girard et al. (2011) observed, that if even slight humidity is present during the heat treatment cracks in soda-lime silicate glass heal better than without humidity.
For the own investigations which are presented in the following the experience in heat treatment given by the past research will be taken into account. Therefore, two temperatures were chosen: lower temperature of 300 • C from the studies of Wiederhorn (1969) and elevated temperature of 550 • C from other studies (Holden and Frechette 1989;Girard et al. 2011). As material, commercial soda-lime silicate glass is used for the investigations presented here. It is assumed, based on the results of Girard et al. (2011) that the glass transition temperature of this glass is at 550 • C. After heat treatment the specimens are tested via double ring bending test at room temperature. Since the furnace design and the experimental set-up for heat treatment, the procedure of pre-damaging and strength test form the basis for a comprehensible experimental procedure, particular importance is given in this publication to describing the used experimental methods in detail.
Theory of the axisymmetric plate
For the calculation of the stresses caused by double ring bending (see Fig. 1a, b) at room temperature, the theory of the axisymmetric plate with consideration of a linear elastic material law may be applied. The deformations that occur in the experiment are relatively small (w/2r 2 1), which is why effects from geometric nonlinearity can be omitted. In EN 1288EN -1 (2000 the analytical Eq. (1) is given to calculate the tensile stresses arising in the double ring bending test. In EN 1288-1 (2000) the influence of geometry (r 1 , r 2 , r 3 ) and Poisson's ratio is summarized with the factor K 1 . Fig. 1 a Sketch of the test setup for the double ring bending test for small surfaces according to EN 1288EN -5 (2000 and b sketch of the test setup in plan view For the test setup R30 according to EN 1288EN -5 (2000 with consideration of Poisson's ratio ν = 0.23, K 1 results to 1.09 and Eq. (1) may then be simplified to Eq. (2). The samples used here had a nominal diameter of 70 mm and deviate from the normative specification (d = 66 mm). If the diameter of 70 mm and a Poisson's ratio of 0.22 (assumption) is used to determine K 1 , a value of 1.069 results for K 1 , which is 2% lower than 1.09.
Experimental investigations
3.1 Pre-damaging and storage of the samples In the first step of pre-treatment, the specimens were pre-damaged with the aid of the Universal Surface Tester (UST, see Fig. 2a). The UST is typically used to scan surfaces for creating surface profiles, indentation and scratching. For the investigations, a conically milled diamond with an angle of 120 • and a 5 μm radius of curvature at the tip of this cone was used as an indenter (see Fig. 3a, b) to induce a scratch (artificial flaw) on the glass surface (air or tin side of specimen). Ultraviolet light was used to determine the tin side of the sample. The tin ions embedded in the surface by the float process light up brightly under the ultraviolet light. The induced scratch (see Fig. 2b) is intended to represent the influence of surface flaws, which can be caused by flat glass production itself, transport and handling of glass products.
With the presented settings in the list below (Hilcken 2015) the artificial flaw was induced in the glass surface. This type of artificial flaw causes, when performing double ring bending tests, fracture stresses which correspond to the 5% quantile value of the fracture stress of float glass defined in standards [45 MPa according to EN 572-1 (2016)]. The parameters for predamaging were selected as follows: • Indenter: Diamond with an angle of 120 • and 5 μm radius of curvature at the tip • Force: 500 mN • Velocity of the indenter: 1 mm/s • Scratch length: 2 mm During the initiation of the scratch, the specimen is fixed on the support table (see Fig. 2a) by means of backside vacuum. The surrounding environment during scratching was standard climate (23 • C, 50% RH). Finally, the table is moved unidirectionally by 2 mm with a velocity of 1 mm/s. Simultaneously, a force of Schula (2015) and b cross-section of the indenter 500 mN acts on the indenter and thus on the glass surface. The scratch resulting on the specimen's surface can be seen exemplary in Fig. 2b. The fracture origin of specimens flawed with the presented technique is typically located at this artificial flaw (assuming that the flaw lies within the load ring) when performing double ring bending tests. In the next step of pretreatment, the specimens were stored at least for one week in a standard climate (23 • C, 50% RH) (Hilcken 2015). Then, in the last pre-treatment step, the samples were heat treated in a radiation furnace. The heat treatment is intended to study a possible increase of fracture strength by healing the induced scratch. Furthermore, the heat treatment serves to harmonize the material samples in order to eliminate any residual stresses (Shinkai et al. 1981;Wiederhorn 1969) in the glass that may occur as a result of the induced scratch (Assmann et al. 2019). Heat treatment studies were carried out, due to a furnace change and the determined fracture stresses, which are presented in Sects. 3.3 and 3.4.
Experimental test setup for strength tests: double
ring bending test at room temperature For the determination of the fracture strength of the heat treated soda-lime silicate glass specimens, the double ring bending test was conducted at room temperature and around 50% RH. The specimens used in the studies were circular in shape with a nominal diameter of 70 mm and a nominal thickness of 4 mm or 6 mm. The samples were cut from a flat glass at the factory and the cut edges were coarsely ground. The air or the tin side of the specimens was exposed to tensile stress. A universal testing machine was used for this purpose. Figure 4a, b show the test setup, whereby it should be mentioned that the sample was bonded with a foil Test setup for the double ring bending test at room temperature for small surfaces according to EN 1288EN -5 (2000 on the bending pressure side in order to hold the fragments of the specimen together after fracture. The test setup R30 was used on the basis of EN 1288-5 (2000), whereby the nominal diameter of 70 mm deviates from the standard (d = 66 mm). The tests were performed force-controlled with a load rate of 28 N/s for the 4 mm thick specimens (64 N/s for the 6 mm thick specimens). The analytical solution of the double ring bending test at room temperature, see Sect. 2, was used to determine the stress on the glass surface. If force and glass stress are known and a linear elastic material behavior is present (room temperature), the required load rate to obtain a stress rate of 2 MPa/s (EN 1288(EN -5 2000 can easily be calculated by Eq. (3).
Study of heat treatment-Method A
The following sections describe the first study for the heat treatment of the tested material specimens prior to the performed double ring bending tests with the test setup according to Sect. 3.2. The material samples were pre-damaged (flaw on the air side of the specimen) and stored according to Sect. 3.1.
Experimental setup for heat treatment
In this first study-Method A, three test series with ten specimens each with a nominal thickness of 6 mm were prepared. The background for this study was to check how far the heat treatment of the specimen is related to the fracture stress. In order to investigate the fracture stress of the specimens after heat treatment, double ring bending tests were performed at room temperature for all 30 specimens with the test setup presented in Sect. 3.2. The following list gives an overview of the series for the study: • KN_V1:10 specimens: scratched, stored (23 • C, 50% RH) • KN_V2:10 specimens: scratched, stored (23 • C, 50% RH), heat treated with target temperature of 300 • C • KN_V3:10 specimens: scratched, stored (23 • C, 50% RH), heat treated with target temperature of 550 • C After 30 samples were stored for at least seven days (Hilcken 2015) in standard climate, the samples of the KN_V2 and KN_V3 series were heat treated with the aid of the radiation furnace shown in Fig. 5a, b. Since a series contained ten samples and five specimens could be placed on each grate (see Fig. 5b), one test series was always heat treated together. The initial temperature calculated cooling rate where the circle marks the time when natural cooling started; for heat treatment with target temperature of 300 • C for the heat treatment was around room temperature. The specimens were placed on the grates with the predamaged air side (where the scratch is located) facing upwards. The background was: if the flawed side lies directly on the grate, the handling of the specimens may result in further flaws, which may be more severe than the already applied scratch. One issue was that the humidity inside the furnace chamber could not be recorded during the heat treatment. It is assumed that the relative humidity inside the furnace chamber at the beginning of the heat treatment (room temperature) was around 30 to 40% RH.
For the heat treatment it was planned, that the samples should be exposed to the respective target temperature for half an hour as scheduled (see solid lines in Figs. 6a, 7a). However, the test showed that, according to the air temperature shown on the display of the furnace (the temperature measured by the furnace itself by means of a permanently installed thermometer), the furnace reached the target temperature (300 • C or 550 • C) after approximately 10 min. After the 10 min of heating, the desired target temperature was maintained for another half an hour. Afterwards the furnace was switched off manually and the furnace cooled down naturally due to its insulation. An independent thermocouple (recording frequency of f I ≈ 0.006 Hz) was installed afterwards for a second experiment to check the temperature which was measured by the furnace itself. It should be noted that, during the temperature measurements shown Figs. 6a and 7a just the grate without specimens was inside the furnace chamber, because there were no further test series foreseen at this stage. Due to the missing mass of the glass it may be possible that the heating ramp profile could change. As can be seen from the graphs the target temperature of 300 • C respectively of 550 • C was nearly reached after approximately half an hour. A maximum temperature of 285 • C respectively 525 • C was measured. From the graphs it can be observed, that the samples have not been exposed to the desired dwell time of half an hour at the target temperature. The fact that the furnace has finished heating up after approximately 10 minutes, based on the temperature measured by the furnace itself, can also be analyzed by the heating rates shown in Figs. 6b and 7b. To determine the heating and cooling rates, the slope of the measured temperature curves in Figs. 6a and 7a was calculated. In Figs. 6a, b and 7a, b the X marks the point when heating ramp ended and the dwell time began. The end of the dwell time, when the furnace was switched of manually is marked with a circle in the diagrams in Figs. 6a, c and 7a, c. The heating rate which resulted for the 300 • C heat treatment was around 45 K/min (for 550 • C heat treatment it was around 55 K/min). It should be noted that the time axes shown in these diagrams represent shortened time segments of Figs. 6a and 7a.
By manually switching off the furnace after half an hour of dwell time (as scheduled) a natural cooling rate resulted, which was initially-14 K/min for the 300 • C heat treatment (− 6 K/min for the 550 • C heat treatment) and further decreased by temperature decrease. For the sake of illustration: the cooling rates used during thermal toughening reach initial values in the range of multiples of 1000 K/min (Barr 2015), which also decrease strongly and non-linearly. Due to the fact that the specimens cooling down with a comparatively low rate, it is assumed that the samples were not thermally toughened. Figure 8 shows the fracture stresses determined via double ring bending tests in comparison to the temperature during the heat treatment. The fracture stresses were calculated by Eq.
Experimental test results of the fracture stress at room temperature
(1). The specimens within this study-Method A were tested on the pre-damaged air side. In Table 1 the mean values of the test series are shown, whereby only eight specimens could be used for the test series KN_V1 (one specimen tested with different load rate, another was broken during installation). It can be seen that the heat treatment at measured 525 • C results in higher fracture stresses (comparing KN_V1), which can probably be linked to a healing of the induced scratch by elevated temperatures in combination with the moisture in the air of the furnace chamber (Holden and Frechette 1989). Comparing the mean values of Table 1 it can be seen, that the heat treatment can increase the fracture stress up to 41% (comparing KN_V1 and KN_V3) of the pre-damaged specimen. Even a heat treatment at a lower temperature of 285 • C results in higher fracture stresses. An increase of the fracture stress of around 12% (comparing KN_V1 and KN_V2) can be observed. One possibility is that, also at lower temperatures in combination with the moisture in the air inside the furnace chamber crack healing effects occur. It should be mentioned, that it is assumed that there was no thermal toughening of the specimens (KN_V2 and KN_V3), because the cooling rates in the furnace shown in Sect. 3.3.1 were far below cooling rates normally used in thermal toughening glass (Barr 2015). In addition, the temperatures used in heat treatment presented here were lower than those typically used in thermal toughening (620 • C, Barr 2015).
Summary of the preliminary study-Method A
In the study-Method A investigating the influence of heat treatment on the fracture stress of soda-lime silicate glass, it was shown that the heat treatment of pre-damaged soda-lime silicate glass specimens can increase the bending strength extraordinary. In the experiment, where an elevated temperature was present (measured 525 • C), an increase of fracture stress of about 41% was observed. The past research of Holden and Frechette (1989) and Girard et al. (2011) could also observe crack healing at these elevated temperatures. In the second case, where the temperature was lower (around 285 • C) also an increase of fracture stress could be observed, which does not seem logical, because the temperature for crack healing was too low (compared to Holden and Frechette 1989;Girard et al. 2011). For both experiments presented here it could also be shown, that even a very short dwell time at low or elevated temperatures may increase the fracture stress of the soda-lime silicate glass as float glass. Since the furnace for heat treatment of the material samples was changed in the further procedure, further studies of heat treatment (Method B) were carried out with a different furnace. These studies are presented in the following paragraphs.
Study of heat treatment-Method B
In the second study-Method B, a different radiation furnace (not identical in construction see Figs. 5,9) was used, so further investigations on heat treatment were carried out. As in the first study-Method A, the specimens used in this study were pre-damaged using the method described in Sect. 3.1 and stored for at least seven days in standard climate. The following list gives an overview of the series for this study: Fig. 9 a Radiation furnace used in the second study-Method B of heat treatment, b test setup without radiation shielding and when measuring the air temperature in furnace chamber and c test setup with radiation shielding and when measuring the air temperature within aluminum enclosure Fig. 10 a Arrangement of the thermocouples when measuring the air temperature in the furnace chamber resp. within aluminum enclosure and b arrangement of the thermocouples when mea-suring surface temperature of the specimens without aluminum enclosure • KN_V4: 8 specimens: scratched, stored (23 • C, 50% RH), heat treated with target temperature of 300 • C with radiation shielding • KN_V5: 8 specimens: scratched, stored (23 • C, 50% RH), heat treated with target temperature of 300 • C without radiation shielding Figure 9a shows the used radiation furnace for the second study-Method B. The target temperature at which the heat treatment was scheduled had an upper limit of 300 • C in accordance to Wiederhorn (1969). To do so, the heating rate of the furnace was set to 10 K/min at the furnace control so that the air temperature will reach 300 • C after 0.5 h. The temperature of 300 • C was then kept almost constant for 4 h. After 4 h the furnace cooled down naturally due to its insulation. When comparing the walls of the two furnaces (Figs. 5b, 9b), it can be seen that the arrangement of the spiral-wound filaments within the chamber is different. In the first furnace, the filaments are located on the left and right Fig. 11 a Temperature measurement without radiation shielding for 300 • C target temperature, b calculated heating rate and c calculated cooling rate walls of the furnace chamber. These filaments hang freely in front of the wall (see Fig. 5b). In the second furnace, the filaments are located on the side walls and the top of the furnace chamber (see Fig. 9b). Here, the filaments are embedded in a temperature-resistant insulating material. The different design of the furnace chamber is expected to result in a different temperature profile (measurements). Due to the grate size of the furnace only eight material samples could be placed on the grate. Different temperature measurements by use of four type K thermocouples (see Fig. 10a) were carried out:
Experimental setup for heat treatment (with and without radiation shielding)
• Air temperature measurement without radiation shielding, Sect. 3.4.2 • Specimen surface temperature measurement without radiation shielding, Sect. 3.4.3 • Air temperature measurement with radiation shielding, Sect. 3.4.4 The thermocouples were inserted through the grate from below and recorded the air/surface temperature with a frequency of f II = 0.1 Hz near the specimen or on its surface. In order to check which temperature would be reached on the glass surface without radiation shielding, another measurement was carried out using two material samples. To do so thermocouples were bent onto the glass surface so that there was direct contact between thermocouple and glass surface (see Fig. 10b). The initial temperature for the heat treatment was around room temperature. The samples were placed on the grate with the pre-damaged tin side (where the scratch is) facing upwards according to Sect. 3.3.1. One issue is that the humidity inside the furnace chamber could not be recorded during the heat treatment. It is assumed that the humidity inside the furnace chamber at the beginning was around 30 to 40% RH.
Heat treatment: without radiation shielding
The specimens were placed on the grate without protection against radiation (see Fig. 9b). The air temperature within the furnace chamber near the specimens was measured with four thermocouples (see Fig. 10a). It should be mentioned that the aluminum sheets to the left and right in Fig. 10a were not present. From the four measurements the mean value of air temperature, which is shown in Fig. 11a, was calculated. The corresponding heating and cooling rates, which are shown in Fig. 11b, c, were calculated with the recorded time and mean temperature. It should be noted that the time axes in Fig. 11b, c represent sections of the axis from Fig. 11a. As can be seen from Fig. 11b, the target of heating the furnace at 10 K/min could not be achieved due to a non-optimized (optimization regarding electric power) furnace control. After half an hour, the heating ramp ended as scheduled at a measured mean air temperature of around 280 • C. After 4 h dwell time at 300 • C target temperature, the furnace switched itself off and cooled down naturally.
Heat treatment: without radiation shielding-measured surface temperature
In order to determine the temperature that occurs on the glass surface of the specimens during heat treatment, another temperature measurement was carried out on two specimens. For this purpose, thermocouples were bent onto the glass surface of the samples Fig. 12 a Temperature measurement the on surface without radiation shielding for 300 • C target temperature, b calculated heating rate and c calculated cooling rate so that the thermocouples were in direct contact to the surface (see Fig. 10b). The two specimens were used from the KN_V5 series, so that finally only six specimens (see Table 2) were available for evaluation of this series. If Figs. 11 and 12 are compared with each other, it can be seen that the qualitative trends are quite similar. However, at the maximum temperature measured during the heating ramp, it can be seen that the air temperature reaches a maximum value of approximately 330 • C (Fig. 11a-single air temperature) and the surface temperature a value of approximately 354 • C (Fig. 12a-single surface temperature).
A difference of 24 K (temperature overshoot) between air and surface temperature and a difference of 54 K between target and surface temperature can be observed. These differences show the occurrence of higher surface temperatures during the heating ramp due to a non-optimized furnace control. A second observation shows that, after the thermal equilibrium was reached (around 1 h after the beginning of the experiment), the surface temperature reached the target temperature of 300 • C. A result of the observations is that the radiant energy emitted by the spiral-wound filaments generates a comparatively higher surface temperature than the air temperature. In order to exclude the temperature overshoot during the heating ramp, as shown in Fig. 9c and as already mentioned before, a radiation shielding, which was built using aluminum sheets (hereinafter also called aluminum enclosure), was provided inside the furnace. This created a chamber within the furnace which massively disturbs the convection within the furnace chamber, which otherwise would have been free to develop. Due to the installation of the aluminum enclosure inside the furnace chamber, the experimen-tal setup for heat treatment had changed and a further measurement of temperature was performed.
Heat treatment: with radiation shielding
The specimens were placed on the grate protected against thermal radiation (see Fig. 9c) with the help of the aluminum enclosure. The aluminum sheets were placed around the specimens and build a radiation shielded room within the furnace chamber. The air temperature within this room was measured with four thermocouples near the specimens (see Fig. 10a). For clarification, the upper cover of the aluminum enclosure, which is not shown in Fig. 10a, was also present during this air temperature measurement. From these four measurements the mean value, which is shown in Fig. 13a, was calculated. The corresponding heating and cooling rates, which are shown in Fig. 13b, c, were calculated with the recorded time and mean temperature. In Fig. 13a it can be observed that due to the disturbed convection inside the furnace chamber it took around three hours (from the beginning of the experiment) when the thermal equilibrium was reached within the aluminum enclosure. This can be observed considering the mean air temperature curve which slightly increases (curve between 0.5 and 3 h in Fig. 13a) after the heating ramp ended. The specimens that were heat treated with the aluminum enclosure thus underwent a temperature of approximately 200 • C. There is a difference of 100 K (comparing surface temperature measured in Sect. 3.4.3 and air temperature measured here) between the heat treatment with radiation shielding and without radiation shielding. Considering Fig. 13a, a smaller Fig. 13 a Temperature measurement with radiation shielding for 300 • C target temperature, b calculated heating rate and c calculated cooling rate overshoot is shown in comparison to the previous air temperature measurements. Furthermore, it should be mentioned that, the installation of the thermocouples did not allow the furnace door to be closed completely, resulting in a small gap which allows a comparatively higher air exchange than when the furnace door is completely closed. It is assumed that a slight exchange of air is possible even when the oven door is closed.
If the heating rates shown in Figs. 11b and 13b are compared, the effect of radiation shielding also becomes visible. The heating rates in the single heating periods when the furnace is heated up in the beginning of the heat treatment reach only half the values with radiation shielding as without radiation shielding. When considering the cooling rates, the difference is smaller and does not play as an important role as the heating rate difference.
Experimental test results of the fracture stress at room temperature
In order to determine to what extent, the heat treatment of the second study-Method B affects the fracture stress of the material specimens, double ring bending tests were carried out at room temperature as in the first study-Method A. Figure 14 shows the fracture stresses versus the used technique (and subsequent temperature) in heat treatment. The fracture stresses were calculated by Eq. (1). The specimens within this study-Method B were tested on the pre-damaged tin side. In Table 2
Summary of the study-Method B
In the second study-Method B several observations could be made. The first both measurements showed that due to the furnace design (radiation furnace) and the furnace control of heating it is possible that the surface temperature can exceed the target temperature (300 • C for Method B) set in the furnace control unit. A difference of 54 K between the surface and the target temperature could be observed. The second observation is that the air temperature and the surface temperature reached a difference of 24 K. These experiments have shown that there can occur a temperature overshoot on the glass surface. How large this overshoot will be, when using elevated temperatures (550 • C) cannot be stated at this time. To overcome this temperature overshoot, the aluminum enclosure was introduced. The use of the aluminum enclosure during the measurements showed, that it has an influence (lower temperature than target temperature) on the resulting temperature profile. But still a relative overshoot during the heating ramp is present, which indicates that amount of electric power or the heating ramp rate (10 K/min) which can be regulated by the furnace control unit need to be lowered. From the results of the third measurement (heat treatment with radiation shielding) it could also be observed that a longer time span is needed for reaching the thermal equilibrium within the furnace. The time needed for thermal equilibrium within the first both measurements was at around 1 h (from the beginning of the experiment), in the third experiment it was reached after approximately 3 h. How the time needed for thermal equilibrium will change for other temperatures cannot be estimated at this time, because several experiments including measurements have to be conducted therefore.
In the subsequent determination of the fracture strengths, the influence of the different temperatures also became apparent, as in Method A. The samples that underwent a heat treatment at 300 • C (KN_V5) yielded on average higher fracture stresses than the samples that underwent a heat treatment at 200 • C (KN_V4, 8% of increase) or that were untreated (KN_V1, 13% of increase). When comparing the mean values of the fracture stresses between KN_V1 (untreated) and KN_V4 (200 • C) nearly the same mean values of fracture stresses result, so it is possible that no crack healing during heat treatment occurred. At this stage of research, it is not possible to make a statistically reliable statement as to whether heat treatment at 200 • C results in higher fracture strengths, because the test series contained too less specimens.
Conclusions
The experimental investigations carried out so far showed that the heat treatment of pre-damaged sodalime silicate glass as float glass can increase the fracture strength of the glass. In the study-Method A, where especially an elevated temperature of around 525 • C for a short time period (lower than 15 min) was used, an increase of the mean value of the fracture stress of around 41% could be observed comparing mean values of fracture stress of KN_V1 and KN_V3. Also, during heat treatment at lower temperatures (around 300 • C, both Method A and Method B) without radiation shielding, an increase of the fracture stress of the glass from approximately 12% (Method A) to 13% (Method B) could be observed, comparing with the untreated specimens of KN_V1. It is not yet possible to make statistically sound statements on the relationship between heat treatment temperature and fracture strength at the current state of research, as the sample size of the test series with six to ten samples was very small. Nevertheless, the investigations have shown that the heat treatment can have an influence on the resulting fracture strength of the pre-damaged soda-lime silicate glass as float glass, which can be linked to a healing of the induced scratch. It could also be shown by surface temperature measurements (without radiation shielding) that the surface temperature of the glass samples is higher than the air temperature inside the furnace chamber, which can be explained by the furnace design (radiation furnace). At the current state of the investigations it is not yet possible to predict how large the temperature differences between air and surface temperature can become if elevated temperatures (e.g. 550 • C) are used for heat treatment. It could also be shown that the overshoot of air temperature during the heating ramp also occurs (relatively) when the aluminum enclosure is applied. Another observation which was made is, that the time needed for thermal equilibrium when using a radiation shielding increases from 1 h to around 3 h (from the beginning of the heat treatment at 300 • C target temperature), which results from the disturbed free convection. The measurements of air and surface temperature have also shown that the natural cooling of the furnace leads to cooling rates that are far below the rates used in the thermal toughening process. It is therefore obvious that the material samples were not thermally prestressed by the heat treatment prior to the double ring bending test, which might have been interpreted as a result of higher fracture stresses.
Outlook
For future research concerning crack healing of predamaged soda-lime silicate glass as float glass as a result of heat treatment, various aspects have arisen on the basis of the present work which will be considered for future experiments. Past research has already shown that, heat treatment can be used to increase the resulting fracture strength of glass, although the approaches of the various sources differ from each other and also differ from the method of pre-damage and strength determination presented here. The literature (Holden and Frechette 1989;Girard et al. 2011) has shown that especially the moisture in combination with elevated temperatures are the driving factors for crack healing in soda-lime silicate glass. At the current state it was not possible to measure the moisture inside the furnace chamber. For future experiments the moisture in the surrounding environment will be measured, that afterwards the mass of water which is solved in the air within the furnace chamber can be calculated.
A further aim for future studies is to improve the heating ramp in such a way that a temperature overshoot does not occur. Therefore, the heating ramp defined in the furnace control unit of 10 K/min will be reduced to a lower value. It may then be possible to remove the workaround of the aluminum enclosure. Further temperature measurements will be conducted afterwards to ensure that the air temperature and the surface temperature are nearly equal. Further experiments on heat treatment at elevated temperatures (500-550 • C) will be carried out in order to be able to make statistically sound statements on the influence of heat treatment at elevated temperatures on the fracture strength of soda-lime silicate glass with the aid of a larger sample size and Weibull analysis. Another objective for future experiments is that heat treatment experiments at lower temperatures beneath 500 • C will be performed, because the results presented here indicate that already at lower temperatures (300 • C) an increase of the fracture stress can occur. For the different heat treatment temperatures it is also foreseen that different dwell times of the specimens within the furnace at given temperature will be studied. | 9,046.8 | 2020-07-28T00:00:00.000 | [
"Materials Science"
] |
Digitalisation and Sustainable work: obstacles and pathways
The aim with this article is to identify obstacles and find pathways for sustainable work in a digital future. We are all concerned about how our work will be in the future; will we be able to handle the new technology or will technology control us? The development is often described in black and white, either as God's gift to mankind or as the wolf is coming . However, the question is not that simple. New technology, such as digitalisation, seldom has in itself a particular way to change our work, whether positive or negative. Future work is shaped here and now, and the development is always possible to influence and control. Based on the vision of Industry 4.0 and observations of the latest technological development that already concretely affects workplaces and people, we have, with the help of theories of sustainable work, discussed what digitalisation can mean for work of the future. We have identified four critical issues that need to be discussed further: 1) The Swedish labour market model under attack, 2) Upskilling, deskilling, or reskilling, 3) Changed gender patterns and 4) Shaping an A and B labour market. The theories of sustainable work are well known and used in working life, in Sweden as well in many other countries, but the road towards digitalisation is complex and filled with traps and pitfalls that need to be handled. To enable positive development, the technical and organisational development needs also to include knowledge of the society, the human and the working environment.
Introduction
In this article we will discuss some obstacles and pathways to sustainable work in the context of digitalisation."The wolf is coming" and "God's gift to mankind" are two common positions or reactions that follow many technical innovations.This also applies to today's debate on digitalisation, automation and artificial intelligence in working life."The wolf is coming" indicates a fear that our lives will be deprived of something we want to maintain, while we neither can nor really want to refrain from the digitalised society.Here we can recognise the fear that the robots will take over, and that our jobs will diminish."God's gift to mankind" emphasises the advantages and new opportunities that facilitate and enrich our lives.Here we find techno-optimistic and often technology driven ideas.Society has participated in technological development with these mixed emotions over the last 20 years, and now there are clear signs digitalisation will take a greater leap into not only our everyday lives, but also our work lives in very concrete ways.Conditions that have been considered as given may not be so sustainable in the future.In other words, future work is shaped here and now.In order to find pathways to handle the new technology and design sustainable workplaces for the future, we need to get a picture of what is happening, but we also need a vision of where we want to go and how to get there.In these times of change, we as researchers have to take on the role of the wolf and ask the uncomfortable questions, but also to go between or beyond the two positions "The wolf is coming" and "God's gift to mankind".
The role of work in a digital industrial context
The German's vision Industry 4.0 (Lasi et al., 2014), and its Swedish companion Smart Industry: a strategy for new industrialisation for Sweden (Regeringskansliet, 2016), paint a bright picture of future working life, where smart machines continuously exchange information with each other, as well as with human workers.The industrial worker will be an expert who makes sure that production runs smoothly.The worker may no longer be "locked" in a control room; instead, the real-time process data and status of machines follow the worker as she moves around the factory.She can solve problems on the spot by remotely interacting with other production operators, experts, suppliers, or customers in multicompetent teams, or she can interact with a humanoid robot that assists in decision-making and analyses.Production control can be done in a digital model far away from the factory.In short, the augmented worker has extended senses and extended memory through technology that takes advantage of and supports human skills, increasing situational awareness, for example, through sensors embedded in the operator's clothes, while keeping an uninterrupted operational vigilance.
An interesting, and perhaps in part a scary, vision is presented by Romero et al. (2016) who, based on the technical core of Industry 4.0, form a typology of the future operators, Operator 4.0.This typology is built on eight characteristics that can be seen as the effects or possibilities of the new technology: Super-Strength Operator (physical interaction) using biomechanical support for increased limb movement, increased strength, and endurance; Augmented Operator (cognitive interaction) using Augmented Reality (AR) for integrating information from the digital to the physical world; Virtual Operator (cognitive interaction) using Virtual Reality (VR) for simulation and training of real situation that might contain risks; Healthy Operator (physical and cognitive interaction) using wearable sensors for monitoring health-related metrics as well as GPS location; Smarter Operator (cognitive interaction) using Intelligent Personal Assistant (IPA) for interfacing with machines, computers, databases, and other information systems; Collaborative Operator (physical interaction) using Collaborative Robots (CoBots) for performing repetitive and non-ergonomic tasks; Social Operator (cognitive interaction) using Enterprise Social Networking Services (E-SNS) for interaction between operators and between operators and Internet of Things; and Analytical Operator (cognitive interaction) using Big Data Analytics for discovering useful information and predict relevant events.
The classification points to the numerous possibilities of integrating Industry 4.0 with human labour: some good and some bad.Nevertheless, there is an urgent need to investigate not only how these technologies are designed, chosen and implemented, but also their impacts on work in industry.There are a number of questions that need to be asked, and, as academics, we have a mission to be the social prosecutor who poses the uncomfortable questions.We have identified four such critical issues to discuss further in this article: • The Swedish labour market model under attack
The Swedish labour market model under attack
Over the years we have witnessed an increase in labour flexibility, the decline of standard labour contracts, sub-contracting or outsourcing of work (Taylor, 2010), increasing selfemployment, and mounting insecurity (Thompson, 2013).However, it is the use of digital platforms by global enterprises to crowd-source labour to small and micro sized companies all over the world that is reshaping work and employment conditions in the most visible way so far.
The term crowdsourcing was coined by Howe in 2006, and was presented as a new level of sub-contracting.For example, rather than relying on offshore jobs at low-cost locations, companies can outsource functions, once performed by employees, to an amorphous and generally large pool of individuals, using an open call over the Internet (Howe, 2008).The most significant differences between crowdsourcing and a traditional workforce are the higher levels of flexibility, scalability, access to a broad range of skills, and experiences at significantly less cost, coupled with the lack of employment regulations.This strategy appeals to industrial firms, as they are able to access a labour force that can expand and contract on demand, without any significant transaction costs or logistical hurdles.Management control is simultaneously 'at a distance' while remaining all-powerful when directing work tasks and determining the nature of reward.Relationships are fleeting and largely anonymous, with no obligation to provide support or facilities for the workforce.
Another aspect of the new technology is related to Scandinavian industrial sociology.In this field, Lysgaard's (1961) book on the workers' collective is regarded as seminal, one of the classics of its time.Although it is well researched and documented that workers act collectively in the workplace, the term 'workers' collective' is rarely used in current Nordic research.It is, for example, well-known that the workers' collective functions as a set of norms, controlling the workers' relations to each other as well as the extent to which deviations from these norms (e.g., a certain type of masculinity, negative attitudes to management, and technological change) are counteracted or accepted.Materialised by this normative system, the workers' collective is based on a culture of resistance that attempts to gain informal control over the work situation.It can also function as a protector of practical and hard physical work, referred to as 'embodied competence' or 'body capital'.Consequently, new technology and new management models are often resisted by the collective system.In this context, Industry 4.0, automated factories, and Internet of Things represent a new technological and managerial landscape to which several reactions are possible.There is a need to analyse the opportunities and challenges represented by the current technological and organisational development, and to create a theoretical platform for the understanding of the transformation of work and workers, based on the workers' collective.
On an aggregated level, this is about the survival of the Swedish labour market model.The Swedish labour market is one of the most harmonious in the world, based primarily on bilateral agreements between the parties, rather than on legislation.In a global internet-based labour market, there is hardly any space for collective agreement and the Swedish labour market model, instead the legislative path seems to be the only way possible.Here is an interesting opening where the Swedish trade unions have long been more co-operative than their European colleagues.Relationship to new technology has often been characterised by "If you can´t beat them, join them" (Johansson et al 2013).
Upskilling, deskilling, or reskilling?
The visions of fully automated factories, Industry 4.0, and Internet of Things not only change the technological landscape of industrial workplaces and organisations, but also cause a qualitative knowledge transformation: from bodily and tacit into more abstract and theoretical knowledge and skills.In the optimistic view, we can read that Industry 4.0 requires workplace learning, as well as continuous education and systems that make use of the workers' skills: i.e., a learning organisation.Using Kern and Schumann's concepts (1974), we can see a clear transformation from the craftsman-like qualification into more technical qualifications.The new demands for teamwork, responsibility, and comprehensive understanding of production flow can be seen as a movement from qualifications dependent on the process, to qualifications more independent of the process (cf.Kern & Schumann, 1974, 1987;Bright, 1958;Blauner, 1964;Johansson, 1986).What was earlier the workers' tacit knowledge (Polanyi, 1967) will be formalised into theoretical knowledge, digitalised, and used in computers and smart phones.In this transition, we can see contradictory movements of upskilling: rapidly changing skill demands and more theoretical, comprehensive, and communication tasks: and deskilling, fragmentation of individual craft knowledge and whole tasks (Abrahamsson & Johansson, 2006).
Whether it is a question of upskilling, deskilling, or reskilling, the transformation of knowledge affects workplace cultures, community of practices, and identities.Individuals and organisations will have to create and recreate qualifications, identity, and gender, when meeting new technology in a changing context.For example, the new knowledge and skills needed may be more abstract and theoretical, but still based on bodily and tacit knowledge, although in new and less physically demanding forms.A common optimistic scenario gives women and other previously underrepresented groups a chance to enter and master different types of industrial work, such as in mining and process industries.Given that this scenario is realised, it does not entail a smooth and unproblematic process.The identity and symbolic aspects of work often lag behind the developments in, for example, technology and qualification demands, resulting in restoring responses during processes of organisational changes (Abrahamsson, 2014).As the workers' collective (cf.Lysgaard, 1961;Fältholm, 1998) is built and sustained by processes of homosocial interaction and identification and on norms controlling likeness between workers, there is reason to investigate how new technology affects these processes.The seemingly robust gender and power relations will be challenged, renegotiated, and ultimately transformed.
Changed gender patterns
One of the hopes of technological development in the industry is that it will allow for changed gender patterns: a better work environment combined with higher qualification demands that will enable more women to work in the industry, creating better gender equality.But the picture is not so clear-cut.At many industrial workplaces where digitalisation is taking place, it is quite common that technology is associated with masculinity (Berner, 2003;Mellström, 2004).This masculinisation of technology is evident in the discourse of the technology, as well as in the culture of these companies.At traditional male-dominated industrial workplaces, even if the workplaces undergo digitalisation, the connection to masculinity lingers, because of the old strong symbolic links to a traditional blue-collar masculinity (Abrahamsson, 2006;Andersson, 2012;Eveline, 2001;Lahiri-Dutt, 2007, 2012, see also Collinson, 1992;Whitehead, 2002;Willis, 1979).For example, the work is often associated with explicit expressions of a special type of masculinity, "macho-masculinity", which is almost difficult to take seriously and analyse (Somerville & Abrahamsson, 2003).The fear of being seen as less masculine is a common theme in these kinds of workplaces.Here men, more than in other workplaces, find it difficult to be associated with competences, attitudes, or behaviours that have a female gender-code (Eveline, 2001(Eveline, , 1989;;Gherardi & Nicolini, 2000;Ely & Meyerson, 2008;Somerville & Abrahamsson, 2003) or have associations with unmanliness (Connell, 1995).As a result, we can see an interesting and seemingly paradoxical tendency that workplaces and work tasks introduced as a result of automation, computerisation, and robotisation can undergo a process of "feminisation" while the men hang on to the old technology (Olofsson, 2010).One example of this is when the mining workers underground, half-jokingly give the remotecontrol workers sitting above ground nicknames such as "the velour workers" (Abrahamsson & Johansson, 2006;Andersson, 2012), meaning that they are of a soft unisex type of men, almost feminine, and not 'real' workers.On the one hand, this trend opens up new gender constructions in industry; on the other hand, this trend can be seen as a symptom of a conservative organization, i.e., barriers to implementing the new technology, and therefore important to study and understand.
At workplaces with a more gender-balance, male workers may attempt to restore the existing local gender order, by telling macho-masculine stories, refusing to do 'women's work' or 'womanish work', and openly resisting women at the workplace (Abrahamsson, 2014;Eveline & Booth, 2002;Lahiri-Dutt, 2012).In these workplaces, ideas about gender: femininities and masculinities, often are so conservative they can create trouble during organisational changes and the implementation of new technology (Abrahamson, 2002;Hollway, 1996;Collinson & Hearn, 1996).
Gender is something people do and construct in social interactions (Gherardi, 1994;West & Zimmerman, 1987, 2009), embedded in work identities, work organisations, and technology (Acker, 1990), formed by complex societal processes and notions of masculinity and femininity.Many attitudes, norms, and cultural symbols at work that are learned through workplace socialisation are connected to gender and the (unequal) gender order (Hirdman, 1988(Hirdman, , 2001)).Tacit collective agreements and a continuous dramatization of gender both restore and change our ways of seeing masculinity and femininity.This play does not become really visible unless the existing masculinity and femininity are threatened (Butler, 1990(Butler, , 1993)), such as in the transformation towards a digital industrial context.Even if such processes often are connected to the restoration of the unequal gender order they are situated in, these processes are continuously changing, and there is a possibility to challenge and transform these processes (Abrahamsson, 2014).
Shaping an A and B labour market
In the optimistic visions smart systems, automation, and remote control will take over dangerous as well as routine work, so that production personnel can focus on learning, creating, and valuing work tasks in a safe environment (Gill, 2014).Even if the development will not be as the positive visions predict, depending on how the new technology is developed and interpreted, there will most likely be new types of industrial work, new types of work environments, and thus new work environmental problems.For example, digital technology and remote control, together with the emerging global and sometimes boundary-less work, not only results in increased freedom to decide how and where to work, but also results in higher demands of availability, perhaps 24 hours a day, seven days a week.This change may blur the boundaries between work and private life.Moreover, since the ability to control and monitor the individual increases, there will be a risk of new psychosocial stress.An increased information flow and accessibility could also lead to anxiety and job strain (Hoonakker & Korunka, 2014).
Other examples come from enhanced possibilities of production distribution, decentralisation, and outsourcing, both locally/regionally and in the global context.This creates dynamic systems of contractors, agency staff, and other actors temporarily active in the same physical workplace or in the same virtual/digital workplace.As mentioned above, the employment form as we know today might dissolve and be replaced with crowdsourcing and what can be called liquidised employment (Holtgrewe, 2014), complicating the coordination of work environment interventions and responsibilities (Johansson et al., 2010).
We might also expect that old work environmental problems will appear in new contexts, and for other groups of workers.Some workers may participate in shaping the systems, while others will become machine assistants, or handle the repetitive and low qualified work tasks that could not be integrated into the automated and smart systems and the learning organisation.Maybe it is time to revive the old debate about the A and B labour market (Braverman, 1974;Kern & Schumann, 1974)?
Future work: pathways and implications
For citizens in a democratic societal context, it is a civil right to be involved in shaping their own future.For many, however, in organisational work contexts characterised less by democracy and more by hierarchical power asymmetries and (increasingly precarious) wage labour contracts, the diffusion of new technology into their working life is sometimes perceived as a rather deterministic process, where their discretion is viewed as very limited.Our ambition is to create awareness of what the new technology can mean and for whom, and at the same time generate knowledge that development is possible to influence and control.There is always room to manoeuvre, for shaping how new technologies can be useful and relevant to people and society.The social dimension must have a prominent place in this process, both in designing the technology and in analysing it from several perspectives.However, there is no lack of knowledge about the significance of the social dimension.Based on extensive and relatively coherent international research on work environment and work organisation, it is possible to formulate a summary list of requirements, almost a utopian vision, of what constitutes sustainable work (cf.Johansson & Abrahamsson, 2009).Such a list could for example include demands that, not only are physical risks and problems eliminated, and equipment and work sites are adapted to suit people's different physical and psychological set-up, and designed to make work easier, but employees also enjoy autonomy and a sense of participation and influence in matters both large and small.These involve being able to influence the division of duties and the pace and method of working, in relation to both other people and to the technical system used.The list could also include that the work and workplace provide physical, intellectual and cultural stimulation, variety, opportunities for social interactions, context and opportunities for learning and for personal and professional development.Here, workloads, demands, and challenges (both physical and psychological) are balanced at a reasonable level.The list would also include gender equality, fairness, respect, trust, democratic leadership, and open communication and opportunities for enjoyment and social support for all employees.There should also be good opportunities for a fair, stable and predictable income and to combine work with a rich and sustainable life outside of work.To conclude, the vision of sustainable work is known and accepted by most people.It is rather the road that is unknown and filled with some dangers and pitfalls.The design of new technology and new work organisation must be harmonised, with both good working conditions and efficient production that can compete in a global market, but the quite optimistic scenario described in the Industry 4.0 texts is not likely to become a reality by itself.New technology has not in itself a particular way to alter the effectiveness or working conditions, whether positive or negative.To enable a positive development, the technical and organisational development needs also to include knowledge of the human, the working environment and the organisation of work, both the formal and informal organising.Industry 4.0, essentially a technology-driven vision, generally refers to a technological revolution with a strong focus on production rationalisation, but we can also see that the organisational recommendations set up for the implementation of Industry 4.0 (e.g., production flow, connected processes and systems, horizontal integrated and flexible organisation, learning and production standardisation, and diagnosis) (see Kagerman et al. 2013) have clear similarities with BPR, The Boundaryless Organisation, Learning Organisation, TBM, TQM, Six Sigma, and Lean.Therefore, there is a need for critical organisational analyses, discourse analyses, analyses of embedded conflicts in Industry 4.0, power shifts, and invisibility of power.In addition, there is a need for analyses related to other current organisational trends (e.g., centralisation, monitoring, requirements for voluntary, storytelling, and corporate branding) and wider social changes.
In general, the technical development is positive, but there are many questions that must be clarified, and we have discussed four of them.The development cannot and should not be stopped, but it requires reflections and considerations, so we do not create more problems than we solve.Research has an important role to play, when new technology should be valued and introduced, but that role is not pre-given to us; we have to mark our position by highlighting issues that are perceived as important and relevant.We cannot let the Industry 4.0's advocates set the discourse, alternative questions must be asked, other type of experts, such as academics, must be engaged, and alternative issues must be communicated and discussed by a wider audience.In the title of the article, we ask the question: The wolf is coming or God's gift to mankind?In order to experience sustainable work, we as researchers sometimes have to take on the role of the wolf, and ask uncomfortable questions.References Abrahamsson, L. (2002) . Restoring the order: Gender segregation as an obstacle to organisational development, Applied Ergonomics, Volume 33, Issue 6, November 2002, pp.549-557 Abrahamsson, L. (2006).Exploring construction of gendered identities at work, pp 105-121.In Billet, Stephan; Fenwick, Tara & Somerville, Margaret (eds.).Work, Subjectivity and Learning.Understanding Learning through Working Life.Dordrecht: Springer. | 5,126.8 | 2021-03-05T00:00:00.000 | [
"Computer Science"
] |
A novel Muth generalized family of distributions: Properties and applications to quality control
: In this paper, we propose a novel family of distributions called the odd Muth-G distributions by using Transformed-Transformer methodology and study their essential properties. The distinctive feature of the proposed family is that it can provide numerous special models with significant applications in reliability analysis. The density of the new model is expressible in terms of linear combinations of generalized exponentials, a useful feature to extract most properties of the proposed family. Some of the structural properties are derived in the form of explicit expressions such as quantile function, moments, probability weighted moments and entropy. The model parameters are estimated following the method of maximum likelihood principle. Weibull is selected as a baseline to propose an odd Muth-Weibull distribution with some useful properties. In order to confirm that our results converge with minimized mean squared error and biases, a simulation study has been performed. Additionally, a plan acceptance sampling design is proposed in which the lifetime of an item follows an odd Muth-Weibull model by taking median lifetime as a quality parameter. Two real-life data applications are presented to establish practical usefulness of the proposed model with conclusive evidence that the model has enough flexibility to fit a wide panel of lifetime data sets.
Introduction
In real-life circumstances, there is always an element of uncertainty which always makes the applied researchers have jitters regarding the selection of an appropriate model.Thus, in order to be on the safe side, applied practitioners always prefer classical distributions such as the Exponential, Weibull or Gamma distribution.To add to the misery, theoreticians generally propose generalizations and modifications of such classical models in order to resolve discrepancies among them.There is an abundance of generalizations of such orthodox distributions as it the discretion of researchers to select the model which they want to explore both theoretically and in applied form.
Despite their importance in the literature, there are a number of distributions that have yet to be fully investigated.The functional complexity of the models may be the most plausible rationale, with the improvement of computational capabilities and numerical optimization techniques such as MATLAB, Python and the R language, this claim is easily refuted.In our perspective, the statistical literature should include these overlooked models that are seldom employed.For distributions that are not regularly discussed in the literature, the authors in [1] provided a comprehensive list.This motivated us to investigate such models or suggest long-overlooked generalizations based on such models.One such model is the Muth distribution, with the name pioneered by the authors in [1].For a continuous univariate distribution, a random variable X is said to follow a Muth distribution such that X ∼ Muth(a) with the following distribution function: where parameter a ∈ (0, 1).According to the authors in [2], it was Tessiér (1934) who initially studied this distribution in the context of an animal ageing mechanism.However, Muth (1977) pointed out instances where it appears as a good model to study the stochastic nature of the variable under consideration as compared to established models.In [3], the authors studied the scaled version of the Muth distribution and established its superiority over the existing distribution by using meteorology data.A few other works related to the Muth distribution have been esented in [2][3][4][5][6][7].The reader is referred to [2], in which an excellent review of the Muth distribution in chronological order has been conducted by the authors.
In this article, we propose a generalization of the Muth distribution.Regarding the generalization of conventional models, the Transformed-transformer T-X approach, introducted in [8], is an integral part for the construction of generalized families of distributions.The distribution function (cdf) of the T-X family is defined by The pdf corresponding to (1) is where the pdf of any baseline distribution is g(x; ξ).
To the best of our knowledge, very few generalizations of the Muth distribution have been proposed in the literature.These include the Muth-G family by Almarashi and Elgarhy [9] using the T-X methodology, the Transmuted Muth-G class of distributions by [10] using quadratic rank transformation and the New Truncated Muth generated (NTM-G) family of distributions [31] in the context of a unit distribution.This further intrigued us to formulate a generalization of the Muth distribution via an odd random variable, denoted as odd Muth-G (OMG for short), in Eq (2.1) and study its mathematical properties.Similar generalizations based on odd ratios are odd Weibull-G in [11], odd generalized-exponential-G in [12], alternate odd generalized exponential-G in [13], odd gamma-G in [14], odd Lindley-G in [15], odd Burr-G in [16], odd power-Cauchy-G in [17], odd half-Cauchy in [18], odd additive Weibull-G [19], odd power-Lindley-G [20], odd Xgamma-G [21], etc.For a comprehensive review on generalized families, the reader is referred to [22,23].
For a more apt background of the T-X approach, readers are referred to [8].Further motivations to propose the OMG class include the following: The inverse distribution function, median, moment generating function and characteristic function of the Muth distribution are not mathematically tractable, though these properties exist for the OMG family; when the shape parameter a → 0, the Muth distribution converges to the exponential family.Thus, there exists a relation between the OMG and exponential families such as exponentiated-G (EG) by [24] and exponentiated generalized-G (EGG) by [25]; the OMG class improves the flexibility of the tail properties of the baseline distribution in terms of improving the goodness of fit statistical criterion and the ability to fit symmetric as well as asymmetric real life phenomena; the Muth distribution is applied for the first time in the context of quality control, which is an integral part of reliability analysis.
The manuscript is structured as follows.In Section 2, the odd Muth-G family and its reliability properties are defined.The general properties of the proposed family are depicted in Section 3. Parameters estimation of the proposed family is illustrated in Section 4. A special model called odd Muth-Weibull (OMW) is presented in Section 5 with some essential properties.Section 6 is based on simulation analysis, while Section 7 showes the mathematical and numerical illustration of the group acceptance sampling plan (GASP).The application to real-life data is presented in Section 8. Section 9 ends the manuscript with some concluding remarks.
Layout of the proposed family
In this section, the odd Muth-G (OMG) family of distributions and its reliability properties are defined.
The following are the expressions of cdf, pdf, reliability function (rf), hazard rate function (hrf) and cumulative hazard rate function (chrf) of the OMG family, respectively: and (2.5)
Proposed family and its properties
Here, we derive some basic properties of the OMG family.
The expression of quantile function
The following expression shows the quantile function (qf) of the OMG: The above expression contains the Lambert-W function of the negative branch.
Densities expansion
In this section, we present a useful expansion for Eq (2.1) by using exponential series expansions, as By using the above exponential series on Eq (2.1), it reduces to Using reciprocal power series expansion (see [26], p. 239) on Eq (3. 2), we are given the following result: where L 0 = 1/b 0 when k = 0, and After incorporating results in Eq (3.2), the expression for linear representation will become where and b k = (−1) k j k .The expression for the density function after taking the derivative of Eq (3.3) will become where h j, k = ( j + k)g(x) G(x; ξ) j+k−1 is a linear combination of the exp-G family, and one can obtain the various properties by taking into account Eq (3.4).
Moments
By using Eq (3.4), the rth ordinary or raw moment of the OMG family is given by By using Eq (3.5), one can get the actual moments and cumulants for X as respectively, where κ 1 = µ 1 .By using the relationship between actual moments and ordinary moments, one can get the measures of skewness and kurtosis.The rth incomplete moment of OMG can be expressed as where I r j, k (t) = t 0 x r h(i j, k) d x , and the incomplete moments are vital in order to compute the wellknown namely Bonferroni and Lorenz curves.
The expression of probability weighted moment
The expression of (r, q)th probability weighted moment (PWM) can be founded as ρ r,q = ∞ 0 x r F(x) q f (x)dx. (3.7) Inserting Eqs (2.1) and (2.2) in Eq (3.7), and using the generalized binomial series expansion, ρ r,q can be expressed as Applying the power series expansion defined in Section 4 on Eq (3.8), it will become Applying a power series expansion on quantity A, it will reduce to exp a(c The expression for ρ r,q after incorporating the result of quantity A, can be expressed as Using generalized binomial series expansion on the above equation, After incorporating the result of the above equation, the expression for ρ r,q can be expressed as Integrating (3.10), we can obtain the expression of PWMs, where
Entropy
The entropy measure is important to underline the uncertainty variation of a rv; let X be a rv having pdf f (x).The Rényi entropy can be found by the following expression: where δ > 0, δ 1, and Inserting Eq (2. 2) in f δ (x), gives Applying a power series yieldes After incorporating the result in Eq. (3.11), the expression for Rényi entropy will reduce to where
Estimation
Here, we demonstrate the estimation of parameters by taking into account the maximum likelihood approach.The log-likelihood (LL) function (Ω) for the vector of parameters Ω = a, ξ can be expressed as The first partial derivatives of Eq (4.1) with respect to a and ξ are where are derivatives of column vectors of the same dimension of ξ.
The OMW distribution
Here we consider Weibull as a baseline model with cdf and pdf, respectively, given as G(x; ξ) = 1 − e −αx β and g(x; ξ) = β α x β−1 e −αx β , where α > 0 is a scale, and β > 0 is a shape parameter.Then, the cdf, pdf, rf, hrf and chrf of the proposed OMW model, respectively, are given by The graphical illustrations of pdf and hrf based on some selected parametric values of OMW are depicted in Figure 1 and reveal that the OMW model has flexibility in both pdf and hrf.
Properties of OMW model
First, we will derive a linear expression of the OMW density to get the useful mathematical properties of this new model.
Several properties of the OMW model can be yielded by using Eq (6. 2) because it is a linear combination of Weibull densities.
The qf of the OMW distribution is given as 3) The expression of rth moments is given by The graphical illustrations of skewness and kurtosis are depicted in Figure 2 for the OMW distribution.The expression for the rth incomplete moment can be written as where γ(s, x) = ∞ 0 x s−1 exp(−x)dx.The expression for the PWMs can be written as where t s = (−1) s j+p s ∞ j,p=0 V j,p ( j + p + 1) .The expression for Rényi entropy can be written as where
Estimation
Let there be a sample of size n from the OMW model given in Eq (5.2).The LL function = (θ) for the vector of parameters θ = ( α, β, a) is − a (6.8) Equation (6.8) can be easily maximized using the computational software R or Mathematica.The components of the score vector U(θ) are One can yield MLEs by setting these equations equal to zero and solving simultaneously.
Group acceptance sampling plan (GASP)
This section is based on the illustration of GASP under the assumption that the lifetime distribution of an item follows an OMW model with known parameters α and β having cdf in Eq (8.2).In a GASP, say, n is the randomly selected sample size and distributed to g groups, and r for a preassigned time r items in a group are tested.If more than c failures occur in any group during the experiment time, the performed experiment is truncated.The reader is referred to Aslam et al. [29] and Khan and Alqarni [30] for a simple illustration of GASP and an application to real data.Designing the GASP reduced both the time and cost.Several lifetime traditional and extended models are used [10,29,[33][34][35] in designing the GASP by taking into account the quality parameter as mean or median; usually, for skewed distributions median is preferable [29].
The GASP is simply the extension of the ordinary sampling plans i.e., the GASP reduces to the ordinary sampling plan by replacing r = 1, and thus n = g [32].
GASP is based on the following process.First, select g (the number of groups) and allocate predefined r (group size) items to each group so that the sample of size of the lot will be n = r × g.Second, select c and t 0 (the experiment time), respectively.Third, do experiment simultaneously for g groups and record the number of failures for each group.Finally, a conclusion is drawn either accepting or rejecting the lot.The lot is accepted if there no more than c failures occur in each and every group and otherwise the lot is rejected.The probability of accepting the lot is represented by the following expression: where the probability that an item in a group fails before t 0 is denoted by p and yielded by inserting (6.3) in (8.2).Let the lifetime of an item or product follow an OMW with known parameters α and β, with cdf given by for t > 0 for convenient we used the qf of OMW model using (3.1) is given by and if p=0.5 yielded the median of the lifetime distribution of the product is not smaller than the specified median value.
and by taking η as Eq (8.3) is obtained by writing α = m/η and t = a 1 m 0 .The ratio of a of product mean lifetime, the specified life time m/m 0 can be used to express the quality level of the product.Replacing the α = m/η and t = m 0 a 1 in Eq (8.2) yields the probability of failure, given by From Eq (8.2), for taking the values of a and β, p can be determined when a 1 and r 2 are specified, where r 2 = m/m 0 .Here, we define the two failure probabilities, say, p 1 and p 2 corresponding to the consumer risk and producer risk, respectively.For given specific values of the parameters a , β, r 2 , a 1 , β * and γ, we need to determine the values of c and g that simultaneously satisfy the following two equations: and where the mean ratio at consumer's risk and at producer's risk, respectively denoted by r 1 and r 2 and the probability of failure to be used in the above expression as follows and Tables 4 and 5 are based on arbitrary values of parameters to underline the effect of design parameters.When r = 5, from Table (4), with β * = 0.1, a 1 =0.5, r 2 =4, there should be 185 items needed for testing (37*5=185).On the other hand, under the same condition when r=10, there should be 60 units tested.So, here, we should prefer when r=10, which significantly reduces the number of units that need to be tested.Table 4. GASP under OMW, when a = 0.5, β = 1, showing minimum g and c.
Empirical investigation
The practical implementation of the proposed model is carried out in this section by considering two real-life data sets.The first and second data sets are taken from [27,28] [36], Kumaraswamy Weibull (KwW), exponentiated generalized Weibull (EGW), beta Weibull (BW) and Weibull (W) are applied to these data sets.
The analysis of both data sets revealed that the proposed OMW model outperforms the comparative models, as per the least information criterion and higher P-values.The estimated parameters along with standard errors are depicted in Tables 6 and 8, whereas the accuracy measures are given in Tables 7 and 9.The graphical illustrations from Figures 3 and 4 are showing good agreement between the actual and fitted results.
The probability density functions of the comparative models are as follows:
AIMS Mathematics
Volume 8, Issue 3, 6559-6580.When r = 5, from Table 10, with β * = 0.1, a 1 =0.5, r 2 =4, there should be 860 items needed for testing (172*5=860).On the other hand, under the same condition, when r=10 there should be 240 units tested.So, here, we should prefer when r=10, which significantly reduces the number of units that need to be tested.
From Tables 11 and 12, when the true median life increases, the number of groups decreases, and operating characteristics values increases.For data 1 when β * = 0.05, a 1 = 1, r=10, α = 0.3201 and β = 0.7953 and for data 2 when β * = 0.05, a 1 = 1, r=5, α = 0.5360 and β = 1.5825 are the proposed GASP, when a lifetime of an item follows a OMW model.We introduced the new odd Muth-G family of distributions with essential properties.A special model called the odd Muth-Weibull is presented with some useful properties.Further, a design of a group acceptance sampling plan is proposed under the OMW model by considering median life as a quality parameter.Real data application revealed that the proposed model yielded better fits compared to some commonly well known models.
Figure 2 .
Figure 2. Graphical illustrations of Skewness and Kurtosis of OMW model at varying parametric values.
Figure 3 .Figure 4 .
Figure 3. Plots of estimated density, estimated cdf, estimated hrf and P-P for the Aircraft Windshield Data.
Table 6 .
Summary of the estimated parameters along with SEs of aircraft windshield data.
Table 7 .
Summary of the goodness of fit statistic for the aircraft windshield data.
Table 8 .
Summary of the estimated parameters along with SEs of Fiber strength.
Table 9 .
Summary of the goodness of fit statistic for the Fiber strength data. | 4,202.8 | 2023-01-01T00:00:00.000 | [
"Mathematics"
] |
Splitting Strategy for Simulating Genetic Regulatory Networks
The splitting approach is developed for the numerical simulation of genetic regulatory networks with a stable steady-state structure. The numerical results of the simulation of a one-gene network, a two-gene network, and a p53-mdm2 network show that the new splitting methods constructed in this paper are remarkably more effective and more suitable for long-term computation with large steps than the traditional general-purpose Runge-Kutta methods. The new methods have no restriction on the choice of stepsize due to their infinitely large stability regions.
Introduction
The exploration of mechanisms of gene expression and regulation has become one of the central themes in medicine and biological sciences such as cell biology, molecular biology, and systems biology [1,2]. For example, it has been acknowledged that the p53 tumor suppressor plays key regulatory roles in various fundamental biological processes, including development, ageing, and cell differentiation. It can regulate its downstream genes through their signal pathways and further implement cell cycle arrest and cell apoptosis [3][4][5][6]. The qualitative analysis as well as numerical simulation has become an important route in the investigation of differential equations of genetic regulatory networks (GRNs) in the past few years [7][8][9][10]. Up till now, algorithms used in the simulation of GRNs have primarily been classical Runge-Kutta (RK) methods (typically of order four) or Runge-Kutta-Fehlberg embedded pairs as employed in the scientific computing software MATLAB [11][12][13]. However, if we are required to achieve a very high accuracy, we have to take very small stepsize. Moreover, the traditional Runge-Kutta type methods often fail to retain some important qualitative properties of the system of interest. This prevents us from acquiring correct knowledge of the dynamics of genetic regulatory networks.
Geometric numerical integration aims at solving differential equations effectively while preserving the geometric properties of the exact flow [14]. Recently, You et al. [15] develop a family of trigonometrically fitted Scheifele two-step (TFSTS) methods, derive a set of necessary and sufficient conditions for TFSTS methods to be of up to order five based on the linear operator theory, and construct two practical methods of algebraic four and five, respectively. Very recently, You [16] develops a new family of phase-fitted and amplification methods of Runge-Kutta type which have been proved very effective for genetic regulatory networks with a limit-cycle structure.
Splitting is one of the effective techniques in geometric integration. For example, Blanes and Moan [17] construct a symmetric fourth-and sixth-order symplectic partitioned Runge-Kutta and Runge-Kutta-Nyström methods and show that these methods have an optimized efficiency. For a systematic presentation of the splitting technique, the reader is referred to Hairer et al. [14]. The purpose of this paper is to develop the splitting methods for GRNs. In Section 2 we present the system of differential equations governing the GRNs and basic assumptions for the system. In Section 3 we describe the idea and formation of the approach of splitting strategy which intends to simulate exactly the characteristic part of the system. Section 4 gives the simulation results of the new splitting methods and the traditional Runge-Kutta methods when they are applied to a one-gene network, a twogene network, and a p53-mdm2 network. We compare their accuracy and computational efficiency. Section 5 is devoted to conclusive remarks. Section 6 is for discussions. In Appendix, the linear stability of the new splitting methods is analyzed.
In particular, we are concerned in this paper with the following two simple models.
(I) The first model is a one-gene regulatory network which can be written aṡ ( ) = − ( ) + ( ( )) , where ( ( )) = /(1 + ( ) 2 / 2 ) represents the action of an inhibitory protein that acts as a dimer and , , , , and are positive constants. This model with delays can be found in Xiao and Cao [18].
(II) The second model is a two-gene cross-regulatory network [7,19]:̇1 where 1 and 2 are the concentrations of mRNA 1 and mRNA 2, respectively, 1 and 2 are the concentrations of their corresponding products protein 1 and protein 2, respectively, 1 , and 2 represent the maximal transcription rates of gene 1 and gene 2, respectively, 1 and 2 are the degradation rates of mRNA 1 and mRNA 2, respectively, 1 and 2 are the degradation rates of protein 1 and protein 2, respectively, are the Hill functions for activation and repression, respectively, 1 and 2 are the Hill coefficients, and 1 and 2 are the thresholds. It is easy to see that the activation function ℎ + is increasing in 2 and the repression function ℎ − is decreasing in 1 .
A p53-mdm2
Regulatory Pathway. Another model we are interested in is for the damped oscillation of the p53-mdm2 regulatory pathway which is given by (see [20]) where represents the concentration of the p53 tumour suppressor, (mdm2) is the concentration of the p53's main negative regulator, is the concentration of the p53-mdm2 complex, is the concentration of an active form of p53 that is resistant against mdm2-mediated degradation, ( ) is a transient stress stimulus which has the form ( ) = − , = , * ( * = , 0, 1) are de novo synthesis rates, * ( * = , , ) are production rates, * ( * = , ) are reverse reactions (e.g., dephosphorylation), is the degradation rate of active p53, and is the saturation coefficient.
Runge-Kutta Methods.
Either the mRNA-protein network (1) or the p53-mdm2 regulatory pathway (6) can be regarded as a special form of a system of ordinary differential equations (ODEs): where = ( ) ∈ and the function : R → R is smooth enough as required. The system (7) together with initial value (0) = 0 is called an initial value problem (IVP). Throughout this paper we make the following assumptions.
(ii) The steady state * is asymptotically stable; that is, for any solution ( ) of the system (7) The most frequently used algorithms for the system (7) are the so-called Runge-Kutta methods which read where is an approximation of the solution ( ) at , = 0, 1, . . ., , , , = 1, . . . , , are real numbers, is the number of internal stages , and ℎ is the step size. The scheme (8) can be represented by the Butcher tableau: or simply by ( , , (])), where = ∑ =1 for = 1, . . . , . Two of the most famous fourth-order RK methods have the tableaux as follows (see [13]): which we denote as RK4 and RK3/8, respectively.
Splitting Methods.
Splitting methods have been proved to be an effective approach to solve ODEs. The main idea is to split the vector field into two or more integrable parts and treat them separately. For a concise account of splitting methods, see Chapter II of Hairer et al. [14]. Suppose that the vector field of the system (7) has a split structure Assume also that both systems = [1] ( ) and = [2] ( ) can be solved in closed form or are accurately integrated and their exact flows are denoted by [1] ℎ and [2] ℎ , respectively.
Definition 1. (i) The method defined by
is the simplest splitting method for the system (7) based on the decomposition (11) (see [13]).
Theorem 5.6 in ChapterII of Hairer et al. [14] gives the conditions for the splitting method (14) to be of order .
However, in most occasions, the exact flows [1] ℎ and [2] ℎ for [1] and [2] in Definition 1 are not available. Hence, we have to use instead some approximations or numerical flows which are denoted by 1 and 2 .
Splitting Methods for Genetic Regulatory Networks Based on Their Characteristic
Structure. For a given genetic regulatory network, different ways of decomposition of the vector field may produce different results of computation. Thus a question arises as follows: which decomposition is more appropriate or more effective. In the following we take the system (1) for example. The analysis of the p53-mdm2 pathway (6) is similar. Denote ( ) = ( ( ), ( )) . Then the -gene regulatory network (1) has a natural form of decomposition: Unfortunately, it has been checked through practical test that the splitting methods based on this decomposition cannot lead to effective results. To find a way out, we first observe where ( * ) is the Jacobian matrix of ( ) at point * and ( ( )) = ( * + ( )) − ( * ) ( ) − ( * ).
Computational and Mathematical Methods in Medicine
We employ this special structure of the system (16) to reach the decomposition of the vector field: where ( ) = ( ( ), ( )) . The systeṁ= [1] ( ) here is called the linearization of the system (1) at the steady state ( * , * ). [1] in (17) is the linear principal part of the vector field which has the exact flow [1] ). However, it is not easy or impossible to obtain the exact solution of [2] ( ( ), ( )) due to its nonlinearity. So we have to use an approximation flow [2] ℎ and form the splitting method: When [2] is taken as an RK method, then the resulting splitting method is denoted by Split(Exact:RK). Hence we write Split(Exact:RK4) and Split(Exact:RK3/8) for the splitting methods with [2] taken as RK4 and RK3/8, respectively.
Results
In order to examine the numerical behavior of the new splitting methods Split(Exact:RK4) and Split(Exact:RK3/8), we apply them to the three models presented in Section 2. Their corresponding RK methods RK4 and RK3/8 are also used for comparison. We will carry out two observations: effectiveness and efficiency. For effectiveness, we first find the errors produced by each method with different values of stepsize. We also solve each problem with a fixed stepsize on different lengths of time intervals. Table 1 gives the parameter values which are provided by Xiao and Cao [18]. This system has a unique steady state ( * , * ) = (0.6, 2) where the Jacobian matrix has eigenvalues 1 = −1.2500+2.9767 , 2 = −1.2500 − 2.9767 , where is the imaginary unit satisfying 2 = −1. Since the two eigenvalues both have negative real parts, the steady state is asymptotically stable. In order to apply the splitting methods Split(Exact:RK4) and Split(Exact:RK3/8), the vector field of the system (3) is decomposed in the way of (16) as [1] ( ( )) = ( − − 2 * / 2
Then we solve the problem with a fixed stepsize ℎ = 2 on several lengths of time intervals. The numerical results are given in Table 6. Table 7 gives the parameter values which are used by van Leeuwen et al. [20]. For simplicity, we take the small function ( ) ≡ 0. This system has a unique steady state ( * , * , * , * ) = (9.42094, 0.0372868, 3.49529, 0). Since the eigenvalues 1 = −38.4766, 2 = −0.0028 + 0.0220 , 3 = −0.0028 − 0.0220 , and 4 = −0.2002 of the Jacobian matrix at the steady state all have negative real parts, the steady state is asymptotically stable.
Then we solve the problem with a fixed stepsize ℎ = 2 on several lengths of time intervals. The numerical results are given in Table 9.
Conclusions
In this paper we have developed a new type of splitting algorithms for the simulation of genetic regulatory networks. The splitting technique has taken into account the special structure of the linearizing decomposition of the vector field. From the results of numerical simulation of Tables 2, 5, and 8, we can see that the new splitting methods Split(Exact:RK4) and Split(Exact:RK3/8) are much more accurate than the traditional Runge-Kutta methods RK4 and RK3/8. For large steps when RK4 and RK3/8 completely lose effect, Split(Exact:RK4) and Split(Exact:RK3/8) continue to work very well. On the other hand, Tables 3, 6, and 9 show that for comparatively large steps, RK4 and RK3/8 can solve the problem only on short time intervals while Split(Exact:RK4) and Split(Exact:RK3/8) work for very long time intervals.
We conclude that, for genetic regulatory networks with an asymptotically stable steady state, compared with the traditional Runge-Kutta, the new splitting methods have two advantages.
(a) They are extremely accurate for large steps. This promises high efficiency for solving large-scale systems (complex networks containing a large number of distinct proteins) in a long-term simulation.
(b) They work effectively for very long time intervals. This makes it possible for us to explore the longrun behavior of genetic regulatory network which is important in the research of gene repair and gene therapy.
The special structure of the new splitting methods and their remarkable stability property (see Appendix) are responsible for the previous two advantages.
Discussions
The splitting methods designated in this paper have opened a novel approach to effective simulation of the complex dynamical behaviors of genetic regulatory network with a characteristic structure. It is still possible to enhance the effectiveness of the new splitting methods. For example, higher-order splitting methods can be obtained by recursive composition (14) or by employing higher order Runge-Kutta methods; see II.5 of [13]. Another possibility is to consider Table 4: Parameter values for the two-gene network. embedded pairs of two splitting methods which can improve the efficiency; see II.4 of [13].
The genetic regulatory networks considered in this paper are nonstiff. For stiff systems (whose Jacobian possesses eigenvalues with large negative real parts or with purely imaginary eigenvalues of large modulus), the previous techniques suggested by the reviewer are applicable. Moreover, the error control technique which can increase the efficiency of the methods is an interesting theme for future work. There are more qualitative properties of the genetic regulatory networks that can be taken into account in the designation of simulation algorithms. For example, oscillation in protein levels is observed in most regulatory networks. Symmetric and symplectic methods have been shown to have excellent numerical behavior in the longterm integration of oscillatory systems even if they are not Hamiltonian systems. A brief account of symmetric and symplectic extended Runge-Kutta-Nyström (ERKN) methods for oscillatory Hamiltonian systems and two-step ERKN methods can be found, for instance, in Yang et al. [26], Chen et al. [27], Li et al. [28], and You et al. [29].
Finally, a problem related to this work remains open. We observe that, in Tables 3 and 9 for the p53-mdm2 pathway, as the time interval extends, the error produced by Split(Exact:RK4) and Split(Exact:RK3/8) becomes even smaller. This phenomenon is yet to be explained. | 3,425.8 | 2014-02-02T00:00:00.000 | [
"Biology",
"Computer Science",
"Mathematics"
] |
Keratinocyte Progenitor Cells Reside in Human Subcutaneous Adipose Tissue
The differentiation of adipose-derived stem cells (ASCs) towards epithelial lineages has yet to be demonstrated using a standardized method. This study investigated whether keratinocyte progenitor cells are present in the ASC population. ASCs isolated from subcutaneous adipose tissue were cultured and examined for the expression of the keratinocyte progenitor markers p63 and desmoglein 3 (DSG3) by immunofluorescence microscopy and flow cytometry. In addition, p63 and DSG3 expression levels were assessed before and after differentiation of ASCs into adipocytes by real-time PCR and western blot analysis, as well as in subcutaneous adipose tissue by real-time reverse transcriptase polymerase chain reaction. Both markers were expressed in ASCs, but were downregulated after the differentiation of ASCs into adipocytes; p63-positive cells were also detected in subcutaneous adipose tissue. ASCs co-cultured with human fibroblasts and incubated with all-trans retinoic acid and bone morphologic protein 4 showed an upregulation in DSG3 level, which was also increased in the presence of type IV collagen. They also showed an upregulation in cytokeratin-5 level only in the presence of type IV collagen. These results provide the demonstration that keratinocyte progenitor cells reside in subcutaneous adipose tissue.
Introduction
The skin is a multilayered organ that protects the organism against external environmental stressors. Stem cell populations within the skin including the interfollicular epidermis, hair follicles, sebaceous glands, and sweat glands not only maintain skin homeostasis but also repair damaged areas. Stem cells in the basal layer of the epidermis give rise to short-lived progenitors, which amplify the keratinocyte population and migrate upwards as they differentiate [1]. In contrast, hair follicle stem cells can behave as multipotent stem cells during physical injury and participate in re-epithelialization [2][3][4]. Most notably, bulge stem cells contribute to the repair of the interfollicular epidermis when it has sustained damage [3,[5][6][7].
Stem cells include embryonic stem cells, induced pluripotent stem cells and adult stem cells. There are no ethical concerns related to the use of the latter. Among them, multipotent mesenchymal stem cells (MSCs) are non-hematopoietic cells of mesodermal origin that are present postnatally in various organs and connective tissues. Adipose-derived stem cells (ASCs) are among the most promising MSC populations for therapeutic applications, since human adipose tissue is easily obtained in large quantities with little donor site trauma [8]. Although ASCs can potentially generate an infinite number of somatic cells of any type, their differentiation towards epithelial lineages has yet to be demonstrated by a standardized method. The identification of keratinocyte progenitor cells is necessary and their potential for differentiation from ASCs must be determined before they can be considered for use in skin regeneration. The aim of this study was to investigate whether keratinocyte progenitor cells are present in ASC populations.
Ethics statement
Informed, written consent was obtained from all study participants. The documents of participant consent are preserved in each patient's medical records. The study protocol was approved by the Ethics Committee of Juntendo University. Data were analyzed in blinded fashion and procedures were carried out according to the principles of the Declaration of Helsinki.
Isolation and culture of ASCs
After obtaining the consent, subcutaneous adipose tissue was obtained from disease-free donors under local anesthesia and was washed extensively with phosphate-buffered saline (PBS). The extracellular matrix was digested at 37°C for 45 min with collagenase (SERVA Electrophoresis, Heidelberg, Germany). Enzyme activity was neutralized by adding control medium (Dulbecco's modified Eagle's Medium (DMEM) (Gibco, Life Technologies, Carlsbad, CA, USA) containing 10% fetal bovine serum (FBS)); the cell suspension was filtered through a 40-μm nylon mesh to remove debris and centrifuged at 1200 rpm for 10 min to obtain a high-density stromal vascular fraction pellet, which was resuspended in 5 ml control medium. The resulting cell population consisting mostly of ASCs were seeded in bare 60-cm 2 culture dishes and maintained at 37°C in a humidified atmosphere of 5% CO 2 in control medium.
After 7 days of culture, cells were harvested using a standard trypsinization protocol (0.25% trypsin/ethylenediaminetetraacetic acid [EDTA] for 3 min), washed with PBS, and incubated with FITC-conjugated anti-human antibodies against cluster of differentiation (CD)34, CD44, CD90, and CD105 (all from Becton-Dickinson, San Diego, CA, USA), for 30 min. Labeled cells were washed and analyzed using a FACSCalibur flow cytometer (BD Biosciences, San Jose, CA, USA).
Adipogenic differentiation of ASCs in vitro
ASCs were tested for their ability to differentiate into adipocytes. Cells were plated in 6-well plates at a density of 3 x 10 5 cells/well and allowed to adhere for more than 24 h in stromal medium (DMEM/Ham's F12 containing 10% FBS and antibiotics) at 37°C in a CO2 incubator. When cells reached between 80% and 90% confluence, the medium was replaced first with differentiation medium (DMEM/Ham's F12 containing 3% FBS, 3-isobutyl-1-methylxanthine, biotin, panthothenate, rosiglitazone, dexamethasone, and human insulin) [9] for 3 days, and then with adipogenic medium, which had the same composition as the differentiation medium but without 3-isobutyl-1-methylxanthine [9]. The adipogenic medium was changed every 3 days until mature adipocytes were obtained (day 12).
Adipogenic differentiation was assessed by Oil Red O staining. The degree of staining was quantified by destaining the cells with 100% isopropanol for 15 min and mesuring the optical density of the solution at 540 nm. Differentiation was also confirmed by real-time PCR detection of adiponectin, leptin, peroxisome proliferator-activated receptor γ2 (PPARγ2), lipoprotein lipase (LPL), and fatty acid-binding protein 4 transcript expression. Total RNA was extracted from cultured cells using the RNeasy Plus Micro kit (Qiagen, Hilden, Germany) according to the manufacturer's protocol. A total of 2 μg RNA was converted to cDNA using the ReverTra Ace qPCR RT kit (Toyobo, Osaka, Japan). TaqMan Master Mix (Applied Biosystems, Foster City, CA, USA) was used to amplify 1 μg cDNA for 45 cycles on a Step One Plus system (Applied Biosystems). The expression of adiponectin, leptin, PPARγ2, LPL, and fatty acid-binding protein 4 (using primers Hs00605917_m1, Hs00174497_m1, Hs01115513_m1, Hs00173425_m1, and Hs00173425_m1, respectively; Applied Biosystems) was normalized to β-actin levels, and the comparative cycle threshold (Ct) method using the formula 2 -ΔΔCt was used to calculate relative mRNA levels.
Immunocytochemical detection of keratinocyte progenitor cell markers
The expression of keratinocyte markers in ASCs was detected by immunocytochemistry. Undifferentiated ASCs were fixed for 30 min in 4% paraformaldehyde at room temperature, and blocked with PBS containing 0.1% Triton X-100 and 10% goat serum (Jackson ImmunoResearch Laboratories, West Grove, PA, USA) for 1 h at room temperature before overnight incubation at 4°C with primary antibodies against p63 and desmoglein 3 (DSG3) (both at 1:1000, from Santa Cruz Biotechnology, Santa Cruz, CA, USA). Samples were washed, then incubated with secondary antibody (1:1000; Life Technologies) for 45 min at room temperature in the dark, then washed three times in PBS. Nuclei were counterstained with 4',6-diamidino-2-phenylindole (Vector Laboratories, Burlingame, CA, USA). Samples were visualized under a Keyence BZ-9000 fluorescence microscope (Osaka, Japan). Normal human epidermal keratinocytes (NHEKs) were used as a positive control.
Keratinocyte progenitor cell marker detection by flow cytometry
Undifferentiated ASCs were harvested using a standard trypsinization protocol, washed with PBS, and fixed with 4% formaldehyde in PBS for 10 min at 37°C. Ice-cold methanol was added and the cell suspension was mixed and left at -20°C for 30 min. The cells were then centrifuged, washed with 1% bovine serum albumin (Sigma-Aldrich, St. Louis, MO, USA) in PBS for 10 min, and incubated with phycoerythrin-conjugated antibody against p63 (1:800; Cell Signaling Technology, Danvers, MA, USA) and an FITC-conjugated antibody against DSG3 (1:1000; Abcam, Cambridge, MA, USA) for 30 min. Cells were washed and analyzed by flow cytometry with NHEKs used as positive control.
Real-time PCR analysis of p63 and DSG3 mRNA expression in ASCs
The expression of keratinocyte lineage markers before and after the differentiation of ASCs into adipocytes was evaluated by real-time PCR. Total RNA was extracted from cultured cells on days 1 and 12 using the RNeasy Plus Micro kit according to the manufacturer's protocol. A total of 2 μg RNA was converted to cDNA using the ReverTra Ace qPCR RT kit (Toyobo, Osaka, Japan). TaqMan Master Mix (Applied Biosystems, Foster City, CA, USA) was used to amplify 1 μg cDNA for 45 cycles on a Step One Plus system (Applied Biosystems). The expression of p63 and DSG3 (using primers Hs00978343_m1 and Hs00951897_m1, respectively; Applied Biosystems) was normalized to β-actin levels, and the comparative cycle threshold (Ct) method using the formula 2 -ΔΔCt was used to calculate relative mRNA levels.
Quantitative analysis of p63 and DSG3 expression in ASCs by western blotting
The expression of keratinocyte markers before and after differentiation of ASCs into adipocytes was assessed by western blotting. ASCs were lysed in IGEPAL Nonidet P-40 in the presence of Halt Protease and Phosphatase Inhibitor Cocktail (both from Sigma-Aldrich). Proteins were separated by 10% Tris-glycine SDS-PAGE (Bio-Rad, Hercules, CA, USA) under denaturing conditions and transferred to a nitrocellulose membrane. After blocking with 3% bovine serum albumin in Tris-buffered saline, the membrane was incubated with primary antibodies against p63 (Cell Signaling Technology) and DSG3 (Santa Cruz Biotechnology) overnight at 4°C. The blot was proved for β-actin using a monoclonal antibody (1:2000; BioLegend, San Diego, CA, USA) as a loading control. The membrane was then washed, incubated with anti-mouse or -rabbit peroxidase-conjugated secondary antibody (1:1000; Santa Cruz Biotechnology and Cell Signaling Technology, respectively) at room temperature for 45 min, and developed with Luminate Forte western horseradish peroxidase substrate (Merck Millipore, Billerica, MA, USA).
Detection of keratinocyte progenitor cells in subcutaneous adipose tissue
Subcutaneous adipose tissue was collected from donors under local anesthesia. Total RNA was purified from the tissue, with normal human keratinocytes serving as positive controls, using the RNeasy Plus Micro kit. Reverse transcriptase (RT)-PCR was performed with cDNA synthesized using the Moloney murine leukemia virus (M-MLV) RT kit (Invitrogen). The following components were included in the reaction: 1μl oligo (dT) [12][13][14][15][16][17][18] (500 μg/ml), 1 μl of 10 mM dNTP mix (both from Invitrogen), 50 ng total RNA, and sterile distilled water to 12 μl. The mixture was incubated at 65°C for 5 min and immediately chilled on ice, and 4 μl of 5x firststrand systhesis buffer, 2 μl of 0.1 M dithiothreitol, and 1 μl RNaseOUT recombinant ribounclease inhibitor (40 U/μl) (Invitrogen) were added. The mixture was incubated at 37°C for 2 min and immediately chilled on ice; 1 μl of 200 U M-MLV RT was added and the mixture was incubated for 10 min at 25°C, followed by 50 min at 37°C and 15 min at 70°C. To remove RNA complementary to the cDNA, 1 μl of 2 U Escherichia coli ribonuclease H (Invitrogen) was added, followed by incubation at 37°C for 20 min. The amplification reaction consisted of 45 μl Platinum PCR SuperMix High Fidelity (Invitrogen), 200 nM primer solution, 100 ng genomic DNA template, and 1 U Platinum Taq DNA polymerase (Invitrogen). The following primers were synthesized by Invitrogen: for p63, 5'-GGT CCC CAC AGA GCA AGA-3' and 5'-TGC AAT GAC AGC CCT TGA-3'; for DSG3, 5'-CAA AGC TGC CTC AAA TGT CA-3' and 5'-TGC AAA CTG CAT CTT TTT CG-3'; and for the positive control glyceraldehyde-3-phosphate dehydrogenase, 5'-TGG GCT ACA CTG AGC ACC AG-3' and 5'-CAG CGT CAA AGG TGG AGG AG-3'. The reaction conditions were as follows: 94°C for 2 min; 35 cycles of 94°C for 30 s; 58°C, 61°C, and 64°C for 30 s each; 68°C for 30 s; and 72°C for 5 min. PCR products were resolved by electrophoresis on 2% and 1.2% agarose gels (Nippon Gene, Tokyo, Japan) in 1x TAE buffer (40 mM Tris; 20 mM acetic acid; and 1 mM EDTA, pH 8.0). For each pair of gene-specific primers, semi-logarithmic plots of the intensity of amplified DNA fragments as a function of cycle number were used to determine the range of cycles over which linear amplification occurred, and the number of PCR cycles was kept within this range.
Differentiation of ASCs into keratinocyte-like cells
A co-culture system was used to differentiate ASCs into keratinocyte-like cells. Normal human dermal fibroblasts (5 x 10 4 cells) were seeded in the bottom chamber of 6-well plates and cultured in DMEM containing 10% FBS for 24 h, while ASCs (10 5 cells) were seeded on 0.4-μm Millicell hanging cell culture inserts (Merck Millipore) coated with type IV collagen (Nitta Gelatin, Osaka, Japan) that were placed in the plates; 1 μM all-trans retinoic acid (ATRA) (Sigma-Aldrich) was added to the upper chamber, and cells were cultured for 72 h. Bone morphogenetic protein 4 (BMP4) (R&D Systems, Minneapolis, MN, USA) was added at 25 ng/ml to the upper chamber. After 4 days, the ATRA-and BMP4-containing medium was replaced with keratinocyte serum-free medium (Invitrogen) for 7 more days. ASC remnants were removed and analyzed by real-time PCR for DSG3 and cytokeratin 5 (K-5) expression. ASCs cultured without ATRA or BMP4 or with neither, and ASCs co-cultured with fibroblasts on non-type IV collagen-coated transwell inserts were used as controls.
Cell viavility assay
Cell viability of ASCs co-cultured with fibroblasts on type IV collagen coating was assessed by collecting the media from the 6-well plates and adding 270 μl 3-(4,5-di-methylthiazol-2-yl)-2,5diphenyltetrazolium bromide (MTT) to each well and incubating the plates for 1 h at 37°C. The supernatant was removed and 1 ml of dissolving solution (Cayman Chemical, Ann Arbor, Michigan, USA) was added to each well. Absorbance was read at 570 nm using a microplate reader.
Statistical analysis
Data were analyzed by analysis of variance and are presented as mean ± SD. Differences were considered statistically significant at P 0.05.
Isolation and adipogenic differentiation of ASCs
ASCs adhered to the dish and became spindle-or stellate-shaped cells (Fig. 1A) that were positive for CD34, CD44, CD90, and CD105, as determined by flow cytometry (Fig. 1B).
ASCs cultured in adipogenic medium exhibited a greater variety of cell morphologies and a time-dependent increase in intracellular lipid vacuoles that appeared after only 4 days, with cell size and the number of lipid vacuoles increasing steadily thereafter (Fig. 1C). The absorbance at 540 nm of Oil Red O-stained cells increased markedly over this time course, while adiponectin, leptin, PPARγ2, LPL, and fatty acid-binding protein 4 transcript levels were upregulated. These results demonstrate the differentiation of ASCs into adipocytes (data not shown).
ASCs express keratinocyte markers
After 7 days of culture, ASCs expressed p63 and DSG3, as determined by immunofluorescence microscopy ( Fig. 2A, B) and flow cytometry (Fig. 1C); control NHEKs were also positive for these markers. Without intracellular staining procedure, p63 and DSG3 were not detected by flow cytometry (data not shown). These observations were consistent across three independent experiments performed using ASCs from three different donors.
Keratinocyte marker expression decreases upon differentiation of ASCs into adipocytes
Real-time PCR (Fig. 3A) and western blot (Fig. 3B) analyses revealed that undifferentiated ASCs were positive for p63 and DSG3. In addition, the expression of these markers was reduced after differentiation of ASCs into adipocytes as compared to undifferentiated cells. These results were consistent across three experiments performed using ASCs from three different donors.
Keratinocyte marker expression in human subcutaneous adipose tissue
Human subcutaneous adipose tissue expressed p63 but a lower level than in NHEKs, as determined by RT-PCR (Fig. 4); however, DSG3 mRNA was not detected. These results demonstrate that p63-positive keratinocyte progenitor cells are present in adipose tissue.
ASCs transdifferentiate into keratinocyte-like cells
To assess the epithelial differentiation potential of ASCs co-cultured with fibroblasts, the expression of DSG3 and K-5 was evaluated by real-time PCR. Treatment with ATRA and BMP4 had no effect on the expression of DSG3 and K-5 in ASCs cultured separately as monolayers (Fig. 5A, B). ASCs co-cultured with fibroblasts on non-type IV collagen-coated transwell inserts had high level of DSG3 expression; type IV collagen coating, moreover, increased the expression of DSG3 and K-5. These results suggest that the extracellular matrix and dynamic cross-communication between fibroblasts and ASCs modulate ASC transdifferentiation. Cell viability was assessed by the MTT assay. ASCs were viable in the co-culture system and also when grown on type IV collagen coating (Fig. 5C), indicating that both conditions induce morphological changes in ASCs without adversely affecting cell viability.
Discussion
Human bone marrow-derived MSCs can differentiate into functional epithelial-like cells in vitro [10,11]. However, MSCs can also be isolated from adipose tissue. The advantages of using adipose tissue-derived ASCs, which are one type of MSC, include their abundance in a given donor and the ease with which they can be obtained using relatively noninvasive methods. On the other hand, the differentiation of ASCs into unexpected lineages is a significant concern. The present study investigated whether ASCs have the potential to differentiate into keratinocytes.
ASCs were isolated from human subcutaneous adipose tissue and were cultured for 2 weeks to assess their potential for differentiating into adipocytes, which was evaluated by the detection of epidermal marker expression. The p63 protein has been proposed as an important transcription factor in the development of squamous epithelia, and there is substantial evidence for p63 as a stem cell determinant in epithelial cell types [12,13]. In human epidermis and epidermal cultures, p63 expression is restricted to cells with high proliferative potential in the basal layer [14]. DSG3 is a cadherin-type cell membrane protein that mediates cell-cell adhesion by coupling to keratin intermediate filaments in the skin, which depends on keratinocyte location and maturation. Based on the present observations that p63 and DSG3 are expressed in ASCs and their expression is downregulated after the differentiation of ASCs into adipocytes, we speculate that ASCs are keratinocyte stem/progenitor cells. Interestingly, DSG3 as well as p63 were detected intracellularly in ASCs by flow cytometry.
It was recently reported that ASCs co-cultured with keratinocytes differentiated into keratinocyte-like cells [15]. In the present study, ASCs were co-cultured with human fibroblasts; under these conditions, ATRA and BMP4 treatment or the presence of type IV collagen stimulated increased expressions of DSG3 and K-5. In contrast, type I collagen had no effect on keratinocyte progenitor cell marker expression (data not shown). Basement membrane proteins such as type IV collagen can accelerate the differentiation of various types of cells [16]. Thus, the presence of fibroblasts combined with the extracellular matrix stimulate the differentiation of ASCs into keratinocytes. Wound healing is a complex process involving many well-coordinated events such as inflammation, cell proliferation and migration, matrix production, and angiogenesis. The balance between proliferation and differentiation-which controls tissue homeostasis in the epidermis-is shifted towards proliferation upon skin injury and must be restored after wound healing is completed. Wound closure is mediated not only by contractile granulation tissue produced by fibroblasts and macrophages, but also involves re-epithelialization via the Treatment with ATRA and BMP4 had no effect on DSG3 or K-5 expression in ASCs cultured as a monolayer, but induced an increase in the transcript expression of DSG3 gene in ASCs co-cultured with fibroblasts on non-type IV collagen-coated transwell inserts. Type IV collagen coating increased DSG3 and K-5 expression in ASCs co-cultured with fibroblasts. (b) Cell viability in co-cultures with or without type IV collagen coating was assessed by the MTT assay. The type IV collagen coating had no adverse effects on cell viability. proliferation and migration of keratinocytes at the wound margin [17]. Full-thickness wounds resulting from tumor resection or injury are often treated with skin grafts that may not survive due to persistent infection, inflammation, and bleeding during the early postoperative course. However, in some cases, epithelialization begins long after the disappearance of the grafted skin, which should contain not only a normal epidermis but also a sufficient number of keratinocyte stem cells for long-term epidermal renewal. However, in addition to the basal stem cells required for normal epithelial homeostasis, other progenitors may also contribute to epithelial layer regeneration. ASCs may be mobilized to sites of injury where a subset differentiate into keratinocytes. Additionally, ASCs can also enhance wound repair by creating a microenvironment that promotes local regeneration of cells in the affected tissue.
Conclusion
This study demonstrated that keratinocyte progenitor cells reside in human subcutaneous adipose tissue, suggesting that this tissue has the capacity to produce keratinocytes. The results also revealed that both co-culturing and an extracellular matrix are needed for ASC differentiation. | 4,674.6 | 2015-02-25T00:00:00.000 | [
"Biology",
"Medicine"
] |
The Structure of Online Information Behind Social Crises
The adaptive nature of the social system allows it to overcome the challenges imposed by its environment as well as to overcome those internal pressures. This adaptive process is associated with an increase in complexity manifested in a greater diversity of its components, new forms of organization, among other transformations. However, these adaptations have a cost and need to be administered, otherwise, they can trigger social unrest and crisis processes. Currently, the adaptive process of social systems has been accelerated and magnified by the emergence of information technologies. In this work, we explore the close relationship between adaptation, complexity, and crisis, showing it expression in a digital social environment, although with some particularities. Specifically, we have observed expected behaviors, such as the polarization of society and negative sentiment of messages during times of crisis, however, our results show something interesting. Despite the loss of order in the social organization questioned by the crisis, we observe the emergence of new complex ephemeral structures of information which seem to be early-warnings signals of profound social transformations.
INTRODUCTION
Society evolves with increasing complexity [1]. As a Complex adaptive system, it is constantly gathering information, restructuring and adapting for its survival. However, it is the same acquired complexity which enables the occurrence of events where the social organization is questioned due to its failure to manage it, giving rise to the phenomenon of social crises [2,3], affecting fields of politics, economy, and society in general. On the other hand, it is the same complexity which limits the prediction of crises events since there is no clear relation between its precursors and final magnitude.
To face the limits of prediction, and other characteristics of this kind of complex and collective phenomenon, during recent decades Complexity Theory has been providing models with more complete meanings and theoretical coherence for social systems [4,5]. Human (collective) behavior, and social crises in particular, are many times decentralized processes that emerge as the result of a bottom-up process where social links play an important role, in much the same way that social rules may govern complexity in the society.
Although social crises have accompanied humanity since its origins [2,[6][7][8], for some years we have witnessed a series of social crisis events of a global nature, of great magnitude and more frequent than in past decades, which could have its origin in the arise of the so-called Networked Society [9] due to the increase in social complexity given the emergence of information technologies and the Internet, which has broken down geographical barriers, strengthened globalization and significantly increased social interaction as well as the flow of information [10]. It is for this reason that today, online social networks such as Twitter among others, have become a projection of material 1 interactions, sharing signs and developing their own particularities, taking on an unusual role in the development, and even the genesis of some of these social crisis events [11].
In this work we propose a methodology to observe and describe these common signs between the material society and digital society behavior that occurs in times of crisis. Our objective seeks to clarify the relationship between these two "societies", where society expresses itself in the manifestation of this type of phenomenon. To achieve this, we have analyzed the Twitter activity of Chilean society, which has experienced for several years, and in particular since October 2019, an acute social crisis which presents in the near future a series of challenges (as the creation of a new Constitution). We have analyzed the activity in the online microblog from two perspectives: users and content, with the aim to approach the phenomena of crisis from those who participate in this, but also from the content or information that they use. To do this, we are using Network and Information theories in order to detect changes (decrease, conservation or increase) in the complexity of the online social system.
We started our analysis from the basis that any critical social moment presents a state of ?maturation? [4], a kind of increase in social temperature. It is for this reason that we daily monitor the ? hot? topics that circulate on Twitter for a specific territory (i.e., Chilean Trending Topics in the case of this study), harvesting the tweets associated with them in order to construct and analyze networks of users and topics in addition to other typical measures for analysis of this type (e.i., sentimental analysis, polarization, etc.). Thus, we pretend to obtain a multidimensional metric that characterizes the digital society in moments of critical behavior.
The work is structured as follows. In Section 2 we present the characteristics of the phenomenon of social crises described from traditional sociological and psychological theory. Section 3 describes the methodology developed to achieve the objectives of this work. The results of our study are shown in Section 4. Finally, in Section 5 we sum up the highlights and present some concluding remarks.
SOCIAL CRISES. A BRIEF VIEW FROM SOCIAL SCIENCES
Few concepts refer to such diverse connotations as crisis, to the point that it ends up being used to denote various situations, among them very different in scope, depth, and effects. However, the idea of associating the crisis with "something" (a space, a property, an interest, an affectation, etc.) that is perceived, understood, intuited, etc., as "critical", seems to be a point in common in many of the definitions. Furthermore, it seems clear that any of these definitions consider the phenomenon as a "process"? which, according to [12] for example, occurs in stages: integration, disintegration, rupture and reintegration.
The conjunctural desectorization of the social space means that, given the critical conjuncture of the social system, its formal structure is diluted, admitting subtle frontiers of sectoral differentiation, which hinders the interaction of the actors and their sectoral logic, together with the decompartmentalization from the themes that are now released to broader spaces of intervention. Likewise, there is a reduction in the autonomy of the actors and a displacement of the arenas of confrontation, generating a loosening of the links between arenas and issues of confrontation. All this determines serious difficulties for the realization of the calculations that the actors must carry out in anticipation of the effects of their eventual plays, installing a determining factor in the possibility of their success or failure. Thus arises the inability to perform adequate evaluations for the management of the crisis. In psychological terms, the usual styles of resolution are not enough to face the phenomenon, whose scope is mediated by the severity of the events, their unexpected nature and the degree of perceived risk [24].
A second property is structural uncertainty and it manifests itself both as loss and/or confusion of those pre-existing reference indices 2 , collapsing traditional definitions and generating loss of effectiveness of the evaluation instruments used in moments of a routine situation (i.e., non-crisis state). This can cause important skidding of certain crises, driven by polarization dynamics in the plays and behaviors of the actors, also accompanied by certain psychological modifications that are expressed in this. In emotional terms, the mediation of the emotional meaning of the crisis is collective [25]. Although narratives become personal through a narrative "engagement", these emotions motivate social actions. In cognitive terms, the crisis is associated with a confirmation bias (i.e., a tendency to discard opinions inconsistent with one's own), motivated reasoning (believing that one's opinion is the best of all and ignoring opposing data) [26], or the priming effect, related to the predisposition to associate certain ideas and stimuli according to those that temporality precede it [27].
Finally, a third property refers to processes of deobjectification of the relations both between sectors and also between actors and sectors, being one of the most interesting vulnerabilities of political systems, generating certain states of liberation in the phenomena of multisectoral mobilizations, or "madness"? or "creative effervescence"? and in the actors certain behaviors assigned to "collusive transactions"? as a formula to obtain certain control of the dynamics that the critical juncture (crisis) acquires.
However, the focus of our concern is whether the digital environment of social interaction represents, in moments of critical juncture, the multiplicity of properties and characteristics described by the theory of social sciences. This is linked to the idea of how far the digital society is a projection of the material society or if the material one is an effect or consequence of the digital society. Furthermore, is it possible to think that the digital society constructs autonomous phenomena and properties in its dynamics, distancing itself from being just a reflection of the social material system, which could rather be insinuated as an autonomous creative capacity that would even allow anticipating the concretion of realities exposed real world.
These questions place us in the identification and reading of the behavior that Twitter has in the face of a critical juncture that unfolds in real time in both types of society, and places us in the analysis of multiple metrics built to try to identify some of these characteristics and get closer to infer something from what is proposed in these questions.
For the Chilean context it is important to highlight that 82% of inhabitants have Internet connection, and 79% of them use online social networks where Twitter stands as one of the most widely used social network, surpassed only by Facebook [28]. As [29] suggests, the country's "digital elite" participates in Twitter, attracting 13% of its population.
The foregoing shows that one of the characteristics associated with crises, such as the displacement of the arenas of confrontation, allow us to understand why online social networks have become a space for the expression of multiple and diverse actors who not only debate about associated ideas but also, they judge, legitimize, approve, reject, confront or construct new realities that affect the game, and move the social system to critical thresholds, thus generating the emergence of its own dynamic.
The structural uncertainty of the crisis is also manifested in online social networks where new reference appear. In fact, traditional referents do not have the exclusive role that they used to have when referring to critical social situations on digital platforms. On the other hand, the loss of sectoral logic, typical of the crisis, is also observed in the digital social environment where any user can comment on any topic, as well as disseminate the associated information much more efficiently.
Finally, the evident social polarization generated by online social networks [30] is another of the characteristics of the crises described by the social sciences that manifests itself in digital environments. In fact [31] suggests that online social networks generate individual political alignments that shape personal consumption of apparently non-political products. On the other hand [32] associate digital polarization with a lower semantic diversity of the subjects treated by individuals and a greater lexical diversity. That is, in polarized digital environments, few issues are discussed but in multiple ways.
While it is true that there are these and other similarities between material and digital societies during a crisis phenomena, we must not forget that the social digital environment has its own rules that generate its own particularities. Among these, the immediacy in the availability of information, the accelerated flow of it, the possibility of anonymity when commenting on the situations and the existence of thematic connecting vehicles such as hashtags, among others, stand out.
Context Research
We have developed our work analyzing the digital activity of Chilean people in a context of deep social crisis. In fact, Chile has not been immune to the unstable social behavior manifested by different countries around the world.
Despite his young age (little more than 200 years), the history of Chile has been characterized by various social crises that have determined changes and transformations in the organization of its social, political and economic systems. According to Kenneth [33], the state of stability, or routine situation [13], that characterize the country since the end of the military dictatorship in 1990, began to change to a new state of crisis, or fluid critical conjuncture [13], with the so-called ?Penguin Revolution? in 2006, when thousands of students and their supporters took the streets to protest inequalities and lack of quality in Chilean education. This challenge to the sociopolitical scenario was extended and reach high instability between 2011 and 2012 with the so-called "Student Movement", which highlighted several challenges of the Chilean educational system along with a series of other demands against institutionalism, authorities and their decisions, as well as diverse social, political, economic, environmental and health issues, among others. Starting a logic situation, a climate, a prégnance [34] in Chile, which floods the system and manifests itself through a series of critical projections, which seem at first sight to be unrelated, but which form part of the same process. All these conditions seem to converge in October 2019 in a highly unstable generalized scenario with typical characteristics of a sociopolitical crisis such as those faced by the country at other times in its history.
Considering the current crisis scenario that Chile is going through, we have developed a multidimensional analysis to detect signals of crisis that appear in the digital society that are in resonance with signals of the social material crisis.
Data Harvesting and Networks Construction
From August 27th to October 26th, 2020, we daily monitor Twitter in the search of Chilean Trending Topics, harvesting three times each day (morning, evening and night) the tweets associated with these trending topics. The data, extracted automatically using the Twitter API 3 , corresponds to 453,564 Chilean tweets (i.e., eliminating foreigners) during the entire period. In each harvest of Trending Topics the average of tweets collected was 4,183.5.
Using the information of these tweets we construct two types of networks: thematic and users.
Thematic Networks
T(H, L) correspond to networks composed by H hashtags and L edges between them. In the thematic network T an undirected link between hashtag h i and h j is created when they appear together in the same tweet. Thus T(t) corresponds to the topic network at harvest time t composed by all the co-occurrent hashtags during t (Figure 1). The amount of tweets collected that contained hashtags to build this type of network was 204,795 (45.15%).
Users Networks
We will call U(P, L) to the networks composed by P people and L edges between them. We define three types of networks U: reply, Frontiers in Physics | www.frontiersin.org April 2021 | Volume 9 | Article 650648 4 mention and retweet networks. In the reply network, U r , a directed link from user i to j is generated when p i responds a tweet posted by p j . Thus, the U r (t) corresponds to the reply network at harvest time t composed by all the users that respond to others during t. The mention network, U m , is similar but considers mentions instead responses. Finally, in the retweet network U rt , a directed link from user i to j is generated when p i retweets a message from p j . As well as the previous networks, U rt (t) corresponds to the retweet network at harvest time t composed by all the users that retweet to other users during t (Figure 2).
Characterizing the Digital World, New Metrics
We have analyzed various metrics, some of them are completely new following the ideas of the concept of a crisis developed and discussed in the previous sections. We have separated this measures into two subsets: structural and content metrics.
Structural metrics correspond to a set of measures that depend exclusively on the structure and topology of the networks that are being analyzed. Specifically, we have considered the following structural measures: network complexity, normalized conditional degree matrix (NCD matrix), and polarization. For the content metrics we have considered the presence of critical concepts, sentiment analysis on messages, and duration for trending topics. Local metrics such as ratio followers/friends for Twitter users was also used in this work.
Structural Metrics
We have applied a series of analyzes to T and U networks, focusing our attention on the Giant Connected Component for each harvest. A brief description of these measures is presented below.
Giant connected component (GCC): is the basic structure of networks T and U analyzed in this work due to the importance in percolation processes [35,36]. It corresponds to a sub-structure of a network that contains the major proportion of nodes where between each pair of nodes there is a path.
Complexity: the Complexity of T networks is defined by [37] as the product between the network entropy S and network disequilibrium Q according to the following equation where entropy is based on the assessment of probabilities to jump between nodes when randomly traveling through the network. Thus, the entropy S i for each node i is computed based on the distribution P i with entries p i → j that give the uniformly distributed probability to jump from node i to node j along an edge between them in exactly one step. For example, if the i is connected to three nodes, then P i will be one third, for details see [37]. The network entropy S corresponds to the average normalized entropy taken over all nodes i according to where N corresponds to the total number of nodes of the GCC. On the other hand, the disequilibrium Q is measured in terms of the Jensen-Shannon divergence [38], taking as a reference network the Erdös-Rényi network, see Eq. 3. Q takes low values for systems that are close to equilibrium and high values for ordered systems according to where Q 0 1/log(2) to ensure Q i ∈ [0, 1]. The probability distribution P i again denotes the probabilities to jump between neighboring nodes i and j when randomly traveling through the network, as in Eq. 2. P e,i denotes the same but for a random system (e.g., Erdös-Rényi network). Thus, Q is computed as the mean of all per-nodes values Q i according to where N corresponds to the total number of nodes of the GCC network.
Conditional degree matrix (CD matrix): when studying social networks, we have been able to verify, as already indicated in [39,40], that metrics referring to local properties (such as the degree of a node) do not capture the general richness of network topology. One way to further characterize the structural properties of the studied networks T is to define the conditional degree matrix, Q i , for the degree of each node: where N k,j if the number of nodes in the network with degree k connected to nodes with degree j. While N t is the total number of degree's connections ensuring the normalization property k,j P k,j 1 Using the proposed probabilities, similar metrics to those mentioned above can be defined: entropy, disequilibrium and complexity. Important for this work is the definition of the actual domain of this probability matrix, i.e. what array elements of P k,j are not null. We will call Ω the total number of elements P k,j > 0. Indeed, omega will be a metric that will be very useful to give an idea of the type of existing connections between nodes. The important insight of this matrix, P k,j , is the possibility to explore the characteristic of the node and its environment (its near neighborhood). That is, the importance is expressed in terms of disseminating information. The rows of the matrix then show the probability that nodes with a given degree connect with other nodes in the network and their importance in the network will be weighed by the frequency of occurrence of these connections. Polarization: another metric used in this work was the polarization of Twitter users in U networks for each time interval analyzed. To infer the opinion of the users participating on the Twitter conversation and measure the resulting polarization we use the methodology introduced in [41]. This methodology develops a model to estimate the opinions of users who interact on a social network from a minority of hubs whose opinion is known. This model has already been used in [42] to measure the political polarization of Twitter users in the Chilean presidential elections of 2018. In our case, the two elites of users with opposing opinions have been selected automatically, assigning n nodes from the two largest communities obtained through the greedy modularity communities algorithm. The model is initialized by assigning an opinion value X of -1 or 1 to each elite and initial value X O to each listener. The opinion of each listener is iteratively updated as the mean opinion value of her outgoing neighbors. Thus the opinion at time step, t, of a given listener i, is given by the following expression: where A ij represents the elements of the network adjacency matrix, which is 1 if there is a link from j to i, and k out i corresponds to her out-degree. The process is repeated until all nodes converge to their respective X i value, lying in the range −1 ≤ X i ≤ 1. Thus, the results of the model are given in a density distribution of nodes' opinion values P(X). In our case the network of the model is represented by the retweet network, reply network and mention network independently. We generate a network for each harvest and the corresponding adjacency matrix for each harvest is given by the following equation: Polarization was calculated for each harvest obtaining a measure from the resulting density distribution of nodes? opinion values P(X). The polarization is given by the following expression: where |ΔA| |P(X > 0) − P(X < 0)| (10) and 2d is the distance between positive and negative average opinions. This formula gives ρ 1 when the distribution is perfectly polarized. In this case the opinion distribution function is two Dirac delta centered at −1 and +1, respectively. Conversely, ρ 0 means that the opinions are not polarized at all.Ratio Followers/Friends: we use the amount of followers and friends of users who participated in twitter during the harvests in order to classify them into groups according to the ratio between both quantities: commons (Followers/Friends x1), followers (Followers/Friends < 1) and leaders (Followers/ Friends ≫ 1). The ratio [followers/friends] have been used as a measure to classify users on Twitter in [43,44] given its ability to classify the user profile according to their historical activity on this social network, what we are looking for in this study. Due to the dynamism of communications in Twitter, this classification does not seek to classify users according to their daily or recent activity in which they could have a high/low level of connectivity or a high/low centrality in the network.
Content Metrics
Sentiment analysis: is an automatic task of massive classification of documents, which focuses on cataloging the documents according to the positive or negative connotation of the language used in it.
We have used the python sentiment-spanish library [45] to infer the positive and negative sentiments of each tweet harvested. This library uses a convolutional neural network to predict the feelings of words in Spanish. This model was trained using more than 800,000 user reviews from various websites, such as eBay and Film affinity. This library delivers sentiment values between 0 and 1. In this work, values closer to 1 indicate negativity of the message and values closer to 0 indicate positivity of the message. Presence of specific words: we quantified the presence of words "charged" of anger, fear and social critical relevance for Chilean context. In this case, we used the NLTK corpus WordNet in order to increase the probability of finding words of this type.
Topic relevance: we developed a web-crawler to extract from Trendinalia.com the duration (hours) of trending topics analyzed in each harvest. This metric denotes the importance of the topics analyzed in the Chilean context.
Order, Disequilibrium and Diversity (ODD)
In order to capture the order, disequilibrium, diversity of T networks analyzed, as well as the topic importance, we introduce the metric ODD that combine them according to the following equation where C corresponds to the Complexity of the T network (Eq. 1), Ω corresponds to the total number of T network nodes P k,j > 0 normalized by N 2 (Eq. 5), and Δ to the duration in hours of the trending topics analyzed weighted by α parameter.
Metrics and Social Theory
Finally, the metrics proposed in this section try to quantify some expressions of the properties described in Section 2. Table 1 shows our proposal about the relation between these metrics and the theory behind social crises.
RESULTS
It seems to be clear which are the characteristics associated with the phenomenon of the crisis, at least from the social sciences point of view. However, it is not entirely clear in those disciplines, what are the conditions that allow its manifestation. We are not referring only to precursors or early-warning signals, where there is practically unexplored terrain, but to those contexts which appear as multiple and unclear. The problem of detecting early warnings in social networks has been investigated in various ways, and even in this work we present different perspectives, from a sociological and qualitative point of views, using network theory and complexity tools. Berestycki et al. [4] show that before the social explosions associated with crisis, society needs to be "ripe", charged with negativity and violence. This behavior is manifested in the case of our study. Figure 3 shows the analysis of the messages associated with the trending topics of the moment, issued by Chilean Twitter users.
The result of the sentiment analysis of the messages seems be fairly obvious for crisis situations: messages are usually negative in character. In addition, the result is complemented with the analysis of the presence of words full of anger for the Chilean context, which in some cases coincide with moments of high tension in Chilean society marked with four vertical stripes of color: National Truck Stoppage (Purple), case of extreme police violence (Green), social outbreak anniversary (Yellow) and, plebiscite for a new constitution (Grey). The width of vertical stripes denotes the duration (i.e., significant presence) of the events in Twitter.
This negative verbal context coincides with a highly polarized digital society (upper plot of Figure 4), highlighting the tension between conservatives and progressives regarding the future of the country. It can be seen that, like the sentiment analysis, user polarization of U networks was high throughout the period of analysis.
Something similar happens with the distribution of participating user types, which does not vary during the period. Notwithstanding the foregoing, it is interesting to note that during the entire period, those leading users are Frontiers in Physics | www.frontiersin.org April 2021 | Volume 9 | Article 650648 not opinion leaders (Followers/Friends ≫ 1) but rather the vast majority are common users (Followers/Friends x1). It is important to note that we can rule out spammers in our analysis since these users generally have a very small followers/friends ratio ( ≪ 1) [44].
A polarized society, and negative and violent verbal language, seem to reflect the state of a society [46]. But, do they allow us to forewarn a crisis or a critical moment for the society? Apparently not. The results show minimal variations in these parameters during the period studied, even during those moments of high social tension manifested by the material and digital society, which had important consequences.
It would seem suggestive to think that these moments of high tension are associated with greater activity in the digital society, however, this is not the case either. Figure 5 (lower plot) shows that during these moments the number of users as well as tweets associated with the hot topics of the moment, do not show variations either. Nothing special is observed in user activity either. The average number of tweets by user does not match the critical moments that society experienced either.
At this moment our results about structural properties of thematic networks T become relevant. Upper plots of Figure 6 show the Complexity (A plot), NCD Matrix (B plot) and the interest (hours) generated by the trending topics obtained in each harvest (C plot), for the thematic networks T during the period studied. Fluctuations can be observed in all cases during the period studied, which in some cases coincide with moments of high social tension.
What is relevant appears when considering these measures in order to rescue broad changes in the structural complexity of thematic networks. Thus, by combining the entropy of the thematic system, its structural disequilibrium, its diversity in terms of connectivity, and its impact, four major fluctuations are clearly appreciated in this constructed metric ODD, which coincide with periods of high social unrest in the country (color mark) that resulted in important social transformations. That is, during critical moments, and in particular before they manifest themselves in the material society, thematic networks become more complex, with a high degree of order, far from structural equilibrium and with a wide diversity in the connectivity between these themes. This work explored the digital behavior of Chilean society in the midst of a deep social crisis. The analysis of the messages associated with the main trending topics used by Chilean Twitter users, suggest that the crisis that the country is experiencing is expressed not only in the so-called material society through multiple expressions, but is also expressed in the digital society in which the inhabitants of the country communicate preferentially for the treatment of these and other issues.
The results show that the digital activity of Twitter reflects the tension of events that occurred in the material society, while the digital activity "feeds" this tension. Consequently, this relationship is clearly reciprocal. Nevertheless, our results suggest that digital activity would allow alerting about critical events with the potential to generate social transformations. For example, the first critical moment detected in our analysis (pink region in Results section figures) resulted in the accusation and subsequent departure of the prime minister of Chilean government [47]. The second moment (green region) had consequences for the restructuring of the national police, the arrest of several people and even threats towards judges investigating the case associated with the event [48]. The third moment (yellow region) was the anniversary of the so-called "social outbreak" associated with several riots around the country [49], and the fourth moment (grey region) resulted in a historic vote that meant rewriting the national constitution [50].
Traditionally, online social network analysis focuses on users and sentiment analysis of the messages. However, in this work we don't observe a strong correlation between the activity intensity of users and critical moments ( Figure 5), nor with the polarization (upper plot of Figure 4), or the usage of negative/violent language that remains constant throughout the period studied ( Figure 3). What our results show is that at critical moments preferably common and follower users share information (bottom plot of Figure 4), taking away the traditional role of the media and other echo chambers. Nevertheless, the most important result of our work is that the organization of information, posted by these kind of users, seems to be the key to anticipating critical events with the potential to generate social transformations. In fact, the increase in the order, disequilibrium and diversity of hot topics relationships, seem to be a signal of the beginning of a critical moment with unexpected results, at least that is what our results show for a polarized digital society that communicates with violent and negative language.
The novel proposed methodology, based on the analysis of thematic networks, allows us to observe the aforementioned reciprocal relationship between digital and material societies. Thus, from our perspective, users become only agents for the transmission of information forming a decentralized collective that generates and maintains the energy associated with information related to critical events. In critical moments, the information (topics) is organized in a non-trivial way and it seems to capture the social tension as well as its subsequent relaxation ( Figure 6). Thus, the thematic networks T would allow access to representations and ideas about reality at a particular moment. These networks would self-organize through the emergence and dynamics of hot topics as objects of reference [51] in the exchange of opinions within Twitter.
The emergence of order in the information that flows through online social media prior to critical moments seems to enrich the social theory of crises from an adaptive social perspective. The (apparent) loss of structure described by social theory (i.e., the conjunctural desectorization of the social space, structural uncertainty, and the processes of deobjectivation) actually signifies a restructuring of order engendered by critical events. In fact, the deep social crisis manifested by the Chilean society has shown an evident loss of structure in part of its organization; however, other parts of the social system seems to reorganize itself into new structures. The complex behavior observed in critical moments such as the ones described in this work, along with others in which society is organized against the established order, included the future national constitution, would be the manifestation of the spontaneous increase of complexity that the systems manifest in its adaptive process. Thus, the complexity of the adaptive system is maintained and even increased during the process. This is a hypothesis that may be probed in a future as well as a deeper understanding behind the observed correlation between the organization of information in online social networks and social crisis events.
DATA AVAILABILITY STATEMENT
Publicly available datasets were analyzed in this study. This data | 7,842.8 | 2021-04-28T00:00:00.000 | [
"Sociology",
"Computer Science",
"Political Science"
] |
Mobile Learning Model of Tour Guide Business in Universities from the Perspective of Distributed Cognition
In order to promote the better development of tour guide business, this article takes the tour guide business teaching in colleges and universities as an example and analyzes the current situation and the effect of students’ learning in the tour guide business course through investigating and researching the current situation of ideological and political teaching of the tour guide business course. It also proposes corresponding improvement measures for the existing problems, so as to improve the ideological and political teaching effect of the tour guide business course. To this end, this study relies on the powerful functions of UMU platform and builds a hybrid mobile learning mode based on UMU platform by improving the traditional teaching method of “face to face instruction + online lecture.” Although the UMU-based blended mobile learning model is formally divided into online learning and offline activities, in the actual teaching process, there are both you and me. In the process of online learning, students can realize the convenient learning through mobile APP terminal anytime and anywhere, or they can sit comfortably at the study table through the computer; in the offline activity classroom, students can sit in the classroom of UMU and communicate with teachers face to face, or they can use their cell phones to project their check-in, opinions, test results, etc. to the big screen. In the whole UMU-based hybrid mobile learning model, there is no clear boundary between online learning and offline activities, and online and offline are integrated with each other and crossed according to the actual learning needs to maximize learning efficiency.
Introduction
e campus culture construction in colleges and universities is constantly updated and advanced with the progress of time, and in order to better regulate the effective integration of curriculum thinking and politics with other courses, General Secretary Xi Jinping pointed out that the main channel of classroom teaching should be used to make all kinds of courses and ideological and political theory courses go in the same direction and form a synergistic effect [1]. It can be said that political education on the curriculum and understanding the political development of the country as well as the society are not only an effective way to improve the political consciousness of college students, but also an important initiative to promote the work of ideological and political education in colleges and universities [2]. Curriculum ideological and political education is the development of teaching contents and integration of political elements through the guide business course in order to improve students' ideological awareness in compliance with the national political regulations as well as the educational and teaching tasks of colleges and universities and students' own cognitive development capabilities [3].
Construction and improvement of tour guide business as the main course in tourism have become the main goal of the curriculum of tourism management. e close integration of professional education and civic affairs helps students to create professional goals and a sense of responsibility, while developing profound humanistic, value, and scientific thinking [4]. At the same time, it provides guidance and demonstration for other professional courses. e purpose of this paper is to summarize the current teaching situation of tourism management professional courses after the integration of the elements of ideology and politics in teaching, analyze the current situation of ideological and political teaching in tour guide business courses, and propose corresponding strategies for the existing problems to promote the reform and development of ideological and political education in tour guide business courses.
First of all, the work of tour guide staff will have a greater probability of receiving foreign tourists, so tour guides are required to pay attention to their words and deeds when receiving foreign tourists, to be associated with the maintenance of national image, and to consciously safeguard the interests of the motherland and the dignity of the nation [5]. Secondly, the tour guide should love the long history, splendid culture, and magnificent mountains and rivers of the motherland. rough vivid explanation during the tour, tourists can experience the profoundness of Chinese culture while viewing the stunning scenery of our country and enhance the national pride [6].
In the course of a tour guide business, the quality of tour guides requires that tour guides should have the core values of "tourist-oriented, sincere service" [7]. e teacher can tell the advanced needs of excellent tour guides when explaining the content of the teaching materials. e teachers can enhance the students' understanding of the principles of tour guide service and guide them to pay attention to the quality of service sincerity by telling the advanced deeds of the excellent tour guides and the cases of how the tour guides are tourist-oriented and how to serve the tourists sincerely [8,9]. e term "career planning" is familiar to everyone. Teachers start the course from freshman year, encouraging students to start from themselves and to talk with them about their school experience, schooling experience, and major work experience, and guide them to draw their own career blueprint [10]. Next, students can interact with the topic "What are the requirements to become a qualified tour guide?," analyze the actual needs of enterprises and the general content of recruitment, and finally adopt the method of situation analysis (Strengths Weaknesses Opportunities reat, SWOT) to conduct a self-analysis and give students a clear picture of their own career [11,12]. SWOT for selfanalysis helps them make a career plan for themselves that can be achieved by jumping in the near future. e timely and reasonable integration of relevant ideological content in the teaching content is not only conducive to students' deeper understanding of the professional knowledge of the tour guide business course [13,14].
In the mid-1980s, the author of [15] in a critique of traditional cognitive science focused on the environment and social culture in which individual cognition takes place and proposed a new paradigm that triggered a multidisciplinary rethinking of cognitive activity-distributed cognition. e research perspective of [16] differs from previous researchers who confined the study of cognitive phenomena to be done and conducted only in the laboratory; they tried to explain that the cognitive processes of cognitive subjects have gone beyond the scope of the brain through real everyday work scenarios and then turned to the environment, social culture, and the interplay of various groups of influential elements in the process. By studying the working environment and the process of positioning a ship at sea and the process of speed fixation in the cockpit of an airplane in real scenarios, they fully explained that the completion of cognitive activities depended on internal representations of the cognitive subject and external representations such as the environment and tools located outside the subject, and they argued that cognitive behaviors should be specific situational behaviors, thus developing a distributed cognition theory. Since then, related theories influenced by distributed cognition, such as distributed knowledge, situated cognition, activity theory, and organizational learning, have been widely applied [17,18].
In order to promote the better development of tour guide business, the article takes the tour guide business teaching in colleges and universities as an example and analyzes the current situation and the effect of students' learning in the tour guide business course through investigating and researching the current situation of the tour guide business course ideological and political teaching. It also proposes corresponding improvement measures for the existing problems, so as to improve the ideological and political teaching effect of the tour guide business course [19,20]. To this end, this study relies on the powerful functions of UMU platform and builds a hybrid mobile learning mode based on UMU platform by improving the traditional teaching method of "face to face instruction + online lecture." Although the UMU-based blended mobile learning model is formally divided into online learning and offline activities, in the actual teaching process, there are both you and me. In the process of online learning, students can realize the convenient learning through cell phone APP terminal anytime and anywhere, or they can sit comfortably at the study table through computer; in the offline activity classroom, students can sit in the classroom of UMU and communicate with teachers face-to-face, or they can use cell phones to project their check-in, opinions, test results, etc. onto the big screen.
Development of Distributed Cognitive
eory. Nowadays, Western scholars also continue to study distributed cognition theory from daily work situations and also devote themselves to apply it to educational teaching systems outside the fields of psychology and computers, creating such results as distributed learning modules [21].
With the rapid development of information technology, multimedia, mobile devices, etc. have a certain influence on people's cognitive behavior, and people gradually realize the importance of environment and tools on cognitive process, so distributed cognitive theory is also gradually paid attention to. e author conducted a literature search for the theme of "distributed cognition" through the Internet and found that there were 1921 related papers as of March 2020. Among them, the number of Chinese literatures is 377, including 219 journal articles and 149 master's and doctoral dissertations [22]. e research in the field of distributed cognition in China is also in-depth year by year. According to the number of citations and the authority of literature sources, the authors of [23] have introduced the concept and historical origin of distributed cognition, explained the relationship between distributed cognition and individual cognition, and illustrated the value of the theory of distributed cognition in practical applications, so as to provide researchers with an overview of distributed cognition and ideas for applying distributed cognition to computer, education, and other fields under the rapid development of information technology. e research data on distributed cognition in China can be broadly classified into the following areas [24,25]: (1) Research on learners or learning perspectives under technology support: the main manifestations are the impact of distributed cognition on learning and its theoretical significance, the conversion of online teaching models in distributed cognitive contexts, the construction of collaborative communities and spaces for simulated learning, distance course learning, and interrelationships under the basic theory of distributed learning, the establishment of Internet-supported learning models, the design and development of software under mobile learning, etc. (2) Design and strategies related to learning environments: the salient features are the importance of communication among individual learners, the important role of learning tools and media in the cognitive process, the forms of knowledge representation and visualization of learning tools, etc. e research explores how to build individual learning environments for different groups and their technological support, the design of teaching learning environments for different disciplines, the construction of individual learning environment models, etc. (3) Research on network transmission capability and resource allocation in the field of computing is based on distributed cognitive wireless networks, and distributed cognitive resource models in coordinated human-computer interaction and other technologies are proposed.
Research on Mobile
Learning. In general, research on mobile learning can be divided into two aspects: theoretical research and practical research. e theoretical research on mobile learning in foreign countries is relatively small, and the main feature is that it mostly starts from practical applications, reflects and evaluates the practice introduced by new technologies and new ideas, improves and sublimates the theory according to the results, and finally uses the theory for practice as a whole trend [26]. In this process, a large number of studies on specific applications, related empirical evidence, and evaluation of mobile learning emerge. e United States has been at the forefront of mobile learning research. 1994 saw the [27], which focused on the use of PDAs in the classroom. In 2001, Stanford University conducted similar research, focusing on foreign language learning, using mobile communication devices with question testing, voice interaction, and other features for the university's language teaching. e practical application of mobile learning in foreign countries mainly involves the field of education, and its main research contents can be divided into the following aspects: (1) Experiments to verify the feasibility of mobile devices in practical teaching and learning and the effectiveness of using mobile technology to assist learning: For example, the verification of the novelty and curiosity brought to learners in the new technology-supported teaching model in the experiment and the learning effect of learners provide good prerequisites for the research related to the application of mobile learning [27]. (2) Research and development for digital learning resources: For example, the University of Helsinki in Finland has developed applications that enable access to school curriculum resources anywhere and anytime through mobile terminals such as cell phones. e M-Learning Research Program, undertaken by five organizations in the United Kingdom, Sweden, and Italy, creates mobile learning environments based on mobile communication and develops mobile learning resources such as courses, services, and products suitable for learners [28].
(3) Experiments on teaching and learning based on short messages: e Short Message Service (SMS) system developed by Kingston University in the UK can verify the superiority of SMS over emails and web pages by sending information such as course schedules and exams. e University of Helsinki in Finland applied the SMS system to teacher training and achieved satisfactory experimental results. e concept of mobile learning was first introduced to China by the Irish distance educator Keegan in 2000, which has since triggered many domestic researchers and scholars to pay attention to mobile learning. After reviewing relevant information, the author found that the research contents and trends of mobile learning in China have shown certain characteristics and stages. 2000-2005 can be classified as the first stage, and the main research contents were theoretical research on mobile learning, research on the prospect of mobile learning, review-type research, exploration of models, etc. In addition to theoretical research such as research trends, 2006-2011 began to involve platform development and research on mobile learning. In addition to theoretical studies such as research trends and technical systematic studies such as platform development, terminal selection and application design began to be conducted in 2011, and there were also preliminary studies on teaching design. 2011-2018 saw a large number of studies on specific applications of mobile learning, such as mobile library, MOOC, WeChat platform, rain classroom, and other platforms applied to teaching and learning [29]. ere are also studies on the application of mobile learning in teaching and learning, as well as research studies on different groups. e research on mobile learning in China is mainly at the level of basic theory or a more detailed and in-depth study of a certain branch of mobile learning, but in recent years, research on specific applications and learning platforms of Discrete Dynamics in Nature and Society 3 mobile learning has been emerging in the field of education. e research direction of the relevant literature can be divided into the following aspects of mobile learning.
(i) eoretical studies on mobile learning
It is mainly reflected in the research on the basic theory, definition, current situation, and development trend of mobile learning, including the more authoritative research on introducing mobile learning, the research on proposing the roadmap of mobile learning system environment, etc. (ii) Technology research on mobile learning For example, in the area of wireless communication technology, they designed a mobile learning platform supported by Android system to realize online learning and learning community functions and verified the results. In the area of resource development technology, they designed and developed a learning resource system for English words under mobile development technology and evaluated it based on the basic model and method of mobile learning resource design. In the area of WAP2.0 supported mobile learning system technology development, they analyzed the feasibility of mobile learning application for teaching and learning under 4G and 5G network system and designed a specific application model [30]. (iii) Research on mobile learning e research mainly focuses on the current situation of mobile learning for college students or the use of certain types of software, but also for master's students, primary and secondary school students, teachers, and other groups, and the research for international students mainly focuses on the use of some mobile Chinese learning software. (iv) Research on the application of mobile learning Domestic research on mobile learning applications in universities is mostly focused on adult education and continuing education. For example, Shanghai Jiaotong University has developed a mobile learning system with the functions of live teaching course, learning resources download, and automatic question and answer. In addition, there is also research on the application of intelligent training systems for enterprises. In the past two years, the application of WeChat and WeChat public platform to learn and teaching research has shown a rapid development rate [31].
Construction of a Blended Mobile Learning Model.
is study relies on the powerful functions of UMU platform and builds a hybrid mobile learning mode based on UMU platform by improving the traditional teaching method of "face-to-face instruction + online lecture" of Anhui University of Finance and Economics, as shown in Figure 1. Figure 1, the UMU platform-based blended mobile learning model consists of three main components: pre-preparation, online learning, and offline activities.
As shown in
First, the preliminary preparation: One is to prepare for teaching analysis, and the other is to prepare for the design and development of learning resources, in which teaching analysis includes the analysis of teaching objectives, teaching objects, and teaching contents. Second, online learning: Online learning mainly relies on the UMU platform for synchronous or asynchronous online learning, and the teacher's role changes from that of the main speaker to that of the leader and guide of online learning, leading students in preclass preparation, guiding them how to conduct effective online learning, providing them with learning resources, and setting up learning tasks [31]. Students learn online through teaching videos (knowledge transfer), case studies (internalization and expansion), and online self-assessment (result curing).
ird, offline activities: e offline activities are based on the UMU platform for the design of teaching activities at the classroom site, organizing students to actively participate in classroom communication, task operation, group discussion, and result display and dynamically displaying the links of on-site sign grouping, video playback of important knowledge points, data overview of group discussion ideas, group collaboration task result display, and ranking of on-site assessment results through the large screen to achieve effective interaction between teachers and students at the classroom site [32]. e UMU-based blended mobile learning model emphasizes student-centeredness, and students are the main subjects of both online learning and offline activities, but this study argues that while emphasizing student-centeredness, the teacher's leading role in the entire learning process cannot be ignored. In each specific aspect of online learning and offline activities, in order to enable students to achieve more efficient learning outcomes in less time, teachers need to implicitly lead the whole learning process through appropriate interactions [27,30]; specifically, if there is some kind or several kinds of deficiencies in social presence, cognitive presence, or pedagogical presence in the online or offline learning process, teachers need to provide the necessary timely instructional scaffolding, and when a certain sense of presence is no longer missing, the teacher timely withdraws the instructional scaffolding.
Preliminary Preparation.
e preliminary preparation of the UMU-based blended mobile learning model includes pedagogical analysis and the design and development of learning resources, in which the pedagogical analysis includes the analysis of pedagogical objectives, objects, and contents. e teaching objectives of the UMU-based blended mobile learning model are continuously specified in the task list of online learning and offline activities, and each objective interacts and links with each other to form a complete general system of teaching objectives of UMU-based blended mobile learning. It also serves as a guide for the design of teaching activities in UMU-based blended mobile learning, directly guiding the direction, intensity, and duration of teaching behaviors, promoting active behaviors between teachers and students, and serving as a basis for evaluation to promote optimal improvement of teaching effectiveness.
Before starting the UMU-based blended mobile learning model, students need to be characterized in order to understand their prior knowledge and cognitive level [32,33], mainly in terms of their initial abilities and basic characteristics, in order to understand their motivation and basic characteristics and then to design appropriate, feasible, and effective UMU-based blended mobile learning model teaching activities.
Design and Development of Learning Resources.
e learning resources for blended learning are very important, and there are two main ways to design and develop blended mobile learning resources based on UMU, as shown in Figure 2.
As can be seen from the above figure, in the UMU-based hybrid mobile learning resource library, part of it is from the introduction and adaptation of the existing resources of the National Open University, and the other part is from the self-built learning resources produced and integrated.
(1) Introducing and transforming existing resources of the National Open University: In the blended mobile learning mode based on UMU, high-quality learning resources on the learning network platform of the National Open University or the highquality open course resources already built by the high-quality courses team of [29] are introduced or transformed to make efforts to adapt them to the results of the preliminary teaching analysis, so that students can make effective use of the learning resources, thus enhance the learning effect, and also promote the sustainable development of the UMU platform. (2) Teachers analyze students' characteristics, their needs for learning resources, and the current situation of learning resources according to the needs of teaching contents and combine their own information technology ability level to make their own suitable learning resources and integrate them into the UMU resource library. e whole process of resource development is completed through the process links of development such as teaching analysis, curriculum planning, resource design, the release and implementation, evaluation and reflection, and resource optimization [34,35].
Online Learning.
e UMU-based blended mobile learning model of online learning is mainly based on the UMU platform to achieve mobile online synchronous or asynchronous learning. Teachers are the leaders and instructors of online learning, leading students to prepare for classes, guiding them to conduct effective online learning, providing them with learning resources, and assigning learning tasks, and students learn online through teaching videos for knowledge transfer, case studies for internalization and expansion, online self-assessments for results curing, etc. Discrete Dynamics in Nature and Society In the mobile blended learning mode, students can access diversified media resources and targeted personalized learning paths through smartphones and other devices on the UMU platform to achieve mobile online asynchronous learning or synchronous learning. Asynchronous learning on the UMU platform refers to students directly watching teaching videos, micro-lessons, graphic materials, and other learning resources released by teachers in advance on the platform to learn independently and complete knowledge transfer anytime and anywhere. Moreover, synchronous learning generally relates to live classes, which students can watch on both cell phones and computers without installing APP and any plug-in, and mainly solves the key points and difficulties in teaching and problems in students' independent learning in live classes.
Offline
Activities. UMU-based blended mobile learning model offline activities, relying on the UMU interactive platform for classroom site teaching design, organize students to actively participate in classroom communication, task operation, group discussion and results display, on-site sign-in grouping, explanation of important and difficult points and student feedback problems, group discussion data overview, group collaboration task results display, onsite assessment results ranking, and other links through the large screen. e dynamic display of classroom interaction between students and teachers is realized. e offline activity classroom supported by UMU changes the status quo of "students cannot use their cell phones in class" and interconnects students' cell phones with the teacher's screen, transforming the traditional "only one person can communicate with the teacher at the same time" into "multiple people expressing their opinions at the same time." It can change the traditional "only one person can communicate with the teacher at the same time" to "multiple people can express their opinions at the same time," and all the important keywords in the opinions can be displayed on the big screen in the fastest and most clear way, making the classroom teaching more vivid and efficient.
us, although the UMU-based blended mobile learning model is divided into online learning and offline activities; in the actual teaching process, there are both you and me. In the process of online learning, students can realize the convenient learning through mobile APP terminal anytime and anywhere, or they can sit comfortably at the study table through the computer; in the offline activity classroom, students can sit in the classroom of the university and communicate with the teacher face to face, and they can also use their cell phones to project their check-in, opinions, test results, etc. onto the big screen. In the whole UMU-based hybrid mobile learning model, there is no clear boundary between online learning and offline activities, and online and offline are integrated with each other and crossed according to the actual learning needs, maximizing learning efficiency. Figure 3, this paper first performs through six student volunteers the learning interest experiment of the tourism course of this paper program. It can be seen that through the evaluation of the students through the pre-course in the course content "digging," in the current affairs events "selection," the teachers should integrate the content of ideology and politics, such as the principles of doing things, the Chinese dream of achieving the great rejuvenation of the Chinese nation, and the core socialist values, into the teaching of Xi Jinping ought on Socialism with Chinese Characteristics for a New Era. At the same time, teachers should make full use of the teaching links such as "understanding" in vivid cases and "practicing" in practical activities to integrate the civic and political elements into the teaching process and stimulate the students' patriotism and responsibility. Teachers should also fully implant the code of ethics for tour guides and the case of gold medalist tour guides into the whole teaching process and guide students to objectively compare and analyze their career plans while learning from the shining points of the role models, so as to cultivate strong cultural confidence, national sentiment, and good professional ethics [4]. Students' interest in learning has been high in student 1. e probability of learning the distribution of interest in the tourism course in this paper is shown in Figure 4, giving a random variable X as the length of time in minutes. Over time, students begin to realize that many things in nature and real life often behave similarly, with variables sharing a distribution, or having the same density function (or similar functions changing some of these constants). e teaching method focuses on Outcome Based Education (OBE) throughout, presenting a student-centered tour guide business classroom with ideological and political elements. e teaching format can be in the form of group discussion, group debate, role play, group PK, brainstorming, blue-ink voting, etc., so that students can really participate in the classroom on their own, actively thinking and reflecting. For example, for a topic of " e rise of online tour guide, are you willing to try it?," through the debate, both sides of the argument can cultivate the spirit of cooperation and for the correct values.
Experimental Effects. As shown in
In Figure 5, the assessment of different teachers' guide business teaching that integrates the elements of civics involves the ideological and political parts, and teachers can use a combination of self-assessment, mutual assessment, and teacher assessment for dynamic assessment, such as submitting learning reports, case study reports, reflection reports, and learning file record forms to stimulate students' interest in learning and facilitate teachers' grasp of students' learning dynamics and changes. Preachers themselves must first understand and believe in the way. Teachers must dig deeper into the ideological and political education elements contained in professional knowledge, organically integrate such civic and political elements as family and country sentiment, awareness of the rule of law, social responsibility, humanistic spirit, and benevolent heart, and silently guide students to closely link their personal growth with the future and destiny of the motherland. Although there is a break in the middle of the Teacher 4 course, the subsequent teaching interest is based on a high level. e tour guide business course combines the teaching reality of tourism management majors, and while teaching knowledge, it also pays attention to guiding students to establish ambitious political ideals and ideological aspirations, establish a correct outlook on life and values, cultivate students' cultural confidence in their hometowns, regions, and national countries, tell the world the Chinese story, spread the Chinese voice, explain the Chinese characteristics, and establish a sense of home, the overall situation, professionalism, and moral conduct.
Conclusion
In order to further strengthen the organic integration of the professional course of tour guide business and the ideological and political education course, the tour guide business course takes Anhui Province attractions and school campus as the carrier to learn the content of tour guide service, which not only fits the course content but also expands the professional ability, and more importantly, the unique charm of Chinese history and culture in the study. e research on the curriculum of the tour guide business needs to be further improved in the following aspects: to further realize the automatic integration of data and accurate pushing; to continuously enrich the cloud tourism resources to meet the needs of the new era of Internet development; to further expand the integration of "curriculum + ideology and politics + hybrid teaching." Data Availability e datasets used in this paper are available from the corresponding author upon request.
Conflicts of Interest
e authors declare that they have no conflicts of interest regarding this work. | 6,930 | 2021-12-09T00:00:00.000 | [
"Education",
"Computer Science",
"Business"
] |
Black hole non-uniqueness via spacetime topology in five dimensions
The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess non-trivial 2-cycles. We discuss how this may lead to a gross violation of black hole uniqueness, beyond the existence of black rings, even for solutions with two commuting rotational symmetries. We illustrate this with a simple example in minimal supergravity; a four parameter family of supersymmetric black hole solutions, with spherical horizon topology and a 2-cycle in the exterior. We show there are black holes in this family with identical conserved changes to the BMPV black hole, thereby demonstrating black hole non-uniqueness in this context. We find a decoupling limit of this family of black holes that yields spacetimes asymptotic to the near-horizon geometry of a BMPV black hole which contain a black hole and an exterior 2-cycle.
Topology of black hole spacetimes
Topological censorship implies that the domain of outer communication of any globally hyperbolic asymptotically flat spacetime is simply connected [1]. In four dimensions this is sufficient to guarantee that any spatial hypersurface Σ has the trivial topology R 3 \B, where B is the black hole region. This can then be used to show that ∂B must be homeomorphic to a sphere S 2 , an important ingredient of the black hole uniqueness theorem [2]. For higher dimensional spacetimes, topological censorship is not as restrictive. In particular, spatial hypersurfaces Σ may have non-trivial higher homology groups H p (Σ), for p ≥ 2. This raises the question: are there black hole spacetimes whose domain of outer communication is topologically non-trivial?
For static black holes this cannot be the case; there is a uniqueness theorem [3,4] that generalises the four dimensional case which shows the only solution is the Schwarzschild metric, or charged versions thereof, so Σ ∼ = R D−1 \B. Therefore, if there are any solutions with Σ non-trivial they must be not be static.
In this note we will focus on five-dimensional asymptotically flat stationary spacetimes with two commuting rotational Killing fields, containing a single black hole. In this case it has been shown that the topology of the domain of outer communication is R × Σ, where 1 Σ ∼ = R 4 #n(S 2 × S 2 )#n ′ (±CP 2 ) \B, (1.1)
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for some n, n ′ ∈ N and B is the black hole region, where the horizon H ∼ = ∂B must be one of S 3 , S 1 × S 2 , L(p, q) [5][6][7][8]. The integers n, n ′ determine the 2-cycle structure of Σ. The known solutions consist of the Myers-Perry black holes and the black rings, which have horizon topologies H ∼ = S 3 and H ∼ = S 1 × S 2 respectively, see [9] for a review. Both of these solutions have trivial topology in the exterior, i.e. n = n ′ = 0 (see [10] for more detail on their topology). Thus, a more refined question is: are there black hole spacetimes with a domain of outer communication given by (1.1) for some n, n ′ = 0?
The above class of spacetimes belong to the generalised Weyl solutions [11]. These have been well studied and their classification is understood in terms of a so-called 'rod structure' [5,11,12]. The rod structure is equivalent to the specification of the orbit spacê Σ ∼ = Σ/ U(1) 2 , which turns out to be a manifold with boundaries and corners, together with a pair of integers and a real number for each boundary segment. These numbers correspond to the linear combination of Killing fields which vanishes along a given boundary segment and the length of the boundary segment.
In particular, it has been shown that vacuum black hole spacetimes in this class are uniquely specified by their angular momenta and their rod structure (their mass is determined by these) [5,6,13]. The known solutions mentioned above possess the simplest possible rod structure compatible with their horizon topology. However, these results do not address the general existence problem: that is, for what rod structures do black hole solutions actually exist? In fact, this is a further refinement of the question posed above. This is because the orbit space and the integers for each boundary segment determine the manifold Σ together with the U(1) 2 -action, which in turn gives the integers n, n ′ in the decomposition (1.1).
An analogous uniqueness result for Einstein-Maxwell theory is known, under some restrictive assumptions, which reveals one must also specify the magnetic flux through any 2-cycles to uniquely characterize the solution [14]. Various uniqueness results are also known in minimal supergravity (Einstein-Maxwell with a Chern-Simons term) for spherical black holes [15], for black rings [16] and for multiple black holes [17]. However, all of these assume the simplest possible rod structure -and hence exterior topology -which is compatible with the assumed horizon topology.
It is clear that the existence of black hole spacetimes containing non-trivial 2-cycles, often termed 'bubbles', would represent a gross violation of black hole uniqueness beyond black rings. We emphasise this is even compatible with the R × U(1) 2 symmetry possessed by the known explicit solutions. This possibility does not appear to have been discussed before.
For vacuum gravity, the only mechanism available to 'support' the bubbles from collapsing is rotation. However, it is unclear whether new vacuum black holes of this kind actually exist. We emphasise though that there does not appear to be any convincing reason why not; indeed, it is tempting to conjecture their existence. For Einstein gravity coupled to a Maxwell field, a more obvious mechanism is available for supporting bubbles: magnetic flux. Indeed, it is much easier to envisage a vast set of black hole solutions with bubbles in the exterior supported by magnetic flux.
In the absence of black holes, soliton spacetimes with bubbles supported by flux are well known to exist, with a number of supersymmetric (see the review [18]) and non-
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supersymmetric examples [19][20][21]. These spacetimes carry positive energy. The relationship between the mass of these spacetimes and their fluxes is expressed in a Smarr-type formula, as observed for BPS-solitons by Gibbons and Warner [22]. Recently, it was shown that on-shell variations of the mass and magnetic fluxes for general soliton spacetimes are governed by a 'first law' formula [23].
Furthermore, one can derive a generalised mass and mass variation formula for R × U(1) 2 -invariant spacetimes containing a black hole with an arbitrary number of bubbles in the exterior region. Similarly to the soliton case it was found that on top of the usual terms for a black hole, extra terms due to the bubbles are present. However, in contrast, these bubble terms are most naturally expressed in terms of an 'electric' flux charge. For Einstein-Maxwell theory, possibly with a Chern-Simons term, the mass formula is [23], and the first law of black hole mechanics is, In the above [C] is a basis for the second homology of Σ, [D] are certain disc topology surfaces which extend from the horizon, Φ are magnetic potentials and Q are certain 'electric' fluxes defined on these surfaces. This shows that non-trivial spacetime topology plays an important role even in black hole thermodynamics, thus providing further motivation to study such objects beyond the question of black hole uniqueness. The purpose of this note is to point out that asymptotically flat black solutions with non-trivial exterior topology do exist. We will illustrate this by writing down and analysing an explicit supersymmetric example.
A supersymmetric example
Large families of supersymmetric smooth solitons with bubbles have been constructed in the 'fuzzball' literature [24]. Because of supersymmetry, it is a simple matter to 'add' a black hole to such 'bubbling' geometries. This has not really been emphasised in the literature, presumably because the focus of the fuzzball program has been on smooth geometries rather than black holes.
We will discuss the simplest possibility of an asymptotically flat black hole solution to minimal supergravity with S 3 horizon topology possessing one exterior bubble. We will first write down the solution and then discuss its salient features.
Solution
Supersymmetric solutions of ungauged minimal supergravity are well understood: they take the form
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where V = ∂/∂t is the supersymmetric Killing vector field and ds 2 M is a hyper-Kähler base [25]. We choose the base M to be a Gibbons-Hawking space where x i , i = 1, 2, 3, are Cartesian coordinates on R 3 , the function H is harmonic on R 3 and χ is a 1-form on R 3 satisfying ⋆ 3 dχ = dH.
As is well known [25], such solutions are then specified by 4 harmonic functions H, K, L, M , in terms of which where The Maxwell field is then where the 1-form ξ satisfies ⋆ 3 dξ = −dK. Now we write the R 3 in polar coordinates Following [24], consider the solution given by the harmonic functions where r 1 = r 2 + a 2 1 − 2ra 1 cos θ, r 2 = r 2 + a 2 2 − 2ra 2 cos θ (2.10) are the distances from the origin to the 'centres' x 1 = (0, 0, a 1 ) and x 2 = (0, 0, a 2 ) respectively. We assume 0 < a 1 < a 2 . We will use a shift freedom in the harmonic functions to set m 0 = 0 without any loss of generality [24]. The explicit form of the solution involves determining the 1-forms χ andω defined above. Integrating, we find
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where, and c is an integration constant. It is also worth noting that the 1-form ξ which determines the Maxwell field is where c ′ is a constant. For a suitable choice of constants this solution is asymptotically flat. Defining r = ρ 2 /4, it is easy to check the Gibbons-Hawking base for ρ → ∞ looks like which is therefore asymptotically R 4 provided ∆ψ = 4π, ∆φ = 2π and 0 ≤ θ ≤ π. Now, it is also clear that f = 1 + O(ρ −2 ). Furthermore, it is easily verified that ω ψ = O(ρ −2 ) and ω φ = O(ρ −2 ) provided one chooses the constants respectively. With these choices, which will be assumed henceforth, our five dimensional spacetime is asymptotically flat R 1,4 . The above solution to supergravity is simply the explicit form for a supersymmetric solution whose harmonic functions possess three 'centres'. If the parameters of the solution are chosen so the three centres are smooth timelike points, the resulting solution is the known soliton with two bubbles [24]. Instead, we will choose one of the centres to correspond to a horizon, and the other two to be smooth points. We note the above 3-centred solution is the simplest possibility for a black hole with an exterior 2-cycle.
Before moving on, we observe that if we 'remove' two of the centres by taking the limit a 1 → a 2 and setting k 1 = k 2 = ℓ 1 = ℓ 2 = m 1 = m 2 = 0 the solution reduces to the 1-centred BMPV black hole [26,27].
Regularity and causality
Let us first examine regularity at the centres x 1 and x 2 . We wish to impose that the spacetime metric at these centres is timelike and smooth.
To examine the behaviour of the metric near each of the centres we first introduce spherical polar coordinates for the R 3 base adapted to each centre: Then one finds the Gibbons-Hawking base It is convenient to rewrite the base as Observe that the metric in the square brackets on the first line is R 4 in spherical polar coordinates, provided we make the same identifications on the angles as required for asymptotic flatness discussed above. Also, it is easily verified that so that the terms in the square brackets on the second line are subleading. This shows that, up to an overall sign, the base near the centres looks like a regular origin of R 4 . Of course, we only require the spacetime metric to have the correct signature.
To examine smoothness near the centres it is useful to introduce the coordinates in terms of which Observe that ∆φ ± i = 2π and X i , Y i are radial variables in two orthogonal planes of R 4 , so any U(1) 2 -invariant smooth function on R 4 must be a smooth function of X 2 i , Y 2 i alone. Indeed, it can be checked that F i , G i are analytic in X 2 i and Y 2 i and in partic- In these coordinates, the terms in the square brackets on the second line of (2.18) are, where to obtain the equality we have used the behaviour of F i , G i near the centre. This is indeed smooth at the origin of R 4 and thus shows that the base metric is smooth at each centre.
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Now, since V 2 = −f 2 , demanding the centres to be timelike requires f = 0 at the centres, which corresponds to setting Then we see that in order to get the correct signature for the spacetime metric we will need f | x=x 2 > 0 and f | x=x 1 < 0. Again, subleading terms of f are analytic in X 2 i , Y 2 i , so the function f is smooth at these centres.
Enforcing smoothness of the metric near the centres also requires the invariant V ·∂ ψ = f 2 ω ψ to vanish at these points (since ∂ ψ degenerates at these points). Firstly, requiring ω ψ to be non-singular at the centres, and using (2.22), implies Then, requiring that ω ψ actually vanishes as x → x 1 and x → x 2 , implies and respectively. Note that these two constraints on the parameters have been simplified using (2.15), (2.22), (2.23). These are the analogs of the 'bubble' equations for solitons [24]. Using the constraints on the parameters (2.24), (2.25), it may now be verified that near the centres, with higher order terms analytic in X 2 i , Y 2 i . Hence the 1-form ω is also smooth at the centres. We have thus derived necessary and sufficient conditions for the spacetime metric to be smooth and timelike at the centres.
Next, we examine the Maxwell field (2.6) near the centres. From the discussion above d(f (dt + ω)) is smooth at each centre. One can also verify that with subleading terms analytic in X 2 i , Y 2 i ; hence this 2-form is smooth at the centres. We deduce that the full Maxwell field is smooth at the centres.
Next we consider regularity of the spacetime away from the centres. It is clear from (2.3) that f is smooth everywhere away from the centres provided, (2.28) Notice that this also implies that f has the same zeroes as H. Remarkably, it turns out that (2.28) also guarantees that the full spacetime metric away from the centres is smooth and Lorentzian with a smooth inverse, even on surfaces where f = 0. Furthermore, this condition also guarantees the Maxwell field is smooth away from the centres. It is clear JHEP10(2014)082 that (2.28) is satisfied asymptotically r → ∞ and we will examine this condition in the interior later.
Let us now turn to causality of our spacetime. We will require our spacetime to be stably causal with respect to the time function t. The condition for this is Clearly this is satisfied in the asymptotically flat region since g tt → −1 as r → ∞. We will examine this condition in the interior explicitly later. At this stage we remark that generically it imposes inequalities on the parameters of the solutions.
To summarise, we have found a family of asymptotically flat spacetimes which are smooth even at the centres x 1 and x 2 and look like the origin of R 1,4 near these points. The solutions are parameterised by (a 1 , a 2 , k 0 , k 1 , k 2 , ℓ 0 ) subject to the constraints (2.24), (2.25) and any inequalities arising from (2.28), (2.29). Thus, generically we have a 4-parameter family of solutions. Generically, the constraints can be easily solved for (k 0 , ℓ 0 ) since they are linear in these parameters. However, we will refrain from doing so at this stage, since this involves imposing certain restrictions on the parameters. Later we will discuss various non-trivial special cases in which they can be solved.
Black hole and near-horizon geometry
We will now show that one can choose the parameters in our solution such that r = 0 is an event horizon. As we will see, this actually imposes less constraints on the parameters, than had we imposed this to be a smooth centre. It is convenient to define the constants Near r → 0, to leading order we find Hence our spacetime is smooth and stably causal near r = 0 if and only if j > 0, λ > 0. Furthermore, we will show that r = 0 is a regular horizon if and only if are both satisfied.
To this end, we transform to new coordinates (v, r, ψ ′ , θ, φ) defined by where A 0 , A 1 , B 0 are all constants. We will need the following Laurent expansions about r = 0, where β, γ,γ, δ are constants whose precise form we will not need. It is then easy to check The g rr component of the metric contains singular terms 1/r 2 and 1/r, whereas the g rψ ′ component contains 1/r terms. Demanding that the 1/r 2 term in g rr and the 1/r term in g rψ ′ vanish, is equivalent to choosing the constants A 0 , B 0 to be This gives where the sign of g vr is positive (negative) if A 0 < 0 (A 0 > 0). Finally, demanding that the 1/r term in g rr is absent determines A 1 to be The metric and its inverse are now analytic at r = 0 and can therefore be extended to a new region r < 0. The supersymmetric Killing field V = ∂/∂v is null at r = 0 and This shows that the hypersurface r = 0 is a degenerate Killing horizon of V . The upper sign choice corresponds to a future horizon, whereas the lower sign choice to a past horizon. It remains to verify that the Maxwell field is regular on the horizon. In fact the gauge field A may be read off from (2.6). Changing to the above coordinates we find The A r component of the gauge field has a singular 1/r term; however the coefficient multiplying this is a constant and therefore it is pure gauge. We conclude that there is a gauge in which A is analytic at r = 0 and therefore F is analytic at r = 0, as required.
The near-horizon geometry is now easily extracted from the above by replacing (v, r) → (v/ǫ, ǫr) and letting ǫ → 0. The result can be written as It is easy to see this is isometric to the near-horizon geometry of the BMPV black hole. This was in fact guaranteed by a near-horizon uniqueness theorem proved in [28].
Geometry of the axes
The axes of rotation corresponds to the z-axis of the R 3 base of the Gibbons-Hawking base. Due to the sources in the various harmonic functions, this axis naturally splits into four intervals: It is easy to see that along this axis where the + sign occurs for I + and I D and the − sign for I C and I − . Remarkably, it can be checked that anywhere along the z-axis the one-form This is a non-trivial identity which requires use of the constraints (2.24), (2.25) in various combinations depending on the interval one is in. It then follows that the induced metric on the axis is where ψ ± = ψ ± φ and φ ± = φ depending on which interval we are in. We also find the induced Maxwell field is We remark that the stably causal condition (2.29) on the axis reduces to just −f −2 + f Hω 2 ψ < 0. Therefore, we deduce that, at least away from fixed points of ∂ ψ ± , stable causality follows from simply imposing |∂ ψ ± | > 0.
We will now examine the geometry on the axis in detail. The precise details depend on the interval in question, although in all cases we show that regularity and causality reduce to the positivity of various polynomials in the given interval. Later we will examine various special cases where one can demonstrate positivity of the various above polynomials is equivalent to certain inequalities on the parameters.
Semi-infinite axes
The semi-infinite intervals I ± correspond to the two axes of rotation which extend out to asymptotic infinity. In particular, along I + the Killing field ∂ φ + = 0, whereas along I − it is ∂ φ − = 0. At the endpoint z = a 2 of I + the Killing field ∂ ψ + must degenerate smoothly due to the general regularity conditions we imposed at the centres. On the other hand, at the endpoint z = 0 of I − this axis meets the horizon.
We now examine the geometry on I + in detail. At z = a 2 the Killing field ∂ ψ + degenerates resulting in a conical singularity; it is easy to see this is removable since ∆ψ + = 4π. Now consider z > a 2 . One finds, using (2.22), where P + (z) is a cubic. Observe that H > 0 for z > a 2 . Smoothness of f requires P + (z) > 0 and therefore we also deduce f > 0 on I + . We also find, where Q + (z) is a 7th-order polynomial. Therefore we also require Q + (z) > 0 for all z > a 2 . We thus deduce that (2.52) is a smooth Lorentzian metric for z > a 2 if and only if P + (z) > 0, Q + (z) > 0. Finally, the Maxwell field (2.53) is also smooth on I + . To see this, note f is smooth and the following holds: where R + (z) is a cubic. Hence, given P + (z) > 0, this function is smooth for all z > a 2 and smoothness of the Maxwell field follows. Similar conclusions hold for I − . Consider first z ′ = −z > 0. One finds, using (2.22), where P − (z ′ ) is a cubic. For z ′ > 0, note that H > 0. Smoothness of f requires P − (z ′ ) > 0 and thus f > 0 for z ′ > 0. Also we find, where Q − (z ′ ) is a 7th-order polynomial. Thus we also require Q − (z ′ ) > 0 for z ′ > 0. We deduce that (2.52) is a smooth Lorentzian metric for z < 0 if and only if P − (z ′ ) > 0, Q − (z ′ ) > 0. As z ′ → 0 we see f vanishes; this corresponds to where I − meets the event horizon. Turning to the Maxwell field, one finds that the identity (2.57) holds with P + (z) and R + (z) replaced by P − (z ′ ) and a cubic R − (z ′ ) respectively. Therefore, the requirement P − (z ′ ) > 0 is sufficient to ensure smoothness of the Maxwell field on I − .
Bubble
Now consider the interval I C . Along this interval ∂ φ − = 0, whereas ∂ ψ − must degenerate at the endpoints z = a 1 , a 2 smoothly due to regularity at these centres. To see this explicitly define ρ 2 = |z − a i | and f i = f z=a i for i = 1, 2. We then find that as ρ → 0 is indeed free of conical singularities at both endpoints since from above ∆ψ − = 4π. However, since regularity at the centres requires f 1 < 0 and f 2 > 0 there must be a point z 0 ∈ (a 1 , a 2 ) where f z=z 0 = 0. Using (2.22) we find that Therefore, we deduce that z 0 = √ a 1 a 2 and P C (a i ) > 0 to ensure the correct signs of f at the endpoints. Furthermore, smoothness of the invariant V 2 = −f 2 requires P C (z) > 0 for all z ∈ [a 1 , a 2 ]. We also find, which therefore also changes sign in the interval in such a way that g zz = H/f > 0 and smooth for z ∈ (a 1 , a 2 ). Next, we find the remarkable simplification where Q C (z) is a complicated 7th order polynomial. Therefore smoothness requires Q C (z) > 0 for all z ∈ (a 1 , a 2 ). Putting all this together, we find that (2.52) is a smooth Lorentzian metric for all z ∈ (a 1 , a 2 ) if and only if P C (z) > 0 and Q C (z) > 0. Given these inequalities, we have shown that any constant time slice extends to a smooth inhomogeneous S 2 . Therefore our black hole solution possesses a non-trivial 2cycle C in the domain of outer communication.
Furthermore, the Maxwell field (2.53) is also smooth on C. To see this it is sufficient to note the identity where R C (z) is a cubic. Therefore, given P C (z) > 0, this function is smooth for all z ∈ [a 1 , a 2 ], which guarantees the Maxwell field is smooth on C.
Disc
Finally consider the interval I D . Along this interval ∂ φ − = 0, whereas ∂ ψ − must degenerate at the endpoint z = a 1 smoothly due to regularity at this centre. Indeed defining ρ 2 = |z − a 1 | we find that as ρ → 0 is indeed smooth since ∆ψ + = 4π. On the other hand, as we approach the other endpoint z → 0 we find so ∂ ψ + does not have a fix point there. In fact this endpoint corresponds to the horizon and it is easily see that this agrees with the norm in the near-horizon geometry. Now, since f > 0 just outside the horizon and f 1 < 0, again we deduce there must be a point in the interval z 0 ∈ (0, a 1 ) where f = 0. In this case we find where P D (z) is a cubic. The quadratic z 2 − 2a 2 z + a 1 a 2 is negative at z = a 1 and positive at z = 0, with one root in between at z 0 = a 2 − a 2 (a 2 − a 1 ). Hence we also require P D (z) > 0 for all z ∈ (0, a 1 ]. Similarly, we also find and remarkably where Q D (z) is a 7th order polynomial. Thus we require Q D (z) > 0 for all z ∈ (0, a 1 ). Putting all this together we find that again (2.52) is a smooth Lorentzian metric for all z ∈ (0, a 1 ) if and only if P D (z) > 0 and Q D (z) > 0. Given these inequalities, we deduce that constant time slices extend to a smooth positive definite metric on a topologically disc surface D in the spacetime, whose centre touches C at a point (z = a 1 ) and ends on the horizon. However, note that since H/f ∼ j/z 2 as z → 0, the proper radius of this disc is infinite; this of course should be the case since our horizon is degenerate.
Again, it is easily checked the Maxwell field is smooth on D. Just note the identity where R D (z) is a cubic. It follows that, given P D (z) > 0, this function is smooth for all z ∈ (0, a 1 ], which guarantees the Maxwell field is also smooth on D. We observe that from the above analysis we see that the supersymmetric Killing field V is in fact null on the circle z = √ a 1 a 2 in C, and also on the circle z = a 2 − a 2 (a 2 − a 1 ) in D. This is why our black hole solution evades the black hole uniqueness theorem for BMPV [28], since that assumes V is strictly timelike in the exterior region.
Physical properties
The conserved global charges of our asymptotically flat solution are easily computed. We find the electric charge is, It is easily checked the mass M = − 3 32π S 3 ⋆dV = √ 3 2 Q satisfies the BPS bound. The angular momentum with respect to a rotational Killing field m is given by J[m] = 1 16π S 3 ⋆dm. We find that with respect to ∂ ψ and ∂ φ it is given by, respectively. It is easily seen that for any BPS black hole in minimal supergravity the surface gravity κ and angular velocities Ω i of the horizon all vanish, whereas the electric potential on the horizon Φ H = √ 3 2 . Also we find that the area of the horizon is and the electric charge and angular momentum of the horizon are and respectively. Thus we see that the parameters k 0 , ℓ 0 are related to the conserved charges on the horizon. Our black hole solution also carries local magnetic flux charge due to the presence of a non-trivial 2-cycle C in the domain of outer communication of the black hole. Using the expression for the Maxwell field induced on this bubble (2.53) we find the magnetic flux is Furthermore, due to the presence of a horizon and 2-cycle, a disc topology region D connecting the two also exists on which we can define a flux charge [23]. Similarly, we find this is This gives a physical interpretation to the parameters k 1 , k 2 in our solution.
We have not been able to prove smoothness and stable causality away from the axis for general values of r (of course in the two asymptotic regions r → ∞ and r → 0 we
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have showed this earlier for the general solution). However, we have performed extensive numerical checks and not found any violation of the inequalities (2.28) and g tt < 0 for this solution. In brief, our strategy was to treat K 2 + HL and g tt as a function of four variables (r, θ, a 1 , a 2 ) and sample it over a variety of hyper-grids in the domain r > 0, 0 < θ < π and a 2 > 2a 1 > 0. Therefore, we believe that this solution is indeed smooth and stably causal if and only if (2.86) is satisfied.
Recently, a Smarr relation and first law of black hole mechanics were derived for black hole spacetimes with non-trivial topology, see equations (1.2), (1.3). For minimal supergravity, the 'electric' flux charge appearing in these laws is given by and similarly for Q [D]. Using the general form for a supersymmetric solution [25], it is a simple exercise to check the integrand . Then, using the behaviour of the solution near the various centres, it follows that Therefore, the extra terms in the Smarr relation and first law in fact vanish for such supersymmetric black holes. Thus these mass formulae reduce to the standard BPS bound.
Static horizon
Consider the special case in which the horizon carries no angular momentum. From (2.77), we deduce that this special case can be achieved by setting 2 Inspecting the near-horizon geometry of the general solution, we see that in this case it reduces to the static AdS 2 × S 3 near-horizon geometry, as one would expect. Thus we obtain a three parameter family of stationary, but non-static, black hole solutions with the same near-horizon geometry as extreme Reissner-Nordström solution. This illustrates the point that a static near-horizon geometry [29] need not arise as the near-horizon limit of a static black hole. We believe this is the first such example with spherical horizon topology. 3 In fact, further setting, gives a two parameter family which is particularly amenable to analysis. Observe that physically, this corresponds to setting the magnetic flux through the bubble and disc to be equal and opposite, q[C] = −q [D]. Indeed, in this case we may solve the constraints (2.24), (2.25) explicitly to find Another possibility is ℓ0 = − 2 3 k 2 0 , which also has a regular horizon. We have not investigated this case. 3 The BPS black ring is non-static, but possesses a static locally AdS3 × S 2 near-horizon geometry [30].
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We see that the conditions for regularity of the horizon (2.32) reduce to simply ℓ 0 > 0. Therefore, we deduce a stronger inequality on the parameters, (2.86) For definiteness we will take the positive root k 1 > 0. We now turn to the regularity conditions for the axis, derived in section 2.4. In particular, we have proved that in this special case, the polynomials P ± (z), Q ± (z), P C (z), Q C (z), P D (z) and Q D (z) are strictly positive in their respective intervals, provided (2.86) is satisfied. This establishes smoothness of the spacetime on the bubble C and the disc D and the two semi-infinite axes I ± . As discussed in section 2.4, these conditions are also sufficient to ensure stable causality on the whole z-axis (i.e. θ ∈ {0, π}).
We have not been able to prove smoothness and stable causality away from the axis for general values of r (of course in the two asymptotic regions r → ∞ and r → 0 we have showed this earlier for the general solution). However, we have performed extensive numerical checks and not found any violation of the inequalities (2.28) and g tt < 0 for this solution. In brief, our strategy was to treat K 2 + HL and g tt as a function of four variables (r, θ, a 1 , a 2 ) and sample it over a variety of hyper-grids in the domain r > 0, 0 < θ < π and a 2 > 2a 1 > 0. Therefore, we believe that this solution is indeed smooth and stably causal if and only if (2.86) is satisfied.
It is worth noting some of the physical properties of this special case. Although the near-horizon geometry is not rotating, the black hole spacetime in fact possesses non-zero angular momenta given by from which it follows that J ψ > 0 and J φ < 0. As we discuss in the next section, this in particular means that this black hole spacetime never possesses equal angular momenta with respect to the orthogonal U(1) 2 Killing fields of R 4 . Therefore, its conserved charges are never the same as that of the BMPV black hole (including the non-rotating Reissner-Nordström solution).
Equal angular momenta and black hole non-uniqueness
Here we consider solutions with equal angular momenta with respect to the standard U(1) 2 rotational Killing fields of R 1,4 . Recall that the BMPV black hole solution has this property [26,27]. Define the quantity The BMPV solution exists only if it is 'under-rotating' η > 0. Interestingly, we will show that there exist regular black hole solutions with equal angular momenta which are underrotating η > 0, critical η = 0, or over-rotating η < 0.
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In our coordinates equal angular momenta can be achieved by setting J φ = 0. From (2.74) this allows us to solve for k 0 : We thus obtain a three-parameter family of black hole solutions with equal angular momenta and the same near-horizon geometry as the BMPV black hole. For simplicity consider the two-parameter subset of solutions with In this case we must have k 1 = 0 as otherwise the solution is singular. Then the unique solution to the constraints is given by The conditions for regularity of the horizon (2.32) are positivity of the quantities Therefore we deduce these are met if and only if, For definiteness we take the positive root k 1 > 0 (the choice k 1 < 0 leads to a solution with equal and opposite angular momenta). The analysis of this solution is more involved than the special case described in the previous section. We can prove that the polynomial P C (z) > 0, but for the remaining polynomials Q ± , P ± , Q C , P D , Q D we have relied on numerical methods to demonstrate positivity. Turning to checking smoothness and stable causality away from the axis for general (r, θ), we have done a careful search for violations of (2.28) and g tt < 0. As in the previous case, the method is to sample a large number of points in the parameter space (r, θ, a 1 , a 2 ) with r > 0, 0 < θ < π and 0 < a 1 < a 2 < 2a 1 . We have found no evidence for violations of (2.28) or g tt < 0 and believe the solution is smooth and stably causal if and only if (2.94) holds.
Let us now briefly discuss the physical properties of this solution. We find the angular momentum, and electric charge, (2.96) It is easily checked that in our parameter domain (2.94) J ψ > 0, so these solutions always have non-zero angular momentum.
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Furthermore, it may be verified that The first factor in the square brackets is always positive in our domain. Therefore the sign of (2.97) is the same as the sign of the quadratic in the second factor in square brackets. We thus find that (2.97) is positive if and only if Remarkably, this overlaps with our parameter domain (2.94). Therefore, we have shown there exist black hole solutions with the same conserved charges as the BMPV black hole, the same near-horizon geometry, but are distinct to the BMPV black hole. This explicitly demonstrates non-uniqueness of supersymmetric black holes in minimal supergravity. Furthermore, in the complement of (2.98) within the domain (2.94) we may also have black holes for which (2.97) vanishes or is negative. Therefore we have also shown there exist spherical black hole solutions which fill out parts of the (Q, J ψ )-phase space not occupied by the BMPV solution.
A decoupling limit
Above we showed that the near-horizon geometry of our black hole solution is the same as that of the BMPV black hole. In particular, the non-trivial 2-cycles in the exterior to the black hole are not captured in this limit. Indeed, a general feature of the near-horizon limit of extremal black holes is that it only retains properties of the spacetime intrinsic to the horizon [31]. It is natural to wonder if there is a limit of the solution which focuses near the horizon in such a way to keep the 2-cycles in the exterior. Indeed, it is easy to write down a decoupling limit with this property. 4 Let ǫ > 0 and define new coordinates and parameters by t =t ǫ , r = ǫr, a i = ǫā i (2.99) leaving all other coordinates and parameters the same. It is then easy to see that the solution is equivalent to that constructed from the Gibbons-Hawking base and the four harmonic functions
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it a BMPV near-horizon geometry with the constants j → j ′ and k 0 (k 2 0 + 3 2 ℓ 0 ) → δ ′ . Notice that this is equivalent to the replacements Let us now turn to regularity of our spacetime. One can repeat all the steps performed for the black hole solution and one finds it is smooth with the same topology provided the parameters satisfy (2.22), (2.23) and (2.25). Similarly, our spacetime possesses a regular degenerate horizon with the same near-horizon geometry as obtained in section 2.3. Again, this can be shown by repeating the near-horizon analysis, or more simply appealing to continuity of our limit. It is worth noting that not all solutions to the regularity constraints (2.24), (2.25) of the asymptotically flat solution admit the above decoupling limit. For example, the special cases we examined in sections 2.6 and 2.7 do not, because scaling the a i to zero is not compatible with keeping the k i fixed for those solutions. It may be interesting to investigate other decoupling limits, which in particular are well defined for these special cases.
To summarise, we have obtained a spacetime with the following properties. It is asymptotically the near-horizon geometry of a BMPV solution, possesses an event horizon with a near-horizon geometry of a different BMPV solution (with parameters related by (2.110)), and a 2-cycle in the exterior region. In effect we have thus merely 'decoupled' the asymptotically flat region from our black hole solution, while keeping the exterior topology and near-horizon region intact. We emphasise that this solution is different to the decoupling limit of a multi-centred BMPV black hole in that it represents a single black hole in a near-horizon BMPV background. We also note it differs from the smooth solitons that are asymptotic to a near-horizon BMPV solution previously obtained [32].
Black holes in spacetimes asymptotic to near-horizon geometries of black holes have of course been previously obtained. For example, multi-black holes in AdS 2 × S 2 [39] and AdS 3 × S 2 [40] have been constructed. More recently, a 2-centred solution describing a single black hole in AdS 3 × S 2 has been written down [41].
Discussion
We have presented an asymptotically flat supersymmetric black hole solution to minimal supergravity with spherical horizon topology distinct from the well known BMPV black JHEP10(2014)082 hole [26]. In contrast to the BMPV black hole, the topology of the domain of outer communication is non-trivial and given by (1.1) with n = 1 and n ′ = 0. We have also showed there are regimes in parameter space where the two solutions have identical mass, electric charge and angular momentum. The solutions may be distinguished by local magnetic flux charges defined on the non-trivial 2-cycles in the spacetime. This is the first proof of non-uniqueness of supersymmetric black holes with a connected horizon in minimal supergravity. 5 Furthermore, we believe this provides the first explicit counterexample to spherical black hole uniqueness (for connected horizons) in a theory containing only a Maxwell field.
In fact a uniqueness theorem for the supersymmetric black holes with spherical horizon topology has been demonstrated [28], which assumes the supersymmetric Killing field V is strictly timelike everywhere outside the black hole. This is not the case for our solution; V is null on a circle on the bubble exterior to the black hole, which is how it may evade this uniqueness theorem. We observe that this is not so surprising, due to the fact that soliton spacetimes are also not strictly stationary but have regions where V is null, referred to as 'evanescent horizons' [22].
Although we have only focused on a simple example, it is clear there are more general possibilities. Working within minimal supergravity, it is a simple matter to add more smooth centres to the Gibbons-Hawking base, following the method for pure solitons [24]. This should result in large classes of black holes with more general 2-cycle structure in the exterior region. Furthermore, it should be possible to construct black rings with exterior bubbles using the same method.
More broadly, and as argued in section 1, analogous solutions should exist for nonsupersymmetric black holes both within minimal supergravity but also other five-dimensional Einstein-Maxwell type theories. This could be of particular interest since non-trivial spacetime topology plays a role in black hole thermodynamics [23]. Clearly, however, in the absence of supersymmetry, constructing explicit solutions will be significantly harder. Perhaps progress for extremal, but non-supersymmetric, black holes can be made along the lines of [34,35].
An interesting open question is whether vacuum spacetimes can 'support' non-trivial topology. We emphasise there are no theorems ruling out this possibility. In the context of Weyl solutions this would correspond to taking more complicated spacelike rod structure than has been previously considered.
It would be interesting to investigate the implications of our results for the string theory derivation of the entropy of the BMPV black hole [26,36]. Implicit in these calculations is the assumption that black holes are uniquely specified by their conserved charges. We have demonstrated explicitly this assumption is false, even for spherical black holes in minimal supergravity.
We have also written down a decoupling limit of our solution which focuses near the horizon while retaining the non-trivial topology of the spacetime. It is worth emphasising JHEP10(2014)082 that this decoupling limit may be of interest in its own right. This spacetime can be thought of as interpolating between the near-horizon geometries of two different BMPV black holes. It would be interesting to interpret this as a holographic renormalisation group flow in the context of AdS 2 /CFT [37,38].
Our decoupling limit can also be thought of as a black hole sitting in the near-horizon geometry of a BMPV black hole. It is natural to expect non-BPS generalisations of such solutions, presumably arising as the decoupling limit of a non-BPS version of our asymptotically flat black hole solutions. Such geometries may indicate that the non-existence results obtained for finite-energy excitations of AdS 2 × S 2 and the near-horizon geometry of extremal Kerr [39,[42][43][44], do not generalise to theories in which black hole uniqueness fails. | 10,875.2 | 2014-10-01T00:00:00.000 | [
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A new technique for preserving conservation laws
This paper introduces a new symbolic-numeric strategy for finding semidiscretizations of a given PDE that preserve multiple local conservation laws. We prove that for one spatial dimension, various one-step time integrators from the literature preserve fully discrete local conservation laws whose densities are either quadratic or a Hamiltonian. The approach generalizes to time integrators with more steps and conservation laws of other kinds; higher-dimensional PDEs can be treated by iterating the new strategy. We use the Boussinesq equation as a benchmark and introduce new families of schemes of order two and four that preserve three conservation laws. We show that the new technique is practicable for PDEs with three dependent variables, introducing as an example new families of second-order schemes for the potential Kadomtsev-Petviashvili equation.
Introduction
Consider a system of q partial differential equations (PDEs), where A is a row vector, u has components u α , α = 1, . . . , q, and square brackets around a differentiable expression denote the expression and finitely many of its derivatives 1 . We assume that (1) is totally nondegenerate (see [18]). A local conservation law is a divergence expression, that vanishes on all solutions of (1). The functions F and G are the flux and the density of the conservation law, respectively, and D x and D t denote the total derivatives with respect to x and t, respectively. The conservation law (2) is in characteristic form if there exists a column vector Q such that Div F = AQ, (3) in which case Q is called the characteristic. The space of total divergences forms the kernel of the Euler operator, E, whose α-th entry is Hence if and only if there exists F such that (3) holds. These results generalize immediately to PDE systems with more than two independent variables. The literature on the numerical solution of PDEs is rich in numerical methods that preserve global invariants, but there are relatively few results on the preservation of local conservation laws. Arguably, local conservation laws are more necessary: they hold throughout the domain, apply to the set of all solutions, and provide much stronger constraints than are needed to preserve the corresponding global invariants. Moreover, when the domain and boundary conditions are suitable, conservation of such invariants is automatically achieved.
A new approach for developing finite difference schemes that preserve conservation laws of (1) was introduced recently in [9]. It exploits the fact that discrete conservation laws form the kernel of a discrete version of the Euler operator (4). Discretizations of the PDE (1) having discrete versions of the desired conservation laws are obtained by requiring that a discrete version of condition (5) is satisfied. This requires the symbolic solution of a large system of nonlinear equations that is impractical in general. The complexity of the symbolic calculations can be reduced by introducing compactness requirements on the schemes, and this direct approach has been applied to a range of PDEs with different structure in [9][10][11]. However, the direct approach is greatly limited by the capacity of symbolic computation; it has been applied only to second-order approximations of PDEs with two independent variables.
In this paper we modify the approach in [9] by finding semidiscretizations of (1) that preserve semidiscrete local conservation laws. The reduction to one discrete space dimension significantly reduces the complexity of the computations, to the point that the determining system can be solved easily without introducing any restrictions on the form of the schemes. After this, a suitable integrator in time needs to be chosen to create a fully-discrete scheme; this depends on the form of the conservation laws that one aims to preserve.
If the PDE is equipped with conservative boundary conditions, it is known that the quadratic invariants of its space discretizations are preserved by symplectic Runge-Kutta methods [4,8,20]. In this paper we extend this result to prove that if G is quadratic in [u] then any symplectic Runge-Kutta method preserves the conservation law (2) locally, regardless of the boundary conditions.
There are various results on local conservation for Hamiltonian PDEs, where [u] x denotes u and its spatial derivatives only, D is a skew-adjoint operator that satisfies the Jacobi identity, and H is the Hamiltonian function.
Multisymplectic schemes [3] and their generalizations [21] can preserve local conservation laws with quadratic flux and density. Requiring the flux to be quadratic is however a strong constraint that is not satisfied by local momentum conservation laws of many important equations in physics such as the nonlinear Schrödinger (NLS) equation, the Korteweg-de Vries (KdV) equation, the Benjamin-Bona-Mahony (BBM) equation, the modified Korteweg-de Vries (mKdV) equation, and the Boussinesq equation. The strategy introduced in this paper does not suffer from this restriction, as no assumption is needed about the flux, so it can be applied to the preservation of these conservation laws as well.
Another popular approach is to use a discrete gradient method for the time integration of (6). These are obtained from a semidiscretization of H and a skew-adjoint discretization of D, and preserve a discrete conservation law of the energy [17]. One widely-used discrete gradient method is the Average Vector Field (AVF) method [5,6,19]. We show that the AVF method yields the local conservation law of the Hamiltonian under constraints on the discretization of D that are milder than skew-adjointness. Consequently, conservation of the local Hamiltonian can be achieved for a larger class of discretizations.
Although the discussion so far has focused on PDEs with two independent variables, the approach of discretizing one dimension at a time works equally well for PDEs on higherdimensional spaces. We discuss this and give an illustration.
The paper is organised as follows. Section 2 introduces a method for obtaining conservative spatial semidiscretizations. Section 3 focuses on time integration. In particular, we show the following.
• Conservation laws with quadratic density (without any assumption on the flux) are preserved by any symplectic method in time locally and independently of the boundary conditions. Conservation laws for mass, charge and momentum are typically in this class.
• For Hamiltonian PDEs, the AVF method preserves the local semidiscrete conservation law of the energy for a wide class of semidiscretizations that generalizes the result in [17].
• For other types of conservation law, fully-discrete methods can be found by introducing relatively few parameters and fixing them by requiring that the conservation law is in the kernel of a fully-discrete Euler operator. This approach can be iterated for dimensions, by using a sequence of semidiscrete and discrete Euler operators.
In Section 4 we apply this new approach to the Boussinesq equation and introduce methods of order two and four that preserve three conservation laws. Section 5 describes numerical benchmark tests, including evidence of stability and comparison with other methods from the literature. In Section 6, we apply the new technique to a two-dimensional PDE, the potential Kadomtsev-Petviashvili (pKP) equation and introduce two families of schemes that preserve two conservation laws. Finally, we draw some conclusions in Section 7.
Conservative space discretizations
We begin with a regular spatial grid. The stencil consists of M = B − A + 1 nodes, where x 0 is a generic grid point; let x denote the vector of the nodes. The forward shift operator S m acts as follows on any semidiscrete function f : the forward difference, forward average, and centered difference operators are respectively, where I is the identity operator. The semidiscretizations of u α (x,t) are given by the column vector U ∈ R M q with the (m + αM − B)-th entry The semidiscrete problem is where here and henceforth tildes represent approximations to the corresponding continuous quantities, and square brackets around a semidiscrete expression denote the expression and a finite number of its time derivatives. A semidiscrete conservation law of (9) is a semidiscrete divergence, such that Div The following result is crucial for obtaining semidiscretizations that preserve conservation laws (see [18] and [14] for analogous results in the continuous and totally discrete setting, respectively).
Theorem 1
The kernel of the semidiscrete Euler operator E U , whose α-th entry is , is the space of semidiscrete divergences (10).
such that E U (L) = 0, and consider the derivative Integrating by parts yields ) whose precise expression is not of importance. Substituting this into (11) and integrating over ε ∈ [0, 1] shows that L is a semidiscrete divergence. If L is of the form (10), E U (L) = 0 follows from the linearity of the Euler operator and from the fact that for any k (see, e.g., [12]), Based on the result in Theorem 1, the approach used in [9][10][11] to preserve fully-discrete conservation laws, is adapted here to the preservation of semidiscrete conservation laws of (1) with characteristics Q ℓ , as follows: 1. Select a stencil that is large enough to support generic semidiscretizations for A and every Q ℓ , having the desired order of accuracy. These approximations depend on a number of free parameters to be determined.
2. Find some of the parameters by imposing consistency, up to the desired order of accuracy, p.
3. Use symbolic algebra to determine the values of the free parameters that satisfy for ℓ = 1. This guarantees that the first conservation law is locally preserved. As both A and Q ℓ are accurate to order p, the discrete conservation law has the same order of accuracy.
4. Iterate the previous step, replacing Q 1 with Q ℓ , to obtain further constraints on the parameters. If (12) has no solution for some ℓ, the corresponding conservation law cannot be preserved without violating one of the previous conservation laws. Typically, the more complicated a conservation law is, the more parameters need to be fixed to preserve it.
Remark 1 It might seem appealing to identify a set of conservation laws that one wishes to preserve and use brute force symbolic computation to solve all constraints simultaneously.
(This was our approach initially.) However, this takes far longer than the sequential approach and commonly comes up with a null result, with no indication as to which subsets of conservation laws can be preserved. The sequential algorithm above enables the user to decide which conservation laws should be prioritized. At each iteration, the computation is simplified by the fact that some parameters have already been fixed.
Remark 2 If the algorithm above does not produce any schemes for a given stencil, one could try preserving the same conservation laws using a wider stencil. However, the wider the stencil is, the more the computational cost increases. Moreover, if one finds a conservative semidiscretization, a time integrator that preserves all the conservation laws is also needed. For example, in the next section we prove that some known time integrators preserve conservation laws whose density is either quadratic, or is a Hamiltonian, but to the best of our knowledge there are no methods that preserve both of these types.
Time integration
We begin by considering one-step time integrators. For fully-discrete schemes the stencil is and the forward shift operators in space and time are respectively. The forward difference and forward average operators in space are defined by (8) and the corresponding operators in time are and let u m,n ∈ R q be the column vector with entries u α m,n ≈ u α (x m , t n ), α = 1, . . . , q.
Conservation laws with quadratic density
Here attention is restricted to PDEs of the form where g is linear homogeneous in [u] x ; these include Hamiltonian PDEs. Consider a conservation law of (13) of the form where the density, G 2 , is a polynomial of degree two in [u] x . (Without loss of generality, assume that no terms in G 2 depend on x only.) For many differential problems of importance in physics (such as KdV, NLS and BBM equations), the conservation laws of mass (or charge) and momentum are of the form (14) with linear and quadratic density, respectively. Let P (x) be an invertible operator such that and h(x, t, U) are two column vectors whose (m + αM − B)-th entry is a spatial discretization of the α-th component of g( be a semidiscretization of the PDE (13) with the following approximation to the conservation law (14): Such a semidiscretization can be obtained using the technique in Section 2. The flux and density of (16) have the general form The following theorem shows that symplectic Runge-Kutta methods preserve local conservation laws with quadratic density. The proof adapts Calvo, Iserles and Zanna's proof that such methods preserve quadratic invariants of systems of ODEs [4], to take contributions from the flux into account.
Theorem 2
The solution of any symplectic Runge-Kutta method applied to (15) satisfies a discrete version of (16).
Proof The conservation law (16) amounts to
Solving (15) using a s-stage symplectic Runge-Kutta method, with internal stages we obtain u n = P (x) g n . Moreover, Using (19) to eliminate g n from the first sum and rearranging, gives The condition of symplecticity, and (17) give which is an approximation of (14).
Remark 3 Multisymplectic methods preserve conservation laws whose density and flux are both quadratic. By contrast, Theorem 2 applies to all conservation laws that have quadratic density. As no assumption is needed on the flux, a larger class of conservation laws can be preserved.
The following results follow directly from the proof of Theorem 2.
Corollary 1 Any Runge-Kutta method preserves semidiscrete local conservation laws whose density is linear in [u] x .
Conservation law for the Hamiltonian
We consider here the system of Hamiltonian PDEs (6) defined by a Hamiltonian function H on a domain with periodic boundary conditions. This assumption is introduced only for simplicity: the preservation of conservation laws is local and therefore independent of the specific boundary conditions assigned to the differential problem. The following local conservation law for the energy is satisfied by all solutions of (6): Among the best-known energy-conserving discrete gradient methods is the Average Vector Field (AVF) method [19]. We can use this in two different ways, depending on the number of points, M, in the stencil in (7). If M is odd, let A = −B so that the stencil is centred on x 0 ; we denote a semidiscretization of H ([u] x ) on such a stencil by H(U). The AVF method approximates (6) by If M is even, let A = 1 − B so that the stencil is centred at the midpoint of x 0 and x 1 . Denote a semidiscretization of H([u] x ) as H(µ m U). We define the AVF method on such a stencil to be McLachlan and Quispel proved in [17] that discrete gradient methods preserve a discrete version of (20) provided that D is a skew-adjoint approximation of D. The following theorem proves that the AVF method (21) preserves the local conservation law for the energy (20) under a milder assumption.
Theorem 3 The AVF methods (21) and (22) preserve a discrete energy conservation law if there exists a function f defined on the stencil such that respectively.
Remark 5 Condition (23) is satisfied if and only if
Similarly, condition (24) holds true if and only if Conditions (25) and (26) provide simple practical tests for analysing whether the assumptions of Theorem 3 are satisfied by a given scheme.
Conservation laws of other types and multidimensional domains
Fully-discrete methods that preserve other types of conservation law can be obtained again by using an Euler operator. For simplicity, we restrict the discussion to the case of second-order schemes for a PDE with polynomial nonlinearity. These can be obtained by following the steps below: 1. Let P = r i=1 L i be a polynomial of degree r in the semidiscretization, where without loss of generality L i is a linear approximation of a single monomial factor in the continuous counterpart of P . Therefore, L i can depend on either U or U t . Assuming that the stencil has N points in the time dimension, discretize P using where i j is the i-th digit of the representation of N r − 1 − j in base N, ordered from right to left, and setting i j = 0 if N r − 1 − j has less then i digits. By varying i j one obtains all possible combinations of N digits of length r. At this stage, we assume that the coefficients α j only satisfy the requirements for consistency. For example, in a one-step method linear quantities are approximated by and quadratic quantities by 2. The values of the parameters α j are obtained by solving where A and Q ℓ are the approximations of the PDE and the characteristic obtained after steps 1 and 2, and E u is the difference Euler operator, whose kernel consists of all fully-discrete conservation laws [14].
Remark 7
In total, net of consistency requirements, for each monomial of degree r one needs: • M + r − 1 r parameters for the semidiscretization. After solving (12), only a few of these will still be undetermined.
• N r new parameters for the full discretization (27), to be determined by solving (28).
By contrast, if one searches directly for all full discretizations without semidscretizing first, the strategy in [9] introduces NM + r − 1 r variables for each monomial of degree r. This in general yields a huge nonlinear system whose solution is impractical.
The algorithm above can be iterated, to preserve conservation laws for PDEs with more than two independent variables, by discretizing a single variable at each iteration. At the k-th iteration the Euler operator in (29) is replaced by whose kernel consists in the space of conservation laws of the form The proof is similar to that of Theorem 1.
The Boussinesq equation
We consider here the (Good) Boussinesq equation cast as a system of two PDEs This system can be written in Hamiltonian form, System (31) has infinitely many independent conservation laws [1]. The first four are D with characteristics respectively. When the boundary conditions are conservative (e.g. periodic), integrating in space (32)-(35) gives the preservation of the following invariants, here I 3 and I 4 are the global momentum and the global energy, respectively.
Conservative methods for the Boussinesq equation
We look for semidiscretizations of (31) of the form Solutions of (38) satisfy semidiscrete versions of the conservation laws (32) and (33) with Q 1 = Q 1 and Q 2 = Q 2 . The linear and quadratic terms in (31) and (36) are approximated as and the coefficients α i and β i,j are chosen by requiring the desired order of accuracy and the preservation of the conservation law of either the momentum (34) or the energy (35), according to the strategy outlined in Section 2. We have not found any semidiscrete scheme that preserves both of these conservation laws, as the constraints on the approximations of the nonlinear terms that we have obtained from (12) are not compatible with each other.
In the following, we present the components of (38) and the characteristic Q 3/4 and density G 3/4 of the remaining preserved conservation law. The corresponding flux F 3/4 does not contribute to our global error estimates; in most cases, it has many terms and gives little insight, so we omit this.
Fully-discrete schemes that preserve the local momentum or the local energy are then obtained by applying Gauss-Legendre method or AVF method, respectively. As these are Runge-Kutta methods, the conservation laws (32) and (33) are preserved as a consequence of Corollary 1.
Second-order schemes
Here we introduce new families of second-order schemes that preserve three conservation laws. The stencil in space consists of four points and we set A = −1 and B = 2 in (7). All the free parameters in the formulae below (α, β, γ, ξ) are O(∆x 2 ). Free parameters corresponding to higher degree perturbations are set equal to zero as their contribution is negligible.
Momentum-conserving schemes
We have obtained six families of semidiscretizations that preserve the conservation law (34), split by two different forms of the characteristic and the three parameter values s ∈ {0, 1/3, 1/2}.
The first three families are Three remaining are given by F 1 , F 2 and G 2 as in (39) together with . In the numerical tests section we limit our investigations to the semidiscretions obtained from (38) with (39) and s = α = β = ξ = 0, γ = λ 1 ∆x 2 ; we use MC 2 (λ 1 ) to denote the family of finite difference schemes obtained by using the symplectic implicit midpoint method (Gauss-Legendre method of order two) to discretize in time. The iterative technique described in Section 3.3 also finds these schemes, but no others.
Energy conserving schemes
There is only one family of semidiscretizations of the form (38) that preserves the local conservation law of the energy. For this family, F 1 and G 2 are defined as in (39) and
The resulting system of ODEs can be written in the form
with The operator D is not skew-adjoint, but satisfies (24). Therefore, by applying the AVF method (22) to (41) we obtain a family of fully-discrete schemes that preserve the local conservation law of the energy. We use EC 2 (λ 2 ) to denote the schemes with α = γ = 0 and β = λ 2 ∆x 2 . Again, the iterative technique from Section 3.3 yields only these schemes.
Fourth-order schemes
The families of fourth-order schemes introduced here preserve three conservation laws and depend on free parameters (α, β, γ, ξ) that are all O(∆x 4 ). Parameters introducing only perturbations of higher degree are set equal to zero. For each of the semidiscretizations introduced in this section, the discrete fluxes F j are second-order accurate, but D m F j and the three preserved conservation laws, are approximated with fourth-order accuracy.
Momentum-conserving schemes
On a spatial stencil with six points (A = −2 and B = 3 in (7)) there are two families of semidiscretizations that preserve the local momentum conservation law. Let The first family of semidiscretizations and their preserved conservation laws is given by The second family has F 1 , F 2 and G 2 as in (42), together with We use MC 4 (λ 3 ) to denote the schemes obtained by applying the Gauss-Legendre method of order four to (42), with α = β = γ = 0 and ξ = λ 3 ∆x 4 .
Energy conserving schemes
On the most compact six-point stencil, there are no semidiscretizations of the form (38) that preserve the local conservation law for energy. However, a seven-point stencil (B = −A = 3 in (7)) is more fruitful. For n ∈ N, let and define the operators ν ± m = I ± ∆x 2 6 D 2 m S −1 m and the functions The family of semidiscretizations and conservation laws is as follows: The systems of ODEs defined by (38) with (43) amounts to with The operator D, although not skew-adjoint, satisfies (23). We use EC 4 (λ 4 ) to denote the family of schemes obtained by applying the AVF method of order four (see [19]) to (44) with α = λ 4 ∆x 4 and β = γ = 0.
Numerical Tests
In this section we solve a couple of benchmark problems to show the effectiveness and conservation properties of the numerical methods in Section 4.
The results are compared with the following second-order structure-preserving methods: • The multisymplectic scheme for (30), [22] and equivalent to the well-known Preissmann scheme.
• The energy-conserving scheme for (31) in [16], , obtained using a discrete variational derivative method. This scheme can be obtained also by applying the AVF method to the Hamiltonian system of ODEs defined by To the best of our knowledge, there are no schemes in the literature for the Boussinesq equation that are fourth-order accurate in both space and time. Therefore, we compare the performance of the fourth-order schemes in Section 4 with the following finite difference scheme for (30) introduced in [13]: The scheme FD 4 is fourth-order accurate in space and second-order accurate in time, so to have a fair comparison we will use this scheme with a time step equal to ∆t 2 . We consider (x, t) ∈ Ω ≡ [a, b] × [0, T ] and periodic boundary conditions. We introduce on Ω a grid with I + 1 nodes, x i , in space and J + 1 nodes, t j , in time. Henceforth subscripts denote shifts from the point (x 0 , t 0 ) = (a, 0) (e.g., u i,j ≃ u(a + i∆x, j∆t)).
As the computational time is similar for all the schemes of the same order of accuracy, our comparisons are based on the error in the solution at the final time t = T , evaluated as where · denotes the Euclidean norm. We also compare the errors in the global invariants (37) defined as where α = 1, 2, 3, 4. For the methods introduced in this paper, G α is given in Section 4. For all the other schemes, we set
Single soliton
For the first problem we set Ω = [−60, 60] × [0, 25] and the initial conditions given by the single soliton solution over R, We first examine the convergence and stability of the schemes found in Section 4, setting all parameters to zero. The order of convergence at various step sizes is measured by and error k denotes the error obtained from (45) with ∆x = ∆t = k/10, for k = 1, 2, . . . , 9.
The results in Table 1 and Figure 1 show that all the methods tend to the exact solution with the expected maximum order of convergence as the grid is refined, and are stable also for the largest stepsizes. Table 2 shows the error in the conservation laws and the solution for the different methods with ∆x = ∆t = 0.5. For this problem, the values of the free parameters that minimize the 6.21e-15 1.57e-12 1.47e-08 5.57e-14 1.94e-04 FD 4 (∆t = 0.5 2 ) 9.97e-12 0.0036 1.07e-04 2.84e-04 0.0038 error in the solution of MC 2 (λ 1 ), EC 2 (λ 2 ), MC 4 (λ 3 ), EC 4 (λ 4 ) are λ 1 = −0.21, λ 2 = −0.20, λ 3 = 0.06, λ 4 = 0.03. Such optimization is easy given that the solution is known, but is not currently feasible more generally. Therefore, the results obtained by setting the above parameters to zero are shown for comparison. This benchmark test illustrates that: • All schemes preserve the first conservation law, but only those based on the formulation (31) preserve the second conservation law; • The schemes introduced in this paper preserve three conservation laws up to machine accuracy; • The new second-order schemes compare favourably with the methods from the literature in terms of accuracy in both the solution and the invariants that are not exactly conserved, even without optimising the parameters; • Choosing the optimal value of the free parameter, the error in the solution is roughly four times smaller (or more) than any other second-order method; • The fourth-order methods are all more much accurate than FD 4 with timestep ∆t = 0.5 2 , even for non-optimal parameters.
In Figure 2 Figure 3 shows the difference between the exact solution and the solutions of MC 4 (0.06) and FD 4 (with ∆t = 0.5 2 ). The error in MC 4 is roughly 30 times smaller; is located mainly at the peak of the soliton, and can be ascribed to a small phase error. The error of FD 4 is more widespread.
Interaction of two solitons
We now study the interaction of two solitons over Ω = [−150, 150] ×[0, 50]. The exact solution over R is [15], where We obtain the initial conditions from (46) setting and solve this problem with ∆x = ∆t = 0.5. The optimal values of the free parameters for each of the families MC 2 (λ 1 ), EC 2 (λ 2 ), MC 4 (λ 3 ), EC 4 (λ 4 ) are λ 1 = −0.19, λ 2 = −0.18, λ 3 = 0.06, λ 4 = 0.02. The results in Table 3 are consistent with those in Table 2, and analogous remarks apply. Figure 4 shows the solution of the most accurate second-order scheme, EC 2 (−0.18), on the whole domain Ω (upper plot) and at the final time (lower plot). The schemes MP and DVD produce oscillations (amplitude ≃ 0.005), where the exact solution is flat. These do not occur in the solution of EC 2 (−0.18). Figure 5 shows how the different schemes approximate the peak of the two solitons (omitting the least accurate solution of MP). The solution of EC 2 (−0.18) best reproduces the speed and the amplitude of the two waves.
Finally, Figure 6 compares the difference between the exact solution and the approximations given by MC 4 (0.06) and FD 4 (with ∆t = 0.5 2 ). Just as for the single soliton, the error of FD 4 has a higher amplitude and spreads far from the final location of the two solitons.
The potential Kadomtsev--Petviashvili (pKP) equation
This section briefly demonstrates that the novel strategy described in Section 3.3 is practicable for PDEs with more than two independent variables. We seek to preserve two conservation laws, of the pKP equation, u xt + 3 2 u x u xx + 1 4 u xxxx + 3 4 u yy = 0.
Note: Throughout this section, H i and H i are components of conservation laws, not Hamiltonians.
We introduce a uniform grid in space with nodes (x m , y n ) and use U m,n (t) to denote a semidiscrete approximation of u(x m , y n , t). In this section, D n and µ n are the forward difference and forward average operators acting on the second index, respectively.
The approach in Section 3.3 can be applied to a full 15-point rectangular stencil; this yields a wide range of families of methods. For brevity, we present here only those schemes for which all spatial derivatives are approximated on a one-dimensional spatial stencil consisting of three and five points respectively for the y-and x-derivatives. There are just two one-parameter families, both of the form D m F 1 + D n G 1 + D t H 1 = 0 (50) (so Q 1 = 1), that preserve semidiscrete versions of (48) and (49). The first family is defined by Figure 7: Initial condition (left) and solution of MC 1 (0) at time t = 5.
Numerical test
As a brief test of the above schemes for the pKP equation, we use the following travelling wave solution of (47) [2]: u(x, y, t) = 2 tanh(x + y − 7 4 t + 5) + 2. Figure 7 shows the profile of the wave at the initial time and the numerical solution of MC 1 (0) at the final time t = 5. Both MC 1 (0) and MC 2 (0) simulate the motion of the wave to the required accuracy, with a maximum absolute error in the solution of 3.40 × 10 −4 and 3.41 × 10 −4 , respectively.
Conclusions
In this paper we have introduced a new approach to constructing finite difference approximations to a system of PDEs that preserve multiple conservation laws. This is based on discretising one dimension at a time, using semidiscrete Euler operators to find constraints that simplify the remaining symbolic computations. This is much cheaper than the approach introduced in [9], and can be iterated to apply to PDEs with more than two independent variables. We have proved that any symplectic Runge-Kutta method preserves local conservation laws with quadratic density and that the AVF method preserves the local conservation law of the energy under milder conditions than the skew-adjointness of the discrete operator D.
The new strategy has been applied to obtain methods that preserve either the momentum or the energy of the Boussinesq equation. These are obtained as families that depend on a number of free parameters. Numerical tests have shown that the new schemes are competitive with respect to other methods in the literature and confirmed their conservation properties. Very accurate solutions can be obtained by selecting optimal parameter values. However, these values depend strongly on the choice of initial condition. Finally, we have given an example that the new approach is practicable for PDEs with three independent variables, by finding two new families of schemes that preserve two conservation laws for the pKP equation. | 7,704.2 | 2020-05-14T00:00:00.000 | [
"Mathematics",
"Physics"
] |
How different are offline and online diplomacy? A comparative analysis of public statements and SNS posts by delegates to the United Nations
Introduction This article investigates the evolving landscape of diplomacy in the digital age, focusing on diplomats at the United Nations (UN) Headquarters in New York. The central inquiry revolves around how diplomatic actors use digital tools to complement or augment traditional face-to-face diplomacy. Methods We systematically compare a substantial corpus of X posts (tweets) from UN diplomats with their public statements at the United Nations Security Council (UNSC), employing advanced computational social science techniques. This study applies a range of large-scale text analysis methods, including word embedding, topic modeling, and sentiment analysis, to investigate systematic differences between offline and online communication. Results Our analysis reveals that, while the essence of diplomacy remains consistent across both domains, there is strategic selectivity in the use of online platforms by diplomats. Online communication emphasizes non-security topics, ceremonial matters, and prominent policy stances, in contrast to the operational issues common in UNSC deliberations. Additionally, online discourse adopts a less confrontational, more public diplomacy-oriented tone, with variations among countries. Discussion This study offers one of the first systematic comparisons between offline and online diplomatic messages. It illuminates how diplomats navigate the digital realm to complement traditional roles. The findings indicate that some elements of public diplomacy and nation branding, directed toward a wider audience far beyond the council chamber, have become an integral part of multilateral diplomacy unfolding at the UNSC.
Introduction
As the world rapidly integrates with cyberspace, those responsible for managing its affairs, including diplomatic actors, find themselves in a state of rapid adaptation to this new reality.For instance, since the late 2000s, the United States State Department has actively engaged in various online platforms such as X (formerly Twitter) and Facebook, allocating increasing human and institutional resources to social media activities as an integral part of its public diplomacy (Zaharna and Rugh, 2012;Bjola and Holmes, 2015).Other countries and organizations, including the United Nations, have followed suit.In the academic domains of international relations and diplomatic studies, this swift expansion of diplomacy into cyberspace has generated growing scholarly interest in the realm of "digital diplomacy" and even "hybrid diplomacy" (Bjola and Holmes, 2015;Bjola and Manor, 2022).These scholars have revealed that diplomatic actors are now actively employing online platforms to gain the public's attention regarding their foreign policy stances and/or improve acceptance among the overseas populace.Despite this burgeoning scholarly attention, however, there is a noticeable lack of research that systematically investigates the conduct of diplomacy spanning both the cyber and physical domains.This lack should not be overlooked, as it remains underexplored how the evolving online diplomatic practices function in relation to traditional, dominant, face-to-face practices offline beyond the limited scope of public diplomacy.
The present article addresses this gap, posing the following question: How do diplomatic actors employ digital tools to complement, augment, or even replace traditional face-to-face diplomacy?Exploring this question is vital for understanding the role of digital tools in contemporary diplomacy.To this end, we systematically compare a substantial volume of X posts by diplomats stationed at the United Nations Headquarters in New York with numerous public statements delivered by the same diplomats in traditional face-to-face settings, specifically within the context of policy deliberations at the United Nations Security Council (UNSC).The UNSC, widely regarded as the preeminent multilateral body in global security, provides an ideal case for exploring this question.Its meetings offer opportunities for typical interstate conference diplomacy, with these meetings being characterized by high levels of institutionalization and dominance by major world powers (China, France, Russia, the United States, and the United Kingdom).They consequently stand in stark contrast to the relatively unconstrained realms of cyberspace, open to sovereign states and the general public alike.Our aim is thus to uncover how diplomats, particularly delegates and officials stationed at the UN, leverage this alternative space to conduct their business within the UNSC, an arena historically dominated by face-to-face interactions.
To accomplish this task, we collected and analyzed two distinct sets of text documents under a common methodological framework, fully leveraging advanced computational social science tools.These include over 18,000 speech transcripts extracted from the official meeting records of the UNSC and more than 145,000 X posts by the official X accounts of various countries' permanent missions to the UN and the UN Secretary General.Employing a range of large-scale text analysis methodologies, such as word embedding, topic modeling, and sentiment analysis, we investigate whether systematic differences exist between offline and online communication in terms of semantic content and topic structures.Our analyses reveal that while diplomats do not fundamentally alter the semantic content of their communication-i.e., the meanings they convey when discussing certain concepts-across different domains, they exhibit a high degree of selectivity in their online discourse.In comparison to their offline statements, online posts tend to emphasize non-security matters (e.g., Sustainable Development Goals), ceremonial topics, and policy positions on highly visible issues.Conversely, they generally maintain a more muted stance on operational issues that constitute routine topics in the context of UNSC policy deliberations (e.g., African issues, peacekeeping).Furthermore, the overall tone of online communication is less confrontational and more geared toward public diplomacy and national branding.Notably, significant crossnational variations persist in these and other aspects, underscoring the need for more detailed investigations.
The article is organized as follows: The next section reviews the related literature on digital diplomacy and the UNSC to further illuminate the study's contributions.Section 3 introduces the UNSC speech dataset and the social media posts collected from relevant actors' X accounts.This section also outlines the specific preprocessing and analytical procedures applied to these datasets.Section 4 presents the main findings derived from these procedures (for additional results, see the Supplementary material) and discusses their relevance in the context of existing knowledge on digital diplomacy and council politics.Finally, the last section highlights remaining challenges for this study and suggests promising directions for future research.
Literature review
Diplomacy is defined as "the conduct of relations between states and other entities with standing in world politics by official agents and by peaceful means" (Bull, 2012, p. 156).In the realm of international relations, diplomacy has historically played a pivotal role in preserving global order.However, the actors involved and the nature of their work have evolved over time.Prior to World War I, foreign ambassadors stationed in host nations held central positions in diplomatic affairs.Postwar, there was a shift toward open diplomacy, driven by the recognition that secret diplomacy had contributed to conflicts.Advances in information transparency led to increased scrutiny of diplomatic activities by legislative bodies and public opinion.Furthermore, diplomacy has transformed, with a rise in multilateral diplomacy and a corresponding decline in bilateral diplomacy, due to the proliferation of international organizations.Politicians and professionals outside of traditional diplomats have consequently become more involved in diplomatic endeavors.
One of the most significant factors influencing the evolution of diplomacy is the development of information and communication technologies (ICTs).The nature of diplomacy has changed in response to rapid communication advancements, such as satellites, airplanes, radios, telegraphs, teletypes, and long-distance telephones (Morgenthau, 1973, p. 536).Important negotiations are now often conducted not only by diplomatic representatives but also by special delegates, including foreign ministers, high officials from foreign offices, or technical experts.
In recent years, ICTs, including social media, have continued to advance, profoundly impacting diplomatic practices.The use of ICTs has prompted European Union permanent representatives to redefine national interests by communicating more frequently with politicians in their capitals, increasing the likelihood of reaching compromises through joint editing of drafts, and emphasizing the importance of language skills in online draft editing (Adler-Nissen and Drieschova, 2019).Diplomats in Geneva have streamlined negotiations through communication via WhatsApp (Cornut et al., 2022).
The rise of social media is of particular note, as it has enabled diplomatic actors to directly engage with citizens and amplified the influence of non-state entities.This shift has given rise to the concept of digital diplomacy, defined as the use of social media for diplomatic purposes (Bjola and Holmes, 2015, p. 4).Notably, the covert use of social media allows state leaders to influence politics through propaganda, advocacy of controversial viewpoints, and the spreading of disinformation (Martin et al., 2023).Non-state actors, including rebels (Bos and Melissen, 2019) and non-governmental organizations (NGOs) (Hall et al., 2020), have also harnessed social media strategies in their diplomatic endeavors.
Digital diplomacy has been practiced most prominently in public diplomacy.Public diplomacy involves diplomatic communication between political entities (ancient kings and modern nation-states) and the public, both foreign and domestic (Huijgh, 2016, p. 437).Diplomatic actors are now actively pursuing such communication on various social media platforms to attract the public's attention and influence their perceptions.One reason for this is that social media elicits emotions and influences diplomatic relations by appealing to national identity through text and images (Duncombe, 2019).Resident diplomats have increasingly embraced public diplomacy by engaging with nonstate actors, with social media serving as a facilitating tool that offers a degree of autonomy (Cooper and Cornut, 2019).Moreover, citizens can actively participate in public diplomacy through social networking services (SNS) by posting comments, sharing content, "liking" posts, using hashtags, mentioning others, and participating in online groups (Huang, 2020).
While a growing body of research explores digital diplomacy, most studies focus on how social media has transformed diplomatic practices and mechanisms.As already suggested, however, there is a noticeable lack of research into how digital diplomacy complements or augments traditional face-to-face diplomacy, such as conference diplomacy.
The present study conducts exactly such an investigation.It focuses on permanent representatives at the UNSC and performs a comparative analysis of their speeches in UNSC meetings and their X posts.The analysis aims to illuminate the extent to which permanent representatives use X to complement or emphasize the content of their UNSC speeches.
UNSC meetings represent a typical form of conference diplomacy, defined as multiparty diplomatic negotiations (Meerts, 2016, p. 499).These conferences, often within international organizations, serve as focal points in ongoing negotiation processes and offer relatively stable structures that facilitate successful outcomes (Meerts, 2015, p. 313).While conference diplomacy speeches do involve disseminating information to the public, the structured nature of international organizationbased conference diplomacy may dilute the intended message.Consequently, diplomats may seek to use social media to complement and emphasize their conference speeches.The UNSC, being one of the most important conferences in the international arena, offers an ideal case to examine how permanent representatives of international organizations employ (or do not employ) social media to complement and accentuate their conference speeches.
Previous research on public diplomacy using social media has primarily conducted qualitative analyses of public diplomacy content (Ociepka, 2018), explored the network structure of interactive connections among social media users (Huang and Wang, 2021), or assessed its impact on citizens through survey experiments (Min and Luqiu, 2021).For conference diplomacy in the UNSC, diplomatic communication has been analyzed mostly in a qualitative manner, which is typically based on detailed reading of a limited number of resolutions and speeches in UNSC meetings.A few exceptions employing quantitative text analysis include the use of the Latent Dirichlet Allocation method to analyze council resolutions (Hanania, 2021), speaker-topic network analysis of meeting records on Afghanistan (Eckhard et al., 2023), sentiment analysis to assess the validity of the norm of "the responsibility to protect" (Scherzinger, 2023), and word-embedding analysis to explore the meaning of the "threat to the peace" (Sakamoto, 2023b).These quantitative studies, however, have focused narrowly on the textual materials produced in the physical domain, that is, inside the council chamber.
In contrast, this article employs a series of quantitative text analysis tools to compare the speeches delivered by permanent representatives during UNSC meetings with the online messages posted by these same diplomats on X (formerly Twitter).This analytical approach allows for a systematic comparison and examination of content in both physical and digital diplomatic communication, thereby offering a unique opportunity to illuminate the still-unexplored relationship between offline and online diplomatic practices.
Data and methods . UNSC speeches
We employed the "UNSC Meetings and Speeches" dataset (Sakamoto, 2023a) for our study, which includes English transcripts of all public statements presented by representatives and officials from various countries and organizations during official UNSC meetings.This dataset covers meetings from 1990 to 2021.For the present study, we updated the dataset by incorporating records from 2022 onward.Specifically, we obtained additional meeting records from the Official Document System of the UN website, accessed via hyperlinks embedded within summary tables presented on the Dag Hammarskjöld Library website.These English transcripts of statements in public meetings from January 2022 to July 2023 were merged with the existing dataset.
Furthermore, we focused our analysis on meetings held after 2015, the year by which all of the council's five permanent members (P5) had established their respective X/Twitter accounts.Accordingly, our updated dataset comprises public speeches in UNSC meetings from the 7355th session on January 6, 2015, to the 9390th on July 31, 2023, totaling 18,173 statements or 12,259,937 tokens.These statements are from the P5 members, the United Nations Secretary-General (UNSG), and elected representatives, representing a total of 46 distinct entities (Table 1).
. /fdata. .The total number of speeches (left column) and X posts (right column) delivered/posted by major diplomatic actors, including permanent representatives of the P5 (China, France, Russia, the United States, and the United Kingdom) to the United Nations during the study period (2015)(2016)(2017)(2018)(2019)(2020)(2021)(2022)(2023).The number in parentheses in each cell indicates the total number of words contained in the corresponding set of speeches/X posts."UNSG" denotes the UN Secretary-General, whereas "All" refers to the entire set of diplomatic actors under investigation (46 countries and organizations). .
UN mission X posts
A further component of the present study involved analyzing posts on X, formerly known as Twitter.Initially limited to 140 characters, the character limit was expanded to 280 starting in 2017.X serves as a social networking service primarily focused on text communication but also accommodating photographs, images, and videos.Many governments have established UN Permanent Representative accounts on X for public diplomacy purposes.To align our analysis with discussions relevant to the UNSC, we concentrated on accounts associated with UN missions based in New York, excluding accounts related to activities in other locations such as Geneva and Rome.
For the sake of consistency, we excluded personal accounts of ambassadors, focusing solely on the institutional accounts of permanent missions.While we initially considered including the accounts of the UNSG, we excluded them due to personnel turnover, opting instead for the Spokesperson's account as a stable institutional representation.Our analysis covers posts from January 2015 to July 2023, corresponding, as suggested above, to the period during which all P5 countries had held Permanent Representative accounts.Thus, the UN Permanent Representatives accounts included in our analysis are: (1) accounts from P5 countries; (2) accounts from countries that served as non-permanent members of the UNSC from 2015 onward and maintained active accounts during their term; and (3) the account of the Spokesperson for the UNSG.A total of 49 accounts met these criteria (Supplementary Table 1).
In , the character limit was extended to , characters for users subscribed to the paid service "Twitter Blue." For consistency, we excluded posts written in languages other than English and omitted reposts (commonly known as retweets) and quote posts (also known as quote tweets) during data acquisition.Consequently, our analysis covered a total of 145,345 posts, comprising 4,162,290 tokens (Table 1).
. Text preprocessing and analyses
We applied a common set of preprocessing measures to both corpora, including lowercase conversion, punctuation removal, and spelling conversion from British to American English.For X posts, we also converted flag emojis, frequently found in social media posts by diplomats, to the names of the corresponding countries and organizations while removing other emojis.Additionally, abbreviations such as "int'l" (for "international") and "gov't" (for "government") were expanded.
For analysis purposes, we conducted word counting, word embedding, topic modeling, and sentiment analysis.
. . Word counting and embedding
To explore variations in the usage of relevant concepts across physical and digital domains, we performed frequency analysis of selected words such as "security, " "peace, " "women, " and "sdg."Detailed results are presented in Supplementary Table 2.
We also conducted word embedding for each corpus using the GloVe (Global Vectors for Word Representation) algorithm (Pennington et al., 2014).Following Sakamoto (2023b), we derived "nearest neighbors"-the words whose embedding vectors are the closest to the vector representing a certain notion-for some of the defining notions in council policymaking as well as in broader international relations.These notions include those represented by words such as "threat, " "protect, " and "sovereignty" (word stem: "sovereignti").Words were embedded using a common set of learning parameters.In particular, the size (dimensions) of a vector and the size of the context window (in both reading directions) were set to be 100 and 12, respectively.These values were chosen based on the recommendations of prior work (Rodriguez and Spirling, 2021).
. . Topic modeling
We further examined how different the overall semantic structures are between the offline statements and the online posts.Specifically, we applied Latent Dirichlet Allocation (LDA), which is the simplest and most commonly used Bayesian topic model (Blei et al., 2003), to the combined corpus to estimate the contents Unless mentioned otherwise, the preprocessing and analytical measures described in this section were implemented using Python (ver. .) and its various extensions (e.g., Gensim, NLTK).
Frontiers in Big Data frontiersin.org of topics-groups of frequently co-occurring words-and their prevalence among the diplomats' messages.We then aggregated the estimated topic prevalence in each text (document-topic vector) for the entire corpus as well as its different subsets such as the speech and X post components.We also derived the countrylevel semantic structure for each country by simply averaging the estimated document-level topic prevalence across the texts (speeches and X posts) generated by its representatives.
In LDA, the number of topics (denoted as k) is exogenously given.We broadly manipulated this parameter (from k = 10 to k = 60) and iterated estimation ten times for each k.The next section details the results obtained from the estimation for k=30, whose perplexity-a commonly used metric to evaluate the predictive performance of topic models-was the lowest (indicating the best performance) among the ten iterations.Supplementary Figures 1, 2 display the topic prevalence and its offline-online differences for k = 20 and k = 50, respectively.While the granularity of the estimated topic structure obviously changes with k, the qualitative characterizations of such structure and its offline-online variation given below largely hold for a broad range of k.
. . Sentiment analysis
Finally, we conducted sentiment analysis on both corpora to classify texts as representing "negative, " "positive, " or "neutral" sentiments.We utilized pre-trained sentiment classifiers based on Transformer and its variants (Devlin et al., 2018;Liu et al., 2019).While we did not train classifiers with our labeled data, we manually assessed the performance of various candidate models against hundreds of sample texts from both the speech and X post datasets.We selected a specific model (pipeline name: lxyuan/distilbert-base-multilingual-casedsentiments-student) based on its consistency with our manual classification of the samples.The results obtained with an alternative model are presented in Supplementary Figure 3.
We then applied the selected model to the entire body of texts for classification.As most of the speech texts are excessively lengthy for typical sentiment analysis models to handle, we randomly clipped continuous sentences from these texts (subject to a length limit of around 400 characters) and input these "representative" sentences into the model for sentiment classification.Lastly, we aggregated the predicted sentiment of each text over all sets of speeches, the entire set of X posts, and other subsets of the corpora as sentiment distributions for comparison.
Use of concepts
The word-level analyses reveal that diplomats' usage of different concepts in cyberspace shows no systematic difference from their usage inside the council chamber.In other words, These models are available from the Hugging Face platform (https:// huggingface.co.; last accessed on September , ).
these diplomats are largely consistent in their use of words.
As Supplementary Table 2 illustrates, most of the key concepts in contemporary international relations, including "secur(ity), " "peac(e), " "threat, " and "sovereignti (sovereignty), " appear in their offline statements and online posts in more or less comparable frequencies.Several notable exceptions include "SDG" and "global goals" (both denoting Sustainable Development Goals, SDGs), which have been actively promoted online by many UN missions (as well as the UN itself) but are not necessarily favored topics for traditional security organs such as the Security Council.Word embeddings confirmed the conceptual stability across the cyber and physical domains in a much deeper sense.Diplomats associate a largely similar set of objects and entities with a certain notion, whether they discuss the notion offline or online.Table 2 illustrates this by displaying, for each of the key concepts listed in the first column, its 20 "nearest neighbors"-the top 20 words (stems) whose embedding vectors are most closely located to the vector representing the concept concerned-both offline (second column) and online (third column).For example, the first row indicates that the "threat" notion has been most closely associated with "pose, " "challeng(e), " "terror(ism), " "risk, " "face, " "grow(ing), " and so on when discussed in the council chamber, whereas the same notion has been most strongly associated with "pose, " "challeng(e), " "face, " "risk, " "terror(ism), " "secur(ity), " and so forth when posted online.Notice that the two sets of stems are almost identical to each other in a certain range (the first 10 or so stems in this case).Such extensive overlap tends to be observed as long as the offline and online frequencies of the concept concerned are not excessively divergent from each other (see Supplementary Table 2).
. Topic structure However, the strong similarity between offline and online communication does not extend further beyond the level of individual concepts.We found noticeable discrepancies between the offline semantic structure and the online structure at the corpus level, although there is also a considerable degree of mutual overlap.For example, Figure 1 illuminates the prevalence of the 30 latent topics-the groups of frequently co-occurring word stems listed in Table 3-that were estimated by the LDA.Panel (A) depicts the overall prevalence of these topics over the entire corpus (the speeches and X posts combined), whereas Panel (B) illustrates the relative topic prevalence in the X posts, obtained by subtracting offline topic weights from those online.
A quick comparison of the two graphs reveals that many of the topics that dominate the entire corpus such as topics 2, 20, 28, 5, and 6 have been disproportionately mentioned in the cyber domain.These topics represent the announcement of an upcoming council meeting or a representative's diplomatic statement there (2); daily reminders of a ceremonial event or an anniversary (20); promotion of SDGs (28); a greeting to a fellow member state relating to its work in the UNSC or in the wider UN (5); and information on an event regarding the UN General Assembly (mentioned by "unga") rather than UNSC (6) (see Table 3).Other topics, including those relating to global issues such as climate change and the pandemic (21), the "Women, Peace, Security (WPS)" agenda (18), and the activities The first column lists significant notions in the context of the UNSC policy deliberations.For each of these notions, the second and third columns in the corresponding row display the 20 "nearest neighbors" for the speech dataset and for the X post dataset, respectively.
of the UN Secretary-General, or the UNSG ( 26), also tend to be actively mentioned online.
In contrast, there are also topics that have been disproportionately discussed in the physical domain.These topics concern the UNSC's role in preventing conflict and building sustainable peace (25) as well as its engagement with political processes and elections in places such as Haiti (24).Meanwhile, topic 29 comprises a pool of frequent terms and established expressions in the specific context of the UNSC deliberations.Other topics, including humanitarian aid and protection of civilians in conflict ( 14), peacekeeping operations (4), the Israeli-Palestinian conflict (1), and other specific conflict situations (19,8,15,16,17,12), also show a similar inclination to be discussed more intensely in the council chamber, albeit to a lesser extent.
Notably, some topics, including those concerning Russian aggression against Ukraine (13, 27), have been attracting the active engagement of UN-based diplomats in both domains, so their prevalence is somehow balanced between the speech and X post corpora.These topics constitute a limited area of overlap between the offline and online semantic structures, which are otherwise largely distinct.
As mentioned earlier, the estimations of the LDA and other topic models depend on several factors, among others, the number of topics 'k' and the random seed used for initialization.Therefore, the exact compositions of estimated topics and their quantitative distributions in the speeches and the X posts can vary considerably depending on these conditions.Nevertheless, the overall patterns of semantic divergence and convergence described above hold in a broad range of parameters and iterations, at least qualitatively (see Supplementary Figures 1, 2).These patterns are also partially supported by the aforementioned word frequency analysis.As Supplementary Table 2 displays, some words such as "sdg, " "women, " and "gender" appear distinctly more frequently in the X posts than in the speeches, which is largely consistent with the relative prevalence of the topics these words obviously relate to.Similarly, other words that constitute distinctively "offline topics" for council deliberations-for example, the names of some African countries such as "congo" and "south sudan" (but not "somalia" and "mali")-appear far more frequently in offline statements than in online posts.
These results suggest a considerable degree of selectivity regarding what diplomatic actors talk about when they are online or offline.Inside the council chamber, delegates typically focus on practical security matters that, having been a part of regular meeting agendas for many years, have become almost routine in the context of council politics.These matters concern protracted conflict situations in the Middle East and Africa (topics 1, 8, 15, 19, etc.), and the UN's involvement with these situations through its peacekeeping operations and other endeavors (4,14,24,25).In contrast, the same diplomats appear to focus on more general, broadly discussed topics such as SDGs, climate change, and WPS (5, 18, 28) when they post on X.This clear divergence in the semantic structure of diplomatic communication indicates that the Security Council, by its nature as a conference diplomacy, tends to direct diplomats' attention to narrowly conceived security matters, whereas X, which has a high degree of freedom, may be utilized to transmit more generalized information to a much wider audience.
It should be noted, however, that some of the concrete and traditional security issues typically discussed in the council chamber are also actively mentioned on X.The heatedly debated war between Russia and Ukraine (topics 13, 27) is a prime example.To a much lesser extent, concerns related to weapons of mass destruction-specifically, the use of chemical weapons in Syria (3) and North Korea and Iran's nuclear programs (23)-and global terrorism ( 22) are intensely discussed on the online platform, not just in offline council meetings.These topics appear to be more visible to the general public, especially in the United States and Europe, in comparison with other topics such as conflicts in Africa and the Middle East, which have been disproportionately discussed in the council chamber.These patterns suggest that ./fdata. .The 10 tokens listed in each row are the word stems most strongly associated with the corresponding topic.A number in parentheses denotes the strength (weight) of association.
diplomats might strategically differentiate between security topics best suited for offline, conference-based channels and those more appropriate for online, public channels, according to the target of diplomacy.
. Tone
With regard to the document-level sentiment analysis, we found a striking difference between the two corpora.As Figure 2 FIGURE O ine and online sentiment distributions.The X posts/speeches classified as "neutral," which constitute a negligible portion, were excluded from the figure for readability.
demonstrates, in comparison with the offline policy statements, the online diplomatic posts express less negative and more positive sentiments.In other words, it seems that UN-based diplomats are less confrontational in cyberspace than in the physical domain.This general tendency for a more positive tone in social media was supported by a similar analysis using an alternative sentiment classifier (see Supplementary Figure 3), even though the exact distributions of positive, neutral, and negative sentiments predicted by different models are considerably divergent.The tendency was also consistent with our unambiguous impression gained from a manual reading of X posts and speeches.That is, compared to often-heated exchanges in the council chamber, the X posts by diplomats noticeably contain advertising, forward-looking, and even highly casual expressions.
These features might seem somewhat surprising given the widely held belief that social-media exchanges likely induce and conflict (Martin et al., 2023).However, they can be interpreted through nation branding in a rather straightforward manner.In the realm of public diplomacy, the concept of nation branding is a subject of considerable discussion.Nation branding is "a process by which a nation's images can be created or altered, monitored, evaluated and proactively managed in order to enhance the country's reputation among a target international audience" (Fan, 2010, p. 101).Given that X serves as a tool for public engagement, it is reasonable to hypothesize that nation-branding initiatives may be operational through this channel.It is likewise conceivable that a strategy might be in place to limit negative expressions and highlight positive ones, with the aim of creating a more favorable impression of one's country.Two X posts classified as positive are provided below as an illustration of such nationalbranding strategy.
"Through its membership at #ECOSOC, Indonesia is fully committed to actively contribute to promoting transformative actions to accelerate the implementation of SDGs.#inidiplomasi" (Indonesian Mission UN, 2023)."The United States is deeply committed to preventing and responding to human trafficking around the world.We stand in solidarity with all those around the world working to" #EndHumanTrafficking (U.S. Mission to the UN, 2023).
. Actor-level analyses
We also conducted a preliminary investigation into how the offline-online differences depicted above can vary across different UN missions, especially among dominant permanent members (P5).Although the investigation was far from exhaustive, we gained an indication that there is indeed a considerable degree of cross-national variation concerning the corpus-level semantic structure as well as the distribution of document-level sentiment tones.As a conspicuous example, Figure 3 depicts the sentiment distributions for the offline statements and the online posts by the Russian mission at the UN.A casual comparison with Figure 2 quickly reveals the markedly confrontational posture of Russian diplomats regardless of offline or online status.This posture stands in marked contrast to that of the other permanent members, including China (Supplementary Figure 4) and the U.S. (Supplementary Figure 5).In particular, the sentiment distributions for the Chinese mission indicate the relatively restrained nature of the country's diplomatic messages.
Lastly, Supplementary Figure 6 illustrates another dimension of cross-national difference, namely the relative topic prevalence.Each graph was generated from country-level aggregation of topic prevalence over the X posts and the speeches for k = 30 (Table 3).While the configurations of predominantly offline topics and predominantly online topics are largely similar to that observed for the entire corpus (see Figure 1B), each country features its own emphasis on what it chooses to discuss.For example, in comparison with the other members, China has devoted more attention to topic 16 in the council chamber, emphasizing the Frontiers in Big Data frontiersin.orgcountry's contribution to peace, development, and stability in Afghanistan and the surrounding region.While the U.S. mission has not shown a particularly distinct tendency in this regard, Russia is again notable in that its online messages disproportionately draw on topic 27.This topic largely represents Russia's efforts to justify its policy, and subsequent war, against Ukraine in terms of what Russia sees as the Western attempt to militarize Ukraine.These results indicate significant differences among countries in terms of the channels they use to disseminate information, with such variation potentially reflecting differences in each country's nation-branding strategy.However, our analysis of cross-national dimensions remains preliminary, and more extensive investigation is required to draw any definite conclusion in this regard.
Conclusions
Through the rigorous application of advanced computational social science tools, this study offers one of the first systematic comparisons between offline and online diplomatic messages in the context of the UNSC.These comparisons have uncovered how burgeoning digital diplomacy functionally augments established conference diplomacy.While diplomats maintain consistency in their use of terms and concepts, digital platforms have afforded them an expanded toolkit, enabling more versatile expressions of diplomatic strategies.Inside the council, diplomats engage with policy deliberations on a wide range of security issues in a tightly constrained institutional setting.Conversely, in cyberspace, they can be more selective in what they talk about and more open in how they convey their messages.Specifically, online messages typically emphasize ceremonial topics as well as prominent policy issues, including those not strictly conceived as security matters (e.g., SDGs), rather than other operational issues common in UNSC deliberations.Additionally, online communication adopts a less confrontational, more forward-looking tone, albeit with a considerable degree of cross-national variation.These observations indicate that some elements of public diplomacy and nation branding, directed toward a wider audience far beyond the council chamber, have become an integral part of multilateral diplomacy unfolding at the UNSC.
There are important limitations and remaining challenges following our study.First, it is essential to acknowledge the need for a stricter comparison given the non-identical nature of our two datasets.While the Security Council is one of the most prominent principal organs of the United Nations, the former is nevertheless a part of the latter.Therefore, the discursive range of X posts by UN-based diplomats might inherently be broader than that of their public statements at UNSC meetings, potentially rendering our comparison somewhat unbalanced.Extensive investigation of additional text data from other UN organs, most notably the General Assembly, would likely address this imbalance.
Although the General Assembly and its First Committee (focused on disarmament and security issues) maintain verbatim records, as does the Security Council, records from other primary UN bodies such as the Economic and Social Council are not verbatim.Instead, they are summary records, which present challenges for comparative analysis.
Second, the study is constrained by the preliminary nature of the actor-level analyses and the absence of exhaustive comparisons among countries.This necessitates further research to discern nuanced divergences in diplomatic strategies among different actors.The highlighted disparities in the deployment of topics and tones across platforms and actors advocate for more granular analyses to comprehend the underlying motivations, strategies, and implications of these variances in digital diplomacy.
Third, in addition to more extensive actor-level analysis, there is a need for analysis that is oriented toward the receiving side of diplomatic efforts.For example, there might be systematic differences between diplomatic messages that attract strong public attention (as measured by the numbers of "likes, " "reposts, " and so on) and those that do not.Preliminary analyses indicate that there is indeed such heterogeneity in diplomatic communication.Specifically, while most of the X posts analyzed here have not aroused any strong public reaction, a small number of posts that have amassed a large number of "likes" tend to mention highly contentious issues such as Ukraine, Palestine, and Myanmar in a considerably assertive, even confrontational, manner.This result is instructive because it indicates that diplomatic actors might not employ digital diplomacy solely for national branding.We will further pursue this line of analysis in future work.
Finally, the methodological approaches employed in this study can be fruitfully utilized in more depth.For example, following preceding work on crisis decision making (e.g., Gibson, 2011), these approaches can be applied to online and offline messages on specific policy issues (e.g., climate change, COVID-19, the Russian invasion against Ukraine, the Israel-Palestine conflict, etc.) to examine how different actors at the UNSC, especially the P5, converge or diverge in their views and policy stances.Such analysis might offer useful insights regarding how multilateral conference diplomacy at the UNSC, the effectiveness of which has often been called into question, can adequately function in the face of serious global threats.
FIGURE
FIGURETopic prevalence (k = ).(A) Prevalence across the combined corpus; (B) Di erences in prevalence between the X posts and the speeches.
FIGUREO
FIGUREO ine and online sentiment distributions in the case of Russia.The X posts/speeches classified as "neutral" were excluded from the figure for readability.
TABLE UN
TABLE Estimated topics for the combined corpus (k = ). | 8,405.6 | 2024-04-08T00:00:00.000 | [
"Political Science",
"Computer Science"
] |
Evidence for Stable High-Temperature Ferromagnetism in Fluorine-Treated C60
It is shown by magnetic �eld dependent ac susceptibility, magnetic force microscopy, and ferromagnetic resonance that exposure of C60 to �uorine at 160 C produces a stable ferromagnetic material with a Curie temperature well above room temperature. e exposure to �uorine is accomplished by decomposing a �uorine-rich polymer, tri�uorochloroethylene [F2C–CFCl]n, which has C60 imbedded in it. Based on previous experimental observations and molecular orbital calculations, it is suggested that the ferromagnetism is arising from crystals of C60–F.
Introduction
ere has been much interest in the material science community in synthesizing molecular-based ferromagnetic materials because of the potential to chemically engineer their properties and the possible ease of production. e C 60 molecule has played an important role in this possibility because of a number of reports of ferromagnetism in it. In 1991 a complex of C 60 and the strong electron donor molecule C 2 N 4 (CH 3 ) 8 (TDAE) were found to be ferromagnetic at 16.1 K [1]. Subsequently ferromagnetism having a Curie temperature of 500 K was reported in a two-dimensional polymeric form of C 60 produced by high pressure (6 GPa) and high temperature in the vicinity of 1000 K [2][3][4]. It is known that C 60 when subjected to UV light forms oligomers most of which are dimers [5]. It has been reported that when the photolysis is done in the presence of oxygen the material is ferromagnetic well above room temperature [6,7]. ere are a number of reports of ferromagnetism in halogenated C 60 . C 60 subjected to a heat treatment in the presence of iodine is shown to be ferromagnetic having a Curie temperature of 60 K [8,9]. Doping with a mix of iodine and bromine produced a material which was ferromagnetic below 30 K [10,11].
In this work it is shown by magnetic �eld dependent AC susceptibility, magnetic force microscopy, and ferromagnetic resonance that C 60 treated with �uorine is ferromagnetic well above room temperature. e C 60 was exposed to �uorine by embedding it in a �uorine-rich polymer, polytri�uorochloroethylene, [F 2 C-CFCl] , (PTFCE) and decomposing the polymer-C 60 mix at high temperature to produce �uorine.
Experimental
e paramagnetic and ferromagnetic resonance measurements were made using a Varian E-9 spectrometer operating at 9.2 GHz with 100 KHz modulation. e temperature of the sample was controlled by �owing heated or cold nitrogen gas through a double-walled quartz tube, which is part of an ADP Heli-Tran system. is system is inserted through the center of the microwave cavity. e magnetization was obtained by measuring the magnetic �eld dependence of the ac susceptibility at 350 kHz using a method similar to that described by Clover and Wolf [12]. e system consists of an HP 204C LC oscillator modi�ed to have an external coil. e sample is contained in the coil, which is in a cryogenic dewar between the poles of a magnet. e change in the frequency of the oscillator, which is proportional to the change in susceptibility, is measured as a function of dc magnetic �eld strength using a HP 5314 frequency counter. e relative susceptibility as a function of dc magnetic �eld is measured by taking the difference in frequency between zero �eld and a given applied �eld. is method of measuring the susceptibility is quite sensitive but not widely used. Magnetic force microscope images were obtained using a Veeco Nano scope IV equipped with a magnetic tip. Raman measurements were made using a J. Y. Horiba confocal micro-Raman system employing a 25 mW He-Ne laser having a wavelength of 632.8 nm and focused to a spot of a 15-micron radius.
Crystalline C 60 , having 99.99% purity, was obtained from the Aldrich Chemical Company. Polytri�uorochloroethylene (PTFCE) was obtained from the Halocarbon Products Corporation. In this paper we will report clear evidence for ferromagnetism in a mixture of C 60 and PTFCE subjected to heat treatment. In any report of ferromagnetism in an organic material, the purity of the starting materials is a critical issue, and we have paid considerable attention to sample analysis. It is particularly important to make sure no magnetic impurities are present in the starting materials. e starting C 60 was analyzed by induction coil plasma mass spectrometry (ICP-MS). e results indicated that signals from all metals were less than 1 part per billion (PPB). Electron paramagnetic resonance (EPR) of the C 60 showed no evidence of the presence of magnetic elements or complexes. EPR is sensitive to 1 part in 10 10 . A very narrow line at 000 was detected which has previously been identi�ed as the C 60 anion [13]. e PTFCE was also subjected to detailed analysis. Energy dispersive X-ray spectroscopy of PTFCE showed only the presence of carbon, �uorine, and chlorine, the constituents of the polymer. No other elements were detected. No magnetic species were detected by EPR. ICP-MS showed no magnetic metals above PPB in the PTFCE.
In a typical synthesis, 0.084 grams of PTFCE were dissolved in acetone and 0.040 grams of C 60 added to the solution. e solution, while subjected to sonication, was allowed to slowly evaporate. e resulting residue was dried for some hours at 50 ∘ C to remove any entrapped acetone. e composite was heated to 160 ∘ C for two minutes and then rapidly quenched to room temperature.
PTFCE as a Source of Fluorine.
PTFCE was heated to 160 ∘ C for one hour and the Raman spectra recorded before and aer the heating. No difference was observed between the frequencies of the Raman spectra indicating the material is not decomposing in the condensed phase.
However, the material sublimes at this temperature. In a second experiment the polymer was heated to 160 ∘ C for one hour in a small beaker which was on a hot plate. e beaker had a chilled slide on the top which enabled collection of the condensed vapor. e Raman spectra of the material condensed on the slide is shown at the bottom of Figure 1. On the top are the spectra in the same frequency region obtained from the polymer before heating. e two lines at 1198 cm −1 and 1298 cm −1 , which are due to C-F vibrations, are completely gone in the spectra of the vapor indicating single �uorines are removed from the carbon atoms of the polymer in the vapor phase providing a source of atomic �uorine rather than diatomic �uorine. Figure 2 is a plot of the ac susceptibility versus dc magnetic �eld at 300 K for the heattreated C 60 -TFPCE. e susceptibility has been normalized to the measured value at 3 Kilo Gauss. By comparing with a measurement on a sample of known magnetization, it is estimated the magnetization at 3000 Gauss is 0.07 emu/gm. No �eld-dependent magnetization is observed in the separated starting materials subjected to the same treatment. Figure 3 shows the details at lower �elds for increasing and decreasing dc magnetic �eld to and from 3000 Gauss showing a small hysteresis. Figure 4 presents the temperature dependence of the magnetization above room temperature measured in a 3000 Gauss �eld and normalized to its value at 300 K. � �t of this data to the Bloch equation,
Magnetization Measurements.
yields a value of of 4.1246 × 10 −5 . e temperature at which ( ) is zero, the Curie temperature, is estimated to be 837 K, from this �t. is is likely an overestimate because of deviations from the Bloch law near due to critical �uctuations. �owever, it is close to estimates of the Curie temperature obtained in C 60 photolyzed in the presence of oxygen.
Magnetic Force Microscope Measurement.
e PTFCE-C 60 material which was heat treated was pressed �at on a slide in order to have a smooth surface. Figure 5 shows a magnetic force microscope image of the material. e brighter regions indicate areas of ferromagnetism.
Ferromagnetic Resonance
Measurements. e �uorinetreated material was heated above its melting point and a 4000 G magnetic �eld applied. e material was then cooled below the melting temperature in the magnetic �eld. is aligns and locks in the direction of maximum magnetization parallel to the direction of the applied magnetic �eld. Figure 6 shows the ferromagnetic resonance spectra for the sample oriented perpendicular and parallel to the direction of the cooling �eld. For a particle having axial symmetry, the dependence of the �eld position of the FMR signal is given by [14], where = 4 / is the anisotropy �eld, is the magnitude of the anisotropy constant, and is the magnetization. e angle, , is between the direction of maximum magnetization and the applied dc �eld, is the magnetic �eld at the center of the FMR signal, and 0 determines the value. Because is lower than the parallel orientation compared to the perpendicular orientation, it can be concluded that is positive. Fitting the data in Figure 6 to (2) allows determination of 0 and . e values for 0 and are 2730 G and 93 G, respectively, at 300 K. e value is 2.287. One of the characteristics of an FMR signal as opposed to an EPR signal is a strong temperature dependence of the line width and �eld position of the resonance. Figure 7 is a plot of the temperature dependence of the �eld position for the sample oriented perpendicular to the direction of the cooling �eld showing a pronounced decrease in the �eld position with decreasing temperature. Figure 8 plots the line width as a function of decreasing temperature showing a marked broadening as the temperature is lowered. e data in Figures 7 and 8 con�rm that the signal is an FMR signal.
A Possible Model for the Origin of Ferromagnetism.
ere has been a previous report of ferromagnetism in C 60 subjected to a different �uorine treatment than that used here [15]. It was observed in C 60 ultrasonically dispersed in dimethylformamide (DMF) solution of polyvinyl di�uoride (PVDF), [H 2 C-CF 2 ] . However, the observed magnetism was not stable having a half-life of 30 hours at room temperature. Further the results were only reproducible 1 out of 15 times. In our observation the results are stable over years and reproducible once the correct synthesis conditions are determined. However, an interesting observation in the PVDF solution made material is that ionization time of �ight mass spectrometry showed the formation of C 60 oligomers having �uorine atoms bonded to each C 60 . Previous density functional molecular orbital calculations of the minimum energy structure of the F-C 60 -C 60 -F dimer indicated that the triplet state has a lower energy than the singlet state by 0.55 eV [16,17]. is suggests that the �uorinated dimer could be a possible source of the unpaired spin necessary to form a ferromagnetic state. However a calculation of the bond dissociation energy (BDE) to dissociate the dimer into 2(F-C 60 ) indicates the dimer would not be stable above 400 K in disagreement with experimental observations.
As discussed in the introduction there have been a number of reports of ferromagnetism at lower temperatures in C 60 subjected to heat treatment in the presence of I, IBr, and H [8][9][10][11]. X-ray diffraction measurements of these materials indicated the ferromagnetism was arising from a cubic phase of C 60 where the C 60 was functionalized with halogens or hydrogens. is is a likely possibility for the structure of the ferromagnetic phase of the �uorinated C 60 observed here. A calculation of the BDE to remove F from C 60 gives a value of 4.36 eV indicating that C 60 -F is stable above 400 K further supporting this possibility [17].
ere has been considerable work done on the �uorination of C 60 which has been discussed in a number of reviews [18,19]. �enerally the �uorination is achieved by exposing C 60 to F 2 gas at high temperature, which of course results in C 60 F where is even. An even would have no net spin. e method of synthesis used here is likely exposing C 60 to atomic �uorine produced by the removal of F from the TFPCE polymer. is would result in being odd giving the entity a net unpaired spin.
Conclusion
Field dependent ac susceptibility, ferromagnetic resonance, and magnetic force microscopy clearly show that exposing C 60 to �uorine at high temperature produces a ferromagnetic phase having a Curie temperature well above room temperature. e results cannot be explained by the presence of magnetic impurities such as Fe, Ni, or Co or compounds of them because ICP-MS and EPR of the starting materials indicate that such materials are present at less than one part per billion. While the structure of the ferromagnetic phase is not determined, some possibilities can be considered. Dimers of C 60 have been suggested to be the origin of the unpaired spin. DFT calculations of the BDE of F-C 60 = C 60 -F indicate it unlikely to be stable above 400 K. On the other hand C 60 -F is predicted to be stable at this temperature. is suggests the structure of the ferromagnetic phase may be cubic lattice of C 60 -F, as observed for ferromagnetism in C 60 -I, C 60 -IBr, and C 60 -H. However further work is needed to con�rm this possibility. | 3,109.4 | 2013-01-02T00:00:00.000 | [
"Materials Science",
"Physics"
] |
An Ensemble Classifier with Random Projection for Predicting Protein–Protein Interactions Using Sequence and Evolutionary Information
: Identifying protein–protein interactions (PPIs) is crucial to comprehend various biological processes in cells. Although high-throughput techniques generate many PPI data for various species, they are only a petty minority of the entire PPI network. Furthermore, these approaches are costly and time-consuming and have a high error rate. Therefore, it is necessary to design computational methods for efficiently detecting PPIs. In this study, a random projection ensemble classifier (RPEC) was explored to identify novel PPIs using evolutionary information contained in protein amino acid sequences. The evolutionary information was obtained from a position-specific scoring matrix ( PSSM ) generated from PSI-BLAST. A novel feature fusion scheme was then developed by combining discrete cosine transform (DCT), fast Fourier transform (FFT), and singular value decomposition (SVD). Finally, via the random projection ensemble classifier, the performance of the presented approach was evaluated on Yeast, Human, and H. pylori PPI datasets using 5-fold cross-validation. Our approach achieved high prediction accuracies of 95.64%, 96.59%, and 87.62%, respectively, effectively outperforming other existing methods. Generally speaking, our approach is quite promising and supplies a practical and effective method for predicting novel PPIs.
Introduction
Proteins are fundamental to human life and seldom function as a single unit. They always interact with each other in a specific way to perform cellular processes [1]. As a consequence, the analysis of protein-protein interactions (PPIs) can help researchers reveal tissue functions and structures and identify the pathogenesis of human diseases and drug targets of gene therapy. Recently, various high-throughput experimental techniques have been discovered for PPI detection, including a yeast two-hybrid system [2], immunoprecipitation [3], and protein chips [4]. However, the biological experiments are generally costly and time-consuming. Moreover, both false negative and false positive rates of these methods are very high [2,5]. Therefore, the development of reliable calculating models for the prediction of PPIs has great practical significance.
To construct a computational method for PPI prediction, the most important factor is to extract highly discriminative features that can effectively describe proteins. So far, protein feature extraction methods are based on many data types, such as genomic information [6,7], structure information [8,9], 2 of 15 evolutionary information [10,11], and amino acid sequence information. Of these approaches, sequence-based methods are more readily available, and it has demonstrated that protein amino acid sequence information is important for detecting PPIs [12][13][14][15][16]. Martin et al. used a descriptor called a "signature product" to discover PPIs [12]. The signature product is a product of sub-sequences from a protein sequence and extends the signature descriptor from chemical information. Shen et al. presented a conjoint triad (CT) approach to take the characters of amino acids and their adjacent amino acids into account [13]. Guo et al. proposed an auto covariance (AC) descriptor approach to represent an amino acid sequence with a foundation of seven different physicochemical scales [14]. When they detected Yeast PPIs, prospective prediction accuracy was achieved. Wong et al. employed the physicochemical property response matrix combined with the local phase quantization descriptor (PR-LPQ) to extract the eigen value of the proteins [15]. Considering the evolutionary information of protein, Huang et al. adopted substitution matrix representation (SMR) based on BLOSUM62 to construct a feature vector and achieved promising prediction accuracy [16]. Ding et al. proposed a novel protein sequence representation method based on a matrix to predict PPIs via an ensemble classification method [17]. Wang et al. proposed a computational method based on a probabilistic classification vector machine (PCVM) model and a Zernike moment (ZM) descriptor to identify PPIs from amino acids sequences [18]. Lei et al. employed the NABCAM (the neighbor affinity-based core-attachment method) to identify protein complexes from dynamic PPI networks [19]. Nanni et al. summarized and evaluated a couple of feature extraction methods for describing protein amino acids sequences by verifying them on multiple datasets, and they constructed an ensemble of classifiers for sequence-based protein classification, which not only performed well on many datasets but was also, under certain conditions, superior to the state of the art [20][21][22][23].
Next, the computational methods for PPI prediction can be formulated as a binary classification problem. A number of machine learning-based computational models for PPI prediction have emerged. Ronald et al. proposed a technique of applying Bayesian networks to detect PPIs on the Yeast dataset [24]. Qi et al. employed several classifiers, including support vector machine (SVM), decision tree (DT), random forest (RF), and logistic regression (LR), to compare their performances in predicting PPIs [25].
Of machine-learning-based computational models for PPI prediction, one of the most important challenges is that the high-dimensional features may include unimportant information and noise, leading to the over-fitting of classification systems [26,27]. Previous works have shown that random projection (RP) is a high-efficiency and sufficient precision approach that can reduce the dimensions of many high-dimensional datasets [28][29][30]. However, the performance using a single RP method is poor [31] because of the instability of RP. Therefore, in our study, an RP ensemble method was designed to predict PPIs.
The capacity of the integration model was better and more effective than that of separate runs of the RP approach. Moreover, the ensemble algorithm achieved results that are also superior to those of similar schemes that use principal component analysis (PCA) to reduce the dimensionality of the dataset [32]. The RP-ensemble-based classifier has useful features [33]. Firstly, RP maintains the geometrical structure of the dataset with a certain distortion rate when its dimensionality is reduced. This feature can reduce the complicacy of the classifier and the difficulty of new sample classification. In addition, dimensionality reduction can eliminate redundant information and reduce generalization error. Particularly, instead of relying on a single classifier, the RP ensemble method incorporates several classifiers that are superior to each single classifier. This feature can lead to better and more stable classification results.
In this paper, we propose an RPEC-based approach for detecting PPIs by combining a protein sequence with its evolutionary information. Firstly, a position-specific scoring matrix (PSSM) is used to express the amino acid sequence. Secondly, three 400 dimensional feature vectors are extracted from the PSSM matrix by using DCT, FFT, and SVD, respectively, and each protein sequence is described as a 2400 size of eigen vector. Then, an 1000 dimensionally reduced feature vector is obtained via PCA.
Finally, the RP ensemble model is built by employing the feature matrix of the protein pairs as an input to predict PPIs. Our method is estimated on the PPI datasets of Yeast, Human, and H. pylori and yields higher prediction accuracy of 95.64%, 96.59% and 87.62%, respectively. When compared with the SVM classifier fed into the same feature vector, the accuracies of our method are increased by 0.58%, 1.4%, and 2.57%, respectively. We also compare our method with other approaches. The obtained outcomes prove that our method is much better at predicting PPIs than those of previous works.
Position-Specific Scoring Matrix
A position-specific scoring matrix (PSSM) can be applied to search distantly related proteins. It emerged from a group of sequences formerly arranged by structural or similarity [34]. There are many methods of calculating distances and metric spaces [35,36]. Here, some research on PSSM methods and its relation to amino acids is discussed. Liu et al. [37] discovered that the PSSM profile has been shown to provide a useful source of information for improving the prediction performance of the protein structural class. Wang et al. [38] proposes two fusion feature representations of DipPSSM and PseAAPSSM to integrate PSSM with DipC and PseAAC, respectively. In our method, we predict PPIs based on PSSM. Thus, each protein can be converted to a PSSM by using the Position-Specific Iterated Basic Local Alignment Search Tool (PSI-BLAST) [39].
The PSSM can be described as follows: where N m = (N 1m , N 2m , · · · , N Lm ) T , (m = 1, 2, · · · , 20). With a size of L × 20 PSSM, L represents the length of an amino acid, and 20 is the number of amino acids. In our research, we achieved the experiment datasets by using PSI-BLAST to use a PSSM for PPI detection. In order to achieve a wide and analogous sequences, the parameter e-value of PSI-BLAST was adjusted to 0.001 and opted for three iterations, and the other values in PSI-BLAST were defaults. Finally, the PSSM from a certain protein sequence was expressed as a M × 20 matrix, where M denotes the quantity of residues, and 20 indicates the number of amino acids.
Discrete Cosine Transform
Discrete cosine transform (DCT) is a classical orthogonal transformation, which was first proposed in the 1970s by Ahmed [40]. It is used in image compression processing with lossy signals because of its strong compaction performance. DCT has better energy aggregation than others. It can convert spatial signals into frequency domains and thus work well in de-correlation. DCT can be defined as follows: where The N × 20 PSSM is the input signal, which is x i ∈ R n . Here, we can obtain 400 coefficients as the protein feature vector after the DCT feature descriptor. At the end, we can obtain a feature vector whose dimension is 800 from each protein pair via DCT.
Fast Fourier Transform
Fast Fourier transform (FFT) is a feature extraction method. The simplified energy function for FFT algorithms evaluate in the space of protein partner mutual orientations. The mesh displacements of one protein centroid in regard to another protein centroid can represent the translational space [41].
Here we describe the simplified energy scoring function, as PPIs are defined on a mesh and indicate M correlation functions all possible values of l, m, and n (assuming that one protein is the ligand and the other is the receptor): where Lp(a,b,c) and Rp(a,b,c) are the integral part of the related function defined with protein interactions on the ligand and the receptor, respectively. We can thus use M forward and an inverse fast Fourier transform to calculate the expression efficiently, and the forward and inverse fast Fourier transform can be denoted by FT and IFT, respectively: where a = √ −1, N 1 , N 2 and N 3 are grid sizes of the three coordinates. If N 1 = N 2 = N 3 = N, the complexity of this method is O(N 3 log(N 3 )). Then, we can use FFT to compute the related function of Lp with the pre-calculated function of Rp. The final sum offers the scoring values of function for all probable conversions of the ligands. Finally, we obtained and sorted the results from different rotations.
Singular Value Decomposition
It is a challenge for bioinformatics to explore effective methods for analyzing global gene expression data. Singular value decomposition (SVD) is a common technique for multivariate data analysis [42]. We assumed that M is the size of an m × n matrix. The decomposition for SVD can be expressed as follows: where U means an m × m unitary matrix, S indicates a positive semi-definite m × n diagonal matrix, V represents an n × n unitary matrix, and V* is a conjugate transposed of V. As a result, we can obtain the singular value of the matrix with proteins. The columns of U form the base vector of orthogonal input or analysis for M and are called left singular vectors. Rows of V* form the base vector of orthogonal output for M and are called right singular vectors. Thus, the diagonal element values of S are singular.
Principal Component Analysis
Principal component analysis (PCA) is a data-dimensionally reduced method. PCA is widely used for data analysis, and the variable interacting with information from the dimensionally reduced dataset can persist [43,44]. It embeds samples in high-dimensional space into low-dimensional space, and the dimensionally reduced data represents the original data as closely as possible. The PCA of a data matrix determines the main information from a matrix according to a complementary group of scores and loading diagrams.
Furthermore, PCA converts primitive variables into a linear combination set, the principal components (PCs), which catch the data variables, are linearly independent, and are weighted in decreasing order of variance coverage [45]. This can reduce the data dimension directly by discarding low variability characteristic elements. In this way, all original α-dimensional datasets can be optimally implanted in a feature space with lower dimension.
The concept and calculation of PCA technology is simple. It can be expressed as follows: Given M = A ij (i = 1, 2, · · · , α; j = 1, 2, · · · , β), where A ij denotes the feature value of the j-th sample with the i-th feature. Firstly, α-dimensional means that the full datasets with vector µ j and α × α covariance matrix are calculated. Secondly, the feature vectors and feature values are calculated and sorted according to decreasing feature values. These feature vectors can be expressed as F 1 with feature value λ 1 , as F 2 with feature value λ 2 , and so on. The largest k feature vectors can then be obtained. This can be done by observing the frequency content of feature vectors. The maximum feature values are equivalent to the dimensions which is the large variance of the dataset. Finally, we can construct an α × k matrix X, whose rows denote the number of samples, and k makes up the feature vectors. Afterwards, the lower dimensional feature space's number of k (k < α) was transformed by N = X T M(A). It is thus shown that the representation can minimize the square error criterion.
Random Projection Ensemble Classifier
Machine learning has been extensively applied in many fields. In mathematical statistics, RP is a method for reducing the dimensionality of a series of points that lie in Euclidean space. Compared with other methods, the RP method is simpler and has less output error. It has been successfully used in the reconstruction of dispersion signals, facial recognition, and textual and visual information retrieval. Now we introduce the RP algorithm in detail. Let be a series of column vectors in primitive data space with high dimension. x i ∈ R n , n is the high dimension, and N denotes the number of columns. Dimensionality reduction embeds the vectors into a space R q , which has lower dimension than R n , where q << n. The output results are column vectors in the space with lower dimension.
where q is close to the intrinsic dimensionality of Γ [46,47]. The embedded vectors refer to the vectors in the set Γ.
Here, if we want to employ the RP model to reduce the dimensionality of Γ, a random vector set γ = {r i } n i=1 must be structured first, where r i ∈ R q . There are two choices in structuring the random basis: (1) The vectors {r i } n i=1 are spread on the q-dimensional unit spherical surface. (2) The components of {r i } n i=1 conform to Bernoulli +1/+2 distribution and the vectors are standardized such that r i l 2 = 1 for i = 1, · · · , n.
We generated a q × n matrix R, where q consists of the vectors in γ. n was mentioned in the previous paragraph. The projecting result ∼ x i can be obtained by In our method, RP is used to construct a training set on which the classifiers will be trained. The use of RP lays the foundation for our ensemble model. Now, we illustrate the theory of our ensemble method. A training set Γ is given in Equation (9). We generate a G whose degree is n × N, and G comes from the column vectors in Γ.
We then structure {R i } k i=1 , whose size is q × n, where q and n are introduced in the preceding paragraph, k means the size of ensemble classifiers. The columns are standardized so as to the l 2 norm is 1.
In the ensemble classifiers, we constructed the training sets They are then fed into the base classifier, and the outcomes are a group of classifiers { i } k i=1 . For the sake of classifying a fresh set u with classifier i , firstly, u will be inlaid into the target space R q . It can be obtained by embedding u into R i .
where ∼ u is the result of embedding. The classification of ∼ u can be garnered by i . In this ensemble algorithm, the RP ensemble classifier will use the classification result of all classifiers { i } k i=1 of ∼ u to decide the final result with a majority voting scheme.
In this study, the 1000 coefficients were divided into 100 non-overlapping blocks. We chose the projection from a block of size 10 that obtained the smallest test error with the leave-one-out test error estimate. We used the k-Nearest Neighbor (KNN) as a base classifier, where k = seq(1, 25, by = 3). Prior probability of interaction pairs in the calculated training samples dataset was considered as the voting parameter.
Datasets Construction
We collected the highly reliable Saccharomyces cerevisiae PPI dataset from the DIP database of DIP_20071007 (http://dip.doe-mbi.ucla.edu) [48]. Protein sequences less than 50 residues may be fragments. Thus, we directly removed these protein pairs. In addition, much of the sequence identity of protein pairs is usually deemed as homologous. To eliminate the effects of these homologous sequence pairs, those with ≥40% sequence identity from protein pairs were also deleted. Finally, we used the remaining 5594 protein pairs as a positive PPI dataset and constructed a negative dataset with 5594 other pairs from distinct subcellular localizations. The final Yeast PPI dataset in our experiment was composed of 11,188 protein pairs with 50% positive samples and 50% negative samples.
For the sake of evaluating the universality of our model, we also performed the proposed method on Human and Helicobacter pylori datasets. The Human dataset was gathered from the Human Protein Reference database (HPRD). We also removed protein pairs with ≥25% sequence identity. To construct a golden standard positive dataset, we chose the remaining 3899 interacting protein pairs among 2502 different Human proteins. Because the proteins in diverse subcellular fractions cannot interact with each other, we built a golden standard negative dataset by selecting 4262 protein pairs among 661 distinct Human proteins [49]. Finally, the Human dataset was composed of 8161 protein pairs. Another PPI dataset used in this study was made of 2916 Helicobacter pylori protein pairs, which are mentioned by Martin et al. [12]. In this dataset, there are 1458 interacting pairs and 1458 non-interacting pairs.
Evaluation Measurements
In order to assess the capability of the RP classifier, the accuracy (Acc), sensitivity (Sen), precision (PE), and Mathews' correlation coefficient (MCC) were used as evaluation indexes. They can be described as follows: where true positive (TP) indicates the count of true samples predicted to interact; false negative (FN) is the quantity of interacting samples predicted to not interact; false positive (FP) is the count of non-interacting samples predicted to interact; true negative (TN) is the number of true samples predicted to not interact.
Experimental Environment
In the study, the presented sequence-based PPI prediction system was carried out using MATLAB (R2014a, the Math Works, Inc., Natick, MA, USA) and R programming language (X64 3.3.1, Copyright© 2016 The R Foundation for Statistical Computing). We finished the experiment with a machine with a 2.4 GHz 2-core CPU and an 8 GB memory based on operating system of Windows. We adapted an RP ensemble classifier to predict PPIs and applied an RP ensemble classifier to train the datasets in the experiment, and the k-Nearest Neighbor (KNN) was employed as a base classifier, where k = seq(1, 25, by = 3).
Performance of PPI Prediction
Three different PPI datasets were applied to estimate the results of our presented model. They are Yeast, Human and H. pylori PPI datasets, respectively.
Performance of the Proposed Method with Three Diverse PPI Datasets
In our problem of PPI predictions, the dimension of input features is 2400, which may contain the unimportant information and noise. Thus, the PCA algorithm is used to eliminate noise in the dataset. However, it is hard to determine the optimal number of features to use. Here, we carried out the experiments to find the optimal PCA dimension. For the sake of example, for the H. pylori PPI dataset, the prediction performance of different PCA dimensions is shown in Table 1. As a result, the favorable number of PCA dimensions is 1000-dimensional. For the sake of avoiding over-fitting and of verifying the constancy of the model, 5-fold cross-validations were used, which is part of the sub-sampling test method. More specifically, in 5-fold cross-validation, the entire dataset is split into 5 parts, where 4 parts are applied as training samples and 1 part is used as testing samples. In this way, we obtain five models from the datasets, and each model is a separate experiment. The prediction results of three datasets with the RP ensemble classifier are based on protein sequences and evolutionary information shown in Tables 2-4. As shown in Tables 2-4 The Receiver Operating Characteristic (ROC) curves for Yeast, Human, and H. pylori PPI datasets with five-fold cross-validation are shown in Figures 1-3, respectively. We computed the average AUC (area under ROC curve) values of Yeast, Human, and H. pylori PPI datasets to be 0.9570, 0.9615, and 0.8287, respectively. In conclusion, the higher accuracies and lower standard deviations of these values indicate that our presented approach is feasible and reasonable for detecting PPIs. Compared with the Human and the Yeast PPI datasets, the prediction performance of the H. pylori dataset is lower. It should be noticed that the sample sizes of the Human, Yeast, and H. pylori datasets are 8161, 11,188, and 2916, respectively. We found that the prediction performance, as indicated by the accuracy score, improves as the size of the samples increases.
Performance Comparison between the RP Classifier and the SVM Model
Many machine learning techniques and algorithms are employed to predict PPIs. We compared our RP model with the state-of-the-art SVM model. During the experiment, we extracted the feature values by the same method to ensure fairness. We used the LIBSVM toolbox on http://www.csie. ntu.edu.tw/~cjlin/libsvm/. The radial basis function (RBF) kernel was applied in our experiments. The method of a gridding search was employed to optimize two kernel parameters: C and g.
For the Yeast PPI dataset, we use the optimized parameters C = 0.3 and g = 1. The obtained results as shown in Table 5. For Human and H. pylori PPI datasets, the optimized penalty parameters are 0.06 and 0.5, and the kernel function parameters are 2 and 0.3, respectively. When we predicted the PPIs by applying the SVM classifier on the Yeast dataset, we obtained an average Acc, PE, Sen, and MCC of 95.06%, 95.35%, 94.76% and 90.60%, respectively. Compared with the SVM classifier, the accuracy of our method is higher by about 0.58%. When we predicted the Human PPI dataset, the results based on the SVM classifier of the average accuracy, precision, sensitivity, MCC, respectively, were 95.19%, 94.91%, 95.04% and 90.84%, respectively. Compared with the SVM classifier, the accuracy of our method was higher by about 1.40%. On the H. pylori dataset, the SVM classifier achieved an 85.05% average accuracy and a 91.92% precision, with 76.80% sensitivity and 74.27% MCC. Compared with the SVM classifier, the accuracy of our method was higher by about 2.57%.
Based on data in Table 5, the average accuracy, precision, and sensitivity values of our proposed model are much higher than averages attained by the SVM approach. The higher the standard deviation, the more unstable the algorithm is. Furthermore, we plotted the ROC curves on the three datasets by applying the SVM classifier as shown in Figures 4-6. It can be seen that the AUC areas yielded by our method are higher than those of the SVM classifier.
Comparison with Other Methods
There have been many prediction approaches developed for detecting PPIs. To further estimate the capacity of the proposed model, we compared our method with other existing methods. Table 6 shows the results of diverse approaches to the Yeast PPI dataset. The accuracies obtained by other previous methods range from 86.15% to 94.72%. In contrast, our method achieves an average accuracy of 95.64%. Our method obtained a higher PE and Sen than that of eight other methods. In conclusion, compared with all methods from Similarly, we compared our method with five other existing methods on the Human dataset. Based on Table 7, which shows the results of diverse approaches on the Yeast PPI dataset, the accuracies obtained by other previous methods range from 89.30 to 95.70%. In contrast, our method achieves an average accuracy of 96.59%. Accordingly, our method outperforms better than most other approaches, which are also based on ensemble classifiers. Similarly, we compared our method with five other existing methods on the Human dataset. Based on Table 7, which shows the results of diverse approaches on the Yeast PPI dataset, the accuracies obtained by other previous methods range from 89.30 to 95.70%. In contrast, our method achieves an average accuracy of 96.59%. Accordingly, our method outperforms better than most other approaches, which are also based on ensemble classifiers. Similarly, we compared our method with five other existing methods on the Human dataset. Based on Table 7, which shows the results of diverse approaches on the Yeast PPI dataset, the accuracies obtained by other previous methods range from 89.30% to 95.70%. In contrast, our method achieves an average accuracy of 96.59%. Accordingly, our method outperforms better than most other approaches, which are also based on ensemble classifiers.
Discussion and Conclusions
In the post-genome era, it is quite important to predict PPIs using computational techniques. In the study, we proposed a PPI prediction model by extracting evolutionary information from the position-specific scoring matrix (PSSM) generated by PSI-BLAST. Then, an RP ensemble classifier is used to implement PPI prediction. We conducted experiments on Yeast, Human, and H. pylori PPI datasets. In order to evaluate the capacity of our model, we compared our approach with an SVM-based model as well as other existing methods. The results of our model are quite promising; our model is a beneficial supplement to traditional experimental methods for PPI prediction. Moreover, the RPEC method may also be employed to solve other classification problems. | 6,189.4 | 2018-01-10T00:00:00.000 | [
"Biology",
"Computer Science"
] |
Exact Formulation of the Transverse Dynamic Spin Susceptibility as an Initial-Value Problem
The transverse dynamic spin susceptibility is a correlation function that yields exact information about spin excitations in systems with a collinear magnetic ground state, including collective spin-wave modes. In an ab initio context, it may be calculated within many-body perturbation theory or time-dependent density-functional theory, but the quantitative accuracy is currently limited by the available functionals for exchange and correlation in dynamically evolving systems. To circumvent this limitation, the spin susceptibility is here alternatively formulated as the solution of an initial-value problem. In this way, the challenge of accurately describing exchange and correlation in many-electron systems is shifted to the stationary initial state, which is much better understood.The proposed scheme further requires the choice of an auxiliary basis set, which determines the speed of convergence but always allows systematic convergence in practical implementations.
Introduction
Accurately predicting the excitation spectra of interacting quantum-mechanical many-electron systems from first principles is a notoriously difficult problem, because the variational principle, which underlies such successful groundstate schemes as density-functional theory [1] or quantum Monte Carlo methods [2], cannot be exploited in this case. Furthermore, strategies based on an expansion of the manyelectron wave function are limited to very small systems due to the rapidly increasing number of possible configurations. Under these circumstances, the most successful computational approaches currently rely on correlation functions, which contain the complete and, in principle, exact information about specific classes of excited states and can be directly related to experimental spectroscopies. Well-known examples include the single-particle Green function, which describes the propagation of individual quasiparticles, that is, injected electrons or holes, and the dynamic charge susceptibility or linear density-response function, which gives information about plasmons, excitons, and other chargeneutral optical excitations [3]. Another example, which will be the focus of this paper, is the transverse dynamic spin susceptibility, which describes spin-flip excitations, including single-particle Stoner excitations as well as collective spinwave modes, in systems with a collinear magnetic ground state. Among the properties that can be directly obtained from these correlation functions are the energies, lifetimes, and oscillator strengths of the excitations.
In the context of first-principles calculations, the transverse dynamic spin susceptibility may be constructed using either of two methods. Within many-body perturbation theory, it can be expanded in terms of single-particle Green functions and a kernel that couples the dynamics of electrons and holes with opposite spin [4,5]. In actual implementations, the latter must be drastically simplified and is usually replaced by the static zero-frequency limit of the screened Coulomb interaction, often in combination with additional approximations, such as a Yukawa-potential model [6] or the neglect of interatomic screening in a localized Wannier basis [7,8]. Alternatively, in time-dependent density-functional theory, the spin susceptibility of independent electrons and holes is renormalized with a dynamic exchange-correlation kernel [9][10][11][12]. The former can be expressed in terms of the Kohn-Sham orbitals and eigenvalues; accurate static density functionals exist for this purpose. The functional form of the latter is much more elusive, however. In practice, adiabatic 2 Advances in Mathematical Physics kernels derived from static density functionals are almost exclusively used, but this choice, necessitated by a lack of viable alternatives, entails significant errors. For example, the local-density approximation yields the exact exchangecorrelation potential and hence the exact Kohn-Sham orbitals and eigenvalues, for a homogeneous electron gas, but the adiabatic kernel derived from it neglects both the spatial and temporal nonlocality of the exact exchange-correlation kernel [13]. In both frameworks, therefore, the lack of accurate models for time-dependent exchange and correlation effects in nonstationary systems currently constitutes the main impediment for systematic quantitative improvements. Moreover, inconsistencies between the prevalent static and relatively crude approximations for dynamic two-particle correlation on the one hand and the accurate description of many-body effects on the quasiparticle electronic structure of stationary systems on the other hand give rise to qualitative errors, such as the numerical violation of Goldstone's theorem for the spin-wave dispersion in implementations of manybody perturbation theory [7,14].
In this paper, I develop a different approach that holds the promise of circumventing the above-mentioned problems. Instead of calculating the transverse dynamic spin susceptibility from a Dyson-type integral equation with a dynamic exchange-correlation kernel, as is usually done, the key idea advanced here is to reformulate it as the solution of an initialvalue problem in the time domain. To this end, I derive an exact differential equation that is of first order in the time variable, using the equations of motion of the field operators in second quantization. Furthermore, I show that the initial value can be expressed in terms of the spin-resolved one-particle reduced density matrix. As a consequence, this scheme requires an accurate description of nonlocal correlation in the stationary ground state, which is achievable even without explicit wave functions, but no dynamic exchangecorrelation kernel. To simplify the notation, Hartree atomic units are used throughout.
Derivation
2.1. Definition of the Spin Susceptibility. In collinear magnetic systems, the direction of the magnetization vector is identical at all points in space and varies only in magnitude and sign. In such circumstances, spin is a good quantum number, as each electron has a definite spin orientation with respect to the global quantization axis. The retarded transverse dynamic spin susceptibility is then defined as where the angular brackets indicate the expectation value with respect to the ground-state many-electron wave function in second quantization and is the commutator of two quantum-mechanical operators. The spin-raising and spin-lowering operators are given bŷ and bŷ respectively, in terms of the time-dependent annihilation operator̂ (r, ) for an electron with spin ∈ {↑, ↓} and its adjoint, the creation operator̂ † (r, ), in the Heisenberg picture. The fermionic field operators with equal time arguments satisfy the anticommutation relations [3] {̂ (r, ) , as well as where the curly brackets denote the anticommutator, defined analogous to (2) but with a plus sign instead of a minus sign on the right-hand side. Finally, the Heaviside step function Θ( − ὔ ) in (1) reflects causality and ensures that the spin density at time is only influenced by the magnetic field at times ὔ < , if the dynamic spin susceptibility is interpreted as the linear spin-density response function by means of Kubo's formula.
Equation of Motion.
The time derivative of the retarded transverse dynamic spin susceptibility, which will eventually lead to the desired differential equation, follows immediately from definition (1) and is given by The derivative of the spin-raising operator (3) is in turn given by For a general interacting many-electron system governed by the Hamiltonian Advances in Mathematical Physics
3
where ℎ(r) = −∇ 2 /2 + (r) comprises the kinetic energy and the ionic potential and V(r − r ὔ ) is the pairwise Coulomb interaction, the field operators obey the equations of motion [3] When applied to the single-particle Green function, it is well known that this procedure generates an infinite hierarchy of equations of motion where each Green function is coupled to a higher-order Green function due to the occurrence of terms involving products of three field operators on the righthand sides of the above equations [3]. However, if (10a) and (10b) are inserted into (8), one finds that the terms involving the Coulomb interaction cancel in this case, leading to the remarkably simple result In fact, only the kinetic energy in ℎ(r) yields a nonvanishing contribution, whereas the external potential commutes with the field operators and has no influence. As a consequence, the time evolution of̂ + (r, ) turns out to be to some degree universal, as long as there are no spin-dependent magnetic fields that couple directly to the spin density and give rise to extra terms in (11). In particular, it would be identical if ℎ(r) were replaced by another Hamiltonianh(r) with a different spin-independent local potential̃ (r) instead of (r). This will be turned to an advantage below. It should be noted that although the time evolution of the operator̂ + (r, ) is to some degree independent of the specific system, physical observables derived from it are not, of course, because the expectation values are still formed with a specific systemdependent wave function. The fact that the time derivative of an operator has a generic value is also not unusual in itself; for example, all operators that commute with the Hamiltonian have a vanishing time derivative, irrespective of the specific system. Another example of practical relevance is the continuity equation for the spin-density operator, to which the present result is related. Turning next to the second term on the right-hand side of (7), the commutator can be simplified to by exploiting the anticommutation relation (5). The expectation values of the operators on the right-hand side correspond to the components of the spin-resolved one-particle reduced density matrix and do not depend on the time variable for a stationary system in the ground state. If all terms are collected, one thus obtains the equation of motion which takes the form of a differential equation that is of first order in the time variable. In order to turn it into a practical scheme for calculating the transverse dynamic spin susceptibility, two further problems must still be addressed, however: First, the expectation value involving products of four field operators on the right-hand side must be expressed in terms of +− (r, r ὔ ; − ὔ ) or other, known quantities. Second, an initial value from which the time propagation can start must be established.
Expansion in an Auxiliary Basis.
In order to achieve the first of the two outlined tasks, a set of single-particle orbitals (r) is chosen, with the sole requirement that they are eigenfunctionsh (r) (r) = (r) of a Hamiltonianh(r) = −∇ 2 /2 +̃ (r) with some spinindependent local potential̃ (r). This ensures that the orbitals form a complete orthonormal set, so that other quantities can be expanded in this basis. In particular, the fermionic field operators can be written aŝ † (r, ) = ∑ * (r)̂ † ( ) , (16a) where the annihilation operator̂ ( ) and the creation operator̂ † ( ) now refer to the chosen basis. Inserting these expressions into the definition of the transverse dynamic spin susceptibility (1) yields the representation with the coefficients 4
Advances in Mathematical Physics
Crucially, if one exploits the relations then the hitherto elusive expectation value on the righthand side of (14) can be rewritten in terms of the same coefficients. With the expansion of the one-particle reduced density matrix and the resolution of the identity all terms in (14) can thus be cast into an identical form and written as sums over products of four orbitals. Although the products of the orbitals exhibit linear degeneracies and do not form an orthogonal basis themselves, a sufficient condition for the equation of motion to be fulfilled is that the coefficients inside the sums on both sides of the equation agree, which eventually yields 2.4. Initial Value. From the Heaviside step function contained in the definition of the transverse dynamic spin susceptibility (1), it already follows that +− (r, r ὔ ; − ὔ ) = 0 and hence The discontinuity at = ὔ is described by the second term on the right-hand side of (22), which establishes that the limit from the above equals The same result can also be directly derived from (1), which implies It then follows by inserting the already established simplified expression for the commutator (12) in combination with the definition of the one-particle reduced density matrix (13) and its expansion in the chosen basis set, as described in the previous section.
Starting from the initial value (24), the further forward evolution of the transverse dynamic spin susceptibility is continuous and governed by which only retains the first term on the right-hand side of (22). Taken together, (23), (24), and (26) thus define the initial-value problem that lies at the center of this work. Due to the simple linear form of (26), it can in fact be integrated analytically, yielding the explicit solution Due to the inclusion of the Heaviside step function, which ensures that the solution fulfills (23) and thus respects causality, this formula is valid for all values of the time argument. Its Fourier transformation to frequency space can also be carried out analytically and is given by with > 0. The location of the poles in the lower half of the complex frequency plane is a characteristic feature of retarded (or causal) correlation functions.
2.5.
Discussion. The formal solution of the initial-value problem derived in the previous section takes the form of an expansion in products of orbitals from a complete orthonormal basis, given by (17), for the spatial variation of the transverse dynamic spin susceptibility and a superposition of harmonic oscillations, given by (27), for its time dependence. Despite the very suggestive appearance, especially of the Fourier transform (28), it is important to recall that the parameters do not constitute any actual energy levels of the physical system in question but are instead the eigenvalues of a different, auxiliary problem (15) and thus serve a purely mathematical purpose. For the same reason, the sums in (17) also run over the entire set of basis functions and are not restricted to transitions between occupied and unoccupied states. Even for systems with a finite number of electrons, the sums are thus infinite, necessitating truncations in practical applications. The description of the time dependence as a superposition of an infinite number of harmonic contributions is akin to a Fourier representation.
As pointed out above, the basis set can be chosen freely with the sole requirement that it corresponds to the eigenfunctions of an auxiliary single-particle Hamiltoniañ ℎ(r) with a spin-independent local potential̃ (r). In practical implementations, where truncations of infinite sums are unavoidable, this degree of freedom may be exploited in order to achieve good convergence even with a finite number of terms. The auxiliary Hamiltonian must then be chosen in such a way that the expansion (20) of the one-particle reduced density matrix of the actual physical system is numerically accurate with a manageable, finite number of coefficients. Consequently, it must reflect the characteristics of the specific physical system. Obvious choices are not admissible, however: The noninteracting Kohn-Sham system of spin-densityfunctional theory is ruled out because, for collinear magnetic systems, the effective potential contains an explicit spindependent exchange-correlation field that forces the breaking of the spin symmetry [15], which arises spontaneously even without magnetic fields in the real physical system due to the Coulomb interaction. Likewise, the so-called natural orbitals [16] that diagonalize the one-particle reduced density matrix and thereby enable its most efficient representation cannot be employed; although the natural orbitals constitute a complete orthonormal set, they do not, in general, correspond to the eigenfunctions of a single-particle Hamiltonian with known eigenvalues, and for a collinear magnetic system they are also spin dependent. While generic basis sets like plane waves are always an option, of course, a weighted average of the local effective potentials of the two spin channels, or the self-consistent effective potential obtained from constrained density-functional theory with a non-spin-polarized electron configuration, might be preferable in actual implementations, because fewer basis functions are required for an accurate representation. In any case, although the choice of an optimal auxiliary basis set remains a practical challenge, it ultimately affects only the speed of convergence, whereas the converged results themselves are independent of the basis set.
A key feature of the constructed initial-value problem is that the characteristics of exchange and correlation are contained in the initial value in form of the one-particle reduced density matrix. This is plausible from a fundamental point of view, because the dynamic spin susceptibility equals the linear spin-density response function, which is a property of the stationary ground state. As the one-particle reduced density matrix is not obtained within the present scheme, it must be constructed independently. For practical purposes, it is important that it can in fact be derived self-consistently without explicit recourse to many-electron wave functions by means of reduced density-matrix functional theory [17], a nonlocal extension of conventional density-functional theory. Although the design of reliable quantitative energy functionals is still very much in progress, reduced density-matrix functional theory is already a practically useful scheme [18]. Alternatively, it can be derived from the single-particle Green function, which is obtainable from implementations of manybody perturbation theory, using suitable approximations [19].
Conclusions
In conclusion, this paper takes a new perspective on the calculation of the transverse dynamical spin susceptibility for collinear magnetic systems, which seeks to circumvent current bottlenecks that prevent systematic improvements in the accuracy of quantitative first-principles simulations. Based on the notion that the spin susceptibility is a property of the stationary state and that its inherent time dependence does not arise from external fields but from the internal phases of wave functions of the unperturbed system, it is here reformulated as the solution of an initial-value problem. An essential point in this process is the expansion in an auxiliary orthonormal basis, which allows all occurrent expectation values to be written either in terms of the coefficients of the transverse dynamic spin susceptibility itself or in terms of other observables that can be obtained independently. The time propagation is simple enough to allow a formal analytic solution, while the problem of accounting for exchange and correlation effects is shifted to the initial value. The challenges hence lie in the identification of efficient auxiliary basis sets that make +− ( − ὔ ) an accurate representation of the true result with a manageable, finite number of basis functions and in constructing the initial value, specifically the spinresolved one-particle reduced density matrix, with sufficient quantitative accuracy. Both of these problems are better understood at a fundamental level and appear more accessible than the design of nonadiabatic exchange-correlation functionals for time-dependent magnetic systems needed for further improvements of prevalent implementations based on the solution of Dyson-type integral equations, however.
Conflicts of Interest
The author declares that there are no conflicts of interest regarding the publication of this article. | 4,211.2 | 2018-01-01T00:00:00.000 | [
"Physics"
] |
Modal analysis of the ultrahigh finesse Haroche QED cavity
In this paper, we study a high-order finite element approach to simulate an ultrahigh finesse Fabry–Pérot superconducting open resonator for cavity quantum electrodynamics. Because of its high quality factor, finding a numerically converged value of the damping time requires an extremely high spatial resolution. Therefore, the use of high-order simulation techniques appears appropriate. This paper considers idealized mirrors (no surface roughness and perfect geometry, just to cite a few hypotheses), and shows that under these assumptions, a damping time much higher than what is available in experimental measurements could be achieved. In addition, this work shows that both high-order discretizations of the governing equations and high-order representations of the curved geometry are mandatory for the computation of the damping time of such cavities.
Introduction
In 2012, Serge Haroche and David Jeffrey Wineland were jointly awarded the Nobel prize in physics for groundbreaking experimental methods that enable measuring and manipulation of individual quantum systems [1]. Basically, they succeeded in building devices where quantum particles (such as photons or ions) can be trapped [2]. A few years before, in 2007, Serge Haroche and his coworkers were able to record the birth and death of a photon in a cavity [3,4], by using an ultrahigh finesse Fabry-Pérot superconducting resonator [5]. This open cavity consists of two superconducting (niobium at 0.8 K) toroidal mirrors (see figure 1) with an extremely high manufacturing precision, as shown on the geometrical parameters of table 1.
The cavity is resonant at 51.1 GHz with a measured damping time of approximately 130 ms. Simply put, this high damping time means that, if a photon appears inside the cavity, it will somehow bounce back and forth for a very long time without interfering with the outside world. By taking advantage of the extremely long lifetime of the photon inside the cavity, Serge Haroche and his coworkers were then able to record the birth, life and death of a photon.
In 2014, attempts were made to model the photon cavity, by using the classical time-harmonic Maxwell equations with the finite element (FE) method and a quasimodal analysis [6]. In particular, by analyzing the eigenmodes of the cavity, the resonance frequency as well as the damping time can be recovered. In their paper, the authors were able to compute the resonance frequency of the cavity, but did not reach a numerically converged value for the damping time with respect to the FE mesh density. The purpose of this paper is to compute the damping time of the photon cavity by using a high-order FE method. In addition, by studying an idealized setup, the performance limits of the cavity are assessed. To the best of our knowledge, the following analysis with high-order techniques is performed for the first time.
This paper is organized as follow. First, in section 2, it is explained how classical electromagnetic numerical computations, exploiting the FE method and a perfectly matched layer (PML), can be used to estimate the lifetime of a photon in an open cavity. Furthermore, the use of a high-order FE approach is motivated. Then, in section 3, the numerical setup is presented. The paper continues with some numerical results in section 4. Section 5 discusses the computational bottleneck introduced by the memory scaling. In order to push further our analysis of the cavity, a two-dimensional setup presenting the same limitations regarding the lifetime is studied in section 6. Finally, conclusions are formulated in section 7.
Computation of the lifetime of a single photon: PMLs and high-order FE methods
One of the fundamental problem in computational electromagnetism is to treat open problems, i.e. enforcing an outgoing wave condition. In 1994, Bérenger [7,8] introduced the PML in the framework of the finite difference time-domain method. This method turned out to be extremely efficient and became very popular. It appeared to be equally efficient in the time-harmonic case and it was soon realized that it could be introduced as a complexvalued change of coordinates [9]. It was also applied to the eigenmodes computation of open structures [10] and is indeed a powerful theoretical tool to define the concept of resonance.
Despite the fact that, in that time, it was an innovative technique in computational electromagnetism, this concept was first introduced as a theoretical tool, named analytical dilation, in quantum mechanics [11,12]. From a technical point of view, this technique is well adapted to electrodynamics, since, by using the concept of transformation optics [13][14][15], the change of coordinates can be encapsulated in the material characteristics: the relative electric permittivity e r and the relative magnetic permeability m r .
It may seem paradoxical to use concepts from classical physics to compute the lifetime of a single photon. However, the fact that similar techniques, analytical dilation and PML, can be used to compute resonances of open systems, electrons in the first case and electromagnetic waves in the second case, is not a coincidence. Indeed, electromagnetic fields can be considered cautiously as the wave functions of photons [16][17][18]. In this case, the Maxwell equations are the Schrödinger equations of the photon (relativistic null mass spin one case in the Wigner classification [19]). In summary, a classical electrodynamics computation is legitimate to estimate the lifetime of a single photon. The next step is to set up a proper discretization of the Maxwell operator. In this paper, we use the FE method. It has been proved [20,21] that edge elements, respecting the de Rham complex at the discrete level, provide a correct approach to tackle electromagnetic eigenvalue problems and the so-called spurious modes. In the present cavity quantum electrodynamics (QED) problem with an extremely high quality factor, we need a very accurate computation of the complex-valued eigenfrequency and especially of its imaginary part. For this purpose, high-order mesh elements and high-order FE shape functions [22] are used. As demonstrated hereafter, high-order mesh elements are mandatory for the representation of the toroidal mirror, since they alleviate the artificial roughness present in straight mesh elements. Furthermore, high-order FE shape functions are known to substantially improve the precision of high-frequency simulations, by reducing the impact of the pollution effect [23,24]. A previous attempt [6] has shown encouraging results, but pointed out the need of highorder elements for the proper numerical convergence of the damping time, as shown in figure 2. From these results, it can be directly seen that the computed damping time depends strongly on the mesh density, although this effect is not observed for the resonance frequency. Since we are looking for resonances associated to complex-valued eigenfrequencies, we are led to solve a non-Hermitian eigenvalue problem. Indeed, the equivalent materials introduced to model the unboundedness of the domain (the PML) are non-Hermitian and destroy the Hermitian nature of the initial lossless problem. Unfortunately, it is well known that these problems are hard to solve [25]. Moreover, the FE discretization leads to very large sparse matrices, but, over the last few years, powerful algorithms implemented in open source libraries have been developed [26,27]. Formally, the complex-valued resonance angular frequency is defined as: Cavity Cavity 2 where f Cavity is the cavity resonance frequency, t Cavity the damping time and i the imaginary unit. All these elements together led us to the proposed numerical model for the computation of the lifetime of a photon in a QED cavity.
Computational setup
In this work, we used a homemade high-order FE code 4 , which takes advantage of an efficient assembly technique, as described in [28]. Indeed, quite often with high-order techniques, the computational bottleneck is found to be the assembly of the discrete operator itself. It is worth mentioning that the discrete high-order FE spaces used are those proposed in [22]. Regarding the eigenvalue solver, the developed tool relies on the SLEPc library 5 [26,27]. When an LU decomposition has to be carried out (see section 3.5), the MUMPS 6 [29,30] library is called, and is configured for parallel analysis with the ParMETIS 7 [31] reordering.
Among the eigenvalues in the 51.1 GHz region of the spectrum, we expect to find one with a high ratio between the real and imaginary parts. This eigenvalue corresponds then to a mode where the cavity exhibits a large damping time (or equivalently, a high quality factor): the photon 'trapping' mode. Our objective is to find a numerically converged damping time: i.e. quasi-independent to both an increase of the FE discretization order and the mesh size.
Before going any further, one last point must be raised. Since the mirrors are toroidal, the cavity actually exhibits two resonant modes: one for each radius. They are both TEM 900 modes near 51.1 GHz and are separated by 1.26 MHz [5,32]. In the following, these modes will be referred to as polarization 1 and 2.
Geometry
Let us now discuss the geometry considered for the simulations. In order to reduce the number of unknowns, only one quarter of a single mirror is modeled, as shown in figure 3. Furthermore, the air surrounding the quarter mirror is represented by a rectangular parallelepiped, as shown in figure 4(a). As discussed in section 2, a PML is added to model the surrounding space, as depicted in figure 4(b). As a first guess, the PML thickness is taken as1λ (where l 5.9 mm is the wavelength at 51.1 GHz), and its distance from the mirror is also set to 1λ. More details on the PML can be found in sections 2 and 3.4.
The final geometry is depicted in figure 4(b), and was generated by the OpenCASCADE 8 engine. This library was driven using the python 9 interface provided by Gmsh 10 [33]. Finally, the computational domain is meshed using the Gmsh mesh engine. Since our objective is to use high-order FE discretizations, curved mesh elements are mandatory [34], not only to achieve a precise representation of the curved mirror, but also to keep the number of mesh elements to an acceptable value.
Eigenvalue problem
Our objective is to find the eigenvalues of the photon cavity. In other words, we need to find every possible value of the angular frequency ω, such that 8 Available at: http://opencascade.com 9 Available at: http://python.org 10 Gmsh is a three-dimensional FE mesh generator with built-in pre-and post-processing facilities; available at: http://gmsh.info From a FE point of view, this eigenvalue problem writes [35]: , the space of square integrable functions with a square integrable curl (these function are also commonly referred to as edge elements). The electrical field e is then approximated by: where the coefficients a j are unknown. Thus, the (generalized) eigenvalue problem writes: By identifying the terms in equation (1), we have: 1 containing the degrees of freedom for e; • the matrix In this paper, the eigenvalue problem(1) is solved by the Krylov-Schur algorithm [36,37] from the SLEPc library [26,27]. The relative tolerance of the eigenvalue solver is set to 10 −15 .
Boundary conditions
As motivated above, only one quarter of a single mirror is modeled. To simulate the actual configuration, appropriate boundary conditions have to be imposed on the geometry of figure 4(b). In what follows, n is the unit vector outwardly oriented normal to Ω.
(i) A zero tangential magnetic field on the Oxy-plane: Oxy n c u r l 0 on . r 1 (ii) Depending on whether polarization 1 or 2 is considered.
Polarization 1: a zero tangential magnetic field on the Oxz-plane, and a zero tangential electric field on the Oyz-plane: Moreover, since the mirror is made of superconducting material, we assume that it has a zero resistivity:´= ¶W e n n 0 on .
Mirror
For simplicity, we also consider the frame of the mirror to have a zero resistivity:´= ¶W e n n 0 on . Frame
Perfectly matched layer
Let us now specify the PML used for the considered simulations. Since we chose a parallelepiped to surround the mirror, it is a natural choice to use a Cartesian PML [7,8]. A PML is usually described by its damping functions σ x (x), σ y (y) and σ z (z). In this paper, we chose the following hyperbolic profiles: where ΔX (or ΔY, or ΔZ) is the thickness of the PML in the x (or y, or z) direction, and where X max (or Y max , or Z max ) is the distance between the center of the mirror and the PML in the x (or y, or z) direction. These profiles are inspired from [38], where a a D c 0 (with αä{X, Y, Z}) term is added to remove the jump between the truncated domain and the PML. From these damping profiles, it is then possible to compute an equivalent relative electrical permittivity and relative magnetic permeability in the PML domain:
Spectral transform
In our cavity problem, it is not required to extract the entire spectrum of(1): indeed, only the TEM 900 mode is of interest. Therefore, a spectral transform is used. The idea is to modify the eigenvalue problem, so that the eigenvalues around a given target are easier to compute [39]. In practice, the shift-and-invert transform [39,40] is used. That is, instead of solving(1), the following equivalent (from the eigenvalue point of view) problem is solved: where σ is a well chosen shift and where q w s = --( ) It is worth noticing that the spectral transform involves an LU decomposition of s - C , which is handled by the MUMPS library.
Three-dimensional high-order FE simulations
With all these tools in hand, let us now discuss some three-dimensional high-order FE simulations. It is worth mentioning that in the following results, some data are missing because of memory limitations (see section 5).
Solution convergence: mesh density and FE discretization
Based on the computational setup presented previously, a first set of simulations is run in order to assess the numerical convergence of the computed solutions. In practice, five tetrahedral meshes are generated, with 3 to 7 mesh elements per targeted wavelength (i.e. l 5.9 mm, as mentioned in section 3). In each case, the mesh exhibits a 3rd-order curvature. From the FE point of view, three discretizations are considered: order 3, order 4 and order 5. Each simulation is carried out with 120 MPI 11 processes. Depending on the problem size, these processes are distributed between 5 and 120 computing nodes. On each node, 64GB of memory is available.
For each simulation, three eigenvalues are computed. In each case, only one eigenvalue exhibits a very large damping time and is selected as the resonant one. Figure 5 depicts the numerical convergence of the computed resonance frequencies and damping times for polarization 1.
For the resonance frequency, we may conclude that convergence is achieved: the resonance frequency for polarization 1 is found at 51.0847 GHz. However, for the damping time, convergence is more delicate to assess. Clearly, the 3rd-order simulations did not yet converge. The 4th-and 5th-order simulations seem to converge toward a damping time around 5.6 s. More accurate discretizations would of course be welcome, but, due to memory limitations discussed in section 5, these data are not accessible. Nevertheless, a few indicators suggest that the computed damping time will remain in this range. First, the 4th-and 5th-order curves suddenly saturate around 5.6 s. Secondly, at a mesh density of 5 mesh elements per wavelength, the damping time varies by only a factor of 5% between the two highest-order solutions. Finally, a variation of only 1% is recorded between the best 4th-order estimate and the 5th-order one.
Compared to the damping time of 130 ms determined experimentally, the computed one is 43 times higher. Four major idealizations made in our model could explain this discrepancy. First, our geometry is ideal: the mirrors are exactly toroidal and perfectly aligned. Secondly, our model consists of only the two mirrors floating alone in the void, whereas the mirrors are surrounded by sophisticated equipment in the actual experiment [5], that could introduce additional losses. Thirdly, the residual resistivity of the superconducting material has not been taken into account. Indeed, since we are not operating at absolute zero temperature, some carriers are not in a superconducting state, leading thus to ohmic losses. Furthermore, it can be shown that these losses are increasing with the square of the frequency [41]. And finally, the roughness of the actual mirror is not modeled. As we will see in the following section, this has a dramatic effect on the value of the computed damping time. Let us stress that these issues can be alleviated by technical improvements, while the open nature of the cavity, and the associated computed losses, is an intrinsic property of the device.
To conclude, and for illustration purposes, figure 6 depicts the eigenmode associated to the cavity resonance. For clarity, the vectorial electric field is shown only on the Oxz-and Oxy-planes. It can be directly noticed that this mode exhibits a cylindrical symmetry around the z axis and 4.5 antinodes. Because of the boundary condition on the Oxy-plane, the total number of antinodes is doubled, confirming thus that polarization1 is a TEM 900 mode.
Polarization 2
In the previous convergence test, only polarization1 was considered. Let us now focus on polarization2. Based on the previous simulations, only the 4th-and 5th-order FE solutions are considered. Figure 7 depicts the computed frequencies and damping times for polarization1 and2. In addition, the frequency difference between the two polarizations is provided in table 2.
As for polarization 1, we can directly notice that the cavity resonance frequency has numerically converged to 51.0834 GHz. Moreover, we have reached a frequency difference of 1.26 MHz, which matches the difference measured experimentally [5,32].
For the damping time, we get a result similar to polarization1: the computed damping seems to converge toward a value around 8.1 s. Again, the computed damping time is significantly larger than the measured one. It is worth noticing that the damping time is larger for polarization 2 than for polarization 1. This phenomenon is quite easy to explain, since polarization 2 is associated to the largest radius.
Mesh curvature
So far, the geometry has been meshed with 3rd-order mesh elements. Let us now analyze the impact of the mesh curvature on the simulations. To do so, only polarization1 is considered for simplicity. Moreover, we limit ourselves to FE discretizations of order 4. As done previously, the geometry is meshed with a density of tetrahedra varying between 3 and 7 mesh elements per wavelength. However, this time, the geometrical order of the elements ranges between 1 and 4. Figure 8 shows the computed frequencies and damping times.
By analyzing the data of figure 8, we can directly notice that the damping time does not converge with 1storder mesh elements. On the other hand, there is no significant difference between simulations using high-order meshes. Obviously, straight mesh elements fail to compute the cavity damping time. Since the shape of the mirrors is curved, approximating it with 1st-order elements introduces some kind of numerical roughness on its surface. This roughness does not significantly impact the resonance frequency. However, it can lead to unwanted scattering, destroying the stability of the wave. This problem has been noticed in the previous attempt to simulate the photon cavity [6]. A last question remains: can the lack of curvature of the 1st-order mesh elements be compensated by a better mesh refinement of the mirrors? To answer this question, let us setup the following simulations. A mesh with 5 tetrahedra per wavelength is used everywhere in the computational domain, except on the surface of the mirror, where refinements of 5, 10 and 20 elements per wavelength are used. The geometrical order of the mesh ranges between 1 and 4, and a 4th-order FE discretization is used for the computations. Let us note that only polarization1 is considered. The computed damping times are reported in figure 9.
Based on the results of figure 9, we can directly notice that increasing the mesh density on the surface of the mirror does not help to achieve convergence for the damping time, at least when straight mesh elements are used. Thus, we can conclude that the damping time is highly sensitive to the numerical roughness introduced by the mesh. Therefore, using curved mesh elements is mandatory to simulate the cavity in order to avoid this virtual roughness.
Sensitivity of the solution with respect to the PML
Let us now study the sensitivity of the computed solution with respect to the parameters of the PML: its distance from the mirror and its thickness. For this analysis, the following setup is used: • a tetrahedral mesh of order 4, with a density of 5 mesh elements per wavelength; • a FE discretization of order 4; • a PML thickness ranging from 0.25λ to 2λ; • two distances between the mirror and the PML, 1λ and 2λ.
The computed damping times are shown in figure 10. The mean resonance frequency and the maximum deviation from this mean are given in table 3. Let us start by analyzing the results presented in table 3. Based on the available data, we can conclude that the resonance frequency does not depend on the PML parameters. On the contrary, figure 10 indicates that the damping time is very sensitive to these parameters. Therefore, we cannot conclude that the damping time converged with respect to the PML-to-mirror distance and the PML thickness, since the behavior is too oscillatory. However, the variations of the damping time seem to remain bounded, which indicates that, even though a larger PML (in term of PML-to-mirror distance and thickness) is preferred, the cavity damping lies in the 5.4 s range.
To conclude this subsection, it is also worth mentioning that two additional numerical experiments were carried out. First, in addition to the boundary condition given in section 3.3 for the PML boundary, we also imposed: Secondly, in addition to the PML equivalent materials given in section 3.4, we also tested the following constant PML parameter: In both cases, the same conclusions were drawn. Furthermore, our findings are also supported by additional PML convergence results presented in section 6 for a two-dimensional setup. There, the numerical convergence of the PML is clearly observed, and it is shown that a PML-to-mirror distance of 1λ, as well as a PML thickness of 1λ, already give numerically sharp results.
Simulation time
To conclude the analysis of our three-dimensional high-order computations, let us give some order of magnitude about the wall clock time taken by the simulations. The smallest simulation (3 mesh elements per wavelength with a 3rd-order FE discretization) counted 517556 unknowns and took less than 1 minute. It was run using 5 computing nodes. On the other hand, the largest simulation (7 mesh elements per wavelength with a 4th-order FE discretization) counted 11443760 unknowns and took less than 11 hours. It was run using 120 computing nodes.
Memory scaling
In order to increase the accuracy on the damping time of the previous computations, a higher mesh resolution, FE discretization order and/or PML size are needed. However, for now and with the available computational resources, it is not possible to increase the problem size, since the memory scaling limit of the MUMPS solver seems to be reached. It is worth noticing that the memory scaling problem is not specific to the MUMPS implementation, but affects the entire family of direct solvers. Another approach would be to use instead a preconditioned iterative method. However, this technique is known to perform poorly for wave problems, at least with classical preconditioners [42]. The design of good preconditioners for wave problems [43,44] and of memory efficient direct solvers [45] remains an active field of research.
In the following of this section, two examples are discussed to illustrate the memory scaling performance.
Two fifth-order test cases
Let us look at the two simulations hereafter: • FE discretization of order 5; • mesh curvature of order 5; • two mesh densities, 5 and 6 mesh elements per wavelength; • polarization1.
These two simulations led to, respectively, 8019588 and 13363722 unknowns. The test cases were launched on 120 computing nodes, with 64 GB of memory available on each node. The smallest simulation ran successfully, whereas the largest simulation failed because of a memory deficiency during the LU factorization stage. This latter case was run again with 240 nodes but failed for the same reason. Let us now look at the peak virtual memory allocated by each process for the problem with 8019588 unknowns, as shown in figure 11. Statistics are available in table 4. From these data, we can see that the memory usage is not uniformly distributed across the computing processes. On average, we use 17 GB with a quite low standard deviation. However, we have two spikes above 25.5 GB (i.e. 50% above the mean). It is those spikes that limit the memory scaling of our simulations.
Two fourth-order test cases
Let us take another example: • FE discretization of order 4; • tetrahedral mesh of order 4, with a density of 7 mesh elements per wavelength; • polarization1.
We ran this setup (11443760 unknowns) successfully on 120 and 240 computing nodes. The peak virtual memory distribution is available in figure 12, and statistics are available in table 5. From the above results, we have once again some memory spikes far above the mean value. Let us focus only on the two largest spikes: 46 GB (240 nodes) and 61 GB (120 nodes). We can directly notice that by increasing by 100% the total available memory, the largest spike is decreased by only 25%, thus limiting the scaling performance.
Further analysis with a similar two-dimensional model
As we saw in the previous sections, the memory scaling is the main computational bottleneck of our simulations. In order to push our analysis of the photon cavity further, we built a two-dimensional model. Since the mirrors have different curvature radii, our cavity is inherently a three-dimensional structure, and thus cannot be described in two-dimensions. One of the closest two-dimensional counterparts are infinitely long cylindrical mirrors. Note that this is still an open structure and the very same numerical convergence challenges are expected. Therefore, we consider in this section a similar, but not equivalent, model. An alternative model would be to consider two spherical mirrors with a two-dimensional axisymmetric approach. However, this strategy does not exhibit any additional feature in term of open cavity resonances. Furthermore, the three-dimensional spherical mirrors exhibit a degenerated mode, which is not the case with the infinitely long cylindrical version.
The structure studied hereafter consists of two cylindrical mirrors in the Oxz-plane, that extend to infinity along the y axis. The mirrors have a radius of 40.6 mm (the major radius of the three-dimensional cavity). By applying symmetries, in analogy to the three-dimensional numerical setup, our two-dimensional model consists of only one half of a single mirror. Again, PMLs are used to model the infinite domain, as depicted in figure 13. Finally, let us mention that except from the changes mentioned above, the numerical parameters of the threedimensional cases are reused in the two-dimensional simulations.
6.1. Numerical convergence of the damping time Since our two-dimensional model exhibits fewer unknowns, let us first use larger mesh densities compared to the three-dimensional case, in order to assess the convergence of the damping time. From our previous analysis, we found that 2nd-order mesh elements were sufficient to represent the geometry precisely. Thus only this kind of element is used. The mesh density varies between 5 and 40 mesh elements per wavelength. For the FE discretization, 3rd-, 4th-and 5th-order FE bases are considered. The PML is located at one targeted wavelength of the structure, and its thickness is set to one wavelength. The computed resonance frequencies and damping times are reported in figure 14.
This figure indicates that the computed resonance frequencies are monotonously converging to 49.9804 MHz for increasing mesh densities and FE discretization orders. Regarding the computed damping times, the calculated results are also monotonously converging to 7.2 s. This value is below the 8.1 s found for the three-dimensional polarization 2 case. However, let us recall that this two-dimensional case is modeling a similar, but not equivalent, situation. Furthermore, it is worth mentioning that already with 5 mesh elements per wavelength, with a 4th-or a 5th-order FE discretization, numerically valid damping times are computed. This observation agrees with the analysis performed for the three-dimensional case, and is an additional indicator that the results presented in the sections 4.1 and 4.2 are numerically valid. Finally, it is worth noticing that for both two-and three-dimensional situations, the computed damping time is well above the 130 ms found experimentally. This comforts us in our assumption that the discrepancy between the simulations and the experimental data has to be attributed to our idealizations, rather than in numerical convergence problems.
Sensitivity of the solution with respect to the PML
Let us now analyze the sensitivity of the results with respect to a variation of the PML thickness and position. In this numerical experiment, the following parameters are used: a mesh density of 5 mesh elements per wavelength, 4th-order mesh elements and a 5th-order FE discretization. Based on the previous analysis, we know that these parameters are sufficiently accurate. In this numerical experiment, both the PML thickness and position (with respect to the mirror) are taken equal and in the l l l l l l { } 1 , 2 , 4 , 8 , 16 , 32 set. This parameter sweep leads to the results presented in figure 15 and table 6.
Based on these data, we can conclude that both the computed resonance frequencies and the damping times are not significantly impacted by a change of the PML parameter. It is however interesting to notice that, as expected, the damping time is more sensitive to a PML variation as compared to the resonance frequency. Again, the numerical stability of the results obtained for this two-dimensional case, with a large PML parameter sweep, comforts us that our three-dimensional simulations are correct. In particular, we can directly notice that numerically valid results can be obtained with a PML-to-mirror distance, as well as a PML thickness, of 1λ.
Comparison with a first-order finite element simulation
For this numerical experiment, we compared a 1st-order FE method with our high-order simulations. Figure 16 depicts the computed frequencies and damping times for a mesh density ranging from 5 to 320 straight mesh elements per wavelength. As expected (based on our three-dimensional analysis), the virtual roughness introduced by the straight mesh significantly impacts the numerical results. Indeed, we need at least 160 mesh elements per wavelength to reach a value close to the expected value of 7.2 s.
It is worth noticing that the largest simulation setup leads to 20363036 unknowns, corresponding to a linear system with twice the size of the largest three-dimensional case. Nevertheless, this simulation does not suffer the same memory limitations. This phenomenon is easily explained by the better non-zero structure of the matrices of the two-dimensional computations, resulting in a lower fill-in.
Simulation time
In this section, let us compare the computation time taken by different mesh densities and FE discretization orders. The results are summarized in table 7. As can be noticed directly, the computation time can be reduced by increasing the FE discretization order and decreasing the mesh density at the same time (while keeping the accuracy constant). This leads to a reduction of the number of unknowns, and thus a decrease of the computation time. Figure 15. Two-dimensional resonance frequencies and damping times for a sweep of the PML parameters (both thickness and position are taken equal): 5 mesh elements per wavelength, 4th-order mesh and a 5th-order FE discretization. Table 6. Two-dimensional resonance frequencies and damping times for a sweep of the PML parameters (both thickness and position are taken equal): 5 mesh elements per wavelength, 4th-order mesh and a 5th-order FE discretization.
Moment
Resonance Figure 16. Two-dimensional resonance frequencies and damping times with a 1st-order FE method on straight meshes.
Other modes
For this last part of our two-dimensional simulations, we computed the resonance frequency and the associated damping time for the other 'trapping' modes of the cavity. Based on our previous convergence analysis, we chose to use a 5th-order FE discretization. The mesh exhibits a density of 10 mesh elements per targeted wavelength and a 2nd-order curvature. It is worth stressing that, since the resonance frequencies are different for each mode, the meshes are also different. This is also the case for the actual length of the PML and its distance to the mirror. Let us also note that because of the symmetry conditions, only the odd modes were computed. By analyzing the results displayed in figure 17, we can directly notice the linear dependence of the resonance frequency on the mode number. This can be also observed for the damping time in a logarithmic scale, with the notable exception of the transition between the 7th and the 9th modes, where the slope suddenly decreases. It is worth noticing that, after a deeper investigation, this phenomenon does not seem to come from a numerical problem. Finally, let us recall that in our simulations, the surface resistivity of the superconducting mirrors was neglected. However, this parameter is expected to limit the damping time increase with the mode number, since it grows with the frequency [41].
Conclusion
In this paper, we simulated the photon cavity designed by Serge Haroche and his coworkers, for recording the birth and death of a photon, by using the classical electromagnetic theory, PMLs, and the finite element method. This problem has already been treated in the literature with straight tetrahedral meshes and a second-order finite element discretization. Unfortunately, the authors were not able to compute the damping time, because of its high sensitivity with respect to the mesh refinement.
In this work, we improved the computations substantially, by using curved mesh elements combined with finite element discretizations of high orders. We demonstrated that they are mandatory for tackling the computation of the damping time of the photon cavity, since they alleviate both the virtual roughness introduced by the mesh and the pollution effect impacting time-harmonic wave problems. We also showed that computing the damping time of the cavity is computationally demanding, and pushes the direct solvers and modern computing facilities to their limits. Nevertheless, a satisfactory convergence study was performed in two steps. First, the convergence of the damping time has been established on the basis of a few points in a threedimensional setup. Then, a two-dimensional model, exhibiting the same behavior as its three-dimensional counterpart, has been studied. By enabling finer discretizations, this additional analysis consolidated the numerical validity of the three-dimensional model. Furthermore, thanks to the two-dimensional model, we showed that a classical first-order finite element approach requires at least 160 mesh elements per targeted wavelength in order to reach a sufficient accuracy, whereas a fifth-order discretization gives the same accuracy with only 5 second-order mesh elements per wavelength.
The computed damping times, with either a three-or a two-dimensional approach, are significantly higher than the one found experimentally: the simulations suggests a damping time of about 5.6 s or 8.1 s, depending on the polarization, whereas the experiment shows a damping time in the 0.1 s range. This discrepancy is explained by the simplifications made in our model: we indeed focused only on the losses introduced by the open nature of the cavity. Among these idealizations, (i) we considered perfectly aligned and exactly toroidal mirrors; (ii) we assumed that the two mirrors are floating alone in the void; (iii) we neglected the residual resistivity of the superconducting material; (iv) we did not consider the surface roughness. It is worth noticing that these issues can be alleviated, e.g. by technological improvements in manufacturing and material science. On the other hand, the open nature of the cavity is intrinsic to the device. | 8,369.2 | 2018-04-27T00:00:00.000 | [
"Physics"
] |
Mucosal Tuft Cell Density Is Increased in Diarrhea-Predominant Irritable Bowel Syndrome Colonic Biopsies
Tuft cells are rare chemosensory sentinels found in the gut epithelium. When triggered by helminth infection, tuft cells secrete interleukin-25 (IL-25) basolaterally and subsequently evoke an immune response. Irritable bowel syndrome (IBS) is a common and heterogeneous disorder characterized by bowel dysfunction and visceral pain sensitivity. Dysfunctional gut-brain communication and immune activation contribute to the pathophysiology of this disorder. The study aims were to investigate changes in tuft cell density in non-post-infectious IBS patients. Immunofluorescent labeling of DCLK1-positive tuft cells was carried out in mucosal biopsies from the distal colons of diarrhea and constipation-predominant IBS patients and healthy controls. Tuft cell numbers were also assessed in animal models. Concentrations of interleukin-25 (IL-25) secreted from colonic biopsies and in plasma samples were analyzed using an immunoassay. The density of tuft cells was increased in diarrhea—but not constipation-predominant IBS patient colonic biopsies. Biopsy secretions and plasma concentrations of IL-25 were elevated in diarrhea—but not constipation-predominant IBS participants. Tuft cell hyperplasia was detected in a rat model of IBS but not in mice exposed to chronic stress. Tuft cell hyperplasia is an innate immune response to helminth exposure. However, the patients with diarrhea-predominant IBS have not reported any incidents of enteric infection. Moreover, rats exhibiting IBS-like symptoms displayed increased tuft cell density but were not exposed to helminths. Our findings suggest that factors other than helminth exposure or chronic stress lead to tuft cell hyperplasia in IBS colonic biopsies.
INTRODUCTION
Tuft cells are rare differentiated epithelial cells, anatomically and functionally distinct from other border cells in the gastrointestinal (GI) tract (1). Characterized by long, blunt microvilli, pear-shaped tuft cells are scattered along the crypt-villus axis (2). Uniquely, they express a microtubule linked protein known as Doublecortin Linked Kinase-1 (3) (DCLK1, also known as DCAMK1 (4)] and contain axial bundles of actin filaments supporting the microvilli (5,6). The chemosensory activity and intimate physical contact between tuft cells and enteric nerves (7,8) suggests a role in regulating gut motility and absorpto-secretory function. Tuft cells could also act as cross-epithelial signal transducers (8), informing the host nervous system of changes in the luminal environment. Parasitic infections, in particular (9), uniquely stimulate release of immune cytokines, such as interleukin (IL)-25 (also known as IL-17E), from tuft cells (10)(11)(12). IL-25, in turn, induces secretion of IL-13 from stromal group 2 innate lymphoid cells (ILC2), which promote release of IgE, eosinophilia, goblet cell hyperplasia (13) and, in a feed forward circuit, tuft cell hyperplasia (14).
Irritable bowel syndrome (IBS), a prevalent, chronic and heterogeneous functional bowel disorder, is characterized by abdominal pain, bloating and altered bowel motility (15). Prevalence of IBS is~7-18% of the worldwide population (16), and this includes a subset referred to as post-infectious IBS (PI-IBS) patients, who develop intestinal dysfunction following infectious enteritis (17). Indeed, prior GI infection is a strong predictor of developing IBS (18), with one in ten patients believing their IBS symptoms emerged subsequent to an infectious illness (17). Infection with protozoans as opposed to bacteria conferred a greater risk of developing IBS following resolution of the infection (19).
Although it is plausible that tuft cell numbers could be elevated in patients with PI-IBS, the majority of IBS patients do not report prior GI infection. Rather, a significant proportion of these patients, who may be sub-categorized with diarrhea (IBS-D), constipation (IBS-C) or alternating subtypes of IBS, experience co-morbid anxiety and depressive disorders (20). Thus, it is generally accepted that dysfunction of the bidirectional gut-brain axis underlies symptoms in these patient groups. This study aims to quantify expression of tuft cells in colonic samples from IBS patients who have not, to their knowledge, had prior intestinal enteritis. Tuft cell density was assessed in non-PI IBS patients, in a stress-sensitive rat model of IBS and in mice exposed to a chronic stressor to determine if stimuli other than exposure to parasites contributes to IBS pathophysiology.
Ethical Approval
The protocol for collecting biopsies and blood samples from IBS patients and healthy control volunteers was approved by the University College Cork Clinical Research Ethics Committee (ECM 4 (r) 010316) and was carried out in the Mater Private Hospital, Cork. Informed consent was obtained from all participants.
Experiments using animal tissue were all in full accordance with the principles of the European Community Council Directive (86/609/EEC) as well as the local University College Cork animal ethical committee (#2011/015).
Human Colon Biopsy and Plasma Collection
Patients attending the General Surgery Clinic at the Mater Private Hospital, Cork, Ireland were recruited for the study. Males and females aged between 18 and 65 years of age and able to provide written informed consent were enrolled. Inclusion criteria for IBS patients included confirmed clinical diagnosis of IBS that satisfied Rome III criteria for IBS. No PI-IBS patients were included in this study. Biopsies from age and weight-matched healthy controls were taken from patients undergoing routine colonoscopies that were in good health and negative for bowel disease. Exclusion criteria for participation included acute or chronic co-existing illness, recent unexplained bleeding or prior GI surgery (apart from hernia repair and appendectomy), coeliac or other GI disease, psychiatric disease, immunodeficiency, bleeding disorder, coagulopathy, a malignant disease or any concomitant end-stage organ disease. Subjects were also excluded if they were taking any experimental drugs or if the subject had taken part in an experimental trial less than 30 days prior to this study. Mucosal biopsies from the distal colon were taken from fasting patients at the same time as obtaining a matched serum sample. Samples were assigned a study number, with the key held only by the treating surgeon, so as to preserve patient confidentiality in accordance with the study protocol. The secretory products from biopsies incubated in Dubellco's Modified Eagle Medium (Sigma Aldrich, UK, overnight, 37°C) were used to measure local tissue concentration of interleukin-25 (IL-25)/hu-17E. Mucosal biopsies were subsequently fixed overnight in 4% paraformaldehyde at 4°C, cryoprotected in 30% sucrose and stored at −80°C for immunofluorescent staining.
Animals and Tissue Collecting
Male Sprague Dawley (SD) and Wistar Kyoto (WKY) rats, > 8 weeks of age, were purchased from Envigo, Derbyshire, UK. Given that hormonal cycles in the female are associated with exacerbation of IBS-like symptoms, we used male rodents in this study such that the additional complexity of changing female hormone levels was not a factor in the studies. The Animals were group-housed four per cage and maintained on a 12/12-hour dark-light cycle with a room temperature of 22 ± 1°C with food and water ad libitum. Rats were euthanized by CO 2 overdose and perforation of the diaphragm.
Male adult mice (C57Bl/6J, The Jackson Laboratory, Maine, US) were bred in-house (Biological Service Unit, University College Cork, Ireland). Prior to social defeat sessions (~1 week) mice were singly housed. Singly-housed adult male CD1 mice (Envigo, UK) were used as aggressors for the chronic social defeat stress procedure. Mice were maintained on a 12/12-hour darklight cycle with a room temperature of 22 ± 1°C with food and water ad libitum. Mice were sacrificed by cervical decapitation.
Chronic social defeat stress in these mice has been previously described (21). In brief, mice assigned to the chronic social defeat stress group underwent 10 consecutive days of stress. The same researcher carried out all interventions. All defeat sessions were carried out in the mornings during the light cycle. CD1 aggressor mice were selected based on the shortest latency to attack another CD1 mouse. Test mice were subjected to a different CD1 aggressor mouse each day over the study period. Exposure of the test mouse to the aggressive CD1 mouse lasted until the first attack, expression of submissive posturing or until 5 min had passed, whichever happened first. The test and CD1 aggressor mice were then separated by a perforated transparent barrier for 2 h. The separator was subsequently removed and, after another defeat, mice were transferred back to their home-cage. Control mice were handled but remained in their home-cages over the course of the stress.
Mesoscale Discovery Biomarker Assay
An immunoassay (U-PLEX Human IL-17E/IL-25 Assay, MesoScale Discovery, Gaithersburg, MD, USA) was carried out to determine the concentration of IL-17E/IL-25 in plasma and supernatant samples of IBS patients and healthy control samples (dynamic range: 0.58-9,200 pg/ml). The assay was run in triplicate and an electrochemiluminescent detection method was used to measure protein levels in the samples. The plates were read using MesoScale Discovery plate-reader (MESO QuickPlex SQ 120). A calibration curve was generated using standards, and cytokine concentrations were determined from the curve.
Immunofluorescence and Confocal Microscopy
Cross-sections of rat and mouse distal colon and human distal colonic biopsies, fixed in 4% paraformaldehyde (4°C, overnight), were cryo-sectioned (10 µm in thickness, Leica Biosystems, Wetzler, Germany) and mounted on glass slides (VWR, Dublin 15, Ireland). Rodent cross-sections or human mucosal biopsies were permeabilized with 0.1% Triton X-100 and blocked with 1% donkey serum (Sigma Aldrich, UK). Colonic tissue was immunolabeled with anti-DCLK1 (1:100, overnight at 4°C, anti-DCAMKL1 polyclonal rabbit antibody, Abcam, Cambridge, UK) and a complimentary TRITC-conjugated fluorophore (1:250, 2 h at room temperature, Jackson ImmunoResearch Europe Ltd., Cambridgeshire, UK). This primary antibody recognizes a protein of the predicted size and is blocked by using a DCAMKL1 peptide (22). No non-specific fluorescence was detected in control experiments where tissues were incubated with anti-DCLK1 in the absence of secondary antibodies or secondary antibodies alone. As tuft cells have a unique arrangement of cytoskeletal components, colonic samples were co-stained with a cytoskeletal marker, Phalloidin-iFluor 488-Cytopainter (1:1,000, Abcam, Cambridge, UK), which was prepared in 1% bovine serum albumin in phosphate buffered saline solution (PBS, (in mM): NaCl 137, KCl 2.7 and Na 2 HPO 4 10 at pH 7.4). Tissue sections were mounted using Dakofluorescent mounting medium containing DAPI (Agilent Pathology Solutions Santa Clara, California, USA) and a coverslip placed over all tissue. Images were captured using a FVl0i-Olympus-confocal microscope with Fluoview software (FV10i-SW, Olympus Europe, Hamburg, Germany). At least three different biopsy slices from six different participants per group were compared in the human study. In the animal studies, at least three different cross-section slices from three different animals per group were compared. Analysis was carried out independently by two different researchers and the mean number of cells from each was calculated.
Statistical Analyses
Data was analyzed using GraphPad prism for windows (version 7). Data were plotted as box and whisker plots with 95% confidence intervals. Data were compared using paired twotailed Student's tests or One-way or repeated measures ANOVA with Tukey post-hoc test, as appropriate. P values of <0.05 were considered significant.
Tuft Cell Density Is Elevated in IBS-D Patient Biopsies
Samples from healthy controls (HC, n = 6 (three males, three females)) were compared with samples from diarrheapredominant (IBS-D, n = 6 (one male, five females)) and constipation-predominant (IBS-C, n = 6, (two males, four females)) participants. HC and patient participants were similar in terms of ethnicity (all Caucasian), age-(44.7 ± 4.56 (HCs) versus 40 ± 3.91 (IBS) years, p >0.05) and weight-(72.9 ± 13.95 (HCs) versus 71.83 ± 10.97 (IBS) kg, p >0.05). Gastrointestinal symptoms, such as bloating, abdominal pain and altered bowel habit were consistent with their categorization into the appropriate IBS subtype, as determined by Rome III criteria for diagnosing IBS. Mood disorders were reported in one IBS-D (depression), two IBS-C (depression and/or anxiety) but no HC participants.
Triple-labeling of human colonic biopsies with an antibody against the gastrointestinal tuft cell marker, doublecortin-like kinase 1 protein (DCLK1, red staining) (23), a cytoskeletal marker (green staining) and the nuclear stain, DAPI, facilitated counting of tuft cells as a percentage of total DAPI-labeled epithelial cells in the visual field. The total number of DAPIlabeled cells in biopsies (n = 5 sections from five biopsies) from HCs (476.7 ± 83.3), IBS-D (383.1 ± 17.47) and IBS-C (447.4 ± 60.23) were comparable (p = 0.31, one-way ANOVA F(2, 12) = 1.293). Labeled tuft cells in human biopsies displayed classic pear-shaped morphology (2) with a large central nucleus and strong Phalloidin-labeled cytoskeletal filaments ( Figure 1A). The density of tuft cells in IBS-C biopsies (n = 18 sections from six biopsies) was not different to HC biopsies (p >0.05, n = 18 sections from six biopsies, Figure 1A). However, the prevalence of tuft cells in IBS-D biopsies (n = 18 sections from six biopsies) was elevated as compared to HC samples (p <0.05, Figure 1A).
Circulating Concentrations of IL-6 and IL-8 Are Altered in IBS Patients
Other inflammatory cytokines, such as IL-6 and IL-8 are reported to be elevated in IBS patients (24,25). Thus, to confirm the findings from the previous studies, IL-6 was initially compared between plasma from HCs and pooled samples from both IBS-D and IBS-C. We found that circulating IL-6 was elevated in IBS patients (0.976 ± 0.17 pg ml −1 ) as compared to HCs (0.398 ± 0.15 pg ml −1 , p = 0.06, Student's t-test). When examined by subtype, circulating IL-6 was elevated in IBS-D (1.343 ± 0.35 pg ml −1 , p = 0.04)) but not IBS-C
Colonic Tuft Cell Density Is Elevated in Stress-Sensitive Wistar Kyoto Rats
Immunofluorescence and confocal microscopy were used to determine the presence and prevalence of tuft cells in the colons of IBS-like Wistar Kyoto (WKY) rats as compared to Sprague Dawley (SD) controls. Triple-labeling with DAPI, anti-DCLK1 (red staining) and a cytoskeletal marker (green labeling) was carried out on colonic cross-sections from SD and WKY rats to determine the density of tuft cells in each rat strain. DCLK1labeled tuft cells were readily identifiable in cross-sections of both SD and WKY colons ( Figure 2, red staining, tuft cells indicated by arrows). However, in contrast to tuft cells in human colonic mucosa, rat DCLK1-labeled tuft cells did not strongly express phalloidin-labeled cytoskeletal proteins. They did however, exhibit similar flask shaped morphology ( Figure 2). The overall number of DAPI-labeled cells was comparable between SD (197.7 ± 49.3, n = 3) and WKY (219.3 ± 22.7, n = 3, p >0.05, Student's t-test) rats. However, the number of tuft cells in WKY rats (n = nine slices from three rats) was increased as compared to SD controls (n = nine slices from three rats; p <0.05, Student's t-test, Figure 2).
Tuft Cell Density Does Not Change in Response to Chronic Stress
As sensitivity to stress is a key trait of both WKY rats (26)(27)(28) and human IBS (29), we investigated if chronic stress alone impacted on numbers of tuft cells. Colons from male C57/BL6J control mice were compared to mice which had endured 10 consecutive days of chronic social defeat stress (21). The overall number of DAPI-stained epithelial cells in non-stressed control C57/BL6J mice (452.8 ± 109.6, n = 4) was not different to stressed mice (402.5 ± 94.63, n = 4, p >0.05, Student's t-test). DCLK1labeled (red staining, tuft cells indicated by arrows, Figure 3) tuft cells were evident in the colonic mucosa of these mice, but similar to the rat tissue, strong actin labeling was not evident. The density of mucosal tuft cells did not differ between stressed C57/BL6J mice and their non-stressed comparators (n = 15 slices from five mice, p >0.05, Student's t-test, Figure 3).
DISCUSSION
Tuft cells have been proposed as chemosensory sentinels important in the host response to exposure to common eukaryotes, such as helminths and protists (11). Although not well elucidated, mechanisms involving basolateral release of immune or neuromodulatory factors from these cells may result in modulation of gut function (9) through interaction with enteric neural plexi (7,8). We have examined tuft cell density in colonic mucosal biopsies from patients with IBS, diagnosed in the absence of previous known enteric infection. Increased density of tuft cells was detected only in diarrheapredominant IBS biopsies. Thus, tuft cell hyperplasia may represent a potential biomarker for this subtype of IBS. The intestinal profile of IBS patients exhibits lower bacterial diversity that healthy individuals (30,31). Moreover, transfer of faecal microbiota from IBS-D patients is sufficient to evoke changes in gut function, low-grade inflammation and the expression of anxiety-like behaviors in germ-free mice (32). However, studies focussed only on bacteria cannot explain the heterogeneity of IBS symptomology (33,34). Given that the human microbiome includes many other non-bacterial microorganisms such as viruses, fungi, archaea and protozoans; other luminal residents have the potential to contribute to the pathophysiology of this functional bowel disorder. Indeed, the mycobiome differs in IBS patients (35) and viral infection has been linked to increased risk of developing IBS (36). The prevalence of protozoans is also increased in IBS patients (37) with some, such as Dientamoeba fragilis (38) and Giardia intestinalis (39) actually inducing IBS-like symptoms such as abdominal pain and looseness of stools. Chemosensory activation of tuft cells, which are in close proximity to the neuronal plexi that regulate gut function (7,8), could therefore potentially contribute to IBS symptom manifestation.
Immunofluorescent labeling of tuft cells in mucosal biopsies revealed rare DCLK1-expressing cells which displayed classic pear-shaped morphology (2) and a strong cytoskeletal component. Similar to other studies (1), we found that these tuft cells made up less than 0.4% of DAPI-labeled epithelial cells in control subjects. Biopsies from the distal colon of patients with IBS-C had a similar prevalence of tuft cells to healthy study participants, however, in the absence of any change in total epithelial cell number, IBS-D patients exhibited tuft cell hyperplasia. Although an active helminth infection can induce more than ten-fold increase in tuft cell numbers in the upper intestine (12), our more modest results (< 2 fold) are present in the absence of any documented history of enteric infection.
Helminths and protists evoke a type 2 innate immune response, which is characterized by secretion of ILC2 cytokines. In particular, IL-25, which, in the intestine, is uniquely secreted by tuft cells, is a key signalling molecule secreted in responses to helminth infections (40,41). IL-25 subsequently stimulates ILC2 to secrete IL-5, IL-9 and IL-13. IL-13 promotes goblet cell hyperplasia and in a feed-forward cycle, tuft cell hyperplasia. Increased goblet cell activity and mucus secretion has been reported in IBS patients (42) and we now provide evidence of tuft cell hyperplasia in IBS-D colonic mucosal samples.
Interestingly, in one study, biopsy-secreted IL-13 was decreased as compared to controls in PI-IBS patients, who had a history of acute gastroenteritis with diarrhea and/or vomiting, (43), although in contrasting results, stimulated lymphocytes from IBS patients secreted more IL-13 as compared to controls, leading the authors to conclude that exposure to bacterial products led to a shift from a Th1 to a Th2 type of cytokine production (44). Our study has detected increased epithelial tuft cell numbers in IBS-D colonic biopsies. Concentrations of local and circulating IL-25 are also elevated in IBS-D samples, which could be related to tuft cell hyperplasia, although no statistical correlation was detected. However, small sample sizes of each IBS subtype could underlie this finding, which is a recognized limitation of the study. Overall, plasma concentrations of IL-25 were notably higher than local secretions, which likely reflects cumulative tuft cell secretion throughout the gut.
We have previously reported changes in cytokine profiles in IBS patients from this geographical region (24,25), with elevated concentrations of IL-6 and IL-8 in pooled plasma samples from all IBS subtypes. We were able to reproduce these findings in pooled samples, however, subtype-specific analysis determined that IL-6 was only significantly increased in IBS-D subtypes. In contrast, plasma concentrations of IL-8, was elevated only in IBS-C samples. No differences in local concentrations of IL-6 or IL-8 were detected in secretions from colonic biopsies and indeed, there was no statistical correlation between tuft cell density and concentrations of these cytokines. IL-6 and IL-8 both have neurostimulatory actions in the enteric nervous system and also modify gut function (27,45,46). While tuft cells have been linked with enteric neuronal function (7,8), and IL-25 receptor immune-reactivity has been detected in central neurons (47), further studies are needed to explore if this cytokine can modify activity in enteric neurons or gut function. Indeed, if this is found to be the case, it could be through indirect mechanisms, such as through stimulation of mucosal mast cells (48) or other immune cells (10,11,49) which are activated by IL-25.
Validated animal models of IBS have been very useful in understanding the pathophysiological changes underlying bowel dysfunction. One such model is the WKY rat, which exhibits visceral hypersensitivity, raised corticosterone in response to a challenge (50) and increased stress-induced defecation (26,27). Moreover, WKY rats exhibit altered colonic morphology including elevated levels of mucus-secreting goblet cells (26). We determined that distal colonic mucosal sections display DCLK1-immunostained tuft cells with a prevalence of <0.4% in control SD rats. In contrast to the human biopsies, these tuft cells did not express overly strong cytoskeletal proteins. Nonetheless, tuft cell hyperplasia was apparent in the WKY rat model of IBS. In contrast to the human study participants, who may have unknowingly been exposed to parasites resulting in altered bowel function and changes to mucosal cells, the controlled environment in which laboratory animals are maintained, allows us to say with confidence that these animals have not been exposed to helminths or protists. Thus, some other factor may contribute to the increase in tuft cell numbers in WKY rats.
It is generally accepted that psychological stressors are complicit in the onset (51), exacerbation and prolongation of IBS symptoms (52,53). Stressors can also modify gut morphology and permeability (54). Sensitivity to stress is a key trait in WKY rats, but modified cytokine profiles indicate that immune activation (55), among other factors, also contribute to the overall phenotype. Two groups of C57/BL6J mice, reared under controlled conditions and protected from helminth exposure, were compared to explore if stress alone modifies expression of epithelial tuft cells. A control, non-stressed group was compared to mice which were susceptible to the stress associated with ten consecutive days of chronic social defeat stress. A previously published study using these mice demonstrated that susceptible mice exhibited elevated levels of corticosterone and adrenal gland weight, reflecting dysregulation of the hypothalamic-pituitary-adrenal axis (21). Stressed mice did not exhibit changes in the numbers of colonic epithelial tuft cells, suggesting that activation of the stress axis per se does not lead to tuft cell hyperplasia. However, as these mice did display some changes in innate immunity (21), the chronic stressor clearly impacts other systems apart from the stress response.
These studies have determined that tuft cell hyperplasia is evident in patients with IBS-D with no history of enteric infection. A parallel increase in secreted and circulating IL-25 was also observed. Although no statistical correlation was detected between tuft cell density and IL-25 concentrations, this may be detected with a larger sample size. Tuft cell hyperplasia was replicated in a rat model of IBS, which was not exposed to microbes such as helminths or protists. Activation of the stress response, which is central to symptom manifestation and prolongation in functional bowel disturbances, had no impact on tuft cell densities in mice, suggesting that stress, in of itself, does not contribute to tuft cell hyperplasia. The clinical diagnosis of IBS is hampered by the lack of specific biological biomarkers, necessitating a symptombased diagnosis following exclusion of other organic diseases. Our findings contribute to gathering evidence of subtype-specific changes in intestinal epithelial morphology in IBS patients.
DATA AVAILABILITY STATEMENT
All data for this study is included in the article/supplementary files or on request from authors.
ETHICS STATEMENT
The studies involving human participants were reviewed and approved by University College Cork Clinical Research Ethics Committee (ECM 4 (r) 010316). The patients/participants provided their written informed consent to participate in this study. The animal study was reviewed and approved by University College Cork animal ethical committee (#2011/015).
AUTHOR CONTRIBUTIONS
JA and MC performed the research and analyzed the data. JB contributed human samples. DO'M designed the research study, sourced funding, prepared and reviewed the manuscript. | 5,549.6 | 2020-05-15T00:00:00.000 | [
"Medicine",
"Biology"
] |
Test Case Prioritization For Embedded Software
Electronic devices used daily contain software, which may have errors due to human factors during coding. Testing is essential before release, especially as software complexity increases with diverse user needs. Testing new features separately and then in combination multiplies test cases. Rerunning all tests after each change is costly. The aim of this study is to develop a test case prioritization method to decrease the time to find software errors in embedded software systems. For this purpose, we extracted the basic features that characterize embedded software systems and tests that run on them. The proposed method calculates prioritization scores for test cases utilizing these characteristics. The test cases will then be arranged in a systematic manner according to their respective scores. This prioritization strategy is designed to minimize error detection time by promptly finding and resolving errors throughout the initial stages of the testing process. The proposed prioritization strategy was tested on an embedded software system, and it was evaluated using the metrics APFD (average percentage of faults detected) and APFDc (APFD with cost). The results indicate that the proposed method based on the attributes of software systems and related tests reduces the time required to find the majority of the errors.
INTRODUCTION
Embedded control systems are electronic systems designed for autonomous control, management, and monitoring of specific operations.They are usually employed in systems like cruise control, backup sensors, automotive navigation, aerospace, and defense systems.Embedded systems comprise hardware and software components, including microprocessors, sensors, input/output interfaces, and actuators.Embedded software runs on the microprocessors within these control systems, governing all connected systems.It receives sensor inputs to respond to changing environmental conditions, interpreting the data and executing desired operations, such as sending outputs to other devices or users.
Software systems typically consist of multiple functions that are not necessarily coded at the same time.While the core features are initially defined at the project's outset, there may be subsequent requests for new functions or changes to existing ones.These functions can be added incrementally, either at different times or by different software developers.Even when it is confirmed that the newly added or modified functions work correctly within the software, it is imperative to ensure that these changes do not introduce errors in other aspects of the software.This kind of testing is known as regression testing, which involves four primary methods: retesting all, test case minimization, test case selection, and test case prioritization [2].
This article presents a novel approach for prioritizing test cases for embedded software systems to detect numerous bugs in a short period of time.First process of prioritizing the test cases is extracting the general characteristics of embedded software and their associated test cases.Test cases for the given embedded software system are collected and used to create datasets containing extracted features.All analyses and assessments were performed based on these datasets.The features that can be utilized to score each test case are identified after the dataset development process is finished.In the selection of scores from extracted features for the dataset, features that are only used for description and are independent of the prioritization process, such as test name, etc. and features used for evaluation (e.g.test status, identified errors) are excluded.For the remaining features, the minimum and maximum value ranges that each feature could take are determined.Throughout the remainder of the article, these features will be called score features (SFs).Since the range of values for each SF differs, in calculating the overall test case score, each SF is individually normalized to produce scores between 0 and 1.While some of the SFs received a fixed score based on experimental findings, others were assigned by software or test engineers to assign values compatible with normalization.For those assigned features, flexibility is provided because of user knowledge about the parameters, messages, and scenarios associated with the changing software in future versions, which can directly affect changes in the software.The main idea here is that before the test cases are run, test case prioritization is done with the help of SF values through the test case scoring process.In this experimental process, the most influential score features (SFs) are identified through the conducted experiments.Then, the values that give the best results for all score features at the same time are examined to see how much they contribute to the prioritization process in all versions.The evaluation of the results employed the use of APFD (average percentage of faults detected) and APFDc (average percentage of faults detected per cost) metrics.The execution time of test cases for each test is used to calculate the test cost value required for the APFDc metric.Additionally, the severity values for all identified errors are established by test engineers.
RELATED WORKS
Askarunisa et al. [2] propose two test case prioritization methods: coverage and cost-oriented.Coverage methods include loop, statement, branch, and condition-based coverage, while cost-oriented methods rely on test case cost, test case coverage, and fault severity values.The experiment involves creating test cases for basic software, introducing faults using mutation testing, and assigning weights based on real-time test case cost and fault severity.Younghwan et al. [5] employ historical data for a two-stage test case prioritization approach.The first stage involves statistical analysis of test history to identify failure patterns for each test case.The second stage, executed during regression testing, interrupts the process upon an error, initiating the reordering of test cases based on the analyzed data.Ali et al. [14] leverage swarm optimization for test case prioritization, aiming to minimize execution time and maximize fault detection.Three datasets are utilized, and results are compared among unordered, randomly ordered, and the proposed algorithm.Zhang et al. [7] present a prioritization algorithm aiming to detect the maximum number of faults early in the testing process.The algorithm initially orders all test cases by the number of faults, then selects the test case with the highest fault count as the first in the prioritized list.Subsequent test cases are reordered based on faults found in the selected test case, eliminating those covering already identified faults.This process continues until all test case faults are covered, ensuring efficient fault detection in the early stages of testing.Thillaikarasi et al. [15] introduce an algorithm for test case prioritization based on weight factors, including time, defect, requirement, and complexity factors.The weighted prioritization value (WPV) is calculated using these factors, and a total prioritization weight (WP) is derived.Natarajan et al. [12] introduce a weighted prioritization method utilizing coverage-based techniques, including statement, function, path, branch, and fault coverage.The experiment collects information for all test cases, and weights are calculated using a formula based on coverage information.Kwon et at.[9] propose a prioritization technique that first uses the regression test selection (RTS) technique to reduce the testing time and then uses the Bloom filter, which is a fast data structure for test case prioritization (TCP).Bertolino et al. [3] propose prioritization techniques based on ML and RL algorithms.Ten different ML algorithms are used to prioritize the test cases.The algorithms used are K-NN, Random Forest, LambdaMART, MART, RankBoost, RankNet, Coordinate ASCENT, Shallow Network, Multiplayer Perceptron and Random Forest (RL-RF).Biswas et al. [4] propose four fault-based algorithms for Test Case Prioritization (TCP).The optimized version of bug detection-based TCP prioritizes test cases.If some have the same fault, it prioritizes test cases that have another fault that has been detected by prioritized test cases before.The second, HDFDC, categorizes test cases based on fault detection capability.The third, Exp-TCP, prioritizes test cases by their expected bug detection potential.The fourth, Bayesian TCP, calculates and compares the average probabilities of detecting faults for each test case, selecting those with the highest probabilities for prioritization.Ozawa et al. [13] proposed an algorithm, which is a subclass of a model-based technique named operational profile-based test (OPBT).In the requirement phase of software, some information about the software is collected for OPBT.This information is used to increase the quality of test cases.The aim of the research is to find code metrics that affect TCP.Luo et al. [10] [8]propose a weighted requirements method for test case prioritization, where weights are assigned based on customer preferences.The K-means algorithm is used to cluster test cases, and a priority percentage is calculated.The K-Medoids method then categorizes test cases into high, medium, and low priorities based on cost and priority percentage.Further division into sub-clusters is determined by time and complexity measures within the main clusters.Ali et al. [1] proposed an algorithm that uses component critically (defined with a fuzzy inference system), test case critically, and ant colony optimization.Using a fuzzy inference system, the criticality of software components is decided.Component code coverage information is used to determine the criticality of test cases.To prioritize the test cases, ant colony optimization is used with the test critically, the fault detection history, and execution time parameters.
There are numerous approaches to test-case prioritization that have been attempted in the literature.The methods mentioned are coverage [2,12], historical data [5], swarm optimization [14], bloom filter [9], machine or reinforcement learning [3], model-based [13], ant colony optimization [1], and weighted based approaches [8,12,15].The weighted-based approach is applied in this paper to test case prioritization.Features such as time factors, requirement factors (customer-assigned priority, implementation complexity, etc.), defect factors (defect occurrence and defect impact), and complexity factors (the total effort to execute one test case) are selected for weighting in the paper [15].The study [8] utilizes customer preferences to assess the weight of the test cases and the study [12] uses a coverage-based methodology.When examining the research findings that used the weighting method, it is clear that features based on time limits for test preparation or execution, errors or how they affect the software, the cost of running a single test, or user-based priorities are all used.Also, the code coverage approach or user requests were employed for certain weightings.As the software test cases are conducted as black box, it is not possible to acquire code coverage information.Therefore, the paper did not utilize the weighing procedure using the code coverage approach.This article identifies qualities that differ from those often used in other weighing articles, based on the operational principles of embedded software.The attributes encompass UsedSubsystemCount, Age, ErrorRate, and other similar characteristics.Section 4 offers a comprehensive description of every utilized function.
BACKGROUND 3.1 Testing Process
In this study, we consider automated software tests using a blackbox test design.Black-box testing does not involve any knowledge of the code; the scenarios under which the software is expected to operate are known based on the input parameters and the expected output parameters.Automated testing, preferred for continuously evolving software, allows the same test cases to be reused for efficiency.Automated tests ensure consistent verification of parameters, minimize the risk of human error, and save time.When one of the test cases is run, a system is taken through all the necessary processes from scratch until it reaches the desired state.
In the case of constantly changing software, regression tests are performed to check the current state of the software.This makes testing significantly more expensive.In this paper, a test case prioritization technique is proposed to efficiently detect the maximum errors in minimal time.By executing the test cases in the specific sequence established by the prioritization method, it is possible to identify a greater number of problems within a shorter duration.Elbaum et al. [6] have described the test case prioritization problem as follows: Problem Statement of Test Case Prioritization:Given: T, a test suite; PT, the set of permutations of T; f, a function from PT to the real numbers.Problem: Here, PT represents the set of all possible prioritizations (orderings) of T; T" and T' are some of the test cases that exist at PT; and f is a function that, applied to any such ordering, yields an award value for that ordering.The definition assumes that higher award values are preferred over the lower ones.
Embedded Control Systems
Embedded control systems are defined as systems that enable the autonomous execution of control, management, and monitoring functions in embedded systems.These systems are responsible for communicating with predefined parameters and external factors with which they can interact to fulfill predetermined functions.
Typically, these systems consist of microprocessors (controllers), sensors, actuators, input/output interfaces, and software.The working logic of an embedded control system is illustrated in Figure 1.The controller (microprocessors) receives data from sensors and processes this data using the controller algorithms embedded in its software.Based on the processed data, it makes a decision and As an example of the mechanism of embedded control systems, Figure 2 provides a representation of basic messages and flows that can be used in an automatic braking system.There are four systems in the example presented in Figure 2. One is the main software that controls the other systems (controller).It decides whether to break or not by looking at sensor data.A sensor system is used to collect data from the outside of the car.An automatic braking system is used to brake the car when some obstacles are seen by sensors.The user interface is used to view the status of the sensor and braking systems and to select the use case of the sensor or auto-brake systems.
Embedded software refers to software that is capable of executing physical actions on hardware, operates in real time, and is subject to certain memory limitations.The embedded software have the ability to interface with several subsystems.It has established precise message structures with distinct boundaries that facilitate communication amongst the subsystems that interact with it.Given the real-time functionality of embedded software, effective handling of the timing of messages in software test cases is crucial.Embedded software mostly operates via a scheduler.An interrupt operation is executed whenever another function has to be performed at any given moment, allowing the execution of the desired function.On the other hand, other software like application software does not possess such prerequisites.Typically, application software engages in action-oriented tasks.For instance, when the user activates a button on an application, the program does the necessary function.The test cases designed for embedded software are tailored to meet the specific functionalities inherent to the program and are commonly employed in the field of embedded software.These features encompass the ability to manage the operational state of the hardware or software of the interconnected subsystems through ongoing message transmission.
For example, the main software is the system that is being tested.The message flow between the sensor and the main software is shown in Figure 2. First, the sensor system periodically sends live messages to the main software.Then the sensor system sends the sensor status data.If there's no error, it sends the parameter as OK, otherwise, it sends it as Not OK.In the presence of an obstacle, the sensor sends a SensorDataMessage to the main software periodically.The main software algorithm processes the sensor data and determines the presence of an obstacle.If an obstacle is detected, it sends an AutoBrakeDataMessage (Figure2b) to the automatic braking system, causing the car to slow down or stop.
Evaluation Metrics
APFD(Average Percentage Fault Detected).This metric can be used to determine how early the errors were discovered in the TFi is the position of the first test case in all test cases T, that exposes fault i, m is the total number of faults exposed under T and n is the total number of test cases in T [6].
APFDc(Average Percentage of Faults Detected per Cost).Different than APFD, this metric also considers test case costs and fault severities.In our study, the test execution time in milliseconds has been determined to be the cost value of test cases.Additionally, the test engineer provides severity values for each fault, and these weights are assigned to each fault based on how much of an impact the fault has on the user.
Let T be a set of test cases that contains n test cases with cost t1, t2,. . . . . .., tn.F is a set of m faults inside the T, and f1,f2. . ...,fm are the severity levels of those faults.Let TFi be the first test case in an ordering T' of T that reveals fault i [11].
Figure 3 illustrates the process of matching fault severity.
To illustrate the use of APFD and APFDc metrics, an example is provided in Table 1.The system in this example consists of 5 test cases and 4 faults.The cost values for each test and severity values for each fault are also displayed.The calculations, based on the formulas provided earlier, are as follows.
PROPOSED TECHNIQUE
When a new version of a software system arrives, new test cases are added, old ones are updated, or some scenarios are removed from the test cases to be run for that version.After these processes are completed, the test cases can be prioritized to find more errors in a short time before the test cases start running.In the method proposed in this article, the test case prioritization process is repeated before each new version.Figure 4 presents the general operation of the proposed prioritization method.The details of the modules are explained in the following sections.UsedModes: This parameter shows the modes in which the message can be used.This mode belongs to the software to which the message is sent.When it comes to embedded software, it's not always desirable for certain functions to happen simultaneously with others.A few modes are defined in the software to make sure that these operations don't happen simultaneously.Although some messages are compatible with all modes, others are limited to specific modes of operation.This parameter is repeated as many times as messages can be sent in some mode.
CountOfMessageRule: This parameter shows if the message has a sending rule.For example, some messages can send only one specific message comes.This parameter can take a value of 0, indicating no rule, or a value greater than 0 to specify the number of rules.
CountOfOtherSubsystemWhichMessageSend: This parameter indicates the count of how many other subsystems receive information about a message sent from any subsystem to the main software.For instance, if Sys1 sends a message to the main software, and the main software forwards it to one or more of the other five systems, this parameter shows the count of those receiving the information.
• Important Notes: There are some rules about the dataset.1) "ErrorRate" parameters used in the first version Vt-w of the dataset, e.g., V04 are all set to 0.
2) "Subsystems" subsections parameters except for parameter "SubsystemName" are about versions of the test cases, not about the test case.The selection of some of the extracted features is driven by the messaging flow of embedded software, as depicted in Figure 2.For instance, the decision on obstacle detection relies on messages from sensors.A rule dictates that for the brakes to engage (AutoBrakeDataMessage), the sensor must send a SensorDataMessage.In case of a sensor error, a SensorUsageMessage is sent to the main software, triggering a SubsystemStatusMessage to the UI system, defining the CountOfMessageRule feature.Periodically sent messages are identified by the isPeriodic feature.Messages like SensorUsageMessage sent to other systems lead to the selection of CountOfOtherSubsystemWhichMessageSend.These features are essential for understanding the software's behavior and testing scenarios.
The Dataset
Figure 5 shows an example of a single test case of the dataset obtained using collected features.To provide a basic example of the dataset in Figure 5 the Subsystems, FaultsFoundedInThisTest-CaseFromAllFaults, and UsedModes sections have been shortened.These parts normally repeat as many times as the number of subsystems, errors, and modes in the test cases.The dataset can be accessed at the following link: https://github.com/elifgusta/TestCasePrioritizationForEmbeddedSoftware
Score Features and Calculation of Total Test Score
In the prioritization process, we assign a score to each test case using the extracted score features (SFs).The SFs were selected by considering the following properties of the collected dataset.First, the features that are not relevant to prioritization, such as Test Name, Test Version, MessageName, TotalParameterCountWhich-ContainError and Test Result are excluded.Secondly, the features that are used only in evaluation metrics, such as TestTime, and Fault-sFoundedInThisTestCaseFromAllFaults were eliminated.Finally, the remaining features that would be suitable for determining the effectiveness of the test cases were selected.These SFs are Age, UsedSubsystemCount, SubsystemName, CountOfSubsystemScenario, ErrorCountOfSubsystemScenarios, CountOfScenarioChange-Made, TotalSendMessageCount, TotalReceivedMessageCount, Receiver, Sender, IsPeriodic, CountOfParameter, CountOfListParameter, CountOfMessageRule, CountOfOtherSubsystemWhichMes-sageSend, UsedModes.In the method to be applied in the article, to perform the prioritization process before running the test cases, the determined features must be selected from the static properties of the test cases or must be determined based on data before the version under test.Since the ErrorRate and Age features do not comply with the static properties of such test cases, the data of these features were used by looking at the historical data.
Since the range of values for each SFs differs, they must be normalized prior to their use in a single equation that computes We normalized the values of each SF between 0 and 1 in two different ways, depending on their effects on the effectiveness of the test case.If a characteristic with a high value implies that the relevant test case will be more successful, the maximum value of the feature is converted to 1, while the minimum value is represented as 0. In the opposite case, where low values affect the test case positively, the minimum value of the feature is converted to 1, while the maximum value is represented as 0. Figure 6 presents two exemplary normalizations of the features Age and UsedModes.The columns on the left side under each feature represent the real values obtained from the dataset.The columns on the right side contain the corresponding normalized values.The main purpose here is to observe whether prioritizing the test cases by features selected from the dataset by giving them different scores can help shorten the time to find errors.Points are given by increasing or decreasing them in equal proportions at certain intervals only to create the difference between test cases, and the effects of the values determined here on other versions are observed.In these value assignments, attention is paid to whether the left real values side taken from the dataset of SFs were numerical or categorical data.
In the given example, Age has a numerical value, UsedModes has a categorical value.For each range of real values, particular normalized values are assigned in the context of numerical parameters.When it comes to numerical data, real data is always sorted from the smallest to the biggest value.The assignments between 0 and 1 on the right normalized data side of the SFs are set to increase in value at equal intervals according to the number of left real value sides of the SFs.In Equation 3, n is a count of score features to be used in the prioritization process, and denotes the weighted value assigned to each feature.and "pscore" is a score that is given for each SF.
Some SFs are repeated in the form of a list of as many values as are in the test case.These features are located in Subsystems, Messages, and UsedModes under Messages.Since the number of these varies for each test case, the value of test cases with a larger number of list elements was getting higher score values in their calculations.To reduce this effect, after adding up the scores of all elements in the list belonging to that one SF, the result is divided by the number of elements and taken as the result to be added to the overall score for that SF.In this article, the first contribution of SFs to test case prioritization one by one is examined, and then the effects of score features when used all at the same time are examined.One drawback of this approach is that the sorting process cannot begin until all test cases for the version being evaluated are ready.Moreover, several aspects are derived from historical data.In order to leverage the impact of those features on the sorting, it is important to own data from the prior version of the version that is being evaluated.
EXPERIMENTS AND RESULTS
In this study, the software that is used is an embedded system designed to operate on the microprocessor featured in embedded control systems, functioning as a controller.Its primary role is to acquire data from connected sensors and relay this information to specific subsystems responsible for executing predefined functions.The software utilized in this study can accommodate up to six subsystems, comprising the user interface, sensors, and actuators.Notably, the simultaneous connection of all six subsystems is not obligatory.For the experiments to be carried out in this article, datasets were prepared for four versions of the used software.The count of test cases and fault numbers in these versions are shown in Table 2.At the beginning of our experiments, we determined the effect of each SF on the effectiveness of the test cases.First, we normalized a feature by converting its maximum value to 1, and we calculated test case scores using only that feature.Scores for other features were counted as zero.As a result, test cases were prioritized using a single feature.Secondly, we normalized the same feature, converted its maximum value to 0, and prioritized test cases again.By comparing the results, we determined how an SF affects the success of the prioritization.We repeated this analysis for each SF. Figure 8 shows an example of how to adjust the maximum value to 0 (MaxToZero) and to 1 (MaxToOne) for an SF.Table 3 shows the best results of APFD and APFDc scores obtained for each SF using the V07 dataset.Thus, using features and scoring to help with prioritization, the impact of the ideal scores established for V07 on other versions was also observed with these outcomes.After this analysis, the following features are normalized using the MaxToOne technique because their larger values affect the priority of the test cases positively: CountOfSubsystemScenario, CountOfScenarioChangeMade, TotalSendMessageCount, TotalRe-ceivedMessageCount, CountOfParameter, CountOfListParameter, and CountOfOtherSubsystemWhichMessageSend.On the other hand, the following features are normalized using the MaxToZero technique because their smaller values affect the priority of the test cases positively: Age, ErrorRate, IsPeriodic, CountOfMessageRule.The second method employs normalized score values, specifically The optimal MaxToZero or MaxToOne normalizations for each feature are chosen based on the evaluates' results, and these scores are then utilized to prioritize all other software versions.The objective is to assess the effectiveness of applying a fixed normalization value to each feature in the ranking of test cases.The trials demonstrate that the proposed method can obtain success rates ranging from 52 percent to 78 percent across all versions of the score calculation.This result is achieved by utilizing all normalization values that yield favorable sorting results for each feature simultaneously.Looking at the results obtained in related articles Natarajan et al. [12] use a weighted TCP method based on code coverage and APFD was used as evaluation metric.The paper uses multiple code coverage approaches.The results of each coverage range from 74% to 81.82%.Additionally, Askarunisa et al. [2] prioritized test cases using different code coverage methods.That paper used APDF and APFDc evaluation metrics and it was found APFD metrics results in the range of 57.14 to 67.7 percent.In the same study, APFDc was in the range of 53.8 to 84.9 percent.Results show that some coverage strategies perform better than the ones used in this paper, while others perform worse.Ritika et al. [7] examined the proposed technique in three ways.Unsorted, randomly sorted, and algorithmsorted.After comparing the three methods indicated in their study, the proposed method generated better results than the unsorted and randomly sorted methods.The findings show that APFD had a 75% success rate and APFDc 85.64 percent.After reviewing prior research, this paper's APFD results were similar to those of other studies.More improvements are needed to improve APFDc results.
CONCLUSION AND FUTURE WORK
This article presents a method to prioritize embedded software test cases for faster error detection before executing each version.General features found in embedded software and their software tests were extracted for the prioritization process.With the acquired features, software tests of embedded software were used to create datasets.Features that could be utilized for scoring and prioritization were identified from the test-derived datasets.First, it was shown how each determined score feature affected the test case prioritization procedure.Subsequently, the contributions of each score feature to the prioritization are displayed once they are processed at the same time.The obtained results show that each of the determined score features helps to find more errors in a shorter amount of time.Simultaneously, it has been noted that combining these features yields better outcomes than utilizing them separately.The features of the software and the tests themselves can be utilized to help prioritize embedded software test cases.
As a future work, more static features from the current version and additional historical data from previous iterations can be extracted to improve the performance of the prioritization model.Every feature in this study is given the same weight.Future research may assign particular weights to different features.Machine learning techniques can be used to prioritize the test cases using extracted features.
Figure 1 :
Figure 1: Basic Embedded Control System Diagram sends the output to actuators.Actuators, in turn, perform predetermined actions based on the received data.As an example of the mechanism of embedded control systems, Figure2provides a representation of basic messages and flows that can be used in an automatic braking system.There are four systems in the example presented in Figure2.One is the main software that controls the other systems (controller).It decides whether to break or not by looking at sensor data.A sensor system is used to collect data from the outside of the car.An automatic braking system is used to brake the car when some obstacles are seen by sensors.The user interface is used to view the status of the sensor and braking systems and to select the use case of the sensor or auto-brake systems.Embedded software refers to software that is capable of executing physical actions on hardware, operates in real time, and is subject to certain memory limitations.The embedded software have the ability to interface with several subsystems.It has established precise message structures with distinct boundaries that facilitate communication amongst the subsystems that interact with it.Given the real-time functionality of embedded software, effective handling of the timing of messages in software test cases is crucial.Embedded software mostly operates via a scheduler.An interrupt operation is executed whenever another function has to be performed at any given moment, allowing the execution of the desired function.On the other hand, other software like application software does not possess such prerequisites.Typically, application software engages in action-oriented tasks.For instance, when the user activates a button on an application, the program does the necessary function.The test cases designed for embedded software are tailored to meet the specific functionalities inherent to the program and are commonly employed in the field of embedded software.These features encompass the ability to manage the operational state of the hardware or software of the interconnected subsystems through ongoing message transmission.For example, the main software is the system that is being tested.The message flow between the sensor and the main software is shown in Figure2.First, the sensor system periodically sends live messages to the main software.Then the sensor system sends the sensor status data.If there's no error, it sends the parameter as OK, otherwise, it sends it as Not OK.In the presence of an obstacle, the sensor sends a SensorDataMessage to the main software periodically.The main software algorithm processes the sensor data and determines the presence of an obstacle.If an obstacle is detected, it sends an AutoBrakeDataMessage (Figure2b) to the automatic braking system, causing the car to slow down or stop.
(a) Sensor -Main Software (b) Brake -Main Software (c) UI -Main Software
Figure 2 :
Figure 2: Messaging Flow in an Exemplary Embedded Software for an Automatic Brake System
Figure 4 :
Figure 4: The General Structure of the Proposed Test Case Prioritization Technique
Figure 5 :
Figure 5: Simple Representation of Dataset for a Single Test Case the test case's score.We normalized the values of each SF between 0 and 1 in two different ways, depending on their effects on the effectiveness of the test case.If a characteristic with a high value implies that the relevant test case will be more successful, the maximum value of the feature is converted to 1, while the minimum value is represented as 0. In the opposite case, where low values affect the test case positively, the minimum value of the feature is converted to 1, while the maximum value is represented as 0. Figure6presents two exemplary normalizations of the features Age and UsedModes.The columns on the left side under each feature represent the real values obtained from the dataset.The columns on the right side contain the corresponding normalized values.The main purpose here is to observe whether prioritizing the test cases by features selected from the dataset by giving them different scores can help shorten the time to find errors.Points are given by increasing or decreasing them in equal proportions at certain intervals only to create the difference between test cases, and the
Figure 6 :
Figure 6: Exemplary Normalizations of The FeaturesDue to the inability to sort categorical data numerically, a single value is assigned to each category instead of allocating unique normalized values to distinct ranges.Hence, the MaxToOne or MaxToZero approaches are inapplicable in this context.The test or software engineer is responsible for inputting the normalized values of categorical features such as SubsystemName, Receiver, Sender, and UsedModes.Figure7shows how the user-defined normalized values can be done.
Figure 7 :
Figure 7: Example of User Defined Score Values For Subsys-temName
Figure 8 :
Figure 8: Example of Assigning MaxToZero and MaxToOne Normalized Values
•
Age: The test case age is determined by the version number it corresponds to.For instance, if a test case is used in all four versions (V04 to V07) of a project, the parameter is set to 1 in the dataset for V04, indicating its first use.In the subsequent version V05, this parameter is set to 2 for the same test case, and so on.It takes an incrementable value between 1 and 4 in the dataset, reflecting the number of software versions tested in this article.• ErrorRate: This historical feature indicates the error rate of the test case.It is obtained from the previous versions of the software to be tested.Let the version under test be denoted as V07, and our previous test version is referred to as V06.To assign a parameter to a test in V07, an initial check is made to determine the existence of the test in the V06 version.If the test is not found in V06, its value is set to zero in V07.If the test exists in V06 and is deemed accurate, the value from the V06 dataset is transferred directly to V07.In cases where the test is present in V06 but is found to be faulty, its value in V06 is adjusted according to the scoring criteria, and the updated value is then written to the V07 dataset.• UsedSubsystemCount: This is the subsystem count used in the test case.
• Subsystems: This parameter is repeated for each subsystem used in the test cases.It comprises four sub-parameters: Sub-systemName, CountOfSubsystemScenario, ErrorCountOf-SubsystemScenarios, and CountOfScenarioChangeMade. These parameters are version-dependent and have the same value for all test cases within a version.Each subsystem used in the test case has its set of these parameters, with values varying based on the subsystem name.SubsystemName is the name of a subsystem.This parameter can take values Sys1,Sys2,... etc. Receiver: The subsystem name of the receiver of this message.Sender:The subsystem name of the sender of this message.IsPeriodic: This parameter indicates whether the message is sent periodically.It has two options: Periodic (1) or Nonperiodic (0).CountOfParameter: This parameter displays the total count of parameters in the message, excluding a list of them.CountOfListParameter: This parameter shows the total list parameter count of this message.
Table 2 :
Count of Test Case and Total Faults
Table 3 :
Results of APFD and APFDc of V07 for each SF normalized values from one version to all other versions.Table4presents prioritized test case results for all versions using all features to calculate test case scores.The version of the software for which we determined the effect of each feature was software version V07.The APFD and APFDc values of the test cases of V07 are 0.78 and 0.72, respectively, which are calculated after the MaxToOne, MaxToZero, or UserDefined normalized values that give the best results for each feature are determined and test cases sorted with their score calculation.
from the MaxToZero or MaxToOne options of V07, which yields optimal results.This method aims to assess the impact of simultaneously utilizing all features for test case prioritization in the software under test.Additionally, it aims to evaluate the influence of applying
Table 4 :
Results for All Versions Software with Normalized | 8,454.6 | 2024-02-01T00:00:00.000 | [
"Computer Science",
"Engineering"
] |
Nocardioides: “Specialists” for Hard-to-Degrade Pollutants in the Environment
Nocardioides, a genus belonging to Actinomycetes, can endure various low-nutrient conditions. It can degrade pollutants using multiple organic materials such as carbon and nitrogen sources. The characteristics and applications of Nocardioides are described in detail in this review, with emphasis on the degradation of several hard-to-degrade pollutants by using Nocardioides, including aromatic compounds, hydrocarbons, haloalkanes, nitrogen heterocycles, and polymeric polyesters. Nocardioides has unique advantages when it comes to hard-to-degrade pollutants. Compared to other strains, Nocardioides has a significantly higher degradation rate and requires less time to break down substances. This review can be a theoretical basis for developing Nocardioides as a microbial agent with significant commercial and application potential.
Introduction
Several pollutants, including heavy metals, petroleum, and organic pollutants such as aromatic compounds, etc., are currently polluting the environment [1].These pollutants are highly toxic, stable, and challenging to degrade [2] and have potent carcinogenicity [3].They pose a severe threat to the environment and public health [4].Physical transfer adsorption, chemical precipitation oxidation, biological precipitation dissolution, etc., are used to treat common pollutants [5].Extraction, adsorption, and membrane separation are the often-used physical remediation methods.Nonetheless, they are ineffective, expensive, and prone to secondary pollution [6].Chemical precipitation, electrolytic oxidation and reduction, and photochemical remediation are examples of chemical remediation methods [7].Applying chelated precipitation and chemical modifiers makes it easy for the soil's environmental structure to become damaged and produce secondary pollution [8].The microorganisms that make up bioremediation technology are used to adsorb, degrade, or transform environmental pollutants into other harmless substances [9].According to the chosen mechanism, there are now three standard microbial remediation techniques: (1) biosorption and enrichment [10]; (2) biodegradation [11]; and (3) biological precipitation and dissolution [12].Adsorbed ions in microbial cells can be categorized into three groups based on how they are distributed: through internal, external, or surface adsorption [13].Biosorption is frequently used to treat heavy metals.For example, Bacillus NMTD17 can reach cadmium (Cd 2+ ) biosorption equilibrium after 60 min, and its maximum Cd 2+ adsorption capacity is 40 mg/L [14].Biodegradation uses its metabolic capacity, including membrane transport, enzyme degradation, and carbohydrate metabolism [15].For example, Clostridium sp. can metabolize trichloroethylene (TCE) into the less toxic dichloride [16].Similarly, the fungi represented by Candida tropicalis can degrade phenol using their pheAencoded phenol hydroxylase [17] and catechol 1-dioxygenase [18] encoded by catA.Organic acids secreted by organisms help dissolve and precipitate pollutants through biological precipitation and dissolution.For example, Acidithiobacillus can produce sulfuric acid, and it can convert the insoluble metal in soil into soluble sulfates by acidifying the soil [19].Microbial remediation technology outperforms other remediation technologies in terms of efficiency and cost.For example, petroleum hydrocarbons' microbial degradation costs roughly 50-70% less than chemical and physical methods [20].Second, there is no secondary pollution, and the conditions for microbial degradation are milder [21].Therefore, bioremediation technologies represented by microorganisms should be given priority when solving the problems caused by environmental pollution.
Nocardioidaceae is a family within the order Propionibacteriales, as shown in Figure 1.There are 158 effective species of Nocardioides, a type of rare Actinomycetes with a similar evolutionary relationship and morphology [22].Strains other than Streptomyces are frequently classified as the rare Actinomycetes [23].Nocardioides can use a variety of organic substances as carbon sources, including petroleum hydrocarbons, aromatic compounds, and nitrogen heterocyclic compounds [24].As described in Table 1, Nocardioides can degrade a variety of pollutants.They can be divided into four categories: aromatic compounds, hydrocarbon and haloalkane, nitrogen heterocyclic, and polyester pollutants, such as nitrophenol, cotinine, ritalinic, polylactic acid, etc.This signals that Nocardioides has a wide range of prospects for pollutants.Nocardioides sp.KP7 [25] has the benzene-ring degradation genes phdA, phdB, phdC, and phdD.They can code for the enzymes involved in degradation, which can degrade to phthalates using phenanthrene as their carbon source.This discovery was made as early as 1999.Nocardioides' degradation currently affects several fields, including medicine [26,27], industry [28], materials [29], etc.The common ones include 2,4-dinitroanisole [30], dibenzofuran [27], nitrophenol [21], and ibuprofen [31].Consider the following example: at an initial concentration of 1.5 mg/L, strain CBZ_1T eliminated 70% of ibuprofen in 7 days [32].In addition to degrading organic pollutants, some strains of Nocardioides are known to be effective at carrying out steroid biodegradation and biotransformation.Steroids are biomolecules in higher organisms that perform basic physiological functions [44].Steroids are widely used in different fields of medicine.At the same time, steroids are emerging contaminants (ECs) [45].Steroids are a class of endocrine disruptors that, at very low levels, can lead to some adverse effects such as sex hormone imbalance, decreased reproductive ability, and cancer in organisms, so the problem of steroid hormone pollution in the environment has attracted widespread attention from researchers [46].Nocardioides simplex VKM Ac-2033D has high 3-ketosteroid 1(2)-dehydrogenase activity toward a wide range of steroids, such as androstenedione, progesterone, hydrocortisone, 6α-methylhydrocortisone, cortexolone, and 21-acetyl-cortexolone [47].N. simplex VKM Ac-2033D can convert 92% of hydrocortisone (5 g/L) into prednisolone in 2 h [47].N. simplex VKM Ac-2033D can also convert pregna-4,9(11)-diene-17α and 21-diol-3,20-dione acetates [48].By conducting omics studies on the bacteria, N. simplex VKM Ac-2033D was found to possess genes related to the sterol uptake system and aliphatic side-chain degradation at C17 and A/B-and C/D-ring degradation systems [49].It can introduce a ∆1-double bond in various 1(2)-saturated 3-ketosteroids and perform the conversion of 3β-hydroxy-5-ene steroids to 3-oxo-4-ene steroids, the hydrolysis of acetylated steroids, and the reduction of carbonyl groups at C-17 and C-20 of androstanes and pregnanes, respectively [49].Meanwhile, N. simplex VKM Ac-2033D can completely degrade cholesterol and lithocholate at an initial concentration of 1 g/L in 72 h.The strain is able to grow on cholesterol as well as lithocholate as the sole carbon and energy sources [50].Phytosterol can also be completely degraded by N. simplex VKM Ac-2033D at an initial concentration of 1 g/L in 120 h [51].
This review summarizes the fundamental traits of Nocardioides before focusing on the types of pollutants that Nocardioides can degrade.Simultaneously, the ability of Nocardioides to degrade pollutants is introduced.This review provides the specific degradation pathways for representative pollutants.Researchers require such information in order to develop and apply microbial degradation methods for environmental remediation.
Nocardioides
Nocardioides was first known as Nocardia.It differs from regular Actinomycetes in that it has irregularly branching aerial hyphae, and the transverse septum breaks into rods or globules [52].In 1976, Prauser H [53] isolated seventeen strains of Actinomycetes from soil, each with unique taxonomic traits, and based on their distribution source, morphology, physiological and biochemical characteristics, etc., classified them as a new genus of Actinomycetes.Nocardioides albus served as the type species for the newly recognized genus [53].The LL-2,6-diaminopimelic acids (LL-DAP) and lack of branching acid distinguish Nocardioides from Nocardia.In 1985, Nesterenko et al. established Nocardioidaceae [22].According to phylogeny, the three most recent genera are Nocardioides, Marmoricola, and Aeromicrobium, as shown in Figure 2.
Nocardioides bacteria are aerobic, Gram-positive, and globular or irregularly rodshaped [54].The majority of Nocardioides' aerial hyphae have sparse or irregular branches and measure about 1.0 µm in length [53].Only a few Nocardioides (Nocardioides simplex, Nocardioides jensenii, Nocardioides plantarum, Nocardioides pyridinolyticus, Nocardioides nitrophenolicus, and Nocardioides aquaticus) lack aerial hyphae.As the culture time increases, the cell morphology gradually changes from rod-shaped to cocciform [53].The colony has a smooth and glossy, round, neatly defined edge and a color that ranges from slightly white to light yellow.The best growth temperature is 28-30 • C, and the best growth pH is 7-8.Most organisms require salt but are not halophilic (often isolated from marine and marinerelated environments).These organisms typically need 0.5-6% NaCl to thrive [22].As demonstrated in Figure 3, Nocardioides can also grow and reproduce using various organic chemicals in different contaminated habitats, such as industrial wastewater, contaminated soil, crude oil, etc. Figure 3 summarizes the main habitat types of Nocardioides and the Nocardioides' distribution in different habitats.The size of the circle represents the number of Nocardioides isolated in that habitat, and the shade of color represents the type of habitat.Figure 3 shows that there are eight types of Nocardioides habitats and the main habitats of Nocardioides are contaminated soil and industrial wastewater.Industrial wastewater is the second most common source of isolation for Nocardioides.This signals that Nocardioides has great potential for degrading pollutants.
each with unique taxonomic traits, and based on their distribution source, morphology, physiological and biochemical characteristics, etc., classified them as a new genus of Actinomycetes.Nocardioides albus served as the type species for the newly recognized genus [53].The LL-2,6-diaminopimelic acids (LL-DAP) and lack of branching acid distinguish Nocardioides from Nocardia.In 1985, Nesterenko et al. established Nocardioidaceae [22].According to phylogeny, the three most recent genera are Nocardioides, Marmoricola, and Aeromicrobium, as shown in Figure 2. Nocardioides bacteria are aerobic, Gram-positive, and globular or irregularly rodshaped [54].The majority of Nocardioides' aerial hyphae have sparse or irregular branches and measure about 1.0 μm in length [53].Only a few Nocardioides (Nocardioides simplex, Nocardioides jensenii, Nocardioides plantarum, Nocardioides pyridinolyticus, Nocardioides nitrophenolicus, and Nocardioides aquaticus) lack aerial hyphae.As the culture time increases, the cell morphology gradually changes from rod-shaped to cocciform [53].The colony has a smooth and glossy, round, neatly defined edge and a color that ranges from slightly white to light yellow.The best growth temperature is 28-30 °C, and the best growth pH is 7-8.Most organisms require salt but are not halophilic (often isolated from marine and marinerelated environments).These organisms typically need 0.5-6% NaCl to thrive [22].As demonstrated in Figure 3, Nocardioides can also grow and reproduce using various organic chemicals in different contaminated habitats, such as industrial wastewater, contaminated Through examining the research statistics on Nocardioides from the past 30 years, it was found that research on Nocardioides in the past 5 years has gradually increased.As shown in Figure 4A, the countries where more research has been conducted are China, the United States, Poland, Germany, Russia, etc.The number of Nocardioides publications has also increased dramatically, as shown in Figure 4B.As shown in Figure 5, current Nocardioides research focuses on pollutant degradation.Researchers discovered the nitrophenol-degrading Nocardioides nitrophenolicus sp.NSP41T in 1999.Nocardioides carbamazepini sp.nov.[26] and Nocardioides sp.[18], which can degrade ibuprofen and nitrophenol, were isolated by researchers in 2022.Over the last 50 years, research on Nocardioides has continuously grown, and mining for new species and determining their ability to degrade environmental pollutants have both gained popularity. Nocardioides has also gradually Through examining the research statistics on Nocardioides from the past 30 years, it was found that research on Nocardioides in the past 5 years has gradually increased.As shown in Figure 4A, the countries where more research has been conducted are China, the United States, Poland, Germany, Russia, etc.The number of Nocardioides publications has also increased dramatically, as shown in Figure 4B.As shown in Figure 5, current Nocardioides research focuses on pollutant degradation.Researchers discovered the nitrophenol-degrading Nocardioides nitrophenolicus sp.NSP41T in 1999.Nocardioides carbamazepini sp.nov.[26] and Nocardioides sp.[18], which can degrade ibuprofen and nitrophenol, were isolated by researchers in 2022.Over the last 50 years, research on Nocardioides has continuously grown, and mining for new species and determining their ability to degrade environmental pollutants have both gained popularity. Nocardioides has also gradually demonstrated the ability to degrade pollutants.This suggests that there is more to explore regarding Nocardioides than other Actinomycetes and that it is possible to discover new species and application values.
Applications of Nocardioides
With the gradual discovery of new species of Nocardioides, Nocardioides exhibit good pollutant degrading skills.Notably, some refractory pollutants, such as ritalinic, atrazine, and polylactic acid [40,55], are closely related to different aspects of life, involving medicine, industry, etc.It is important to summarize the type and ability of Nocardioides to degrade these pollutants.This provides more possibilities for microorganisms to repair the environment and protect its ecology.In this review, pollutants are divided into five categories according to their chemical structure: hydrocarbons, halogenated alkanes, aromatic compounds, nitrogen heterocyclic pollutants, and polyester pollutants.A detailed summary of the types and abilities of Nocardioides to degrade pollutants is presented.
The Degradation of Hydrocarbon and Haloalkane Pollutants
Common hydrocarbon pollutants include crude oil [16], butane [56], etc.One of the world's most significant energy sources is crude oil, and as industrialization advances exponentially, demand is growing [57].However, oil spillage during extraction, shipping, and refinement can severely pollute the land [57].The chemical wastewater released by the chemical printing and dyeing industries also contains a variety of petroleum hydrocarbon pollutants, which harm the soil's ecological ecosystem and contaminate the water body [58,59].Petroleum hydrocarbons can also lower crop yield because they accumulate in plants, interfere with their normal physiological processes, and inhibit plant photosynthesis [60].These pollutants risk human health and can harm the respiratory system by entering the human body through various pathways and accumulating in organisms [61].
Many different types of microorganisms in nature can degrade petroleum pollutants, including Pseudomonas spp.[62], Bacillus sp.[61], Nocardioides sp.[57], etc. Alkanes are a carbon source that Nocardioides can use [56].For instance, Hamamura et al. [44] discovered that Nocardioides sp.strain CF8 was found to have butane monooxygenase [62], which may use butane and a variety of alkanes as carbon sources [63].The Nocardioides luteus strain BAFB [63] degrades the C11 alkanes in jet fuel JP-7 by using them as a carbon source in long-chain alkanes.Nocardioides oleivorans sp. and Nocardioides sp. were also isolated from crude oil samples of oil fields by Schippers et al. and Roy et al.Both may utilize crude oil as a carbon source, while Nocardioides oleivorans sp.can adapt to the condition of a
Applications of Nocardioides
With the gradual discovery of new species of Nocardioides, Nocardioides exhibit good pollutant degrading skills.Notably, some refractory pollutants, such as ritalinic, atrazine, and polylactic acid [40,55], are closely related to different aspects of life, involving medicine, industry, etc.It is important to summarize the type and ability of Nocardioides to degrade these pollutants.This provides more possibilities for microorganisms to repair the environment and protect its ecology.In this review, pollutants are divided into five categories according to their chemical structure: hydrocarbons, halogenated alkanes, aromatic compounds, nitrogen heterocyclic pollutants, and polyester pollutants.A detailed summary of the types and abilities of Nocardioides to degrade pollutants is presented.
The Degradation of Hydrocarbon and Haloalkane Pollutants
Common hydrocarbon pollutants include crude oil [16], butane [56], etc.One of the world's most significant energy sources is crude oil, and as industrialization advances exponentially, demand is growing [57].However, oil spillage during extraction, shipping, and refinement can severely pollute the land [57].The chemical wastewater released by the chemical printing and dyeing industries also contains a variety of petroleum hydrocarbon pollutants, which harm the soil's ecological ecosystem and contaminate the water body [58,59].Petroleum hydrocarbons can also lower crop yield because they accumulate in plants, interfere with their normal physiological processes, and inhibit plant photosynthesis [60].These pollutants risk human health and can harm the respiratory system by entering the human body through various pathways and accumulating in organisms [61].
Many different types of microorganisms in nature can degrade petroleum pollutants, including Pseudomonas spp.[62], Bacillus sp.[61], Nocardioides sp.[57], etc. Alkanes are a carbon source that Nocardioides can use [56].For instance, Hamamura et al. [44] discovered that Nocardioides sp.strain CF8 was found to have butane monooxygenase [62], which may use butane and a variety of alkanes as carbon sources [63].The Nocardioides luteus strain BAFB [63] degrades the C11 alkanes in jet fuel JP-7 by using them as a carbon source in long-chain alkanes.Nocardioides oleivorans sp. and Nocardioides sp. were also isolated from crude oil samples of oil fields by Schippers et al. and Roy et al.Both may utilize crude oil as a carbon source, while Nocardioides oleivorans sp.can adapt to the condition of a maximum of 50 mg/mL of crude oil, and it can degrade 40% of 50 mg/mL crude oil as its carbon source.
Halogenated hydrocarbons are byproducts produced when halogen groups replace hydrogen atoms in hydrocarbon molecules.The presence of halogen atoms makes the molecule more poisonous [64].Vinyl chloride (VC), an extremely dangerous and carcinogenic halogenated hydrocarbon, is widely found in groundwater and soil [65].It was included in the 2017 list of class I carcinogens due to its widespread use in the polymer chemical industry [66].VC is a severe hazard to the environment and people's health [67].Dehalococcoides spp.[68], Nocardioides sp.[69], etc., are the common VC-degrading bacteria.According to Mattes et al., Nocardioides sp.strain JS614 may use VC as a carbon source, and the etnE gene encodes epoxy alkyl coenzyme M transferase, which breaks down VC [70].Additionally, Wilson et al. confirmed that Nocardioides sp. may use VC as a carbon source [71].Nocardioides sp. is primarily concerned with the degradation of crude oil and the utilization of VC.Nocardioides can be observed to have various degradation types for hydrocarbon and haloalkane pollutants.
The Degradation of Aromatic Compounds
Aromatic compounds with stable chemical structures, typical carcinogenicity, and mutagenicity have been discovered in various natural habitats, such as soil and water [72].In addition to significantly inhibiting microorganisms, these toxic compounds threaten human health and the natural environment, and preventing this is the primary goal of pollution control [73].Additionally, the quantity of benzene rings in aromatic compounds is positively correlated with the difficulty of carrying out the environmental degradation of aromatic compounds and their toxicity [65].In a study, it was found that their volatility decreased as the number of benzene rings increased, the solubility in fat increased, and the difficulty of environmental degradation increased.Due to their high level of carcinogenicity, teratogenicity, mutagenicity, and ecological toxicity [69], aromatic compounds-which are typically present in water, soil, and sediments [68]-pose a severe risk to human health and the environment [74].Nocardioides has been found to degrade aromatic compounds such as 2-dinitroanisole, ibuprofen, dibenzofuran, and nitrophenol.
2,4-dinitrophenol (DNAN) is a typical aromatic compound.It gradually substitutes trinitrotoluene (TNT) as a low-sensitivity explosive [29].In addition to creating significant acute cytotoxicity during methanogenesis and nitrification, DNAN can also cause damage to algae, microorganisms, and plants.Karthikeyan et al. isolated a Nocardioides sp.JS1661 strain and determined that it could use DNAN as its only carbon source to degrade DNAN and release nitrite through the 2,4-dinitrophenol (DNP) pathway [29].Figure 6 illustrates the degradation pathway.N. sp.JS1661 can adapt to the condition of a maximum of 150 mg/mL of DNAN.Additionally, within 45 h, N. sp.JS1661 can degrade 150 mg/L of DNAN.Rhodococcus erythropolis strain HL 24-1 can degrade 92 mg/L of DNAN.Its degradability is nearly twice that of R. erythropolis strain HL 24-1 [75].The oxygen demethylation of DNAN is the first step in creating DNP and methanol [76].The cleavage of the ether bond to form DNP, the formation of the hydride-Meisenheimer complex from DNP, and the release of nitrite are all processes catalyzed by DNAN demethylase.A study indicated that DNAN has little to no accumulation, nitrite has an almost stoichiometric release, and DNAN can be completely degraded within 20-50 h [30].Microbial degradation is becoming more significant due to the increased use of DNAN.The degradation of polycyclic aromatic hydrocarbons (PAHs) by Nocardioides mainly involves an aerobic pathway, which is carried out by means of the hydroxylation of double oxygenation, dehydrogenation, and ring-opening double oxygenation [77].Ring-hydroxylating oxygenase binds oxygen atoms to PAHs to produce cis-dihydrodiol, which continues to be metabolized and degraded by dehydrogenation and ring-opening steps.Unlike other bacteria, Nocardioides also has a cytochrome P450 monooxygenase pathway [78].The enzyme also converts polycyclic aromatic hydrocarbons (PAHs) to cis-dihydrodiol, dehydrogenates them, converts them to diols, and then epoxides them to form intermediates in the tricarboxylic acid cycle, which is used in cell synthesis or catabolism.Examples of p-nitrophenol-degrading bacteria isolated from industrial wastewater include Nocardioides sp.KP7 [28], Nocardioides nitrophenolicus sp.NSP41T [79], and Nocardioides simplex FJ2-1A [80].With the help of the two enzymes coenzyme F420 and ring-hydroxylating oxygenase, N. simplex FJ2-1A may mineralize and use TNT and DNP [80].The 2,4,6-trinitrophenol requires coenzyme F420 to form a picric acid hydride σ-complex, which combines with DNAN to create a dihydrocomplex [30].
Ibuprofen is also a benzene-ring compound.It is a drug widely used as an antipyretic, pain reliever, etc. [28].Ibuprofen contamination has been discovered in finished drinking water, surface and groundwater, and pollution from other medications and personal care products.Municipal and industrial wastewater effluents are the main entry points for ibuprofen into the environment [32].Increases in ibuprofen use and drug residues eventually cause ecotoxicity [81].The most prevalent bacteria that degrade ibuprofen include Sphingomonas sp., Bacillus sp., Nocardioides sp., etc. Carballa et al. found that at an initial concentration of 1.5 mg/L, in one week, ibuprofen's biological oxidative removal rate was >70% in Nocardioides.Nevertheless, the metabolic byproducts (hydroxyibuprofen and carboxyl ibuprofen) produced by specific strains during oxidation have toxicological effects comparable to those of ibuprofen in the aquatic environment [28].Tibor et al. isolated a strain of Nocardioides carbamazepini sp.nov.from ibuprofen-contaminated water.Nocardioides degrades ibuprofen when glucose and ibuprofen are used as co-substrates.The bacteria can degrade 70% of 1 mg/L ibuprofen within seven weeks.
Dibenzofuran (DBF) is a model compound for studying aromatic compounds' degradation processes and polychlorinated dibenzofurans [82].DBF is a hazardous, hard-todegrade benzene-ring pollutant that can last in the environment for a long time [83].It is frequently used in medicine, disinfectants, preservatives, dyes, etc.The most prevalent bacteria that can degrade DBF include Burkholderia xenovorans strain LB400T [84], Sphingomonas sp.RW1 [85], Pseudomonas resinovorans strain CA10 [86], Rhodococcus sp.strain YK2 [87], etc. Aerobic degradation is the primary form of the biodegradation of DBF by Ibuprofen is also a benzene-ring compound.It is a drug widely used as an antipyretic, pain reliever, etc. [28].Ibuprofen contamination has been discovered in finished drinking water, surface and groundwater, and pollution from other medications and personal care products.Municipal and industrial wastewater effluents are the main entry points for ibuprofen into the environment [32].Increases in ibuprofen use and drug residues eventually cause ecotoxicity [81].The most prevalent bacteria that degrade ibuprofen include Sphingomonas sp., Bacillus sp., Nocardioides sp., etc. Carballa et al. found that at an initial concentration of 1.5 mg/L, in one week, ibuprofen's biological oxidative removal rate was >70% in Nocardioides.Nevertheless, the metabolic byproducts (hydroxyibuprofen and carboxyl ibuprofen) produced by specific strains during oxidation have toxicological effects comparable to those of ibuprofen in the aquatic environment [28].Tibor et al. isolated a strain of Nocardioides carbamazepini sp.nov.from ibuprofen-contaminated water.Nocardioides degrades ibuprofen when glucose and ibuprofen are used as co-substrates.The bacteria can degrade 70% of 1 mg/L ibuprofen within seven weeks.
Dibenzofuran (DBF) is a model compound for studying aromatic compounds' degradation processes and polychlorinated dibenzofurans [82].DBF is a hazardous, hard-todegrade benzene-ring pollutant that can last in the environment for a long time [83].It is frequently used in medicine, disinfectants, preservatives, dyes, etc.The most prevalent bacteria that can degrade DBF include Burkholderia xenovorans strain LB400T [84], Sphingomonas sp.RW1 [85], Pseudomonas resinovorans strain CA10 [86], Rhodococcus sp.strain YK2 [87], etc. Aerobic degradation is the primary form of the biodegradation of DBF by microorganisms [88].According to some studies, DBF is degraded by a ring-opening reaction involving the action of a biphenyl-degrading enzyme; it is hydroxylated by a dioxygenase and undergoes additional ring-opening reactions to 2,2,3-trihydroxy biphenyl, oxygenation to form 2,4-hexadienoic acid and different formations of salicylic acid and dihydroxybenzoic acid, and then into the tricarboxylic acid cycle to achieve complete transformation [89].Previously, Kubota et al. [26] isolated DBF-degrading bacteria from soils and sediments contaminated with various amounts of DBF and discovered that Nocardioides aromaticivorans, a member of the Gram-positive Actinomycetes, was the most prevalent among the culturable DBF-degrading bacteria.Nocardioides has strong potential for dibenzofuran degradation.Simultaneously, N. aromaticivorans can adapt to the condition of a maximum of 33mg/L of DBF.It can also completely degrade 33 mg/L of DBF [26] within 96 h at pH 7 and 30 • C. Pseudomonas sp.strain C3211 was found to completely degrade 0.585 mg/L of DBF within 67 h [90], meaning that the degradation rate was over fifty-six times higher.
Nocardioides can also use several other aromatic pollutants as carbon sources, as shown in Table 1.Nocardioides outperforms different strains in its ability to degrade phenol pollutants by offering more types of degradation and superior degradability.
The Degradation of Nitrogen Neterocyclic Pollutants
Heterocyclic compounds with nitrogen can also serve as carbon sources for Nocardioides.Pyrrole, indole, pyridine, quinoline, isoquinoline, and their derivatives are examples of common nitrogen heterocyclic compounds [88].They are present in industrial wastewater, such as pesticide, coking, dye, pharmaceutical, and dye wastewater [10].Nitrogen heterocyclic pollutants have lower biodegradability and face more difficulty in disrupting metabolic processes than polycyclic aromatic hydrocarbons [91].They seriously impair the environment and people's health and are carcinogenic, teratogenic, and mutagenic [92].In one study, a Korean researcher extracted a new strain of Nocardioides pyridinolyticus sp.nov.which can use pyridine as a carbon source [79].In 2018, Professor Qiu isolated the Nocardioides sp.strain JQ2195 [27] from contaminated wastewater near urban areas.The strain can adapt to the condition of a maximum of 500mg/mL of cotinine.It can also degrade 500 mg/L cotinine in 32 h using pyridine cotinine as the only carbon and nitrogen source.During the degradation process, 50% of the cotinine was converted into 6-hydroxy-cotinine and 6-hydroxy-3-succinylpyridine (HSP) intermediates [55].
Methyl phenylacetate is a drug prescribed for the treatment of deficiency hyperactivity disorder among other promotional drugs [37].Water pollution can result from the presence of ritalinic acid (RA), the primary metabolite of methylphenidate.As a biomarker used to identify the presence of methylphenidate in sewage epidemiology, RA has been proposed [93].Arthrobacter sp.strain MW1 Marta, Phycicoccus sp.strain MW4, Nocardioides sp.[93], etc., degrade RA.Nocardioides sp.strain MW5 [93] 2020, which can alter the N heterocyclic site of RA using RA as the only source of nitrogen and carbon, was also discovered by Woźniak-Karczewska et al. in 2020.Meanwhile, it was found that when RA was used, the bacteria could adapt to the condition of a maximum of 1 g/L RA.Additionally, the bacteria could completely degrade 1 g/L of RA in 4 h.
Triazines, such as triazine herbicides, are six-membered nitrogen heterocyclic molecules frequently used as insecticides [94].Triazine herbicides were initially made available in China in the early 1980s.As their use has grown due to their high toxicity and endurance, they have not only affected the development of subsequent crops but also been found to be carcinogenic and harmful to human health [95].According to some studies, Nocardioides sp.strain C190 could use atrazine as a carbon source [96].Koji Satsuma discovered that N. strain DN36 could adapt to the condition of a maximum of 0.95mg/L of atrazine.It could completely degrade 0.95 mg/L of atrazine (triazine herbicides) in a week [38].Dechlorination, dealkylation, hydroxylation, and ring cracking are some examples of specific degradation processes.The degradation genes of triazine herbicides include atzA, atzB, atzC, atzD, atzE, atzF, and trzN [97].The function of the trzN gene is similar to that of atzA, which regulates dechlorination (step I) and then produces 2-amino-1 pyrrolidone under the control of the atzB gene (step II), followed by ammonia hydroxylation to cyanuric acid under the control of the atzC gene (step III).Then, atzD regulates the formation of cyanuric acid into biuret (step IV) and atzE regulates the removal of one amino group to isopropanoic acid (step V). atzF then generates carbon dioxide (step VI), as shown in Figure 7.
Molecules 2023, 28, x FOR PEER REVIEW 12 of 20 a A, which regulates dechlorination (step I) and then produces 2-amino-1 pyrrolidone under the control of the a B gene (step II), followed by ammonia hydroxylation to cyanuric acid under the control of the a C gene (step III).Then, a D regulates the formation of cyanuric acid into biuret (step IV) and a E regulates the removal of one amino group to isopropanoic acid (step V). a F then generates carbon dioxide (step VI), as shown in Figure 7.In addition, Takagi et al. isolated a strain of Nocardioides and discovered that the strain could adapt to the condition of a maximum of 5.04 g/L of melamine, and it was found to be able to degrade 5.04 g/L melamine (a nitrogen heterocyclic pollutant) [39] entirely in 20 d.Its ability to degrade melamine is nearly 50 times that of Micrococcus sp.strain MF-1 (100% degradation of 100 mg/L melamine) [98].Nocardioides can degrade Ritalin, triazine herbicides, and melamine, and it has a variety of degradation pathways for insoluble nitrogen heterocyclic contaminants.
The Degradation of Polyester Pollutants
Nocardioides can degrade high-molecular-weight compounds such as biodegradable plastics: polyhydroxyalkanoates, polycaprolactone (PCL), poly (3-hydroxybutyrate) [P(3HB)], polylactic acid (PLA), etc. [99].According to estimates, 300 million tons of plastic waste are produced annually worldwide, 79% of which is disposed of in landfills or released into the environment [100].Biodegradation, in conjunction with plastics that degrade through microbial action, has gradually become one of the solutions to this problem [24].Currently, Marinobacter sp., Pseudomonas.stu eri, Shewanella sp., Nocardioides sp., etc., are the microorganisms known to degrade plastics [24].Mi scherling et al. isolated In addition, Takagi et al. isolated a strain of Nocardioides and discovered that the strain could adapt to the condition of a maximum of 5.04 g/L of melamine, and it was found to be able to degrade 5.04 g/L melamine (a nitrogen heterocyclic pollutant) [39] entirely in 20 d.Its ability to degrade melamine is nearly 50 times that of Micrococcus sp.strain MF-1 (100% degradation of 100 mg/L melamine) [98].Nocardioides can degrade Ritalin, triazine herbicides, and melamine, and it has a variety of degradation pathways for insoluble nitrogen heterocyclic contaminants.
The Degradation of Polyester Pollutants
Nocardioides can degrade high-molecular-weight compounds such as biodegradable plastics: polyhydroxyalkanoates, polycaprolactone (PCL), poly (3-hydroxybutyrate) [P(3HB)], polylactic acid (PLA), etc. [99].According to estimates, 300 million tons of plastic waste are produced annually worldwide, 79% of which is disposed of in landfills or released into the environment [100].Biodegradation, in conjunction with plastics that degrade through microbial action, has gradually become one of the solutions to this problem [24].Currently, Marinobacter sp., Pseudomonas.stutzeri, Shewanella sp., Nocardioides sp., etc., are the microorganisms known to degrade plastics [24].Mitzscherling et al. isolated Nocardioides alcanivorans sp.from an environment polluted by plastics and N. alcanivorans NGK65T [101], which can use biodegradable plastics as a carbon source.Some scholars in Japan isolated a strain of Nocardioides marinisabuli OK12 from marine plastic waste which can use Poly-3-hydroxybutyrate (P(3HB)) as its only carbon source.The strain forms a biofilm on the surface of P(3HB).Shewanella sp.degraded P(3HB) at a rate of 47 µg/cm 2 /day, whereas strain OK12 degraded it at 318 ± 75 µg/cm 2 /day [41].The degradation rate was found to be over seven times higher.Additionally, Mistry et al. constructed a combined bacterial agent containing Nocardioides zeae EA12, Stentrophomonas pavanii EA33, Gordonia desulfuricans EA63, and Chitinophaga jiangningensis EA02 that can completely degrade high-molecular-weight PLA film within 35 d [40].
Nocardioides combined with other microorganisms can completely degrade PLA, and P(3HB) impairs plastic significantly faster than different plastic-degrading strains.Several plastic pollution contaminants can be used to isolate Shewanella sp. and a novel species of Nocardioides.Nocardioides has excellent potential for degrading plastics, as has been demonstrated.In the future, Nocardioides is expected to become the "star" of biodegradable plastics.
Conclusions
Natural habitats contain Nocardioides, a rare form of Actinomycetes.Members of Nocardioides have been discovered and used due to the pure culture's widespread use and the polyphasic classification of microorganisms.In most cases, Nocardioides is an aerobic Gram-positive bacteria with broken transverse septa that form rods or globules and uneven aerial hyphae [52].LL-DAP and the absence of branching acid distinguish Nocardioides from Nocardia [22].Presently, 158 effective Nocardioides species are known [22].Nocardioides started relatively late when compared to other conventional Actinomycetes.The abundance of undiscovered new species is one of Nocardioides' advantages.This undiscovered activity fills a gap in the connection of Nocardioides bacterial cultures and suggests we can investigate further undiscovered biological functions.
Additionally, preliminary findings from researchers suggest that it can degrade various pollutants, particularly refractory pollutants, including aromatic compounds, hydrocarbon and haloalkane pollutants, nitrogen heterocyclic pollutants, polymer polyester compounds, etc. Table 2 compares and summarizes the degradation by Nocardioides and other strains of pollutants.Nocardioides outperformed other strains in terms of their ability to degrade poly-3-hydroxybutyrate, dibenzofuran, 2,4-dinitrophenol, pyridine, and melamine, which can all be completely degraded.N. marinisabuli strain OK12 has a degradative capacity for poly-3-hydroxybutyrate that is about 7 times more than Shewanella sp., nearly 10 times as much as Rhizobium sp.NJUST18 can degrade pyridine.Almost 50 times more melamine can be degraded by this strain of Micrococcus sp.than by the strain MF-1.Other degrading bacteria, single degradable pollutants, low degrading efficacy of refractory pollutants, and difficult degrading conditions are disadvantages.Nocardioides has the advantage of dealing with a wide range of pollutants, including those from medicine, industry, materials, and many other fields.Nitrogen heterocyclic compounds can completely degrade refractory pollutants such as plastics, the conditions for degradation are broad and easy to implement, the degradation time is short, and the degradation efficiency is high.Nocardioides is expected to provide materials for environmental bioremediation because of this uniqueness.Pseudomonas sp.strain ISTDF1 (40% degradation of 200 mg/L in 36 h) [102] Pseudomonas aeruginosa FA-HZ1 (100% degradation of 20 mg/L in 70 h) [103] Pseudomonas sp.strain C3211 (100% degradation of 0.585 mg/L in 67 h) [90] Table 2. Cont.
Pollutant Type
The Degradability of Nocardioides sp.
Nocardioides also has other unique applications.Nocardioides can resist metal [107], remove toxins, and affect blooms.For example, Li et al. isolated Nocardioides sp. from Hg-contaminated soil [108].In Hg-contaminated soil, Nocardioides sp. is the dominant flora and can be used as a biological indicator of metal pollution [109].Additionally, Bagade et al. isolated Nocardioides sp.L-37a [110] from an arsenic (As)-contaminated environment with arsenate reductase activity.This indicates that Nocardioides sp. also has significant application potential in the degradation of the carcinogen As and its compounds.YokoIkunaga found that Nocardioides sp.strain WSN05-2 was able to eliminate 1000 µg/L of emetic toxin (DON) within 10 d [43].Nocardioides lacusdianchii sp., which can promote Microcystis aeruginosa growth and induce the formation of a Microcystis aeruginosa population, was isolated by Xiao et al. from a Microcystis aeruginosa culture [111].Additionally, it is essential for the emergence, spread, and reduction of microcystis bloom.In conclusion, Nocardioides offers an excellent research space, and their application prospects in the agricultural, industrial, and pharmaceutical industries are inestimable.
Nocardioides has good contaminant degradation capacity and can biodegrade and catalyze steroids.Their current bioprocessing mainly focuses on microbial degradation and biotransformation catalysis.In terms of biotransformation, Nocardioides has a variety of biocatalytic enzymes.For example, Nocardioides sp.YR527 can produce vanillin on a large scale using eugenol oxidase [112].In terms of pollutant degradation, Nocardioides often forms complex bacteria with other microorganisms [113].For example, a Nocardioides complex can produce biosurfactants that dissolve petroleum hydrocarbons and facilitate microbial utilization [114].In terms of commercial applications, it is expected that Nocardioides will be used to develop microbial agents with application value.In addition, their multiple biocatalytic enzymes can degrade and bioconvert steroids; this opens up new perspectives for the steroid pharmaceutical industry to create effective biocatalysts.
However, with the advancement of bioinformatics, the methods of whole-genome sequencing, genome assembly, and gene function prediction are gradually maturing.This is due to the late start of research on this strain which causes the degradation of environmental pollutants to still evolve.Gene function prediction analysis can be integrated with the gene information of Nocardioides and the functional genes enriched in a particular environment to confirm the functional genes.Therefore, it is increasingly important to study the structure and biological functions of Nocardioides.Simultaneously, Nocardioides is expected to develop into a microbial agent with significant market and application value based on existing strains' excellent pollutant degradation ability.Humans are expected to find new, more valuable Nocardioides species and more biological functions soon.
Figure 1 .
Figure 1.A phylogenetic tree of Nocardioidaceae belonging to the order Propionibacteriales of Actinobacteria.
Figure 1 .
Figure 1.A phylogenetic tree of Nocardioidaceae belonging to the order Propionibacteriales of Actinobacteria.
Figure 2 .
Figure 2. Phylogenetic dendrogram obtained via neighbor-joining using the 16s rRNA gene sequences of Nocardioides and related strains.(The numbers on the branch nodes are bootstrap values.)
Figure 2 .
Figure 2. Phylogenetic dendrogram obtained via neighbor-joining using the 16s rRNA gene sequences of Nocardioides and related strains.(The numbers on the branch nodes are bootstrap values.)
Figure 3 .
Figure 3. Types of Nocardioides habitats and the Nocardioides' distribution in different habitats.
Figure 3 .
Figure 3. Types of Nocardioides habitats and the Nocardioides' distribution in different habitats.
Figure 7 .
Figure 7. Proposed pathway and degrading genes of atrazine biodegradation by Nocardioides.
Figure 7 .
Figure 7. Proposed pathway and degrading genes of atrazine biodegradation by Nocardioides.
Table 1 .
Types of Nocardioides degradation contaminants and their degradability.
Table 1 .
Types of Nocardioides degradation contaminants and their degradability.
Table 2 .
Comparison of pollutant degradation capacity of Nocardioides sp. with other strains. | 8,366.4 | 2023-11-01T00:00:00.000 | [
"Biology",
"Environmental Science"
] |
Isoproterenol Induced Insulin Resistance Leading to Diabetic Ketoacidosis in Type 1 Diabetes Mellitus
Isoproterenol is known to cause insulin resistance and is often used to treat bradyarrhythmias from atrioventricular block. We report a case of isoproterenol induced diabetic ketoacidosis in a 77-year-old female patient treated with isoproterenol for atrioventricular block prior to insertion of permanent pacemaker. Diabetic ketoacidosis (DKA) developed within hours of starting an isoproterenol drip, and there were no other precipitating factors at that time. DKA resolved quickly after discontinuing isoproterenol and starting insulin drip. DKA is a common complication of diabetes mellitus, with about 140,000 hospital admissions for DKA in 2009. While the rate of DKA has increased by nearly 50% between 1988 and 2009, the rate of mortality has decreased. There are many causes of diabetic ketoacidosis, such as medication noncompliance, infection, pancreatitis, stroke, myocardial infarction, and many others. Isoproterenol may lead to diabetic ketoacidosis by increasing insulin resistance.
Introduction
Diabetic ketoacidosis (DKA) is a potentially life-threatening complication of diabetes mellitus. There are numerous known precipitants of DKA, including infection, stroke, myocardial infarction, insulin noncompliance, and medications. Diabetic ketoacidosis occurs at a higher rate amongst younger patients, females, those with lower socioeconomic status, those with poor glycemic control, and those with psychiatric symptoms or depression [1]. Presenting symptoms often include nausea, vomiting, polyuria, and polydipsia. Abdominal pain may occur in 46 percent of patients with DKA [2]. Physical exam may reveal Kussmaul respirations, signs of volume depletion, and findings associated with the precipitating cause of DKA. In some cases, a fruity odor is noted. We describe a case of DKA in a woman with type 1 diabetes mellitus, which was caused by medication-induced insulin resistance.
Case Report
A 77-year-old woman with a history of type 1 diabetes presented to the endocrinology clinic complaining of lightheadedness for several weeks. That morning, she experienced syncope and fell to the ground, striking her head. There were no episodes of severe or symptomatic hypoglycemia at home. She was directed to the emergency room, where a head CT revealed no evidence of hemorrhage and an electrocardiogram showed sinus tachycardia. Blood glucose was 34 mg/dL, so she was treated with intravenous dextrose, 25 grams. The patient was admitted to the telemetry floor. Over the subsequent 12 hours, blood glucose was monitored closely and remained between 179 and 303 mg/dL. She was treated with insulin glargine 24 units and insulin lispro 4 units TID with meals. Additional medications included enoxaparin prophylaxis, ezetimibe, fluoxetine, levothyroxine, lisinopril, potassium chloride, and pravastatin. With elevated blood glucose, she was treated with an additional dose of insulin lispro 5 units. The telemetry monitor demonstrated several 6to 9-second episodes of asystole, with intact P waves. She was transferred to the medical intensive care unit for atrioventricular block and started on an isoproterenol drip. Initial laboratory studies were notable for glucose of 297 mg/dL but otherwise normal. Four hours later, bedside blood glucose measured glucose >600 mg/dL (see Figure 1). Repeat laboratory data showed sodium 99 mmol/L, bicarbonate 11 mmol/L, anion gap 20, and glucose 1,713 mg/dL. Glycohemoglobin was 2 Case Reports in Endocrinology 7.5%. Thyroid stimulating hormone was normal. The patient was started on an insulin drip for diabetic ketoacidosis.
The isoproterenol was discontinued, and a pacemaker was placed. One hour after the discontinuation of isoproterenol, laboratory studies showed sodium 138 mmol/L, potassium 3.9 mmol/L, serum bicarbonate 17 mmol/L, chloride 103 mmol/L, and glucose 510 mg/dL. Venous blood gas revealed pH 7.19, pCO2 44 mmHg, and bicarb 16 mmol/L. Five hours after the discontinuation of isoproterenol, the diabetic ketoacidosis resolved.
Discussion
Isoproterenol is a nonselective beta-adrenoceptor agonist and an effective medication for bradyarrhythmias. We used this agent temporarily to increase the patient's heart rate, pending the placement of a permanent pacemaker. As a beta agonist, insulin resistance is a possible effect of isoproterenol. Thus, we monitored the patient's blood glucose closely, which we observed to increase dramatically, rapidly leading to diabetic ketoacidosis. Fortunately, this metabolic derangement was quickly controlled with continuous insulin infusion and discontinuation of isoproterenol. The following day, she was transitioned to subcutaneous insulin, with good control of blood glucose. Isoproterenol is known to cause glycogenolysis and insulin resistance. It increases serum glucose levels by promoting glycogenolysis, which occurs in a cyclic-GMP mediated fashion. Insulin resistance may be induced by isoproterenol via several mechanisms, including inhibition of resistin gene expression [3], inhibition of insulin mediated tyrosine phosphorylation of the insulin receptor [4], inhibition of localization of the glut-4 receptor to the cell wall [5], and activation of gene expression of SOCS-3 (suppressor of cytokine signaling-3), a negative regulator of insulin [6]. In addition, isoproterenol is known to have counterregulatory effects on sodium potassium chloride channels in skeletal muscle [7].
Tumor necrosis factor (TNF) alpha is produced by adipocytes and is known to cause lipolysis and insulin resistance. Elevated levels of TNF are observed with obesity. Isoproterenol causes a significant increase in TNF alpha levels [8] which may contribute to the medications' impact on overall insulin resistance.
By increasing insulin resistance, isoproterenol may increase the risk of diabetic ketoacidosis. Early recognition and prompt treatment of diabetic ketoacidosis are crucial, because the condition may lead to cerebral edema, severe hypokalemia, and death. Knowledge of this possible adverse event may assist clinicians in the prompt recognition of the complication and may improve outcomes and shorten hospital stays.
Diabetic ketoacidosis is characterized by hyperglycemia, ketonemia, and anion gap metabolic acidosis. While mortality has dramatically improved since the discovery of insulin, all-cause mortality in patients with DKA may be as high as 14%, and the condition is associated with significant morbidity. Several medications have been implicated in precipitating diabetic ketoacidosis, including clozapine, olanzapine, cocaine, lithium, corticosteroids, sodium-glucose cotransporter-2 (SGLT2) inhibitors, and terbutaline. To our knowledge, this case represents the first report of isoproterenol causing diabetic ketoacidosis, which likely occurred via insulin resistance.
Disclosure
This case report was presented as a poster presentation at the American College of Osteopathic Internists Research Symposium, October 27-31, 2016, and the Advocate Research & Innovation Forum, October 19, 2016. | 1,402.8 | 2018-12-17T00:00:00.000 | [
"Medicine",
"Biology"
] |
SELECTED METHODOLOGICAL ASPECTS OF MULTIDIMENSIONAL ANALYSES OF REGIONAL SPACE
The substantial research potential of already existing procedures, their development and proposing of new alternatives, as well as practical usability of taxonomic methods result in practically infinite possibilities in terms of their application in multidimensional analyses of regional space. They may play a significant part in the description, assessment and forecasting of development of individual regions. Having the knowledge, skills and competences, nowadays researchers are able to take advantage of guidance available in literature of the subject and the improving computer software. Nevertheless, due to lack of versatile solutions, every study has to be approached individually, making well thought-out decisions, often arbitrarily. The aim of this paper is to systematize certain methodological dilemma with regard to multidimensional analyses of regional space. The scientific discussion conducted makes it possible to answer questions of who and what is the subject of research of this type and to determine the characteristics of the most frequently undertaken research tasks. #0#
Introduction
Most categories in economy are characterized by spatial diversification, and to make the right socio-economic decisions, it is necessary to get familiar with this phenomenon. Quantitative methods turn out to be of great assistance in this regard. They are widely used in empirical research today, including regional research projects, and their usability is unquestionable. They are widely used in socio-economic analyses and diagnoses, making the Rafał Klóska description and assessment of the way that variables tend to change in time and space substantially more accurate. Therefore, apart from theoretical considerations, which are of great importance, it is recommendable to master the skill of effective use of statistical tools and techniques, which broaden the scope of scientific speculations, allowing for a complex and objective analysis of economic phenomena. These may be simple, describable using a single variable, or complex, requiring at least two -and usually more -variables. The methodology of analysis of simple phenomena is well developed today; multi-dimensional analysis, which is much more complex, and thus more difficult and less developed, has nevertheless been subject to extensive research in the last several decades. The present study puts emphasis on methodological aspects of analyses of this type, associated with determination of the subject of research, quantification of the research field and the specific characteristics of the basic research tasks.
Determination of the subject of research
The basic unit in statistical research is an object. In multi-dimensional analyses of regional space, it is the region. The interdisciplinary nature of this concept, which has been studied by representatives of many research disciplines, and at the same time the differences stemming from characteristics of economy, regional economics and local government finances, as well as economic geography, spatial economy, sociology, ethnography and other fields lead to development of various approaches to the idea. Etymologically, the term comes from the Latin word regio, regionis, which can be translated as 'space', or, more precisely, a direction that delineates a certain area, and as a result of general acceptance for this definition, the word "region" is today used in many countries and languages. In economic literature, the term pertains to certain polarized socio-economic and political-administrative fragments of space, which in terms of their territory fall below the national, but above the local level (Cooke, Leydesdorff, 2006, p. 6). In the vocabulary of the European union, the space of member states has been divided, using the statistical criteria, into the so-called NUTS, distinguishing five individual levels. In Poland, NUTS 1 is equivalent to a macro region, NUTS 2 -to a province, NUTS 3 refers to subregions, NUTS 4 -to districts and cities with district rights, while NUTS 5 pertains to commune; at the same time, the former three levels are referred to as being regional, and the latter two -as being local. The basic regional level, which serves as a basis for the EU regional policy, is nevertheless the second degree domestic administrative unit (NUTS 2) (Korenik, 1999, p. 53;Strahl, 2005, p. 18;Paradysz, 2012, p. 191), which is why in Poland a region is most often perceived as equivalent to a province.
Quantification of the research area
Spatial economy, innovativeness of regions, socio-economic development, competitiveness of regions, regional development -these are just a few of terms that are common today, although they have not been clearly defined, but interpreted implicitly and understood intuitively. Multidimensional phenomena of this kind are complex characteristics, for which a far-reaching consensus with regard to their meaning is assumed. Due to lack of precision and ambiguity of meaning of such terms, despite many attempts made to define them precisely, in everyday practice they function as conventional expressions, lacking, however, any clearly specified measurement methods. The basic problem is selection of specific diagnostic characteristics that would allow for quantification of the research area. Abstractive concepts and general identifiers of the described multidimensional categories require specification that would consist first of identification and then of use of a carefully selected set of measures, and there are no widely accepted, universal solutions in this regard. The complex nature of socio-economic phenomena that emerge in Vol. 28/2, 4/2018 Selected methodological aspects of multidimensional analyses of regional space regional space requires application of various measures, which should reflect all of the key characteristics of the phenomenon being analysed; an additional problem here is posed by difficulties due to lack or limited availability of specific statistical data. There is a generally acceptable notion of the information potential in this regard, which undoubtedly limits the complex description and assessment of regional space. Appropriate measurement requires a careful selection of the set of specific indicators, which should take into account the spatial and temporal scope, as well as the objective of analyses or diagnoses undertaken, and this issue has not been solved unambiguously so far; in empirical research on the subject, the sets of measures applied constitute a compromise between substantive premises and information capabilities and usually result from an arbitrary approach of the research team (Strahl, 2006, pp. 26-32). In other words, a long tradition of compromise between using the already gathered and available statistical data and indicators, which would be perfect for achievement of objective of a specific research project leads to a situation, in which in sets of identifiers for benchmark analyses, the sets of measures are selected according to the principle of the "best possible" choice (Graversen, Siune, 2008, p. 3). S. Wydmus has also underlined that in research of this type, we deal with a number of simplifications and generalizations, which stem from far-reaching synthesis of the multidimensional issues, mostly in the territorial dimension, as application of the same list of diagnostic characteristics applicable to different fields means that we assume that every country or region analysed is characterized by the same specific nature of development or strategy of decisions made despite the differences in their conditions (Wydmus, 1984, pp. 38-39). One should therefore understand that the final results of multidimensional benchmark analyses are determined mainly -apart from the statistical methods discussed further -by the list of variables to be applied in the research project. In many empirical research projects dedicated to the issue, the set of diagnostic variables is limited to a short analysis of characteristics based on substantive premises, or the mode of selection of these characteristics is left without much debate. Apart from substantive analysis of these characteristics, it seems reasonable at least to take into account the postulate of discrimination of features by applying the variability coefficient to elimination of quasi-constant variables. As the subsequent step, it is possible to apply a specific algorithm of formal procedures for formal and statistical selection with regard to the choice of variables proposed. Methods and techniques used at this stage have been widely described in literature, including such recommendable positions in this regard as the works of Z. Hellwig (1981), K. Jajuga (1993), M. Walesiak and E. Gatnar (2004), W. Pluta (1986), T. Grabiński, S. Wydmus andA. Zelias (1982, 1989), E. Nowak (1984Nowak ( , 1990, J. Pociecha, B. Podolec, A. Sokołowski and K. Zając (1988), as well as A. Malina (2004). One has to realize, however, that there is no simple answer to the question whether in selection of the final variables we should apply the criterion of variability or correlation, or perhaps introduce diversified weights, expressing the relative importance of variables, or apply other procedures, allowing, for instance, for grouping of characteristics or selection of their representatives. Potential weighing of features constitutes a separate problem and yet another methodological dilemma. In literature, there have been certain proposals in this regard (Grabiński, 1992, pp. 34-35), and it is also possible to seek expert opinions. Nevertheless, the issue has not been clearly resolved and no generally acceptable procedure has been developed. Therefore, in practice, most researchers attach the same importance to each feature, applying equal weights (Sokołowski, 1985, p. 48).
It should therefore be underlined that every case has to be assessed individually. Using various techniques and tools for selection of the initial variables, we may obtain different sets of characteristics of the objects being analysed. This is why strictly substantive selection is so important in searching for the ultimate list of diagnostic variables. In-depth recognition of the phenomenon being analysed, as well as familiarity with the achievements Rafał Klóska made so far, own reflections and expert opinions, common sense or even experience in research of this type, combined with intuition, are of utmost importance.
The specific nature of basic research tasks
As the aim of regional research is usually description and assessment of sets of object, the main two research tasks, presented in many research papers, are assumed to consist of grouping and linear ordering. The former allows for placing the statistical data in order, and it is limited to dividing the set of objects into groups of units that are similar in terms of the features applied to describe the phenomenon being examined. The second research task -linear ordering -can be brought down to putting the objects being analysed in order according to a specific criterion, which makes it possible to assign them a certain hierarchy. For the purpose of valuation of the objects being compared, an appropriate synthetic measure is applied (Zeliaś, 1991, p. 76;Czyżycki, 2018, p. 207). The substantial research potential of the already developed procedures, their development or proposing new ones creates practically unlimited possibilities of applications, particularly in regional research. In a classical taxonomic approach, multidimensional observations of the diagnostic variables applied in the objects examined allow for spatial analysis from a static (cross-cutting) perspective. Introduction of the additional dimension of time in dynamic research, that is, on the basis of multidimensional observations coming from various points or periods in time allows us to examine a complex issue of this kind from the perspective of the so-called data cube. This has been indicated, among others, by K. Jajuga (1987, pp. 14-16), M. Walesiak (1993, pp. 30-31) and J. Hozer (1987, p. 14). In terms of geometry, this figure can be imagined as a cross-sectional/temporal multidimensional series in a three-dimensional coordinate system, in which individual axes present dimensions of objects, variables and time units, respectively. Space created by sets of: -objects Y = {y 1 , y 2 , ..., y n ), -characteristics X = {x 1 , x 2 , ..., x k ), , -time units (moments or periods) T = {t 1 , t 2 , ..., t N ), and their multi-aspect analysis, enabled by the data cube, results in an enormous field of applicability of the multidimensional statistical analysis methods. Taxonomic issues can then be of simple nature (including the already mentioned classical issue of taxonomy, or grouping of multi-characteristics objects in a time unit), complex (combining two simple problems, allowing for analysis of e.g. time-objects or time-characteristics) or complex (encompassing a total examination of objects, characteristics and time units, taking into account the so-called time-characteristic-objects) (Sokołowski, 1982, pp. 65-71). Thus, a three-dimensional data cube can be used for an examination of: a) an overall approach -encompassing the entire data cube for n objects described using k variables in T time units; b) partial approaches -from the perspective of: object-variable, where n objects are considered from the perspective of k variables in a single given time unit; from the perspective of: time-variable, where the study is focused on a single object with regard to k variables over T time units; from the perspective of: objecttime, where n objects are described in T periods from the perspective of a single specific variable (this is an issue of single-dimensional analysis, not applicable to complex phenomena). Nevertheless, it is necessary to realize that there is no single answer to the question, which procedure is right for a specific empirical research project. Therefore, to be able to use specific taxonomic methods to group and Vol. 28/2, 4/2018 Selected methodological aspects of multidimensional analyses of regional space place in order a linear set of objects, the researcher must have the appropriate knowledge and skill sin this regard. In classification and linear hierarchy of sets of objects, despite numerous methodological guidelines in specialist literature, which has grown very rich, at least some of the decision-making problems have not been clearly solved and require a well thought out, responsible decision, made arbitrarily by the research leader.
Conclusions
The multitude of theoretical research papers, as well as empirical works, indicates clearly the practical usability of multidimensional analyses of regional space. As a result of application of computer software, which is available nowadays, it is relatively easy to use the appropriate statistical method, provided that the researcher is methodically and substantively familiar with the phenomenon being described. A conscious researcher must make well-thought-out decisions and know the level of significance of results obtained when using specific tools. In this article, by pointing out to the selected methodological aspects, the authors have put in order and partially solved the emerging dilemmas with regard to definition of the object of research, quantification of the research area and the specific nature of the research tasks undertaken. While certain problems have been explained, others have been merely indicated and they may serve as a starting point for scientific debate. Undoubtedly, research in this area should be continued. | 3,309.6 | 2018-01-01T00:00:00.000 | [
"Economics"
] |
Implementation of Pascal's Law Learning Media with a Scientific Approach to High School Physics Learning
Physics learning is inseparable from experiments. Some teachers have not been able to provide experimental tools in schools. One of the materials that requires experimental tools is Pascal's Law. The solution provided is in the form of developing a Pascal's law experimental tool using the R & D method. The development is using the ADDIE model which consists of the stages of analysis, design, development, implementation, and evaluation. The aim of this research is to investigate the results of the implementation of the Pascal's law experimental tool. Data collection instruments with pre-test, post-test, student worksheet, and student response questionnaires. The sample was taken from one class of 20 class 11 physics students at West Java. The questions on the pre-test and student worksheet totaled 7 items and 10 questions respectively. The student response questionnaire consisted of four aspects, namely aspects of ease of use, attractiveness, efficiency
INTRODUCTION
The Indonesian government is improving the quality of education by implementing the Independent Curriculum (Rohmadi, 2022;Hamdi, 2022). Implementing the Independent Curriculum is a government effort to restore learning after the Covid-19 pandemic (Natashia & Abadi, 2022;Septiani et al., 2022;Hasibuan et al., 2022). Many studies have revealed the occurrence of learning losses during online learning (Sabates et al., 2021;Schuurman et al., 2021). The Independent Curriculum will help restore and improve student competence (Vidieyanti et al., 2022;Nelisma, 2022). To achieve maximum results, there are nine guidelines that must be completed, namely the basic framework, curriculum structure, learning outcomes, teaching tools, reinforcement projects, assessment learning, operational curriculum, mechanism, and evaluation. These guidelines are being implemented by the government, teachers, students, boards of education, and the community.
Physics learning is often considered difficult for students because learning physics is related to real and abstract natural phenomena (Astra et al., 2015;Sadiah, 2021). Previous research reveals that students find difficulties in learning physics. Some of the reasons are that the teacher does not use interactive learning media in teaching, the teacher does not familiarize students with discovering concepts, the teacher only uses the lecture method in learning and so on Telaumbanua et al., 2021). The proper method used by the teacher to explain Pascal's law material is the experimental method. Physics learning is more appropriate if students practice a lot of experimental activities (Anggerni & Yohandri, 2022). Experimental activities can train students' mastery of concepts, scientific skills, and scientific attitudes (Yulyanti & Pratiwi, 2022). Therefore, teachers should have solutions to make physics learning meaningful and fun for students. Experimental activities can be carried out if the experimental tools and materials are available. In fact, only a few schools and teachers can provide experimental tools like Pascal's Law. Although, Pascal's Law simulation in PhET software is often used as an alternative to learning. But teachers can make simple experimental tools to make it easier for students to understand the concept of Pascal's Law. The advantage of using experimental tools is that students have real experience in measuring and retrieving experimental data. In addition, several scientific skills can be trained in students, such as science process, creativity, critical, problem-solving, collaboration and other skills. Thus, experimental tools have an important role in improving students' skills.
Many previous studies have developed experimental tools, especially Pascal's law. First, research by Reski et al. (2022) reveals that Pascal's law teaching aids are worth trying out in schools. The research is still in the validation stage. Second, Rofiqah et al.'s (2022) research discusses the development of Pascal's hydraulic law press teaching aids for class VIII students at junior high school. Similar to previous studies, the teaching aids developed are still at the validation stage. The validation results and student responses are 83% material validation, 88.3% material validation and 86.5% student responses. Third, research by Maliasih et al. (2015) also discusses the development of hydrolytic kit teaching aids and worksheets. The research results show an increase in students' concepts with an N-gain value of 0.65 (moderate category). Finally, the research by Pangke et al. (2021) shows that differences in the N-gain values in the small and large group tests are 0.90 and 0.92, respectively. This shows that the teaching aids developed can improve student learning outcomes in the concept of Pascal's law.
Based on previous research, there are some deficiencies, namely that there are no teaching aids developed for understanding the concepts of high school students. In addition, most research is still at the product validation stage, so it is necessary to develop visual aids for high school students that have been validated and tested on students. This study aims to develop experimental tools to improve students' understanding of Pascal's law material. The uniqueness of this research produces effective learning media and relevant student worksheets that make it easier for students to understand Pascal's law. In addition, this study describes the results of product development, deficiencies, and implications for further research. (He et al., 2021;Schüler-Meyer et al., 2019). The form of development carried out was the development of Pascal's law experimental tool. The development model used was the ADDIE model, which stands for analysis, design, development, and evaluation (Davis, 2013;Widyastuti & Susiana, 2019). The analysis phase was carried out to determine the students' constraints in learning Pascal's law. The design phase aims to design teaching aids that will be developed based on the problems found in the field. The development stage is important before the tool is tested on students. Next is the implementation stage to determine whether the tool can increase student understanding. Finally, the evaluation stage is needed to see the deficiencies from the previous stage that must be corrected. This study took a sample of 20 students in a high school in West Java. The sample consisted of 10 males and 10 females. Students were taken from different economic backgrounds. In addition, samples were taken from students who had previously studied Pascal's law material at both the junior high and high school levels. At the time of research, students had just studied Pascal's law material a week before the research was conducted. However, some students said they had forgotten the equations in Pascal's law. At that time, the school was still using the 2013 curriculum in learning, especially in class X. Each student was given a Student Worksheet to make it easier to do the experiments.
This study applied a research and development (R & D) method
The data collection instrument used pretest and posttest assessment sheet. A pretest was given to determine students' initial skills before conducting experiments; meanwhile, posttests would show students' skills after conducting experiments with experimental tools developed. Pretest and post-test questions in the forms of multiple choice and essay. Multiple choice questions consist of two items and essays of 4 items. These questions were taken from the results of research on the development of Pascal's legal assessment instruments that had previously been published. The data that has been collected was analyzed using Microsoft Excel and displayed in graphical form.
After conducting the experiment, students were given a practical questionnaire to see their responses after doing the experiment. The practicality questionnaire consists of 4 aspects: easy to use, attractive, efficient, and suitability of the material. The total number of questionnaires was 11 indicators which were distributed through Google Form to students. The questionnaire was given online through Google Form.
Results of the Analysis Stage
The first stage in this research is problem analysis. The problem is related to students' obstacles in learning Pascal's law. The results of interviews and observations with one of the physics teachers at the research school indicate that no real Pascal's law experimental tool is available in the laboratory. In addition, the results show that some students still experience misconceptions about Pascal's law material, as mentioned in the background. The development of this experimental tool is expected to increase students' interest in learning physics.
Results of the Design Stage
The second stage in this research is the design of the tool. At this stage, the criteria for tools and materials are also considered because this tool is a form of development from previous research. The tools and materials used include glass syringes, acrylic glue, sandpaper, bottle caps, pipettes, hose clamps, weights, scissors, acrylic, and hoses. All of these materials are in accordance with the project development design. The initial design of the tool can be seen in Figure 3. The design of the tool uses the usual Microsoft PowerPoint. Initially, researchers will develop two sets of tools, each consisting of 2 pairs of tubes. The first set consists of 1 tube with different diameters and oil fluid. The second set consists of a larger weight mass, and the fluid is water. After that, an initial prototype is made, as shown on the left. However, in this case, constraints are found on the capillary pipe, so the pipe is replaced with a plastic pipe, not a capillary pipe.
Results of the Development Stage
At this stage, the tool is tested internally. The trial of the experimental tool does not only look physically but also at it in terms of conformity with Pascal's law.
Figure 4. Pascal's Law Experiment Tool
The final results of the development of the experimental tool can be seen in Figure 4. Based on the suggestions and input from the supervisor, the original piston from the plastic injection is replaced with glass syringe to reduce the frictional force between the piston and the tube. In addition, previously, the force on the second cross-sectional area is given a load but replaced with a dynamometer. This aims to obtain more accurate data, prove the concept of Pascal's law, and make it easier for students to measure the force on each piston cross-section.
Results of the Implementation Stage
The next stage is the use of tools that have been developed for schools. The sampling students have studied Pascal's law before. To find out the student's skills, seven questions are given as a pretest. Then, after conducting the experiment, processing the data, and concluding the experiment, the students are given the same question again as a posttest. The results of the students' pretest, posttest, and N-Gain analysis can be seen in Table 1. The results of the two tests show a difference, although not significant. The average pretest and posttest scores of students are 77 and 82.5. The N-Gain calculation results obtain 0.24 in the low category. However, it can be seen that the maximum and minimum scores of the students are 90 and 60. If we look again, there are two students who receive high N-Gain categories, 8 students who receive medium N-gain categories, and 10 students who receive low N-Gain categories. The students' N-Gain scores varied quite a bit, ranging from -1.33 to 0.75. A total of three male students obtains N-Gain in the medium category while two other male students are in the low N-Gain category. Meanwhile, for female students, two students receive N-Gain in the high category. Four female students are in the medium category, and the remaining students are in the low N-Gain.
This implementation is equipped with worksheets to make it easier for students to obtain experimental data. A worksheet is designed as attractive as possible for one Pascal's law experiment. The worksheet is equipped with 10 data analysis questions. The results of the worksheet analysis can be seen in Figure 5.
Figure 5. The Results of Students' Worksheet Analysis
The results of processing student data on the worksheet can be seen in Figure 5. Three questions were answered correctly by all students. This question relates to the identification of independent, dependent and control variables in the experiment. The other two questions deal with graph interrogation and experimental conclusions. All students have answered correctly so that the points get full points on the three questions. However, in question number 2, which is related to the factors that affect the pressure in a closed system, only 50% of them are correct. It is necessary to apply the concept of pressure in closed and open systems to students.
The title of the worksheet designed is Pascal's Law Experiment Student Worksheet. Then, it is followed by student identities such as student name, absent number, class, and day/date of experiment. After that, the experiment aims to investigate the factors that affect the pressure in a closed system and determine Pascal's law equation from the experimental results. The tools and materials consist of props developed and variations in load (5 grams, 10 grams, 20 grams). Then, work instructions are given to facilitate students in retrieving data. The observation table consists of two tables for the same cross-sectional area and different cross-sectional areas. Students are asked to complete the calculated force column, the force measured by the spring balance, and the calculated force must be on a large cross-sectional area, followed by data analysis and conclusions, which consist of 5 questions each.
Results of the Evaluation Stage
The last stage is the evaluation stage of the tools that have been developed. At this stage, 11 indicator questionnaires were distributed to determine the practicality of the tools developed based on student responses. The questionnaire consists of 4 aspects, as shown in Figure 6. Figure 6 shows the results of the practicality questionnaire analysis on the development of experimental tools. In the questionnaire, four aspects were given: easy to use, attractive, efficient, and suitability of the material. This aligns with Dwijayani's (2019) research that learning media can increase students' interest in learning. There are a total of 11 indicators in the questionnaire, namely, three indicators for 'easy to use', three indicators for 'attractive', three indicators for 'efficient', and two indicators for 'suitability of the material'. The aspects of easy-to-use and attractive obtained the same percentage of 79.17 in the practical category. While the efficient aspect obtained the lowest percentage, namely 78.47%. But the difference is not too significant with other aspects. The highest aspect is obtained with a percentage value of 81.25% in the practical category. The analysis results of the average of the overall aspects are 79.51% in the practical category. Thus, the developed Pascal's law experimental tool can be used in physics learning.
Discussion
One of the learning media development models is the ADDIE model. The ADDIE model stands for analysis, design, development, and evaluation (Budoya et al., 2019;Almelhi, 2021). Several stages of developing learning media with the ADDIE model are the analysis, design, development, implementation, and evaluation (Spatioti et al, 2022).
The analysis stage is the first step in finding the problem to be solved. This analysis can be obtained from the results of interviews and observations at schools (Samudro et al., 2022). The analysis carried out relates to student learning outcomes, teacher learning media, learning models, and so on. Student learning outcomes can be obtained from daily, midterm, or final Indicator semester scores. Then, these values can be analyzed to determine whether there are misconceptions. Therefore, the analysis stage needs to be done to understand the urgent problems found in the field. The second stage is the design stage of the tool to be developed. Tool development means similar tools already exist. However, its weaknesses are analyzed and used as innovation for further development. In the previous stage, an analysis was carried out, and the tools, materials, and the right design were determined. Learning media that are designed must follow the concepts of physics and are useful for facilitating teachers in delivering learning material (Caleon et al., 2023). The teacher plays a very important role in determining the right learning media to increase student learning outcomes (Nevrita et al., 2020;Puspitasari, 2019). The tools and materials used must consider the security and safety of students in learning. Thus, the design stage becomes the initial solution to the problems that have been found.
The next stage is the tool development stage. The designs that have been designed are then developed into tools that are ready to use (Rosmiati & Siregar, 2021). The tools developed were first tested internally. This aims to find out whether there are still deficiencies in the tool itself. In addition, trials are also carried out by taking initial data internally and calculating how many deviations occurred. From this stage, the tool development stage must be tried out so that students can get good experimental results.
After that, the stage of implementing the tool in schools (Sriwahyuni et al., 2021). The implementation stage is supported by pretest and post-test questions, worksheets, and tools developed. Pretest questions are given before conducting the experiment, while post-test questions are given after conducting the experiment. Meanwhile, worksheets are given to students to guide students in retrieving data (Kadir et al., 2020;Yau & Mok, 2016). The results of the N-gain analysis show that student learning outcomes increase after conducting experiments with Pascal's law experimental tool. However, the results do not improve significantly. This is because the tool developed is only one, so students cannot do experiments with repetition.
Student Worksheets are used to support the application of Pascal's law experimental tools. In addition, worksheets help students collect data, process, and visualize experimental results. In other words, worksheets make it easier for teachers and students in the learning process (Basuki & Wijaya, 2018;Asrizal et al., 2019). The worksheets used previously have been adjusted to the basic competencies of learning. Furthermore, the worksheet is corrected according to the direction of the supervisor. The worksheet includes the title, student name, group name, experiment objectives, tools and materials, data tables, data analysis, further data analysis, and conclusions. Each student is given a worksheet for the smooth running of the experiment.
The last stage is the tool evaluation stage which involves students (Iswati, 2019). The results of student responses indicate that the designed experimental tool is easy for students to understand so that students can improve their understanding of the Pascal concept. This aligns with the opinion of Misbah et al. (2018) that a good worksheet can be used and understood by students well. Several questions are also asked in the worksheet to determine students' understanding of the concept. Worksheets can increase students' interest and creative skills (Hekmatulaini et al., 2020;Ubuz & Erdoğan, 2019;Chien & Chu, 2018). However, on the efficient aspect, not all students obtain accurate data in reading the spring balance scale. Worksheets and experimental tools have been designed according to Pascal's law material.
In general, students can distinguish between independent, dependent, and control variables. The independent, control, and dependent variables are mass, water, and spring balance, respectively. Most students also already know the factors that affect the pressure in a closed system, such as the mass and force exerted on the piston after conducting experiments. However, in describing the graph of the relationship between the force on the first crosssectional area and the second cross-sectional area in the experiment with different crosssectional areas, almost all students are wrong. When interviewed, students said that they were not used to making graphs and visualizing data in graphs. Incorrect graphic images result in errors in interpreting the data in the next question. Furthermore, student errors in reading the measurement results follow the questionnaire students filled out.
This research has several drawbacks. First, experimental tools are limited to a few masses of objects, so experimental tools are needed that are more flexible with large loads. Second, experimental tools are still being tested on a small sample scale, so larger trials are needed for one or two classes. Third, experimental tools can only be used manually on Pascal's law material and only one type of fluid. In further research, it is suggested that there be research related to comparing student achievement by learning with direct experimental tools, such as Pascal's law, with virtual experimental tools, such as PhET simulations.
CONCLUSION
Pascal's law experimental tool should be used by teachers in deepening students' physics concepts. Based on the research results, it is known that there are differences in student learning outcomes before and after using the tool. These results are indicated by obtaining an N-Gain of 0.24 in the moderate category. The results of student responses also show that the tools developed are easy to use, attractive, efficient and follow Pascal's law material. The average student response rate is 79.51% in the practical category. This shows that Pascal's law experimental tool that has been developed can make it easier for students to understand the concept of Pascal's law. In addition, students can also know the factors that directly affect the pressure on a closed system. | 4,776.8 | 2023-05-29T00:00:00.000 | [
"Physics",
"Education"
] |
Electronic Band Structure and Optical Properties of HgPS3 Crystal and Layers
Transition metal thiophosphates (MPS3) are of great interest due to their layered structure and magnetic properties. Although HgPS3 may not exhibit magnetic properties, its uniqueness lies in its triclinic crystal structure and in the substantial mass of mercury, rendering it a compelling subject for exploration in terms of fundamental properties. In this work, we present comprehensive experimental and theoretical studies of the electronic band structure and optical properties for the HgPS3 crystal and mechanically exfoliated layers from a solid crystal. Based on absorption, reflectance and photoluminescence measurements supported by theoretical calculations, it is shown that the HgPS3 crystal has an indirect gap of 2.68 eV at room temperature. The direct gap is identified at the Γ point of the Brillouin zone (BZ) ≈ 50 meV above the indirect gap. The optical transition at the Γ point is forbidden due to selection rules, but the oscillator strength near the Γ point increases rapidly and therefore the direct optical transitions are visible in the reflectance spectra approximately at 60–120 meV above the absorption edge, across the temperature range of 40 to 300 K. The indirect nature of the bandgap and the selection rules for Γ point contribute to the absence of near-bandgap emission in HgPS3. Consequently, the photoluminescence spectrum is primarily governed by defect-related emission. The electronic band structure of HgPS3 undergoes significant changes when the crystal thickness is reduced to tri- and bilayers, resulting in a direct bandgap. Interestingly, in the monolayer regime, the fundamental transition is again indirect. The layered structure of the HgPS3 crystal was confirmed by scanning electron microscopy (SEM) and by mechanical exfoliation.
Exfoliation of HgP S 3 Figure S6a shows how nearly transparent a monolayer is when the microscope is on reflection mode and with its diaphragm open.In the case of few-layers (e.g. 1, 2, 3 layers) one expects very low optical contrast, in such a way that the color of the flakes will be very similar to that of the substrate.One way to assure that the flake is a monolayer is by collecting differential reflectance spectrum between the flake and the substrate (Figure S6b) and check the spectral positions of the A, B and C excitons, which are well established for M oS 2 as well as M oSe 2 , W S 2 and W Se 2 .In the case of monolayer M oS 2 the narrow A exciton is located expected at approximately 1.92 eV, while B is at around 2.03 and the broad C exciton is expected at around 2.81 eV, and these values can vary 10-15 meV from flake to flake [1].The flake indicated by the arrow is therefore a monolayer.
Raman Spectroscopy
To the best of our knowledge, there is no literature regarding the Raman modes of HgP S 3 .Therefore, in this study we present an analysis of its vibrational modes by combining experimental data and DFT calculations.Figure S7a shows Raman spectra of bulk HgP S 3 from 10 to 300 K, and 12 peaks can be identified at low temperature, labeled P1 to P12 from low to high frequency, respectively and indicated by the arrows.In general, all of them undergo a slight shift to lower frequencies as the temperature increases (Figure S7b), apart from the usual decrease in intensity.Nevertheless, 7 out of the 12 peaks are still visible at 300 K. P2, P5, P11 and P12 vanish at around 200 K, while P7 vanishes at 280 K, as shows Figure S7b.Peak frequencies were extracted by Lorentz fits.No peak splitting is observed.These results suggest that the compound does not undergo structural phase transition in this temperature range.Raman spectra of exfoliated crystals of HgP S 3 are presented in Figure S7c.Three flakes were investigated at room temperature, and seven peaks can be observed: P1, P3, P4, P6, P8, P9, and P10, in excellent agreement with the spectrum of the bulk crystal at the same temperature.No significant difference between bulk and exfoliated HgP S 3 phonon modes was noticed.The exfoliated flakes were transferred onto a Si/SiO 2 substrate, and the intense peak at around 515 cm −1 is due to the substrate.Phonon calculations at the Γ point of the Brillouin Zone yielded 27 modes, with irreducible representation Γ = 15A g + 12A u , labeled Ag1 to Ag15 and Au1 to Au12, and marked by black and red vertical lines, respectively, in Figure S8.The main feature is at ≈ 241 cm −1 with a corresponding calculated phonon mode at ≈ 244 cm −1 .According to [2], only A g modes are Raman-active.The corresponding calculated phonon frequencies are given in Table S1, together with the frequencies of the 12 peaks experimentally observed at 10 K.The fact that 12 peaks were observed experimentally might be related to the setup configuration: some peaks might only be visible with parallel scattering configuration (the conventional one, used by us, in which incident and scattered light are parallel to each other), while others might only be accessed in cross-scattering configuration.
Figure S8: Raman spectrum of HgP S 3 at 10 K (blue) and 300 K (green), along with calculated phonon modes A g (black) and A u (red).
Figure
Figure S5: FT-IR spectrum of HgP S 3 .
Figure
Figure S6: a) Optical images of mechanically exfoliated M oS 2 flakes transferred to SiO 2 /Si substrate with 20x magnification.Red arrow indicates a monolayer candidate.b) Differential reflectance from the flake indicated by the arrow, which confirms that it is a monolayer.Dashed lines highlight spectral position of excitons A, B, and C. Inset shows an image of the monolayer with 50x magnification and closed diaphragm for better visualization.Red lines indicate the approximate flake dimensions: 27x17x15 µm.
Figure
Figure S7: a) Raman spectra of bulk HgP S 3 from 10 to 300 K. Spectra has been shifted vertically for better visualization.b) Temperature dependence of the frequency of the 12 peaks marked in a) by arrows.c) Raman spectra of exfoliated HgP S 3 flakes at 300 K. Peaks are labelled according to a).
Figure
FigureS10ashows the energy difference of the valence (3 bands) and conduction (2 bands) bands closest to the energy gap.The blue circles indicate the four lowest energy direct transitions at high symmetry points or local minima that have nonzero transition oscillator strengths (See FigureS10b, which presents specific values of these quantities for the x, y and z polarization components).S10c collects information from the previous figures.The size of the circle indicates the sum of the strength components of the transition oscillators, and the colors indicate the transition between specific bands.Higher energy optical transitions are possible at the Γ point, approximately at a few hundreds meV above the absorption edge.
Figure
Figure S10: a) Lowest energy direct transitions with non-zero matrix elements.b) Oscillator strength of each of the transitions for the x, y and z polarization components.c) combines a) and b): size of the circle indicates the sum of the oscillator strength, and the colors indicate the transition between specific bands.
Figure S11 :
Figure S11: Single particle dielectric function of HgP S 3 obtained by density-functional perturbation theory (DFPT).The inset includes a close-up of the edge with arrows marking the band gap, and the lowest optical transitions with non-zero oscillator strength presented in Figure S10a.
Table S1 :
Calculated phonon modes, the 12 experimentally observed peaks from bulk HgP S 3 at 10 K and corresponding frequencies. | 1,723.4 | 2024-05-23T00:00:00.000 | [
"Physics",
"Materials Science"
] |
Synthesis and evaluation of new fluorinated anti-tubercular compounds.
Treatment of tuberculosis (TB) and the discovery of effective new anti-tubercular drugs are among the most urgent priorities in health organizations all over the world. In the present study, fluorinated analogs of some of the most important anti-TB agents such as p-aminosalicylic acid (PAS), thiacetazone and pyrazinamide were synthesized and tested against TB. The fluorinated analog of thiacetazone was 20 times more potent than the parent compound against M.tuberculosis H37-RV, while the fluorinated p-aminosalicylic acid (PAS) was almost three times less potent than PAS. A few other halogenated analogs of thioacetazone were also synthesized and subjected to anti-M.tuberculosis screening tests. The best halogen substituent was found to be fluorine which has the smallest size from one hand and the strongest electronegativity from the other hand among the halogen atoms. Fluorine therefore could be considered as a golden substituent to improve the anti-M.tuberculosis activity of thioacetazone.
Introduction
Tuberculosis is the oldest documented infectious disease and it remains an important health concern all around the world. As indicated by recent reports of WHO, there were an estimated 8.7 million new cases of TB (13% co-infected with HIV) in 2011 and 1.4 million people died from TB in this year (1). The global resurgence of tuberculosis and development of drug resistance have rekindled the need for the development of new anti-tubercular drugs (2, 3). The results have been a torrent of papers and reports on compounds, which exhibit new mechanism of action or improved efficacy. Fluorine has been an attractive group for medicinal chemists and fluorinated compounds have many advantages that some of them are (4): a. as the second smallest substituent, fluorine most closely mimics hydrogen with respect to steric requirements at enzyme receptor sites, b. the presence of fluorine often leads to increased lipid solubility, thereby enhancing rates of absorption and transport of drugs in-vivo, c. the high electronegativity of fluorine frequently alters electronic properties, and thereby chemical reactivity and physical properties of compounds, d. fluorine imparts increased oxidative and thermal stability because the C-F p-aminosalicylic acid (PAS) and thiacetazone and their activities against M. tuberculosis were evaluated (Figure 1).
Chemistry
Substitution of fluorine on aromatic ring is conventionally performed via diazotization of primary aromatic amines, followed by thermal decomposition of the corresponding diazonium perfluoroborate salt (Schiemann reaction). This method was used for the preparation of 3-fluoropyrazincarboxamide (compound 6) and the desired compound was obtained in satisfactory yield (Figure 2).
In case of PAS and thioacetazone, the aromatic ring is rather electron rich and direct fluorination via an electrophilic aromatic substitution could be considered as the plausible method for the synthesis of their fluorinated bond is stronger than the C-H bond. This also limits enzymatic deactivation, e. in special cases, e.g. 5-fluorouracil, the specific location of the "deceptor" fluorine instead of hydrogen blocks an essential biochemical reaction and leads to its tumor inhibitory behavior.
Fluorinated analog of isoniazide ,as one of the most famous drugs for tuberculosis treatment, has already been synthesized and the results show that introducing fluorine on the pyridine ring drastically decreases the activity against M. tuberculosis (5). However the fluorinated derivatives of other first line medications in tuberculosis treatment i.e. PAS, pyrazinamide and thioacetazone have not been reported yet.
As part of our efforts to find new anti-TB agents, we have synthesized a series of fluorinated derivatives of famous synthetic anti-tuberculosis agents such as pyrazinamide, derivatives.
3 -fl u o r o -4 -a c e t a m i d o b e n z a l d e h y d e thiosemicarbazone (compound 16) was synthesized according to the synthesis scheme depicted in Figure 4. 4-acetamidobenzaldehyde was subjected to direct fluorination by Selectfluor TM in acetonitrile. 3-Fluoro-4acetamidobenzaldehyde thus obtained, was reacted with thiosemicarbazide to obtain compound 16 in satisfactory yield ( Figure 4).
In order to investigate the role of fluorine substitution on the activity of thiacetazone, other halogenated derivatives of this compound were also synthesized and subjected to antimycobacterium tuberculosis screening tests. Figure 5 illustrates the synthetic routes for the synthesis of compounds 17-25 (7, 8). Halogenated derivatives of PAS and pyrazinamide had been reported previously in literature as less active and therefore no attempt was made for their synthesis and anti-tuberculosis tests (9).
Chemistry
All solvents, reagents and catalysts were of analytical grade and used without further purification. The melting points (°C) were determined by open capillary method on an Electrothermal melting point apparatus and were uncorrected. The purity of compounds was confirmed by thin layer chromatography using Whatman Sil G/UV 254 silica gel plates as the
Preparation of methyl 3-aminopyrazine-2carboxylate (3)
To a suspension of 0.06 mol 3-aminopyrazine-2-carboxylic acid (2) in 40 ml methanol was added 8 mL of concentrated sulfuric acid slowly. The mixture was heated under reflux at 65 °C for 1.5 hours and was allowed to cool to room temperature. Enough concentrated ammonium hydroxide solution was added to make the pH basic and the precipitate was filtered and dried, resulting in 4.68 g (51%) of 3 as yellow solid.
Preparation of methyl 3-fluoropyrazine-2carboxylate (4)
A mixture of 0.0215 mole methyl 3-aminopyrazine-2-carboxylate (3) and 0.05 g copper powder in 12.5 mL of 40% tetrafluoroboric acid was stirred at room temperature for 10 minutes. After cooling to -5 °C in an ice-acetone bath, 1.79 g (0.026 mol) sodium nitrite was added in small portions while maintaining the temperature below 5 °C. The suspension was stirred at 0 °C for 15 minutes followed by 1.5 hours at room temperature. The reaction mixture was neutralized to a pH of 5-6 with sodium carbonate at 5-10 °C and extracted several times with 100 mL portions of diethyl ether. The combined ether layers were dried over anhydrous magnesium sulfate and the solvent was evaporated to give 2.75 g of the crude product. This compound was subjected to
Preparation of 3-fluoropyrazine-2-carboxylic Acid (5)
To a solution of 0.3 g (0.0022 mol) potassium carbonate in 7 mL water, was added 0.624 g (0.004 mol) methyl 3-fluoropyrazine-2-carboxylate (4). The mixture was heated at 90 °C under reflux for one hour and then was allowed to cool to room temperature. Enough concentrated HCl was added to bring the pH to 1. The precipitate was filtered and dried to give 0.34 g (60%) of a white solid. Recrystallization of this compound from water gave 0.27 g (42%) of the pure product which was characterized as 3-fluoro-2pyrazinecarboxylic acid monohydrate, mp 106-108.
Preparation of methyl 4-acetamidosalicylate (10)
To a suspension of 4.17 g (0.025 mol) methyl 4-aminosalicylate (9) in 20 mL water, was added 3 mL (0.032 mol) acetic anhydride while stirring. The mixture was heated at 80 °C for 30 minutes and cooled to room temperature. The precipitate was collected and added into 100 mL of 10% hydrochloric acid. This suspension was stirred at room temperature for 10 minutes, filtered and dried and recrystallized from methanol yielding
Preparation of 4-acetamido-3fluorobenzaldehyde (15)
A solution of 20.56 g (0.058 mol) Selectfluor TM in 400 mL acetonitrile was obtained by heating the mixture at 70-80 °C. To this solution was added 4.73 g (0.029 mol) 4-acetamidobenzaldehyde and the mixture was heated at 70 °C under reflux for 72 hours. The reaction mixture was allowed to cool and then added into 500 mL diethyl ether. The mixture was washed first with 3 × 300 mL water and then with 300 mL of saturated solution of sodium bicarbonate, dried over anhydrous MgSO 4 , evaporated and recrystallized from water containing 1 g activated charcoal to yield 0.91 g (19%)
Preparation of 4-acetamido-3-chlorobenzaldehyde (17)
To a solution of 6.43 g (0.039 mol) 4-acetamidobenzaldehyde in 55 mL of glacial acetic acid, was added 100 mL of 5.25% solution of sodium hypochlorite and the reaction mixture was stirred at room temperature for 48 hours. The mixture was poured into 100 mL water and filtered to give
Preparation of 4-acetamido-3-bromobenzaldehyde thiosemicarbazone (20)
A solution of 1.32 mL (0.0265 mol) of bromine in 6.25 mL of glacial acetic acid was added to a solution of 4.07 g (0.025 mol) of 4-acetamidobenzaldehyde in 22 mL glacial acetic acid slowly at room temperature. A precipitate developed in the reaction mixture when almost half of the bromine solution was added. The mixture was stirred at room temperature for one hour further and then poured into 100 mL of water. The mixture was stirred for 30 minutes until the strong yellow color of the solution disapeared. The precipitate was filtered and dried. Several recrystallization from methanol did not yield a pure compound. To a solution of 0.48 g of this mixture in 5 mL of ethanol, was added a solution of 0.182 g of thiosemicarbazide in 6 mL of water containing 0.4 mL of acetic acid at 70 °C. The mixture was stirred at this temperature for 45 minutes. The precipitate was filtered without cooling the mixture to give 0. ,38.11;H,3.50;Br,25.35;N,17.78;S,10.17. Found: C,38.58;H,3.74;Br,24.98;N,17.94;S,11.52.
Preparation of 4-amino-3-iodobenzonitrile (22)
To a solution of 5.9 g (0.05 mol) of 4-aminobenzonitrile in 25 mL of glacial acetic acid was added dropwise a solution of 0.05 mol of iodine monochloride in 5 mL of glacial acetic acid. During the addition the temperature rose to 40 °C. The solution was stirred at room temperature for 20 minutes. A solid developed in the reaction mixture and the deep brown color of the solution started fading gradually. The mixture was poured into 250 mL of water and stirred for 10 minutes to give a solid which was filtered and recrystallized from methanol/water containing 1 g of activated charcoal yielding 9.
Preparation of 4-acetamido-3iodobenzonitrile (23)
A mixture of 8.54 g (0.035 mol) of 4-amino-3iodobenzonitrile (22), 16 mL (0.16 mol) of acetic anhydride and five drops of concentrated sulfuric acid was heated at 70 °C under reflux for 10 minutes. The reaction mixture was poured over 400 mL of cold water and stirred for 5 minutes to give a white solid which was filtered and dried, yielding 9.
Preparation of 4-acetamido-3iodobenzaldehyde (24)
A mixture of 0.0197 mol of 4-acetamido-3iodobenzonitrile (23) 3.6 g of Raney nickel and 55 mL of 75% formic acid was heated under reflux at 85 °C for 1.5 hours. While the reaction mixture was still hot, it was filtered through a cake of filter aid and the residue was washed with 3 × 10 mL of absolute ethanol. The solvent was evaporated and the solid was recrystallized from methanol/water, yielding 4.2 g (73%) of 24
Anti-tuberculosis activity: In-vitro evaluation of anti-mycobacterial activity
Primary screening was conducted at 6.25 µg/ mL of the tested compounds against Mycobacterium tuberculosis H 37 Rv in BACTEC 12B medium using a broth microdilution assay, the Microplate Alamar Blue Assay (MABA) (10). Compounds effecting < 90% inhibition in primary screen (i.e., MIC > 6.25 µg/mL) were not generally evaluated further. Compounds demonstrating at least 90% inhibition in primary screening were retested at lower concentration against M. tuberculosis H 37 R V to determine the actual minimum inhibitory concentration (MIC) using MABA. The MIC is defined as the lowest concentration effecting a reduction in fluorescence of 90% relative to controls.
Concurrent with the determination of MIC, compounds were tested for cytotoxicity (IC 50 ) in VERO cells at concentration ≤ 62.5 µg/ mL or 10 × the MIC for M. tuberculosis H 37 R V . After 72 hours exposure, viability was assessed on the basis of cellular conversion of MTT into a formazan product using the Promega Cell Titer 96 Non-radioactive Cell Proliferation Assay.
For the most active compounds MICs were determined in MABA against M. avium and against five strains of single-drug-resistant (SDR) M. tuberculosis (i.e., each strain resistant to a single TB drug). The minimum bactericidal concentration (MBC) was then determined for M. tuberculosis H 37 R V and Erdman (and for the appropriate drug-resistant strain, for analogs of known anti-tubercular drugs) by subculturing on drug-free solid media and enumeration colony forming units following exposure in supplemented Middlebrook 7H9 media to drug concentrations equivalent to and higher than the previously determined MICs of the respective strains.
Results and Discussion
All the synthesized fluorinated compounds were assayed for their anti-tubercular activities and the results of primary screening are presented in Table 1.
The Bactec media, which is used for these tests, has the pH of 6.5-6.8. Pyrazinamide itself is almost completely inactive at a neutral pH (11). Thus one could expect to get almost no activity for the compounds 5 and 6 which are close derivatives of pyrazinamide.
MIC of p-aminosalicylic acid (PAS) against M. tuberculosis H 37 R V (determined by MABA system) is 1.25 µg/ mL (10), while this value for compound 12 is ≤ 3.13. This means compound 12 is almost three times less active than the parent compound; but it is still considered as a potential candidate and further tests were conducted on this compound and the results are presented in Table 2.
The MIC of thiacetazone against M. tuberculosis H 37 R V (determined by MABA system) is > 2.0 µg/mL (10), while this value for compound 16 is ≤ 0.1. This means compound 16 is about 20 times more potent than the parent compound; and it is an excellent candidate for further tests (Table 2).
Other halogenated thiacetazone derivatives were also assayed for their anti-TB activities and the results of compelementary tests are presented in Table 2.
As it appears from Table 1 and 2, all halogenated derivatives of thiacetazone were more potent than thiacetazone against M. tuberculosis H 37 R V . The higher activities of all halogenated derivatives compared to the parent compound (thiacetazone) could be due to the effect of halogen substituents on electronic and/ or partitioning characteristics of thiacetazone.
Comparison of MIC values for the halogenated derivatives (comp 16-25) shows the following order of activity: The decrease in activity when a halogen substituent is changed with its larger counterpart, might be due to the steric hindrance caused by larger halogen substituents on aromatic ring.
The minimum bactericidal concentration (MBC) for compounds 12 and 16 against a few M. Tuberculosis strains are presented in Table 3.
In summary the result of this study shows that substitution of a halogen group on the phenyl ring in thiacetazone, improves anti-M. tuberculosis activity of this compound. Interestingly the best halogen substituent is fluorine which has the smallest size from one hand and the strongest electronegativity from the other hand among the halogen atoms. This fact reemphasizes the unique nature of fluorine as a golden substituent in medicinal chemistry.
Thiacetazone is a thiocarbamide-containig drug which has been reported to alter the mycolic acid profile of M.bovis BCG (13). Mycolic acids are a complex mixture of branched, long-chain fatty acids, representing key components of the highly lipophilic (hydrophobic) mycobacterial cell wall. Pathogenic mycobacteria carry mycolic acids that contain cyclopropane rings in their structure. The enzyme which is responsible for cyclopropanation of mycolic acid is cyclopropane mycolic acid synthases (CMASs) and it has been proven that thiacetazone and its analogs act directly on CMASs and suppress the biosynthesis of cyclopropane-containing mycolic acids.
Thiosemicarbazone moiety is recognized as the pharmacophore group in thiacetazone scaffold 13-15). Therefore it could be speculated that the new thiacetazone-related compounds (3) (6) (8) (10) This article is available online at http://www.ijpr.ir which are reported in this study, exert their activity by a similar mechanism. While this speculation is attractive, further confirmation is required through complementary mechanistic studies. In-vivo screening will also clarify the effectiveness of these compounds in biological fluids.
Conclusion
In this work, we present the synthesis of fluorinated derivatives of three official anti-M.tuberculosis drugs: pyrazinamide, PAS and thiacetazone. Contrary to pyrazinamide and PAS, the fluoro substituted thiacetazone exhibited higher activity than thiacetazone. Therefore, this study suggests the incorporation of a fluoro substituent on position 3 of thiacetazone in order to better interaction with its possible target cyclopropane mycolic acid synthase (CMAS). Other halogenated derivatives were also more active than thioacetazone but fluoro derivative was the most potent analog.
In summary, this study demonstrated that simple structural modification of the thioacetazone scaffold may lead to a new thiacetazone analog for the potential treatment of tuberculosis as mycolic acid inhibitor. | 3,750.6 | 2014-01-01T00:00:00.000 | [
"Chemistry"
] |
Understanding the Molecular Diversity of GABAergic Synapses
GABAergic synapses exhibit a high degree of subcellular and molecular specialization, which contrasts with their apparent simplicity in ultrastructural appearance. Indeed, when observed in the electron microscope, GABAergic synapses fit in the symmetric, or Gray’s type II category, being characterized by a relatively simple postsynaptic specialization. The inhibitory postsynaptic density cannot be readily isolated, and progress in understanding its molecular composition has lagged behind that of excitatory synapses. However, recent studies have brought significant progress in the identification of new synaptic proteins, revealing an unexpected complexity in the molecular machinery that regulates GABAergic synaptogenesis. In this article, we provide an overview of the molecular diversity of GABAergic synapses, and we consider how synapse specificity may be encoded by selective trans-synaptic interactions between pre- and postsynaptic adhesion molecules and secreted factors that reside in the synaptic cleft. We also discuss the importance of developing cataloguing tools that could be used to decipher the molecular diversity of synapses and to predict alterations of inhibitory transmission in the course of neurological diseases.
INTRODUCTION
One of the most striking aspects of inhibitory synaptic circuits is the remarkable diversity of GABAergic systems. GABAergic interneurons occur in many different subtypes, that play exquisitely precise functions in neural networks . Each type of interneuron is highly selective, making synapses with particular populations of target cells and only with specific subcellular compartments (Huang et al., 2007). Moreover, the diversity of GABAergic interneurons matches a corresponding multiplicity of synaptic and extrasynaptic GABA A receptor (GABA A R) subtypes, that support neural circuit operations under an extensive range of behavior-dependent brain states (Monyer and Markram, 2004;Freund and Katona, 2007;Klausberger and Somogyi, 2008;Olsen and Sieghart, 2009). For example, in hippocampal and cortical circuits, basket cells containing either parvalbumin (PV) or cholecystokinin (CCK) target the cell body of pyramidal cells at synapses containing mainly α1β2/3γ2 GABA A Rs, which display fast kinetics of deactivation, or α2β2/3γ2 GABA A Rs, which have slower kinetics compared to receptors containing the α1 subunit (Klausberger et al., 2002;Klausberger and Somogyi, 2008). While PV-basket cells appear to control the temporal coordination of principal neurons and network oscillations, CCK-positive interneurons modulate synchronous activities by integrating subcortical and local modulatory signals (Freund and Katona, 2007;Sohal et al., 2009;Thomson and Jovanovic, 2010). Notably, these differences can be extended to the level of pathology, as the two types of GABA A Rs appear to be implicated in different types of neurological and psychiatric disorders (Lewis et al., 2005;Freund and Katona, 2007). Similarly, genetic manipulations of individual GABA A R subunits in mice produce selective alterations in behavior, reinforcing the idea that specific neuronal networks characterized by respective GABA A R subtypes are involved in the regulation of defined behavioral patterns (McKernan et al., 2000;Möhler, 2006Möhler, , 2007Whiting, 2006). This extraordinary diversity contrasts with the apparent simplicity in the ultrastructural appearance of GABAergic synapses. When observed in the electron microscope, GABAergic synapses fit in the symmetric, or Gray's type II category (Gray, 1959;Colonnier, 1968;Peters and Palay, 1996). These synapses are characterized by a thin postsynaptic density (PSD), similar in size to the presynaptic active zone. In contrast, glutamatergic synapses belong to the asymmetric, or Gray's type I group, which is distinguished by a prominent PSD. Asymmetric synapses also show a conspicuous electron dense material in the synaptic cleft, which is less obvious in symmetric synapses. Not surprisingly, the morphological differences between type I and type II synapses are proportional to their molecular complexity. Proteomic studies of the excitatory PSD have revealed a number of proteins greater than 1000 (Collins et al., 2005;Bayés et al., 2011), which exceeds by two orders of magnitude the number of molecules that have been found in the inhibitory PSD (Lüscher and Keller, 2004;Charych et al., 2009). It would be hazardous, however, to conclude that all GABAergic synapses share the same basic molecules and mechanisms to sustain their exquisite specificity. In this essay, we review recent work that points to a remarkable heterogeneity of the molecular machinery that regulates GABAergic synaptogenesis in vivo and we provide a personal view of the mechanisms that may underlie synapse specificity during the development of neural circuits.
Understanding these mechanisms is of interest for both basic and clinical neuroscience, as disruption of inhibitory synapse development is now regarded as a major cause of brain disease (Lewis et al., 2005;Südhof, 2008;Charych et al., 2009). A detailed description of the molecular organization of GABAergic synapses falls outside the scope of this paper and can be found in other excellent review articles (Lüscher and Keller, 2004;Tretter and Moss, 2008). Here we rather focus on the evidence that the diversity of GABAergic synapses may be generated by the interplay of multiple molecular mechanisms with partially overlapping functions. We also discuss the importance of a classification scheme that could be used to identify distinct types of synapses based on the differential expression of groups of interacting proteins.
POSTSYNAPTIC SCAFFOLDS OF INHIBITORY SYNAPSES
One of the main achievements in the field of synapse research has been the characterization of the molecular components of the PSD. Molecular investigations of glutamatergic synapses have shown that the PSD is a specialized microdomain characterized by core scaffolding proteins, such as PSD-95, that link glutamate receptors to the subsynaptic cytoskeleton and also interact with different types of regulatory proteins and with cell adhesion molecules via specific PDZ domains (Kennedy, 1997;Ziff, 1997;O'Brien et al., 1998;Garner et al., 2000;Kim and Sheng, 2004;Boeckers, 2006). Importantly, there is increasing evidence that proteinprotein interactions within the PSD are not static and that dynamic modulation of the PSD provides a mechanism for the regulation of synaptic plasticity (Scannevin and Huganir, 2000;Kim et al., 2007;Steiner et al., 2008). The inhibitory PSD cannot be readily isolated, and progress in understanding its molecular composition has lagged behind that of excitatory synapses. The multi-domain, 93 kDa protein gephyrin has emerged as a major scaffolding molecule of the inhibitory PSD Fritschy et al., 2008). Here we briefly summarize the proposed functions of gephyrin and we describe other scaffolding molecules that may contribute to assemble postsynaptic specializations in at least some subtypes of inhibitory synapses.
GEPHYRIN
Gephyrin was originally copurified with the glycine receptor (GlyR; Pfeiffer et al., 1982), and was later found also at postsynaptic sites of GABAergic synapses (Sassoè-Pognetto et al., 1995;. This molecule lacks PDZ domains, but can form aggregates by spontaneous oligomerization, although the precise mechanisms by which gephyrin forms postsynaptic scaffolds is still unresolved (for review, see Fritschy et al., 2008). Gephyrin binds a cytoplasmic loop of the GlyR β subunit (Meyer et al., 1995), and is essential for postsynaptic clustering of GlyRs (Kirsch et al., 1993;Feng et al., 1998). This scaffold protein also contributes to stabilize postsynaptic GABA A Rs, as its knockdown in cultured neurons causes a disruption of GABA A R clusters (Essrich et al., 1998;Yu et al., 2007). Similarly, knockout of the gephyrin gene in mice results in an extensive loss of postsynaptic GABA A R aggregates (Kneussel et al., 1999(Kneussel et al., , 2001Fischer et al., 2000;Lévi et al., 2004).
The precise mechanisms by which gephyrin clusters GABA A Rs are poorly understood, although there is evidence that this molecule restrains the lateral mobility of the receptors in the plasma membrane (Jacob et al., 2005;Thomas et al., 2005). Most likely, this function involves interactions with the cytoskeleton, as gephyrin binds with high affinity polymerized tubulin (Kirsch et al., 1991;Kirsch and Betz, 1995) and serves as an adaptor for regulators of microfilament dynamics (Mammoto et al., 1998;Giesemann et al., 2003;Bausen et al., 2006). Interestingly, the clustering of gephyrin and GABA A Rs are to some extent mutually dependent on each other, since synaptic gephyrin clusters are disrupted after deletion of GABA A Rs (Essrich et al., 1998;Schweizer et al., 2003;Li et al., 2005;Kralic et al., 2006;Studer et al., 2006). Alldred et al. (2005) have identified the fourth transmembrane domain of the GABA A R γ2 subunit as essential to mediate postsynaptic clustering of GABA A Rs, whereas the major γ2 cytoplasmic loop is required for recruitment of gephyrin to GABA A R clusters. Direct interactions between gephyrin and the GABA A R α2 and α3 subunits have emerged only recently (Tretter and Moss, 2008;Saiepour et al., 2010). The binding of gephyrin to the α subunits appears to be detergent sensitive, which may explain why it has been remarkably difficult to reveal these interactions using biochemical approaches. However, whether gephyrin binding to GABA A Rs involves multiple interactions with distinct α and γ subunits is presently unclear. The relevance of the numerous gephyrin isoforms generated by alternative splicing is also not understood (Paarmann et al., 2006;Fritschy et al., 2008). Moreover, gephyrin function may depend on post-translational modifications. Indeed, recent studies indicate that phosphorylation of gephyrin at specific residues contributes to regulate the anchoring of GlyRs and GABA A Rs at postsynaptic sites (Zita et al., 2007;Charrier et al., 2010;Tyagarajan et al., 2011).
A still unresolved issue is whether gephyrin contributes equally to the clustering of all major subtypes of synaptic GABA A Rs (that is receptors that are highly concentrated in the postsynaptic membrane and mediate phasic inhibition). Extensive experimental evidence indicates that receptors containing a γ2 subunit in association with two α and two β subunits (α1β2/3γ2, α2β2/3γ2, and α3β2/3γ2) are the predominant types of synaptic GABA A Rs (for review, see Lüscher and Keller, 2004;Farrant and Nusser, 2005). The analysis of spinal cord sections, retina organotypic cultures, and cultured hippocampal neurons derived from gephyrin knockout mice lead to the idea that gephyrin mediates the postsynaptic accumulation of GABA A Rs containing the α2 or the α3 subunit, and suggested the existence of additional clustering mechanisms (Fischer et al., 2000;Kneussel et al., 2001;Lévi et al., 2004). However, in the brain gephyrin colocalizes with all major types of postsynaptic GABA A Rs containing either the α1, α2, or α3 subunit , indicating that its function is not restricted to α2 and α3-containing synapses. Because gephyrin knockout mice die at birth (Feng et al., 1998), a better appreciation of gephyrin function at distinct types of GABAergic synapses may derive from the study of mouse models with conditional deletion of this protein in selected populations of neurons characterized by the expression of distinct GABA A R subtypes. The complex situation regarding the role of gephyrin in the clustering of different GABA A Rs may also be explained by redundancy between multiple clustering factors with partially overlapping synaptic expression profiles (see below).
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THE DYSTROPHIN-GLYCOPROTEIN COMPLEX
Another postsynaptic scaffold that is present in some GABAergic synapses is dystrophin. This protein belongs to the dystrophinglycoprotein complex (DGC), a large, membrane-spanning protein complex that links the cytoskeleton to the extracellular matrix (Ervasti and Campbell, 1991;Blake and Kröger, 2000;Waite et al., 2009). Dystrophin is derived from a large gene with at least seven internal promoters that enable the expression of several distinct isoforms (for review see Perronnet and Vaillend, 2010). Interestingly, the full-length (Dp427) isoform is derived from three independent promoters with differential expression in muscle, forebrain, and cerebellar Purkinje cells. The N-terminal domain of dystrophin binds to filamentous actin, whereas the C-terminal domain interacts with dystrobrevins (α and β) and syntrophins (α, β1-2, γ1-2), which are also cytoplasmic constituents of the DGC. Several dystrobrevin-binding elements have been identified, including dysbindin, a protein that has been associated with schizophrenia (Benson et al., 2001;Talbot et al., 2009). However, immunohistochemical analyses suggest that dysbindin is not enriched at GABAergic synapses (unpublished observations). Syntrophins are adaptor proteins each containing a PDZ domain and two pleckstrin homology (PH) domains mediating interactions with several other proteins, including kinases, ion and water channels, and nNOS (Waite et al., 2009).
Syntrophin colocalizes with GABA A Rs in cultured hippocampal neurons (Brünig et al., 2002), however the synaptic localization of endogenous syntrophins in unknown. Of particular interest is the fact that the γ2-syntrophin isoform has been reported to interact with the PDZ binding motif of the adhesion molecules neuroligin 3 and neuroligin 4 (Yamakawa et al., 2007), which are present at inhibitory synapses (see below). It is therefore possible that interactions between syntrophins and neuroligins may help organize postsynaptic scaffolds at inhibitory synapses (Figure 1). A core component of the DGC is dystroglycan, which is composed of an extracellular α subunit and a transmembrane β subunit, derived by proteolytic cleavage from a single precursor protein (Ibraghimov-Beskrovnaya et al., 1992). The βdystroglycan subunit contains a single transmembrane domain and its cytoplasmic tail binds dystrophin, whereas α-dystroglycan is a secreted glycoprotein that binds to LNS (laminin G, neurexins, and sex hormone-binding globulin)-domain-containing proteins, such as laminin, perlecan, agrin, neurexin, and pikachurin (Bowe et al., 1994;Gee et al., 1994;Talts et al., 1999;Sugita et al., 2001;Sato et al., 2008). The fact that α-dystroglycan binds neurexin is particularly intriguing, as it suggests that the DGC may mediate trans-synaptic interactions between pre-and postsynaptic specializations.
FIGURE 1 | Postsynaptic scaffolds and adhesion molecules of GABAergic synapses.
The diagram is based on reported molecular interactions (see text), some of which remain to be confirmed in vivo. Gephyrin, S-SCAM/MAGI-2, and dystrophin are shown in the same postsynaptic specialization, although dystrophin is present in only a subset of GABAergic synapses and the in vivo distribution of S-SCAM/MAGI-2 has not been characterized. Gephyrin trimers are believed to aggregate into a submembranous lattice that provides stability to postsynaptic GABA A Rs. Gephyrin also binds collybistin (CB) and neuroligin 2 (NL2), that has been proposed to function as a specific activator of collybistin. Cytoskeletal proteins associated with gephyrin, such as Mena/VASP and microtubules, are not shown. Neuroligin 2 bridges the synaptic cleft and binds to neurexins on the presynaptic terminal. Reported interactions between neurexins and GABA A Rs are also indicated. Neurexins may also interact with α-dystroglycan (α-DG), thus establishing a link with the dystrophin-glycoprotein complex (DGC). One component of the DGC, syntrophin, has been reported to bind neuroligin 3 and neuroligin 4. Finally, there is evidence that S-SCAM/MAGI-2 may establish a link between neuroligin 2 and the DGC by interacting with the intracellular domain of β-dystroglycan (β-DG).
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Immunohistochemical analyses have shown that the DGC is present in a subset of GABAergic synapses, specifically in cerebellar Purkinje cells and in forebrain pyramidal neurons (Knuesel et al., 1999;Sekiguchi et al., 2009;Briatore et al., 2010). Interestingly, both in vitro and in vivo analyses have shown that the synaptic localization of dystrophin and dystroglycan are independent of GABA A Rs and gephyrin, suggesting that the DGC has the capacity to self-assemble at postsynaptic sites (Brünig et al., 2002;Lévi et al., 2002;Patrizi et al., 2008a). The studies that have investigated the function of the DGC at GABAergic synapses have generated partially conflicting results. Deletion of dystroglycan in cultured hippocampal neurons caused a loss of postsynaptic dystrophin, but did not affect the localization of gephyrin and GABA A Rs (Lévi et al., 2002). In contrast, in vivo analyses of mdx mice, that lack the full-length version of dystrophin, revealed a selective deficit in the synaptic clustering of GABA A Rs, but not gephyrin, in cerebellum, hippocampus, and amygdala (Knuesel et al., 1999;Sekiguchi et al., 2009;Vaillend et al., 2010). Similar results have been reported in the cerebellum of double knockout mice lacking both α and β dystrobrevins (Grady et al., 2006). The selective loss of GABA A R clusters, but not gephyrin clusters in mdx mice is surprising, also considering that deletion of GABA A Rs from Purkinje cells causes a severe defect in the clustering of gephyrin without affecting dystrophin and dystroglycan (Patrizi et al., 2008a). However, there is extensive electrophysiological evidence indicating that an intact DGC is required for normal GABAergic inhibition (Anderson et al., 2003;Kueh et al., 2008;Sekiguchi et al., 2009). In short, the available data indicate that the DGC is involved in modulating synaptic function in a subset of GABAergic synapses. However, the precise organization of the synaptic DGC and the specific contribution of its molecular constituents require further investigations.
S-SCAM/MAGI-2
According to a recent study, the synaptic scaffolding molecule (S-SCAM)/membrane-associated guanylate kinase with inverted organization (MAGI)-2 localizes at inhibitory synapses in rat primary hippocampal neurons (Sumita et al., 2007). This is surprising, because S-SCAM/MAGI-2 has a molecular organization similar to PSD-95, harboring multiple PDZ domains, a guanylate kinase, and two WW domains. S-SCAM/MAGI-2 is also present at glutamatergic synapses, where it interacts with NMDA receptors, neuroligin 1, and β-catenin (Hirao et al., 1998;Iida et al., 2004). At GABAergic synapses, it has been reported that S-SCAM/MAGI-2 can interact with β-dystroglycan and neuroligin 2, suggesting that this scaffold molecule may provide a link between the DGC and the neurexin-neuroligin adhesion system (Sumita et al., 2007). Thus it appears that S-SCAM/MAGI-2 and syntrophins may mediate selective interactions between the DGC and, respectively, neuroligin 2 and neuroligins 3 and 4 (Figure 1). Research on S-SCAM/MAGI-2 is still at its beginnings, but it may lead to the discovery of new mechanisms underlying the assembly of the inhibitory PSD. It will be important to characterize the spatio-temporal profile of S-SCAM/MAGI-2 expression in relation to the other molecular constituents of GABAergic postsynapses. In addition, it will be of primary interest to investigate the possible redundancy of trans-synaptic signals mediated by the DGC and the neurexin-neuroligin adhesion system. More in general, in vivo analyses are needed to get a clear picture of the endogenous distributions of these different scaffolding systems and to help dissecting their specific roles in different populations of synapses.
VARIABILITY IN THE MECHANISMS THAT REGULATE THE POSTSYNAPTIC ACCUMULATION OF GEPHYRIN
While gephyrin is expressed almost ubiquitously at inhibitory synapses, recent studies have evidenced an unexpected variability in the mechanisms that control its synaptic localization. For example, in cerebellar Purkinje cells gephyrin is expressed initially at all GABAergic synapses, however during postnatal development gephyrin clusters disappear from perisomatic synapses and remain exclusively at axodendritic contacts (Viltono et al., 2008). While the reasons for this differential regulation are unclear, the loss of gephyrin is mirrored by a structural reorganization of perisomatic synapses, consisting in a reduction in the size of GABA A R clusters and in the length of synaptic appositions.
One protein implicated in the recruitment of gephyrin to postsynaptic specializations is the GEF (guanine nucleotide exchange factor) collybistin, that was identified as a gephyrin-binding protein in a two-hybrid screening (Kins et al., 2000). Collybistin, like other GEFs, is characterized by an N-terminal src homology 3 (SH3) domain, a catalytic tandem Dbl homology (DH) domain and a PH domain. It is believed that collybistin participates in the membrane targeting of gephyrin by binding membrane lipids through its PH domain (Harvey et al., 2004;Reddy-Alla et al., 2010). Different collybistin isoforms (CB1-3) have been identified, which are created by alternative splicing of exons encoding the SH3 domain and three alternate C termini (Kins et al., 2000;Harvey et al., 2004). Interestingly, expression studies have shown that the SH3 domain negatively regulates collybistin function (Kins et al., 2000;Harvey et al., 2004). However, most endogenous collybistin isoforms harbor this region, suggesting that collybistin activity requires protein-protein interactions at the SH3 domain (Kins et al., 2000;Harvey et al., 2004). Indeed, recent investigations have shown that the synaptic adhesion molecules neuroligin 2 and neuroligin 4 can bind to and activate collybistin by relieving the SH3-mediated inhibition (Poulopoulos et al., 2009;Hoon et al., 2011). In addition, all neuroligin isoforms have in their cytoplasmic domain a conserved gephyrin-binding motif that contributes to recruit gephyrin to synapses. It has been proposed that by interacting with gephyrin and collybistin neuroligin 2 can act as a nucleation site for the formation of postsynaptic gephyrin scaffolds that recruit GABA A Rs at postsynaptic sites (Poulopoulos et al., 2009). On the other hand, knockout of neuroligin 2 has only a relatively small effect on the clustering of gephyrin and GABA A Rs, specifically at perisomatic synapses of hippocampal neurons (Poulopoulos et al., 2009). In contrast, deletion of collybistin or GABA A Rs causes an extensive loss of gephyrin clusters (Essrich et al., 1998;Li et al., 2005;Kralic et al., 2006;Studer et al., 2006;Papadopoulos et al., 2007;Patrizi et al., 2008a). These observations question the importance of neuroligin 2 as a major physiological clustering factor for gephyrin and collybistin and suggest that there could be multiple pathways capable of activating collybistin with differential cellular and subcellular specificity.
Mouse genetic studies have revealed that in vivo collybistin is required for the initial localization and maintenance of gephyrin Frontiers in Cellular Neuroscience www.frontiersin.org and GABA A R clusters in a subset of inhibitory synapses in selected brain regions, particularly in the hippocampus and basolateral amygdala (Papadopoulos et al., 2007(Papadopoulos et al., , 2008. Surprisingly, deletion of collybistin did not affect the organization of GABAergic synapses in other regions, nor that of glycinergic synapses. These findings indicate that the mechanisms that control the assembly of the inhibitory PSD are region and synapse-specific. This selectivity may be explained by the fact that the expression of collybistin at inhibitory synapses is highly heterogeneous. In the retina, collybistin is preferentially colocalized with α2-GABA A Rs, and shows limited localization at synapses containing other GABA A R subtypes or GlyRs (Saiepour et al., 2010). Similarly, in brain circuits collybistin has been found in only a subset of gephyrin-positive synapse, although no specific association with particular GABA A R subtypes was found (unpublished observations). These observations suggest that other GEFs or unknown clustering factors may also contribute to cluster gephyrin at postsynaptic sites. Interestingly, a recent study has revealed that SynArfGEF (also known as BRAG3 or IQSEC3), a member of the A-resistant Arf-GEF/IQSEC3 family, localizes at postsynaptic specializations of GABAergic and glycinergic synapses and can interact with dystrophin and S-SCAM/Magi-2 (Fukaya et al., 2011). Thus, SynArfGEF is another GEF expressed at inhibitory synapses, although its precise function remains to be determined. It will be important to understand whether SynArfGEF, like collybistin, is associated with selected subtypes of inhibitory synapses, and whether these two GEFs have differential or partially overlapping distributions.
SYNAPTIC SPECIFICITY DEPENDS ON MULTIPLE MECHANISMS
A crucial and still open question in developmental neurobiology is to decipher the mechanisms that ensure the formation of functional connections between appropriate synaptic partners characterized by distinct molecular signatures. A large number of studies in both vertebrate and invertebrate nervous systems have shown that the specificity of synapses depends on multiple mechanisms, including homophilic and heterophilic interactions between adhesion molecules, secreted synaptic organizers, antisynaptogenic molecules, interactions with guidepost and/or glial cells, temporally restricted expression of transcription factors, and defined patterns of neuronal activity (for a recent review see Margeta and Shen, 2010). To illustrate the remarkable variety of the mechanisms that give rise to connectional specificity, we refer to recent work on cerebellar Purkinje cells. These neurons receive GABAergic inhibition mainly from basket cells, that target the cell body and the axon initial segment (AIS), and from stellate cells, that innervate exclusively the dendritic shafts (Palay and Chan-Palay, 1974). Both types of synapse express the same GABA A R subtype containing the α1 subunit . Studies in transgenic mouse models have shown that stellate and basket cells use different molecular cues to innervate distinct subcellular domains of Purkinje cells. The targeting of basket axons to the AIS depends on a subcellular gradient of neurofascin 186, a cell adhesion molecule of the L1 immunoglobulin family (Ango et al., 2004). This gradient requires ankyrinG, a membrane adaptor protein that is restricted to the AIS and recruits neurofascin. In ankyrinG-deficient Purkinje cells, the neurofascin gradient is abolished, and basket axons lose their directional growth along Purkinje cells, resulting in impaired synapse formation. On the other hand, the formation of stellate cell synapses depends on close homolog of L1 (CHL1), another member of the same family of adhesion molecules, localized along Bergmann glia fibers (Ango et al., 2008). Thus, different members of the L1 family of cell adhesion molecules contribute to axon patterning and subcellular synapse organization in different types of interneurons, although it seems that these molecules are more directly involved in axon guidance rather than in mediating synapse formation. There is also evidence that GABA A Rs play a remarkably selective role in the refinement of perisomatic and axodendritic synapses in Purkinje cells. Deletion of GABA A Rs from Purkinje cells causes a selective decrease in the density of axodendritic synapses without altering the number of perisomatic synapses Patrizi et al., 2008a). Notably, the reduced axodendritic innervation is accompanied by the appearance of numerous heterologous contacts between GABAergic axon terminals and Purkinje cell spines, which retain an asymmetric PSD typical of glutamatergic synapses .
These examples highlight two important aspects of synaptic specificity. First, the selectivity of connections does not depend on a hard-wired process based on exclusive cellular interactions, but rather results from a mechanism of selection among potential synaptic partners. In Purkinje cells, the silencing of GABAergic transmission is sufficient to boost ectopic synapses on spines, suggesting that in this specific case activity-dependent competition is a major determinant of synaptic specificity. Second, different synapses are subject to different regulation, implying that mutations that perturb synapse development in some populations of synapses may leave other synapses unaffected. This heterogeneity must be understood before common principles of synaptogenesis can be defined.
COMPLEX ORGANIZATION OF ADHESION MOLECULES AT INHIBITORY SYNAPSES
Once a synaptic adhesion has been established, it is essential that synaptic specializations recruit the correct complement of preand postsynaptic molecules, including the correct types of neurotransmitter receptors and their anchoring proteins. In the case of GABAergic synapses, it is still unknown how postsynaptic neurons cluster distinct types of GABA A Rs at synapses that can be located only a few micrometers apart. Selective interactions between preand postsynaptic adhesion molecules have been invoked to explain the selectivity in the segregation of different GABA A Rs (Thomson and Jovanovic, 2010). Indeed, there seems to be enough variability in the different families of synaptic adhesion molecules to support this function (Scheiffele, 2003;Yamagata et al., 2003;Washbourne et al., 2004;Craig et al., 2006;Piechotta et al., 2006;Dalva et al., 2007;Arikkath and Reichardt, 2008;Biederer and Stagi, 2008;Brose, 2009;Siddiqui and Craig, 2010;Tallafuss et al., 2010), although none of the known adhesion proteins appears to have a selective localization that would be compatible with a role in segregating distinct GABA A Rs to different synapses. Here we discuss the possibility that synapse diversity may result from the differential co-expression of multiple adhesion molecules with partially overlapping distributions.
Recent studies have evidenced a complex organization of neuroligins at inhibitory synapses. While NL2 is present in practically all inhibitory synapses throughout the brain, other neuroligin isoforms have a more restricted distribution. Thus, NL4 is mainly associated with glycinergic synapses , whereas NL3 is coexpressed with NL2 in subsets of GABAergic synapses (Budreck and Scheiffele, 2007;Patrizi et al., 2008b). These observations indicate that differential expression of neuroligins may confer specific functional properties to individual synapses, although the contribution of each individual neuroligin isoform remains unclear. Interestingly, recent research has indicated that NL2 has quite selective functions at GABAergic synapses, despite its broad distribution. In hippocampal pyramidal neurons, deletion of NL2 decreases the amplitude of IPSCs evoked from PV-positive interneurons, but has no effect on IPSCs evoked from somatostatin-positive cells (Gibson et al., 2009). A similar level of selectivity has been reported also for other cell adhesion molecules. For example, perturbation of the neural cell adhesion molecule (NCAM) produces selective effects on GABAergic synapses in frontal and cingulate cortex and in the amygdala, but not in hippocampus (Pillai-Nair et al., 2005). Together, these data reveal an unexpected variability in the synaptic properties conferred by individual cell adhesion molecules and provide support to the idea that synaptic specificity may be encoded by multiple interactions between selective combinations of synaptogenic proteins.
It is generally assumed that neuroligins promote synapse maturation by interacting with presynaptic neurexins (Ushkaryov et al., 1992;Graf et al., 2004;Chih et al., 2005;Kang et al., 2008). Neurexins occur in six different isoforms (three longer α-neurexins and three shorter β-neurexins), that are further subject to alternative splicing, giving rise to several distinct variants that can bind with different affinities to multiple types of postsynaptic partners, including neuroligins, LRRTMs (leucine-rich repeat transmembrane neuronal proteins), neurexophilins, and the Cbln1-GluD2 (cerebellin 1-glutamate receptor δ2) complex (Ullrich et al., 1995;Missler and Südhof, 1998;Koehnke et al., 2010;Siddiqui and Craig, 2010;Uemura et al., 2010;Wright and Washbourne, 2011). In particular, the presence or the absence of an insert at splice site 4 (S4) appears to be an important determinant of binding partner selectivity (for review, see Craig and Kang, 2007;Siddiqui and Craig, 2010). Co-culture studies support a preferential role of α-neurexins(+S4) in mediating GABAergic synaptogenesis (Boucard et al., 2005;Chih et al., 2006;Kang et al., 2008). Likewise, knockout of all α-neurexins decreases considerably the density of GABAergic synapses in cortex (Missler et al., 2003). Interestingly, α neurexins can also interact with α-dystroglycan (Sugita et al., 2001), which is present in a subset of GABAergic synapses as discussed above. Neurexins have also been reported to interact directly with GABA A Rs, although the importance of these interactions for synapse development is still unclear (Zhang et al., 2010). In summary, although there is clear evidence that both neuroligin 2 and α-neurexins(+S4) promote GABAergic synaptogenesis in vitro, the extensive alternative splicing and numerous binding partners of neurexins suggest that these molecules may regulate synapse development by multiple, and not necessarily shared, mechanisms. As novel studies evidence that neuroligins can regulate glutamatergic synaptogenesis by neurexin independent mechanisms (Ko et al., 2009) and, vice versa, that neurexins induce the formation of glutamatergic synapses by interacting with postsynaptic molecules other than neuroligins (Uemura et al., 2010;Matsuda and Yuzaki, 2011), it appears reasonable to reevaluate the relevance of neurexin-neuroligin interactions in the context of inhibitory synapse development. It will also be of primary interest to understand what is the expression profile of the different neurexin isoforms in distinct types of excitatory and inhibitory synapses.
SYNAPTIC CLEFT PROTEINS PROVIDE A FURTHER LEVEL OF COMPLEXITY
An emerging concept is that proteins localized in the synaptic cleft may act bi-directionally to coordinate selective interactions between the pre-and postsynaptic compartments. By itself, this is not a new idea, as it is well established that at the neuromuscular junction secreted proteins, such as agrin and laminin, serve as synaptic organizers (Kummer et al., 2006;Witzemann, 2006;Rushton et al., 2009). Recently, a novel class of secreted molecules that link pre-and postsynaptic specializations has been characterized in the cerebellar cortex. Specifically, it has been shown that Cbln1 acts as a crucial synaptic organizer that is required for the formation and maintenance of glutamatergic synapses made by parallel fibers with Purkinje cell spines (Yuzaki, 2010). Cbln1 is a glycoprotein of the C1q family that is secreted from cerebellar granule cells. Mice lacking Cbln1 are ataxic and show a surprising similarity to mice lacking the δ2 glutamate receptor (GluD2), which is expressed selectively in Purkinje cells. Both these mutants have a remarkable (∼50%) reduction in the number of parallel fiber-Purkinje cell synapses, with the remaining synapses showing a mismatch between PSDs and presynaptic active zones, as well as impaired LTD (Kashiwabuchi et al., 1995, Kurihara et al., 1997, Hirai et al., 2005. The similarities in the structural and functional abnormalities observed in Cbln1-null and GluD2-null mice have suggested that these two molecules are engaged in a common signaling pathway. Indeed it has been demonstrated that Cbln1 binds to the N-terminal domain of GluD2 (Matsuda et al., 2010), and that the Cbln1-GluD2 complex mediates synapse formation by interacting selectively with neurexins(+S4) (Uemura et al., 2010; Figure 2).
These new exciting findings show that secreted proteins can act as divalent ligands linking pre-and postsynaptic transmembrane components. Accordingly, the synaptic cleft can be regarded as the site in which secreted factors and cell adhesion molecules Frontiers in Cellular Neuroscience www.frontiersin.org mediate trans-synaptic interactions that may contribute to encode synaptic specificity. For example, the ternary interaction between neurexin(+S4), Cbln1 and GluD2 may represent a "protein code" specific for parallel fiber-Purkinje cell synapses (Uemura et al., 2010). Notably, there is evidence that Cbln1 and the closely related Cbln2 can interact with neurexins and mediate synapse formation not only in cerebellum but also in forebrain regions (Matsuda and Yuzaki, 2011). Co-culture analyses have shown that Cbln1 and Cbln2 induce preferentially inhibitory presynaptic differentiation by interacting with neurexin variants containing S4, although the postsynaptic partners remain unknown (Joo et al., 2011). It is therefore reasonable to assume that differential interactions of neurexin variants with neuroligins, Cbln and LRRTMs may be involved in specifying distinct types of excitatory and inhibitory synapses. By analogy, we suggest that trans-synaptic interactions mediated by α-dystroglycan may constitute a molecular code for a specific subset of GABAergic synapses (Figure 2). In short, cross-interactions between synaptic cleft proteins and cell adhesion molecules provide an additional level of complexity that could be exploited by neurons to functionally specify synapses. It is now a key task to increase our understanding of the synaptic extracellular matrix or synaptomatrix (Vautrin, 2010). Ultrastructural analyses have shown that this material is particularly dense, even denser than the neuronal cytosol, and is characterized by periodically organized complexes, suggesting a regular arrangement of cleft proteins (Zuber et al., 2005). Resolving the molecular interactions that occur in the synaptomatrix is likely to provide important insights into the mechanisms that underlie the formation and specificity of synapses.
A MOLECULAR CATALOG OF INHIBITORY SYNAPSES
The studies revised above have revealed an unexpected complexity in the molecules and mechanisms that control the assembly and specificity of inhibitory synapses during the formation of neural circuits. An important insight that has emerged from these investigations is that not all synaptic proteins are expressed equally at all inhibitory synapses, suggesting that synapse diversity is produced by unique combinations of synaptic molecules with FIGURE 2 | Proposed trans-synaptic interactions mediated by synaptic cleft glycoproteins. At parallel fiber-Purkinje cell synapses (left), Cbln1 forms a ternary complex with neurexin variants containing the S4 insert and postsynaptic GluRδ2 receptors (modified from Uemura et al., 2010). At some GABAergic synapses (right), α-dystroglycan (α-DG) may establish a link between α-neurexins and the postsynaptic dystrophin-glycoprotein complex through the transmembrane β-dystroglycan isoform (β-DG). Glycan side chains of Cbln1 and α-DG may also mediate multiple interactions with extracellular matrix molecules.
Frontiers in Cellular Neuroscience
www.frontiersin.org partially overlapping localizations and functions. The combinatorial expression of distinct sets of synaptic molecules may be regarded as a signature that identifies individual synapses and could be used to generate a molecular-based system of synapse categorization (Grant, 2007). A molecular catalog could be used to identify distinct types of synapses based on the differential expression of groups of interacting proteins, each contributing to specific aspects of synapse organization and physiology. While the tremendous complexity of glutamatergic synapses poses a formidable challenge toward the accomplishment of a synapse catalog (Grant, 2007), a molecular characterization of inhibitory synapses appears to be within reach. A main obstacle is that our current list of synaptic proteins is not yet complete. Therefore a crucial step will be the identification of all proteins, including their splice variants and post-translational modifications. Expression screenings in co-culture systems represent a useful method for the identification of novel families of synaptogenic molecules (Paradis et al., 2007;Linhoff et al., 2009). On a larger scale, existing proteomic methods, such as mass spectrometry and protein array tools, can be applied to reveal protein-protein interactions (Husi et al., 2000;Schweitzer et al., 2003;Yuk et al., 2004;Collins and Choudhary, 2008). Bioinformatics tools could also be employed to generate hypothesis of interactions that could be verified experimentally and to construct interaction maps and models that could be used to predict the effects of mutations of single proteins (Armstrong et al., 2006).
Ideally, a categorization of synapses based on molecular markers should be combined with detailed knowledge of synaptic connectivity in situ, the ultimate goal being a convergence of synaptic proteomics with connectomics (Lichtman and Sanes, 2008). Considering the diversity and specificity of synapses, a full appreciation of their molecular complexity can be achieved only by microscopic analyses aimed at individual synapses. In this context, immunofluorescence methods are of particular interest because they combine high sensitivity with adequate resolution, and because they are suitable for large-scale analyses of protein distribution (Schneider Gasser et al., 2006;Sassoè-Pognetto, 2011). Moreover, labeling with multiple antibodies allows to determine whether two or more synaptic proteins colocalize at specific synapses. Recent developments, such as the advent of super-resolution light microscopy (Gustafsson, 2005;Hell, 2007;Nägerl et al., 2008), have considerably expanded the analytical power of immunofluorescence microscopy. In particular, array tomography is a new proteomic imaging method that exploits a combination of light and electron microscopic approaches (Micheva and Smith, 2007). This method consists in immunolabeling and imaging ordered arrays of ultrathin (50-200 nm), resin-embedded serial sections on glass microscopic slides, resulting in the acquisition of very large volume images at high resolution. Moreover, antibodies can be eluted and the sections restained a number of times thus allowing the detection of a large number of antigens in the same sample. Because of its proteomic capabilities and high resolution, array tomography represents a useful method for large-scale exploration of synaptic diversity. This method has been recently used to determine the composition of glutamatergic and GABAergic synapses in somatosensory cortex of Line-H-YFP Thy-1 transgenic mice (Micheva et al., 2010).
The potential of array tomography and other immunohistochemical methods is limited by the availability of antibodies that can be used to stain brain sections. In many cases the extensive sequence homology between related protein isoforms precludes the generation of specific antibodies. These technical difficulties may be overcome by labeling proteins directly by recombinant fusion protein technologies. For example, in a recent study pHsensitive pHluorin tagging was used to distinguish the membrane vs. intracellular pools of engineered neurexin 1α and neurexin 1β in cortical organotypic cultures (Fu and Huang, 2010). In this study, the pHluorin-tagged neurexin isoforms were expressed in PV-positive interneurons, allowing the visualization of their subaxonal localization and dynamics in a specific subset of GABAergic synapses. In another study, PSD-95-GFP was transfected by in utero electroporation in a specific population of cortical pyramidal neurons to monitor in vivo the dynamics of PSD-95 clusters using two-photon microscopy (Gray et al., 2006). While the expression of a tagged protein in isolated neurons may facilitate the visualization of its subcellular localization, the molecular cataloguing of synapses would require that the tagged proteins are expressed in vivo and replicate precisely the distribution patterns and expression levels of the endogenous proteins. Although the technology to perform this is potentially available, there have been no systematic analyses of synaptic protein distribution using this approach.
A full appreciation of the molecular diversity of synapses may help to uncover relationships between molecular composition and functional properties. In this context, the analysis of molecular organization should be complemented by gain or loss-of-function studies aimed at individual synaptic proteins in genetic model organisms. Likewise, a detailed knowledge of synaptic molecular composition may provide an interpretation key for the results obtained in knockout mutants, where the effects of the mutation are often confounded by the co-existence of multiple redundant molecular pathways (Piechotta et al., 2006). A synapse catalog could also be used to predict the consequences of mutations in the context of brain pathology and to identify populations of synapses that are likely to be affected in a particular disease (Grant, 2007). Finally, it will be of prime interest to consider how synapses vary over time, in particular by comparing synapse organization during the period of development and in mature circuits. As the last two decades have witnessed an impressive advancement in the identification of the molecular constituents of synapses (Südhof and Malenka, 2008), a big challenge ahead is to define the spatio-temporal expression profile of the endogenous synaptic proteins, to understand how this large array of molecules assemble into functional units, and to link the molecular data sets with a characterization of the anatomical and physiological diversity of synapses.
ACKNOWLEDGMENTS
Research in our laboratory is supported by Compagnia di San Paolo, Regione Piemonte (Ricerca Sanitaria Finalizzata 2008/bis and 2009), and Italian MIUR (Prin 2008KN7J7J). Giulia Pregno is the recipient of a fellowship from Fondazione CRT (Progetto Lagrange).
Frontiers in Cellular Neuroscience
www.frontiersin.org | 9,319.8 | 2011-04-28T00:00:00.000 | [
"Biology"
] |
Instant fuzzy search using probabilistic-correlation based ranking
Background: Instant search recommends completions of the query `on the fly', and instantly displays the results with every keystroke. It is desirable that these query results be robust against typographical errors that appear not only in the query but also in the documents. Additionally, instant search requires instant response time and ranking of the results to focus on the most important answers. Method: In this study, simple and efficient methods for instant fuzzy single keyword andmulti-keyword search that are resilient to typographical errors and that employ nomore than inverted and forward indices are studied. While computing search results incrementally using the cached results, the answers are ranked based on their relevance to the query using probabilistic correlation based ranking. Findings: Experiments are conducted on data sets DBLP andMedline and the execution time for obtaining answers to instant fuzzy single keyword search is recorded for different prefix lengths. Similarly, the execution time for obtaining answers to instant fuzzymulti-keyword search is recorded for sub-queries of two keywords and three keywords for various prefix lengths on the same data set. Furthermore, in order to measure the usefulness of the proposed correlation based ranking, precision is calculated for the search results. Experimental evaluation demonstrates the efficacy of the instant fuzzy search algorithms and the probabilistic correlation based ranking. Applications: The proposed instant fuzzy keyword search for single and multiple keywords not only improves the efficiency but also the quality of the search results.
Introduction
In instant search, for each keyword or for the keyword that is presently being typed, the search engine must return results not only for the similar words but also for the words whose prefix is similar to the keyword.
One of the earliest examples of instant search is the Unix Shell, which presents the list of all file names starting with the letter that has been typed on the command line. While the purpose of the instant search is finding information, it is also employed in text editors for predicting user input (1)(2)(3) . In the context of information retrieval systems, https://www.indjst.org/ Bast et al. (4)(5)(6) proposed methods for indexing keywords and then querying for instant search. However, these techniques require large processing times and a lot of space. There are also studies on fuzzy instant search that are typo-tolerant and word-order independent (7)(8)(9)(10) . More recently, it is integrated into a number of search engines, for example, Google Instant for searching the web, Facebook that searches for the relevant people, Internet Movie Database that recommends movies, YouTube Instant that suggests the videos, interactive query suggestions within an e-mail system (11) and so on. However, these search engines make use of massive logs of previous queries, and fail to generate appropriate answers if the query posed is not in the log.
An additional challenge in search engines is dealing with massive amounts of documents in the data repository. One of the solutions in dealing with massive amounts of data is ranking query results; because ranking directs attention towards only the most relevant answers. Ranking algorithms are extensively studied in databases and information retrieval. The Ranking models can be classified as vector space models (12) , probabilistic models (13) , statistical language models (14) and hybrid models (15) .
In this article, simple and efficient methods for fuzzy instant search are studied that answer single keyword and multikeyword queries. The methods make use of no more than inverted and forward indices. Moreover, the methods compute answers incrementally using the cached results, and rank the answers based on their relevance to the query using probabilistic correlation based ranking.
The rest of the article is organized as follows: Section 2 presents preliminaries of the study. While Section 3 presents instant fuzzy keyword search, Section 4 describes instant fuzzy multi-keyword search, and Section 5 defines probabilistic-correlation based relevance ranking. Finally, Section 6 demonstrates the experiments conducted and Section 7 concludes the paper.
Preliminaries
Data Set: Let R = {r 1 , r 2 , ...} be a set of records and D = {w 1 , w 2 , ...} be a dictionary that contains the set of all distinct keywords of R. While in Table 1 an example of a set of records is presented, in Table 2 an inverted index of the set of records is given.
Similarity Measurement: In this study, edit-distance is employed to measure the dissimilarity between two keywords, which is defined as the minimum number of edit operations such as insertion, deletion, and substitution of single characters required to convert one keyword to the other. Let us denote the edit-distance between two keywords S 1 and S 2 as edist (s 1 , s 2 ) then the two keywords are similar if edist (s 1 , s 2 ) ≤ τ where τ is the edit distance threshold. Using linear algebra for intelligent information retrieval r 4 Approaches to intelligent information retrieval Freenet: a distributed anonymous information storage and retrieval system r 6 Survivable information storage systems
Instant fuzzy keyword search
Instant fuzzy keyword search consists of searching keywords that have a prefix close to the query string. More formally, given a query string q = c 1 c 2 . . ., instant fuzzy keyword search generates a ranked list of pairs (w i , r j ) such that prefix v of w i is similar to q and w i ∈ D is a keyword of r j ∈ R. In this section, a simple and efficient algorithm for instant fuzzy keyword search is presented where the information system accepts a sequence of queries from the user who is keying in character by character, and computes answers to the query from the answers generated in the previous query in the sequence. The answers generated are ranked based on their relevancy which will be described in Section 5.
Algorithm Description
Let q = c 1 c 2 . . . be the query being typed character by character, and τ be an edit-distance threshold. For the sub queries . . c τ the answer is set of all pairs of (w i , r j ), such that w i ∈ D is a keyword of record r j ∈ R.
For the sub-query q τ+1 = c 1 c 2 . . . c τ+1 the entire inverted index is scanned in order to generate the answer. Let ϕ τ+1 be the answer for query q τ+1 , and v i,τ+1 be the prefix of w i whose length is equal to τ + 1, then for each w i ∈ D the prefix V i,τ+1 is https://www.indjst.org/ anonymous Freenet r 5 8.
intelligent r 3 r 4 10. linear r 3 11. retrieval r 1 r 2 r 3 r 4 r 5 12. storage r 2 r 5 r 6 13. structures r 1 14. survivable r 6 15. system r 5 r 6 16. using r 3 compared against the query q τ+1 , and the pair (w i , r j ) is included in the answer set of query q τ+1 if and only if v i,τ+1 is similar to q τ+1 . In other words, the answer to query q τ+1 is a set of pairs defined as follows: For the subsequent queries q x = c 1 c 2 . . . c x such that x > τ + 1, the answer ϕ x is computed from ϕ x−1 as follows. Instead of scanning the entire inverted index, only the keywords of the pairs included in ϕ x−1 are considered. At first, ϕ x is initialized to be empty, then for each (w i , r j ) ∈ ϕ x−1 , the edit-distance of prefix v i,x of w i whose length is equal to x is computed against the query q x , and the pair (w i , r j ) is included in ϕ x if and only if edist (v i,x , q x ) ≤ τ. Formally, the answer to query q x is a set of pairs defined as follows: The proposed algorithm is typo-tolerant, simple and efficient. The algorithm employs an inverted index that is not scanned in entirety for all the sub-queries. Furthermore, while calculating the edit-distance between the prefix of a keyword and the given query, only the prefix whose length is equal to the length of the query is considered.
Instant fuzzy multi-keyword search
A multi-keyword query q l consists of a sequence of keywords (w 1 , w 2 , . . . , w l ). In an instant search, a query is generated for each character typed in by the user, and instant fuzzy multi-keyword search constitutes of searching records r j ∈ R such that the following two conditions hold: • The record r j has a keyword similar to w i for 1 ≤ i ≤ l − 1.
• The record r j has a keyword with prefix similar to w i .
Algorithm description
Initially, as the user types the query character by character, the answer for the first keyword w 1 is computed using an inverted index as described in Section 3.1. Upon completion of the first keyword the records that match the first keyword are cached. Subsequently, when the user enters a sequence of characters generating multi-keyword query, a sequence of sub-queries are generated for each character being typed and the results of the previous query are cached. Let w l be the keyword being typed where l > 1, then the prefixes similar to the keyword w l are searched in the records of the cached results of the previous query rather than the complete set of keywords. Let R i−1 be the set of records cached for the sub-query q i−1 , then the set of records that contain the keywords similar to w 1 , w 2 , . . . , w l−1 and the keyword with prefix similar to w l is computed for q i as follows. For each r i ∈ R i−1 , forward index is https://www.indjst.org/ used to determine if there exists a keyword with prefix similar to w l in r i . If a keyword with prefix similar to w l exists in r i , then r i is included in R i .
The algorithm described employs an inverted and a forward index. Furthermore, the algorithm is both typo-tolerant and word-order independent. The algorithm is efficient since it does not scan all records for every sub-query.
Probabilistic-correlation based relevance Ranking
Keywords in a record must be associated with weights based on how well it distinguishes a particular record from other records. In general, a keyword that occurs more often in various records is a bad discriminator and must be assigned smaller weight when compared to a keyword that occurs less often in various records.
Correlation between the keywords is a measure of inter-dependence and can be calculated based on conditional probability as follows: It can be noticed that cor (w i , w j ) = cor (w j , w i ). Moreover, cor (w i , w j ) = 1 implies that the keywords w i and w j are interdependent on each other and always appear together in the records; and conversely, cor (w i , w j ) = 0 implies that the keywords w i and w j are independent of each other and never appear together.
More generally correlation of a keyword w i with one or more keywords simultaneously can be calculated as follows: Let R l ∈ 2 R be a set of cached results and W l ∈ 2 D be a set of all distinct keywords in cached results R l . If keyword w i ∈ W l then the correlation of w i given a set of keywords W ⊆ W l over cached results R l is denoted as cor l (w i ,W ), and is computed from the cached results instead of the entire data repository R.
Relevance ranking
Let r ∈ R l be a record in the cached results R l consisting of keywords r = {k 1 , k 2 , . . . , k n } where k i ∈ W l for 1 ≤ i ≤ n ; then the relevance or importance of keyword k i in record r can be defined as follows: It can be noted that 0 ≤ rel(k, r) ≤ 1; and rel(k, r) = 1 implies that the keyword k has higher relevance in r while rel(k, r) = 0 implies no relevance of keyword k in r.
Relevance Ranking of Single Keyword Query Results
Let ϕ x be set of answers to the query q x defined according to (2), then for all pairs (w i , r j ) ∈ ϕ x the relevance of keyword w i in relation r j denoted as rel (w i , r j ) is the rank of the corresponding pair.
Relevance Ranking of Multi-Keyword Query Results
Let q l = (w 1 , w 2 , . . . , w l ) be a multi-keyword query, and R l ∈ 2 R the corresponding set of cached results. Then the relevance of answer r ∈ R l given multi-keyword query q l can be calculated as follows: https://www.indjst.org/
Experiments
The performance of the proposed algorithms is evaluated on two real data sets namely, DBLP and Medline. For this study, 1000 DBLP log queries and 1000 Medline log queries are extracted and the experiments are conducted on Intel i3 CPU @ 2.6 GHz and 2GB of memory. The average time for generating answers to an instant fuzzy keyword search described in section 3.1 is recorded for various prefix lengths and presented in Figure 1A. Similarly, in order to evaluate instant fuzzy multi-keyword search, the average running time for generating answers to sub-queries of two keywords and three keywords are recorded for different prefix lengths in Figure 1B and Figure 1C respectively. It can be noted from Figure 1A, Figure 1B, and Figure 1C that the proposed algorithm constantly performed well for different prefix lengths. To gauge the quality of the answers generated by the proposed algorithms and the ranking method, precision is measured by determining the percentage of the expected results generated by these approaches. Based on the investigation, the precision of instant fuzzy keyword search is 85% and that of instant multi-keyword search is 90%. | 3,413.2 | 2020-03-20T00:00:00.000 | [
"Computer Science"
] |
The Grip Concept of Incisional Hernia Repair—Dynamic Bench Test, CT Abdomen With Valsalva and 1-Year Clinical Results
Incisional hernia is a frequent consequence of major surgery. Most repairs augment the abdominal wall with artificial meshes fixed to the tissues with sutures, tacks, or glue. Pain and recurrences plague at least 10–20% of the patients after repair of the abdominal defect. How should a repair of incisional hernias be constructed to achieve durability? Incisional hernia repair can be regarded as a compound technique. The biomechanical properties of a compound made of tissue, textile, and linking materials vary to a large extent. Tissues differ in age, exercise levels, and comorbidities. Textiles are currently optimized for tensile strength, but frequently fail to provide tackiness, dynamic stiction, and strain resistance to pulse impacts. Linking strength with and without fixation devices depends on the retention forces between surfaces to sustain stiction under dynamic load. Impacts such a coughing or sharp bending can easily overburden clinically applied composite structures and can lead to a breakdown of incisional hernia repair. Our group developed a bench test with tissues, fixation, and textiles using dynamic intermittent strain (DIS), which resembles coughing. Tissue elasticity, the size of the hernia under pressure, and the area of instability of the abdominal wall of the individual patient was assessed with low-dose computed tomography of the abdomen preoperatively. A surgical concept was developed based on biomechanical considerations. Observations in a clinical registry based on consecutive patients from four hospitals demonstrate low failure rates and low pain levels after 1 year. Here, results from the bench test, the application of CT abdomen with Valsalva's maneuver, considerations of the surgical concept, and the clinical application of our approach are outlined.
Incisional hernia is a frequent consequence of major surgery. Most repairs augment the abdominal wall with artificial meshes fixed to the tissues with sutures, tacks, or glue. Pain and recurrences plague at least 10-20% of the patients after repair of the abdominal defect. How should a repair of incisional hernias be constructed to achieve durability? Incisional hernia repair can be regarded as a compound technique. The biomechanical properties of a compound made of tissue, textile, and linking materials vary to a large extent. Tissues differ in age, exercise levels, and comorbidities. Textiles are currently optimized for tensile strength, but frequently fail to provide tackiness, dynamic stiction, and strain resistance to pulse impacts. Linking strength with and without fixation devices depends on the retention forces between surfaces to sustain stiction under dynamic load. Impacts such a coughing or sharp bending can easily overburden clinically applied composite structures and can lead to a breakdown of incisional hernia repair. Our group developed a bench test with tissues, fixation, and textiles using dynamic intermittent strain (DIS), which resembles coughing. Tissue elasticity, the size of the hernia under pressure, and the area of instability of the abdominal wall of the individual patient was assessed with low-dose computed tomography of the abdomen preoperatively. A surgical concept was developed based on biomechanical considerations. Observations in a clinical registry based on consecutive patients from four hospitals demonstrate low failure rates and low pain levels after 1 year. Here, results from the bench test, the application of CT abdomen with Valsalva's maneuver, considerations of the surgical concept, and the clinical application of our approach are outlined.
INTRODUCTION
The occurrence of an incisional hernia indicates the development of a weakness of the sutured abdominal wall caused by mechanical overload, defective wound healing, and/or inadequate scar formation. Patients with an incisional hernia often complain of pain and a gradually increasing hernia size indicating an overstretching of the tissues. The rates of recurrences are still unacceptably high. Some of the main reasons why incisional hernia recur in such high incidence is the inappropriate selection of the adequate mesh, its size and its fixation according to the size of the hernia. Also, abdominal wall elasticity plays an important role, which is rarely examined preoperatively. How can a durable, long-lasting repair of incisional hernias be designed? We wanted to gain insight into the potential of cyclic loading and shakedown analysis for incisional hernia repair.
We conducted a feasibility study to apply continuum biomechanics to incisional hernia repair. A bench test for cyclic loading was developed to characterize the impact-related biomechanics of materials used for repair. Dynamic intermittent strain (DIS) resembling coughs can characterize any influence numerically with relative figures (1,2). The results can be summed up to indicate the critically needed (CRIP) and the gained resistances to impacts delivered by pressure (GRIP) before and during surgery (3). The CRIP gives a threshold for the reconstruction to survive 425 repeated impacts within a period of 4 h on the bench test. The GRIP includes the calculation of a relative value characterizing the retention force of a mesh with its fixation elements at the mesh-tissue interface. We believe that a durable reconstruction requires the GRIP to be higher than the CRIP value.
Computerized tomography of the abdomen at rest and during Valsalva's maneuver gives insight into the overall shift of organs and tissues upon strain and permits the analysis of tissue elasticity preoperatively (4,5).
We applied the concept to consecutively treated patients with incisional hernia as a prospective observational registry study. As the main outcome parameter, recurrences were reported after 1 year. As secondary endpoint, pain levels were observed for 1 year.
MATERIALS AND METHODS
We conducted a feasibility study for a novel biomechanical approach involving a self-built bench test, a CT evaluation developed by our group, and a clinical application based on the worldwide largest hernia registry Herniamed R . We wanted to gain insight into the potential of cyclic loading and shakedown analysis for incisional hernia repair.
The study consists of three steps with each one being a prerequisite of the next step. Without a bench test, enabling cyclic loading shakedown cannot be tested for. Without coefficients derived from the bench test characterizing each influence, individualization is neither possible nor necessary on a scientific basis. Without criteria for individualization, meshes and surgical techniques cannot be tailored. CT scans at rest and with strain demonstrate large interindividual differences in elasticity. Tissue elasticity is the major influence on the bench test. Therefore, individualization is necessary. The prospective observational registry study shows the potential of the approach with each element influencing the design and contributing to the surgical execution of incisional hernia repair.
Description of the Bench Test
The bench test uses hydraulically driven repeated sharp impacts resembling coughing actions (Figure 1). Since the intermittent strain varies dynamically every 4-6 s, the term dynamic intermittent strain (DIS) test was used for the application (1,6). This self-built DIS test was designed in two versions. In the first version, a protruding balloon bulged as a ball. Upon the impacts, a creeping motion of an hernia mesh was observed leading to dislocation of the mesh in about 85% of the reconstructions investigated. In the second version, a polyethylene foil was used as a stamp with a wider contact surface similar to a mushroom cap for the dynamic deliverance of energy to the tissues resulting in comparable effects. Both designs were computer controlled to simulate a coughing or a sharp straining action with <1 s to reach the peak and a relaxation time up to 3 s followed by a resting time of 2 s.
Commercially available hernia meshes and fixation systems such as sutures, tacks, and glue were tested on a self-built bench test (3). Two different tissues were investigated with differences in their elasticity: beef flank was found to be more distensible and to bear more load compared with pig belly (5, 7). Hernia sizes from 5 to 12.5 cm in diameter were investigated in detail with two different mesh positions: sublay/retromuscular and underlay/IPOM. In order to investigate the different mesh positions, meshes were placed between the respective tissue layers. From the results, meshes were classified according to the need for fixation (DIS classes A-C) (8). Fixation devices were graded according to the retention force per single element or, in case of glue, per square centimeter.
At rest, the tackiness of the mesh sticks the textile to the tissue surface. Meshes with high tackiness are less likely to need fixation. The basal pressure of the DIS machine increases the stiction between tissue and textile. Fixation is added as spot or area gluing, as tacks of various kinds or as running or single-knot sutures. Fixation increases the retention force. The pulse transmits energy to the reconstruction, elongates tissue and textile to a different extent, and causes in this way a sliding or creeping force counteracting the retention force. If the reconstruction fails in one spot, failure is likely to occur on the bench test. The results obtained should be reproducible even under unstable conditions.
Consideration for the Clinical Application of the GRIP Concept
In order to assess this balance of power and to address the various influences, a numerical value was derived. This value describes the retention force of the whole reconstruction. The surgeon can use the value to tailor the procedure to the needs of the individual patient. Starting from the mesh-defect-area-ratio (MDAR), such a numerical value was developed (9,10). We choose to multiply the MDAR with coefficients. According to a general description, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression. In the latter case, the variables appearing in the coefficients are often called parameters and must be clearly distinguished from the other variables (Coefficient-Wikipedia). We choose parameters that characterize the tackiness of the mesh, the strength of the fixation, the position of the mesh, the elasticity of the tissues, and other influences. The coefficients available so far are given in Table 1.
The calculations with the coefficients are given in formulas (1) and (1a) and return the gained resistance to impacts related to pressure (GRIP) in relative numbers (3). The gained resistance of a reconstruction toward impacts delivered by pressure was shortened to the acronym GRIP as detailed previously (8).
Grip = MDAR * bonding factor + peritoneum closing factor (1) This value was found useful to assess several 100 different reconstructions so far. The formula has been expanded to include other influences as coefficients as well.
Grip = MDAR * mesh bonding factor * fixation bonding factor * mesh position factor + peritoneum closing factor (1a) Due to ongoing research efforts, it is likely that more coefficients will be included in the future. Missing is a shape factor to better describe the geometry of the defect or the shape of the mesh. The mesh overlap may be detailed with an overlap factor characterizing a retention force needed on the edge. Please note that the coefficients for the various factors have to be determined for each condition with a bench test several times before the factors can be used to plan a reconstruction. For a given mesh, it is possible to describe conditions of 100% stability in a DIS test as a critical resistance of impacts delivered by pressure shortened to the acronym CRIP (3).
The CRIP value can be calculated before the surgical procedure as: CRIP = 0.5 * hernia size + 15 (2) according to (3). Data on the bench test indicate that the tissue elasticity is an important modulator of the CRIP value. With very lax tissue, higher CRIP values are required for stability.
For the clinical application of the GRIP concept, it is not sufficient to transfer the bench test data to the surgical work. The defect area and the tissue elasticity have to be determined in the individual patient. Since the defect area can vary with pressure and muscular contraction, it has to be determined in at least two states-at rest and under load. The same holds true for the tissue elasticity. From the clinical options available, we choose to perform a CT scan of the abdomen at rest and during Valsalva's maneuver.
CT Abdomen at Rest and During Valsalva's Maneuver
The protocol for CT scanning was adapted from a low-dose, nocontrast protocol implemented for symptomatic kidney stones. All CT imaging data were collected twice without contrast medium during deep inspiration. Following the scout for planning, the CT acquired data sequentially (slice thickness 0.6 mm, 110-130 kV). The whole abdomen from the diaphragm to the symphysis was scanned: first in relaxation with the abdomen at rest. As a second step, the patient strained oneself FIGURE 2 | (Top) CT scans of the abdomen without contrast medium of a 35-year-old male with an incisional hernia after liver transplantation at rest (Left) and during Valsalva's maneuver (Right). It can be noted that the lateral musculature contracts, and the abdominal contents bulge forward with a distension of the hernia opening by about 30%. (Middle) CT scans of the abdomen without a contrast agent of a 73-year-old woman with an incisional hernia after pancreatic resection at rest (Left) and during Valsalva's maneuver (Right). It can be seen that the anterior abdominal wall bulges forward, and the hernia sack increases in size without enlargement of the hernia opening. (Bottom) CT scans of the abdomen without added contrast of a 62-year-old man with an incisional hernia after laparostoma and short bowel syndrome resulting from multiple intestinal fistulae after an ileus. The functional state at rest (Left) and during Valsalva's maneuver (Right) corresponds to the two upper rows. It can be recognized that the left lateral musculature is displaced by the abdomen bulging forward opening the hernia base by about 50%. (we acknowledge the help of Samuel Voss in the selection of scans in the upper and lower row).
Examples are given in Figure 2. The data were evaluated as described previously (4,5,11).
Applying the GRIP Concept to the Individual Patient
The GRIP concept was applied to patient care to reduce complication and recurrence rates after incisional hernia repair. The individual patient was evaluated according to the flow chart depicted in Figure 3. More complex hernia cases and/or patient with many comorbidities are primarily eligible for evaluation.
Surgeons in the STRONGHOLD group decided to apply the GRIP concept to smaller hernia sizes for training purposes.
If the hernia size is found to distend markedly on clinical observation, or if more than one incision was present on the abdominal wall indicating a battlefield abdomen, a computed tomography of the abdomen at rest and during Valsalva's maneuver was performed, and the tissue elasticity was evaluated as described above. The tissue elasticity was multiplied with the CRIP value calculated.
The reconstruction was planned to surpass the elasticity-adjusted CRIP value. The planning of the reconstruction started with an estimate on the desired MDAR. According to Kallinowski et al. (8), a DIS class A mesh gives the best retention force due to a high mesh bonding factor as detailed in formula (1a) above. Both DIS class A meshes used here have high retention forces with Progrip R exhibiting a coefficient of 1.44, Dynamesh R Cicat one being 1.0 (10). The bench test is used to continuously test new materials and to derive the respective coefficients. New results are presented in a monthly weblog, www.hernia-today.com [Influences on the GRIP calculation-Hernie heute (hernie-heute.com)]. The variation of the coefficients available so far is summarized in Table 1.
During the planning of the surgical procedure, the GRIP values are adjusted and recalculated selecting other meshes, alternate sizes, different fixation schemes, and so forth until the planned GRIP value is larger than the required CRIP with the desired safety margin. This planning procedure profoundly influences the surgical procedure to be performed. Since the retromuscular position gives the better retention force compared with an IPOM procedure, all repairs intended to place the mesh before the peritoneum behind the musculature. A total of 72 sublay positions with six MILOS approaches and four eMILOS approaches were attempted. A transversus abdominis release was planned in 19 cases. In these cases, peritoneal flap techniques were generally included in the plan to provide large areas for tension-free repair, embedding the required mesh sizes and preventing increased intra-abdominal pressures at the same time. Preperitoneal underlay mesh placements (PUMP) using flipped Progrip R meshes with the lactic acid grips oriented toward the musculature were included in the planning in four patients.
After surgery, the particulars of hernia and mesh sizes and shapes, the kind and number of fixation elements, the position of the mesh within the abdomen, and the closure of the peritoneum are noted and entered into the STRONGHOLD/Herniamed R registry. All patients received a telephone interview after 1, 6, and 12 months. If the patients complained of pain or a protrusion, a clinical investigation was followed by an ultrasound, magnetic resonance imaging, or a CT scan as needed.
The Stronghold/Herniamed ® Registry
Within the Heidelberg surgical community, 96 patients were consecutively treated by 10 different surgeons in four hospitals. The data were included in the Herniamed R registry, which was expanded with a data sheet called STRONGHOLD. Within STRONGHOLD, seven additional items have to be reported taking about 1 min with an algorithm calculating MDAR and GRIP thereafter. We report results after 1 year for the first 96 consecutive patients. The patients were followed by telephone. If pain or bulging was reported, ultrasound and/or CT scans of the abdomen at rest and during Valsalva's maneuver were performed. Pain was rated from zero to 10 according to the commonly used numerical or visual analog pain scales.
The approach reported here is limited by the definition of the load case, the missing load-limit curve, and the lack of a control group. A better definition of the load case requires the analysis of critical confounders in a large cohort, e.g., by propensity score matching. The load-limit curve is evaluated for elastic tissue assessing the peak pressure and the length of the plateau phase. Preliminary results show the length of the plateau phase to be more influential. A control group requires the expansion of the data base, e.g., by randomization or-more cost efficient-by propensity-score matching again.
Statistical Analysis
Data were collected in Excel spreadsheets. The results were depicted with box-and-whisker-plots and as time lines. Descriptive statistics were calculated as needed. The Kruskal-Wallis test was used for the assessment of group differences. Differences were considered significant after a Bonferroni correction on an error probability of 1%. In case of significant group differences, u-tests for non-paired observations were applied to find differences pairwise.
Influence of the Observer on the Results of the Bench Test
No influence was found in repeated experiments as long as the baseline pressure was kept above 4 and below 10 mmHg (Figure 4). For these experiments, a setting with 50% stability for
Preoperative Assessment of the Tissue Elasticity With CT Abdomen at Rest and During Valsalva's Maneuver in Individual Patients
Preoperatively, the elasticity of the abdominal wall of the individual patient was assessed by three to five investigators at least three times as previously described (3,4). The results are depicted in Figure 5 for illustration.
Applying the GRIP Concept to the Individual Patient
Preoperatively, the type of mesh and its size were chosen to reach the desired MDAR. The surgical strategy was planned, and several alternatives to reach GRIP > CRIP were calculated. Intraoperatively, the size of the mesh was adopted to the anatomical findings with an elliptic, round, or square shape as desired. Changes in the hernia and/or the mesh sizes were followed by a recalculation of the MDAR and the number of the fixation elements. The retromuscular space was limited in the sublay area and required a posterior component separation for larger hernia areas in an additional 10 cases to the 19 patients already planned in this way.
FIGURE 5 | (Top)
Changes in the hernia size as a function of the distension of the hernia sac upon Valsalva's maneuver of five patients. The CT scans of five patients were analyzed four times by three different investigators giving a total of 12 readings from each CT abdomen. The evaluation procedure and the interobserver variation has been described previously (4). About half of both parameters change <10% (dots in the shaded circle). In about one quarter, the hernia sac expands with the hernia opening staying almost constant (dotted line). In about one fifth, both the hernia defect and the hernia sac dilate (solid line). In a few readings, the musculature contracts the hernia sac with unpredictable behavior of the hernia size (left side of the illustration). (Bottom) Frequency distribution of measured changes of the hernia area from CT scan of the abdomen at rest and during Valsalval's maneuver of 67 patients analyzed in this manuscript. Each patient was analyzed one to four times by three to six observers giving a total of 253 readings. Marked variation is obvious with most values ranging between no dilatation and 150% enlargement. About half of the hernia areas change <25% in size upon Valsalva's maneuver.
During the surgical performance, anatomical variations or technical aspects necessitated modifications of the planned procedures in 12 cases. In addition, the fixation factor was varied in the majority of cases after intraoperative assessment of the regional instability of the abdominal wall. Sutures were augmented with tacks in 39 cases to safe operation time.
Clinical Application of the Biomechanical Concept
A total of 96 patients were consecutively operated on between July 1, 2017 and July 31, 2019 in four different hospitals. Demographic and comorbidity data are given in Table 2. Half of the patients were still professionally active (mean age ± SD: 62 ± 13; range: 27-92).
The indication for surgery was enlargement of the hernia during time in all cases and disabling pain in 39 patients. Only one emergency case was noted. Primary hernia was prevalent in 78% with 21 recurrent cases (17 first, one second, three fourth recurrence). The width of the hernia was below 5 cm in 18 cases, between 5 and 10 cm in 49 patients, and above 10 cm in 29 orifices. Median hernia openings were noted in 64, purely lateral orifices in 14 cases. Combined median and lateral hernias occurred in 18 cases.
Median hernia size was 39 cm² (mean: 82 ± 94; range: 2-491). In almost all cases, DIS class A meshes were implanted (43 Dynamesh R Cicat, 41 Progrip R , one Ultrapro R , and one Proceed R ). Larger hernia sizes were cared for with Dynamesh R Cicat (median hernia size: 113 cm²; mean: 132 ± 108 cm²; range: 12-491 cm²). Median mesh overlap was 4.5 cm (mean: 4.7 ± 1.7; range: 1.5-10) before closure of the defect, which was attempted at least of the anterior wall in all cases using tissue flaps as needed. This was mainly due to Progrip R needing smaller overlap on bench testing for durable repairs due to its 44% higher gripping power (median Progrip R overlap: 4.5 cm; median Dynamesh R Cicat overlap: 5 cm). Meshes were cut to an elliptical shape in 53 cases, being left square in 41 patients. Two hernia defects were covered with round hernia meshes. In general, the posterior wall was closed (89 cases) with 86 absorbable and two permanent suture materials. In seven cases, the hernia sac was redressed, and the defect was bridged. In one case, a sandwich was constructed In patients who reported a protrusion on follow-up, an ultrasound examination (N = 40) and/or a CT scan of the abdomen at rest and with Valsalva's maneuver were performed (N = 18). No recurrence of the repaired incisional hernia was detected so far with a CT scan of the abdomen including Valsalva's maneuver. One distant abdominal wall hernia after metachronous open cholecystectomy in another hospital, one pronounced rectal diastasis after a weight gain of 25 kg, and two inguinal hernias were diagnosed. Pain levels between NAS levels 1-5 were reported after 1 year by four patients after load bearing in excess of 2 h, none of which required a prescription for pain relief (Figure 6).
DISCUSSION
First, we show that bench tests for cyclic loading can be built (Figure 1). Over time, material coefficients can be accumulated ( Table 1). The data facilitate a biomechanical approach to incisional hernia repair (Figure 3).
Contribution of the Dynamic Bench Test to Durable Incisional Hernia Repair
Because the biomechanical behavior of the abdominal wall is complex, there is a need for an experimental approach to advance surgical science (12,13). A self-built bench test permits the analysis of tissues, hernia meshes, fixation devices, and surgical techniques (3). During the bench test, a model hernia repair is subjected to repeated submaximal dynamic impacts simulating coughs. Plastic deformation of a newly formed compound can take place under these conditions. The deformation results in a shakedown of the structures to bear load or in a breakdown once the load limit is exceeded (14). The data from the bench test are the first application of the concept to incisional hernia repair. Using the data, a measure for dynamic friction called grip can be derived (8).
DIS loading in our bench test puts energy into the incisional hernia repair tested (Figure 1). The retention force of the meshtissue interface can be assessed in relative terms. So far, data on Progrip R , Dynamesh R Cicat and IPOM, Ultrapro R , TiMesh R light, PhysioMesh R , and Permacol R have been published with Progrip R and Dynamesh R Cicat classified as DIS class A meshes ( Table 1) (8). The gripping factor of Progrip R was assessed as 1.44 that of Dynamesh R Cicat being 1.0.
Meshes and other hernia repair material are brought to the market after proof of the mechanical stability, harmlessness to living tissues, and longevity under physiological conditions (15,16). Stress tests of the compounds made with various tissues, meshes, and fixation material have rarely been performed. It has been demonstrated that the wet compound requires a healing period to gain stable conditions (17). Networks from collagen fibers strengthen following cyclic loading (18). Phantom studies depend on the stretch ratio, the stress levels, and other influences (19). Freshly formed collagen fibers need crosslinking for shakedown (20). Since bending can already displace a mesh by several centimeters, a critical load limit has to be surpassed for stability (21). We defined this limit as coughing 425 times with intra-abdominal pressures above 150 mmHg. From published results and our own observations, about one third of our patients pass this threshold in the first 24 h after surgery (1,22,23). The GRIP and CRIP concepts can factor in all aspects mentioned above (8). We conclude that the bench test permits the assessment of the biomechanical properties and possible interactions of tissues and repair materials under pulse load.
Influence of the Observer on the Results of the Bench Test
With the DIS test, the biomechanical properties of each part of an incisional hernia repair can be analyzed independently ( Table 1). Critical parts of the compound can be identified. The results of the DIS test are reproducible (Figure 4). The interobserver variation can be estimated as 10-12%. For the clinical application, the variation of 10% should be built into the safety margin. During the planning procedure, the intended GRIP value should be at least 10% higher than the estimated CRIP (Figures 2, 3).
Preoperative Assessment of the Tissue Elasticity With CT Abdomen at Rest and During Valsalva's Maneuver in Individual Patients
Tissues differ due to age, obesity, comorbidities, collagen composition, and other influences. The hernia orifice varies its position and its width within the abdominal wall. The muscular strength as a stabilizing factor and the unstable , debris-like zone surrounding the hernia orifice differ from patient to patient. Although tissue quality influences the biomechanics to a large extent, a paucity of data is available with no randomized trial reporting this item (24). Our attempt with Valsalva's maneuver during a CT scan of the abdomen gives a clue to the tissue elasticity of the individual patient. In about half the patients, the elasticity of the hernia sac and of the tissue surrounding the hernia orifice differs. The individual tissue elasticity can be considered and accounted for with the GRIP concept (3). The conventional evaluation by man-based segmentation demonstrates high inter-and intraobserver variation (Figures 2, 5). This is mainly due to the subjective differentiation between the hernia area and the debris zone surrounding it (4,5). The debris zone may involve scar formation, neuronal deprivation, or muscular wasting. The consequence is an anisotropic load distribution with potential for a regional instability leading to a recurrence. It is a commonly held belief that the size of an incisional hernia can be reliably given after a single assessment. Our work demonstrates that about 12 readings are necessary to bring the variation below 5% in cases of pronounced instability.
Our practical solution involves multiple readings by different observers. New approaches to reach the area to be repaired more precisely and less time consuming involve artificial intelligence and non-rigid b-spline registration from CT scans done on the individual patient preoperatively (11).
Thirty-one randomized trials were analyzed, and only 14 reported the average hernia defect surface area and 11 the average hernia defect width (24). At this point in time, the size of the hernia orifice derived from CT scans of the abdomen at rest and during Valsalva's maneuver can be used to analyze the critical resistance needed toward impacts related to pressure (CRIP). With increasing size, the CRIP of the reconstruction rises (2). In the future, the position of the hernia orifice should be added (3).
So far, computed tomography was mainly used to image complications of surgery or mesh repair (25). Here, we present evidence that the tissue elasticity, as a major influence on the durability of repair on the bench test, can be analyzed with the aid of an added Valsalva's maneuver in patients (4). In our opinion, the critical load is a worst-case scenario and should consider the area of instability of the abdominal wall rather than a single hernia orifice.
Applying the GRIP Concept to the Individual Patient
Musculoskeletal dysfunction is a consequence of weaknesses of the abdominal wall and should be remedied by incisional hernia repair (26). A multitude of meshes are available, which can be placed in various abdominal planes using open, laparoscopic or robotic approaches (27). The recent years were characterized by the advent of new techniques in an effort to significantly reduce risk factors for recurrence (28)(29)(30). Many discussions imply biomechanical stresses at the mesh-tissue interface to be involved with seroma formation, wound healing impairment, bulging, or recurrence. The shakedown concept might provide a biomechanical theory to analyze these technical differences in more detail as has been shown in synthetic polymer compounds (31).
The surface interaction between mesh and tissues provides adhesion (32). The initial bonding process can be described as tackiness (33). The retention force at a given tackiness is increased by sutures, tacks, and glue. Information about the interaction between mesh surface, fixation elements, and tissue is important to the surgeon during the planning of the procedure. Our approach defines a load case for the planning of the repair. The load case was derived from previous work on static testing using round meshes with a diameter of 15 cm covering a round hernia orifice of 5 cm without fixation elements (34). With cyclic loading, a rapid dislocation of many meshes was observed under these conditions. With the need of additional fixation, we distinguished three different retention strength of the meshes called DIS classes A-C (8). The better the DIS class of a mesh, the less fixation is needed to take up and to reliably dissipate energy.
The retention strength of the fixation materials adds to the tackiness of the mesh. The increase is distinctly different between various materials (8). With information available from the DIS test, several surgical procedures have been successfully tested.
So far, <200 out of about 4,500 surgical techniques have been analyzed. In the rapidly evolving market of hernia meshes with a significant potential for conflict, a premarket surveillance should include the mesh behavior as a compound (https://www.fda. gov/medical-devices/implants-and-prosthetics/hernia-surgicalmesh-implants&prev=search&pto=aue). This is important since more than 70 new hernia meshes were approved for clinical use by the FDA in recent years (35).
The change in the hernia size during pressure should be figured into the needed reconstruction strength in order to counteract the effects of tissue elasticity. In our group, a tissue factor as percent dilatation of the hernia size is multiplied with the hernia size to reach the required CRIP value preoperatively.
Intraoperatively, the regional distribution of tissue weaknesses or scar formations can be observed directly by the surgeon. As a consequence, the safety margin of the procedure might be elevated to reach higher GRIP values, or the distribution of fixation elements might be adjusted as desired. This was necessary in at least 12 reconstructions.
Clinical Application of the Biomechanical Concept
Biomechanically stable repairs of ventral hernias result in low recurrence rates and low pain levels after 1 year (Figure 6). Biomechanically stable hernia meshes can be classified as DIS class A (8). If DIS class A meshes are augmented with sufficient fixation points and are implanted in sufficient size in the required layer of the abdominal wall, clinical results after 1 year are excellent (36).
For more than 80 years, biomechanically stable soft tissue repairs were modeled on the assumption that the strain of each constituent (cells, fibers, matrix, meshes, and fixation elements) equaled the global tissue strain resulting in an affine deformation (37). The results presented here prove that the models have to be extended to anisotropic and non-affine strain distributions. Recent work with finite element analysis provided important insights into the interaction of tissue and mesh (19). Even at low strain rates around 1 mm/min and during uniaxial stress, force accumulation at the suture fixation was observed. The methodology presented here provides a simple and clinically applicable way for the analysis of biomechanical stability during various conditions, such as multiaxial tension, anisotropic force distribution using dry or wet meshes with potentially wide variations of the experimental parameters, or standardized conditions as desired.
On the self-built bench test, about 85% of the combinations of meshes, defects, fixation materials, and closure defects tested failed before 425 DIS impacts. Since one third of our patients cough more often within the first 24 h after surgery, this might be one mechanism to explain failure rates and pain levels of the conventional approaches. The bench test results combined with CT scans of the abdominal wall of the individual patient enable the surgeon to enter a step-by-step assessment of the needs of the patient (Figures 3, 4). A durable repair has been observed after 1 year. The patients reported little or no pain. We plan to follow the patients for several years in the STRONGHOLD/Herniamed R registry.
A durable incisional hernia repair is sought after by many surgeons. One solution might be to use a high MDAR (38). A threshold of 16 was proposed by Hauters et al. (38) analyzing laparoscopic ventral hernia repair with DIS classes B and C meshes not taking into account fixation. Since the largest hernia meshes cover about 2,400 cm², a ratio of 16 limits the hernia size to 150 cm² to be durably repaired by this approach. For a round defect, a radius of 7 cm should not be surpassed according to these authors. A total of 21 patients reported here have hernia sizes above this limit. Our approach included the use of DIS class A mesh and fixation to increase the retention force.
Fixation can contribute to retention strength. An option may be to use an optimal ratio of fixation elements to the mesh area (39). Our approach uses a relative figure to tailor the reconstruction to the needs of the individual patient. As long as a threshold called CRIP is surpassed, there are many options to perform the repair. The study is limited by lacking information such as the minimal overlap related to the shape of the hernia orifice, by the low patient number, the limited observation period, and the lack of a control group.
Repair for giant, battlefield, recurrent, or complex incisional hernia can durably be performed according to the GRIP concept. With many new meshes and fixation devices in the regulatory process to gain market access, DIS testing can confirm a high DIS class of the material. The surgical algorithm provides a step-by-step approach. Stable repairs seem to heal without seroma formation or wound problems even in patients with many comorbidities (Tables 2, 3). The 1-year results of the first 96 patients operated on by 10 surgeons in four hospitals are encouraging for future developments.
CLINICAL IMPLICATIONS AND IMITATIONS
The concept provides a biomechanical point of view to plan both individual incisional hernia repair and studies. At this point in time, only a small fraction of meshes, fixation devices, and glues have been tested. Many coefficients are still lacking as well as contributions from basic sciences. Is the overlap required for a durable repair a stable value, or does it vary with the type of mesh, the form of the hernia opening, and the instability of the abdominal wall? The work done so far will most likely look minute at the end, but it provides a starting point for the investigation of cyclic loading and critical load limits. Since this approach has been successful in compound constructions such as airplane wings, we confidently report our limited data and the first clinical application of a biomechanical-based incisional hernia repair.
CONCLUSIONS
A bench test was designed delivering dynamic intermittent strain (DIS) similar to coughing impacts. A load limit was defined after counting coughs on patients postoperatively: one third of the patients coughed 425 times in 24 h or more often. Using the bench test with 425 DIS impacts as cyclic load, meshes, their position in the abdominal wall, fixation elements, repair techniques, and tissue elasticity were attributed to a relative figure called gained resistance to impacts related to pressure (GRIP). With increasing defect size, GRIP is needed to be raised to reach durable repairs. The minimal GRIP required for a durable repair at a given size was defined as the critical resistance to impacts related to pressure (CRIP). We conclude that the GRIP needs to exceed the CRIP in the repair of large, recurrent, and complex incisional hernia.
Tissue elasticity in the individual patient was assessed with CT scans of the abdomen at rest and during Valsalva's maneuver. The hernia size was found to change upon pressure in about half of the patients up to 250 cm². We conclude that the tissue elasticity and the hernia size under pressure should be assessed before the repair of large, recurrent, and complex incisional hernia.
Both the results from the bench test and from the CT scans gave the opportunity to develop a biomechanical basis for incisional hernia repair. The concept was applied by 10 surgeons in four hospitals. After 1 year, 96 consecutive patients were repaired using conventional techniques taking into account the biomechanical theory of the GRIP concept and the bench test and the CT results. No mortality, a complication rate of 5-7%, no recurrences, and low pain levels were observed. We conclude that the GRIP concept is a structured approach for the repair of large, recurrent, and complex incisional hernia.
DATA AVAILABILITY STATEMENT
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.
ETHICS STATEMENT
The studies involving human participants were reviewed and approved by Universität Heidelberg Ethikkommission der Med. Fakultät No. S-522/2020. Written informed consent for participation as required for this study was obtained in accordance with the national legislation and the institutional requirements.
AUTHOR CONTRIBUTIONS
FK and RN designed and directed all research, conducted some of the series, got the funding, received material support, were the key surgeons, drafted the report, and will do the revision. DG, FH, MS, YL, and RN investigated the tissues on the bench test. VL, TL, JR, and RN were key surgeons and applied the GRIP concept to patients. JG and AG did the CT scans and evaluated the results together with VL, RN, and FK. MV and FK designed the bench test. MV supervised the building process. All authors contributed to the article and approved the submitted version. | 9,384.2 | 2021-04-14T00:00:00.000 | [
"Medicine",
"Engineering"
] |
Poly(lysine) Dendrimers Form Complexes with siRNA and Provide Its Efficient Uptake by Myeloid Cells: Model Studies for Therapeutic Nucleic Acid Delivery
The disruption of the cellular pathways of protein biosynthesis through the mechanism of RNA interference has been recognized as a tool of great diagnostic and therapeutic significance. However, in order to fully exploit the potential of this phenomenon, efficient and safe carriers capable of overcoming extra- and intracellular barriers and delivering siRNA to the target cells are needed. Recently, attention has focused on the possibility of the application of multifunctional nanoparticles, dendrimers, as potential delivery devices for siRNA. The aim of the present work was to evaluate the formation of dendriplexes using novel poly(lysine) dendrimers (containing lysine and arginine or histidine residues in their structure), and to verify the hypothesis that the use of these polymers may allow an efficient method of siRNA transfer into the cells in vitro to be obtained. The fluorescence polarization studies, as well as zeta potential and hydrodynamic diameter measurements were used to characterize the dendrimer:siRNA complexes. The cytotoxicity of dendrimers and dendriplexes was evaluated with the resazurin-based assay. Using the flow cytometry technique, the efficiency of siRNA transport to the myeloid cells was determined. This approach allowed us to determine the properties and optimal molar ratios of dendrimer:siRNA complexes, as well as to demonstrate that poly(lysine) dendrimers may serve as efficient carriers of genetic material, being much more effective than the commercially available transfection agent Lipofectamine 2000. This outcome provides the basis for further research on the application of poly(lysine) dendrimers as carriers for nucleic acids in the field of gene therapy.
Introduction
RNA interference (RNAi) is a biological process in which RNA molecules induce specific inhibition of target gene expression. Its discovery provoked great enthusiasm in the scientific community, and subsequent studies on RNAi resulted in the transition from experimental technology to a powerful therapeutic tool. In 2010, the first case of systemic targeted delivery of short interfering RNA (siRNA) was reported, which gave a solid foundation for the clinical use of this type of genetic material [1]. In recent years, siRNA has become the basis for drug development due to the high level of specificity, limited side effects, and the ease of synthesis of therapeutic molecules [2].
However, before siRNA molecules reach their site of action in the cell cytoplasm, they have to conquer several obstacles, the number of which depends largely on the way of administration, the target tissue, as well as the physicochemical properties of the siRNA itself. The latter involve low stability, negative charge, and high structural stiffness, hampering the transport in body fluids, across cellular membranes, and between intracellular compartments [3]. What is more, siRNA upon entering the bloodstream easily undergoes enzymatic degradation by nucleases or rapid renal clearance [4].
In order to overcome the barriers limiting the transport of genetic material and exploit the therapeutic potential offered by the RNAi mechanism, effective delivery systems for siRNA molecules to their site of action are necessary. These systems, in addition to specific transport and transfection efficiency, should be able to protect siRNA against degradation by nucleolytic enzymes, prolong its blood circulation time, and release genetic material intracellularly, making it easily accessible for RNAi machinery, thus enabling effective silencing of the target gene [5].
In general, the carriers used to introduce nucleic acids into the cells can be divided into viral and non-viral systems. Vectors using genetically modified viruses are capable RNA delivery devices, offering, among others, long-term silencing of gene expression even after a single administration, efficient transfection, or expression of multiple copies of siRNA molecules. However, expensive production and side effects associated with random integration into the host genome (which can lead to the damage of important genes or activation of oncogenes), significant immunogenicity, and the possibility of the virus returning to its wild pathogenic type may limit the use of this group of carriers. Therefore, efforts have been made to obtain synthetic non-viral siRNA carriers, useful for both in vitro and in vivo applications [6,7].
Currently, the most commonly used non-viral siRNA carrier systems are based on nanomaterials. For this purpose, natural and synthetic cationic polymers are often applied [8], including highly branched dendrimers of a well-defined structure. These compounds enable electrostatic interactions with negatively charged siRNA molecules, providing the formation of stable complexes (dendriplexes) that are capable of intracellular delivery of nucleic acids and their protection against the activity of nucleases. What is more, surface groups of dendrimers may be subjected to modifications by functional moieties targeting them to specific locations. Numerous experiments have shown that dendrimers can be successfully used as carriers of various types of genetic material, including plasmids, single strands of DNA, oligonucleotides, and finally RNA molecules, ensuring their improved stability and prolonged blood half-life [9,10].
Most studies on the potential use of dendrimers as carriers for siRNA concern poly(amidoamine) (PAMAM), poly(propyleneimine) (PPI), and poly(lysine) dendrimers (PLL) belonging to the group of peptide dendrimers [10]. The latter are branched polymeric structures in which both the core and dendrons are composed mainly of amino acids connected by peptide bonds [11]. Peptide dendrimers are most often based on lysine, an amino acid that enables the generation of several branching points [12]. PLL dendrimers, due to their flexible structure and protein-like characteristics, such as good biocompatibility and water solubility, as well as high resistance to proteolytic digestion could be used in several biomedical applications. Their properties have been studied over the last few years both experimentally [13][14][15] and in computer simulation [16][17][18][19][20][21]. In particular, they have aroused the interest of several research teams aiming at their use as carriers of nucleic acids [22][23][24][25].
The primary goal of this study was to investigate the formation of complexes of three types of PLL dendrimers (containing additional lysine, arginine, or histidine residues within their structure) with siRNA molecules, to assess the cytotoxicity of dendrimers themselves and the obtained dendriplexes, and finally to evaluate the efficacy of transfection in in vitro-cultured myeloid cell lines.
Results and Discussion
In recent years, various types of dendrimers have been studied in terms of their use as carriers for oligonucleotides and nucleic acids [26][27][28][29]. It has been shown that PAMAM, phosphorus, and carbosilane dendrimers form stable dendriplexes [29,30] that enable effective transfection and enhancement of the cytotoxic effect of siRNA [31].
For the purpose of drug and gene delivery, PLL dendrimers seem to be the most legitimate choice, primarily due to their biocompatibility, structure flexibility, and positive charge, enabling the formation of non-covalent complexes with nucleic acids and their efficient transport in the bloodstream and into the cell cytoplasm without triggering side effects. In this study, we applied three types of PLL dendrimers ( Figure 1): D3K2 (containing two additional lysine residues (Lys-Lys) between each pair of neighboring branching points of the standard lysine dendrimer of the third generation (D3)), D3R2, and D3H2 (containing two additional arginine (Arg-Arg) or histidine (His-His) residues at the same points). Our previous research showed that D3K2 is an excellent carrier of plasmid DNA, with the transfection efficiency comparable to that of the Lipofectamine 2000 [32]. In light of these results, it seemed reasonable to continue the research on the use of PLL dendrimers as carriers for other types of genetic material.
Substitution of lysine residues with different amino acids may bring several benefits to PLL dendrimers considered as a system for gene delivery, changing their flexibility and distribution of charged groups, providing additional interactions with nucleic acids, and affecting cellular uptake levels [24,[33][34][35]. Both lysine and arginine are charged aliphatic amino acids with amino groups that are protonated under biological conditions, which may ensure the efficient delivery of nucleic acid into the cells and its endosomal escape. It has been shown that the insertion of Arg residues between inner Lys branching points made the dendrimer's interior more charged and thus more hydrophilic [34]. What is more, a guanidine moiety of Arg shows high affinity for phosphate groups of DNA, increasing its condensation. On the other hand, His contains an aromatic imidazole group, which can be either cationic or neutral at different pH values, potentially providing additional interactions with nucleic acids and their pH-triggered release [36].
The main goal of this work was the initial characterization of dendrimer:siRNA complexes and evaluation of the in vitro transfection efficiency to determine the optimal conditions for further research.
In the first stage, measurements of fluorescence polarization and changes in the zeta potential of fluorescein-labeled siRNA (siRNA-FITC) under the influence of dendrimers were performed, as well as an evaluation of the hydrodynamic diameter of the obtained complexes. The aim of this step was to determine the optimal molar ratios for complexing siRNA with PLL dendrimers, and the size of the dendriplexes prepared in selected molar ratios.
The formation of the dendrimer:siRNA complexes leads to a significant reduction in the movement of siRNA molecules in suspension, which is observed as an increase in the fluorescence polarization of siRNA-FITC ( Figure 2). This phenomenon enables the determination of interactions between dendrimers and nucleic acid, and estimation of stoichiometric ratios in which stable complexes are formed.
During the addition of subsequent portions of tested dendrimers to siRNA-FITC solution, a constant increase in fluorescence polarization was observed until reaching the plateau phase, indicating the formation of complexes. A similar observation was made for the complexes of carbosilane dendrimers and oligonucleotides [37,38]. For the D3K2 dendrimer, the increase in fluorescence polarization was much lower compared to D3R2 and D3H2, suggesting that the interactions between the first dendrimer and siRNA are weaker.
between each pair of neighboring branching points of the standard lysine dendrimer of the third generation (D3)), D3R2, and D3H2 (containing two additional arginine (Arg-Arg) or histidine (His-His) residues at the same points). Our previous research showed that D3K2 is an excellent carrier of plasmid DNA, with the transfection efficiency comparable to that of the Lipofectamine 2000 [32]. In light of these results, it seemed reasonable to continue the research on the use of PLL dendrimers as carriers for other types of genetic material. Substitution of lysine residues with different amino acids may bring several benefits to PLL dendrimers considered as a system for gene delivery, changing their flexibility and distribution of charged groups, providing additional interactions with nucleic acids, and affecting cellular uptake levels [24,[33][34][35]. Both lysine and arginine are charged aliphatic amino acids with amino groups that are protonated under biological conditions, which may ensure the efficient delivery of nucleic acid into the cells and its endosomal escape. It has been shown that the insertion of Arg residues between the dendriplexes prepared in selected molar ratios.
The formation of the dendrimer:siRNA complexes leads to a significant reduction in the movement of siRNA molecules in suspension, which is observed as an increase in the fluorescence polarization of siRNA-FITC ( Figure 2). This phenomenon enables the determination of interactions between dendrimers and nucleic acid, and estimation of stoichiometric ratios in which stable complexes are formed. During the addition of subsequent portions of tested dendrimers to siRNA-FITC solution, a constant increase in fluorescence polarization was observed until reaching the plateau phase, indicating the formation of complexes. A similar observation was made for the complexes of carbosilane dendrimers and oligonucleotides [37,38]. For the D3K2 dendrimer, the increase in fluorescence polarization was much lower compared to D3R2 and D3H2, suggesting that the interactions between the first dendrimer and siRNA are weaker.
The plateau phase was obtained at the following dendrimer:siRNA molar ratios: 20:1 for D3K2 and D3R2, and 30:1 for D3H2 dendrimer. These results suggest that for the complex to form, the siRNA molecule must be surrounded by the studied dendrimers. In addition, this outcome indicates the need to use higher concentrations of PLL dendrimers for the preparation of dendriplexes in comparison to other dendrimers, e.g., carbosilane, for which the optimal dendrimer:siRNA molar ratio was 4:1 [9,26]. It is worth noting, however, that a higher ratio of dendrimer to nucleic acid may allow a dendriplex with a higher positive charge to be obtained, increasing its affinity for cellular membranes.
To confirm the stoichiometric ratios of dendrimer:siRNA complexes obtained during the fluorescence polarization measurements, and to assess the surface electrostatic potential of the dendriplexes, zeta potential titration was conducted ( Figure 3). Upon the addition of the dendrimers, the initial zeta potential of siRNA-FITC of -14.24 ± 1.59 mV began to rise with the increase of the dendrimer concentration. This trend continued until a plateau was reached at the dendrimer:siRNA molar ratio of 20:1 for D3K2 and D3R2, and 30:1 for the D3H2 dendrimer, which confirmed the stoichiometry of the dendriplex formation determined in the previous stage of study. The plateau phase was obtained at the following dendrimer:siRNA molar ratios: 20:1 for D3K2 and D3R2, and 30:1 for D3H2 dendrimer. These results suggest that for the complex to form, the siRNA molecule must be surrounded by the studied dendrimers. In addition, this outcome indicates the need to use higher concentrations of PLL dendrimers for the preparation of dendriplexes in comparison to other dendrimers, e.g., carbosilane, for which the optimal dendrimer:siRNA molar ratio was 4:1 [9,26]. It is worth noting, however, that a higher ratio of dendrimer to nucleic acid may allow a dendriplex with a higher positive charge to be obtained, increasing its affinity for cellular membranes.
To confirm the stoichiometric ratios of dendrimer:siRNA complexes obtained during the fluorescence polarization measurements, and to assess the surface electrostatic potential of the dendriplexes, zeta potential titration was conducted ( Figure 3). Upon the addition of the dendrimers, the initial zeta potential of siRNA-FITC of −14.24 ± 1.59 mV began to rise with the increase of the dendrimer concentration. This trend continued until a plateau was reached at the dendrimer:siRNA molar ratio of 20:1 for D3K2 and D3R2, and 30:1 for the D3H2 dendrimer, which confirmed the stoichiometry of the dendriplex formation determined in the previous stage of study. [26,30,[39][40][41], as well as for the complexes of carbosilane dendrimers and oligonucleotides (~5-20 mV) [27]. Here, it was also demonstrated that dendriplexes formed by D3K2 and D3R2 dendrimers have a greater surface positive charge compared to D3H2 dendrimer. This is most likely related to the zeta potential values of the dendrimers themselves (Table 1), and suggests that dendriplexes formed by D3H2 dendrimers may have a lower tendency to interact with the cell membrane, and thus, lower transfection efficacy. On the other hand, a high surface positive charge may increase the cytotoxicity of compounds [10]. Interestingly, given the surface potential of the dendrimers under evaluation, it could be expected that interactions with negatively charged siRNA molecules will be the strongest for the D3K2 dendrimer, which is, however, contradicted by fluorescence polarization studies. This may be partially explained by differences in the flexibility of the studied dendrimers, or additional interactions provided by arginine and histidine residues (either hydrophilic, hydrophobic, or hydrogen bonds) [36], and require further studies.
The hydrodynamic diameter of the dendriplexes formed in the determined optimal molar ratios equaled 841.00 ± 21.95 nm, 300.53 ± 12.16 nm, and 249.67 ± 14.02 nm (dendriplexes formed using D3K2, D3R2, and D3H2 dendrimers, respectively). These results suggest that the cellular uptake of D3K2 dendriplexes may be hindered due to the significant size. However, it has been shown that dendriplexes based on PAMAM and carbosilane dendrimers, characterized by similar sizes, can effectively transport siRNA into the cells [26,27,30,31,42].
The results of this stage of research allowed the ability of cationic PLL dendrimers to form complexes with siRNA to be demonstrated, which can protect it against the action of nucleolytic enzymes and enable the transport of negatively charged nucleic acid molecules through cell membranes.
Next, the cytotoxicity of the dendrimers was evaluated ( Table 2). It was shown that the dendrimers exhibit varied cytotoxic activity towards the investigated myeloid cell lines, with D3K2 being the most toxic and D3H2 the least toxic. This outcome is consistent with the zeta potential measurements, indicating the highest positive surface electrostatic potential of D3K2 dendrimer and the lowest in the case of D3H2, suggesting the well-known mechanism of cell death triggered by positively charged dendrimers [43,44]. Due to the observed cytotoxic effects, dendrimers at 1 (D3K2, D3R2) or 1.5 µM (D3H2) concentrations were used for further experiments. These concentrations are required to carry the same concentration of siRNA (0.05 µM) at the optimal dendrimer:siRNA molar ratios. The cytotoxicity of dendriplexes after two different incubation times (24 and 72 h) was also determined (Figure 4). The purpose of this step was to compare the toxicity of the obtained dendriplexes with each other and with the cytotoxicity of transfection complexes obtained using the commercially available agent Lipofectamine 2000. This compound, although used as a standard, has been shown to exhibit significant toxicity towards several cell lines, especially during longer incubation times, thus limiting the possibility of its application [45,46]. commercially available agent Lipofectamine 2000. This compound, although used as a standard, has been shown to exhibit significant toxicity towards several cell lines, especially during longer incubation times, thus limiting the possibility of its application [45,46].
After 24 h of incubation, the lack of a statistically significant difference between the cytotoxicity of dendriplexes and transfection complex formed using Lipofectamine 2000 was demonstrated for both cell lines. Additionally, no statistically significant difference was found when comparing the dendriplexes with each other. After 72 h of incubation, a statistically significant decrease in the cell viability of the THP-1 cell line transfected with Lipofectamine 2000 was observed, relative to D3K2 dendriplex. In addition, a statistically significant difference was determined between the cytotoxicity of the dendriplex formed by D3R2 (decrease of cell viability to 77.5%) relative to the dendriplex formed by D3K2. It is worth noting that, despite the differences shown, the dendriplexes and transfection complex formed using Lipofectamine 2000 are characterized by relatively low cytotoxicity. After 24 h of incubation, the viability in all examined cases did not fall below 95%. The highest decrease in viability was observed after 72 h of incubation for the D3R2 dendriplex and the Lipofectamine 2000:siRNA complex; however, in both cases, cell viability was still high (above 70%). After 24 h of incubation, the lack of a statistically significant difference between the cytotoxicity of dendriplexes and transfection complex formed using Lipofectamine 2000 was demonstrated for both cell lines. Additionally, no statistically significant difference was found when comparing the dendriplexes with each other. After 72 h of incubation, a statistically significant decrease in the cell viability of the THP-1 cell line transfected with Lipofectamine 2000 was observed, relative to D3K2 dendriplex. In addition, a statistically significant difference was determined between the cytotoxicity of the dendriplex formed by D3R2 (decrease of cell viability to 77.5%) relative to the dendriplex formed by D3K2.
It is worth noting that, despite the differences shown, the dendriplexes and transfection complex formed using Lipofectamine 2000 are characterized by relatively low cytotoxicity. After 24 h of incubation, the viability in all examined cases did not fall below 95%. The highest decrease in viability was observed after 72 h of incubation for the D3R2 dendriplex and the Lipofectamine 2000:siRNA complex; however, in both cases, cell viability was still high (above 70%).
In the last stage of the study, the efficacy of siRNA cellular uptake was assessed using flow cytometry ( Figure 5). Increased cellular uptake of siRNA-FITC molecules was demonstrated for all three PLL dendrimers tested as carriers relative to Lipofectamine 2000. For the dendrimers, the percentage of FITC-positive cells of both cell lines was above 94% regardless of the incubation time. The use of Lipofectamine 2000 as a transfection agent allowed for cellular uptake of siRNA molecules at 49.25% ± 1.05%, 64.6% ± 5.45%, and 79.85% ± 0.35% (THP-1 cell line, 24, 48, and 72 h of incubation, respectively), and 60.85% ± 0.45%, 71.7% ± 5.6%, and 76.9% ± 0.5% (U937 cell line, 24, 48, and 72 h of incubation, respectively).
The obtained results showed that regardless of the incubation time, the level of cellular uptake of dendriplexes is much higher compared to the uptake of complexes formed by Lipofectamine 2000, which correlates well with the results of other studies on the use of PLL dendrimers as carriers for nucleic acids [23,47]. Moreover, despite the differences in the dendrimer-siRNA interactions and dendriplex properties, all tested dendrimers were able to transfect cells with comparable efficiency, reaching~100%. Similar results were obtained previously by Dzmitruk et al. [31] for phosphorus dendrimers and siRNA with a scrambled sequence; however, the level of transfection was significantly lower for other types of dendrimers (~10% for PAMAM G3,~60% for PAMAM G4, and~30% for carbosilane dendrimers). Comparing our results with the transfection efficacy of other types of dendrimers, it can be concluded that PLL dendrimers can serve as an extremely efficient tool for the delivery of siRNA into the cells in vitro.
In summary, based on the conducted experiments, it can be concluded that the PLL dendrimers D3K2, D3R2, and D3H2 are capable of forming complexes with siRNA, and the obtained dendriplexes differ in the strength of dendrimer-siRNA interactions and binding stoichiometry, as well as the electrostatic surface potential and size. The tested dendrimers exhibited varied cytotoxicity relative to the THP-1 and U937 cell lines, with the highest toxic effect exhibited by the dendrimer with the highest surface electrostatic potential. The use of PLL dendrimers made it possible to obtain non-toxic and highly efficient siRNA delivery systems in vitro, increasing the cellular uptake of nucleic acid molecules compared to the commercially available transfection agent. In the last stage of the study, the efficacy of siRNA cellular uptake was assessed using flow cytometry ( Figure 5). Increased cellular uptake of siRNA-FITC molecules was demonstrated for all three PLL dendrimers tested as carriers relative to Lipofectamine 2000. For the dendrimers, the percentage of FITC-positive cells of both cell lines was above 94% regardless of the incubation time. The use of Lipofectamine 2000 as a transfection agent allowed for cellular uptake of siRNA molecules at 49.25% ± 1.05%, 64.6% ± 5.45%, and 79.85% ± 0.35% (THP-1 cell line, 24, 48, and 72 h of incubation, respectively), and 60.85% ± 0.45%, 71.7% ± 5.6%, and 76.9% ± 0.5% (U937 cell line, 24, 48, and 72 h of incubation, respectively). The obtained results showed that regardless of the incubation time, the level of cellular uptake of dendriplexes is much higher compared to the uptake of complexes formed by Lipofectamine 2000, which correlates well with the results of other studies on the use of PLL dendrimers as carriers for nucleic acids [23,47]. Moreover, despite the differences in the dendrimer-siRNA interactions and dendriplex properties, all tested dendrimers were able to transfect cells with comparable efficiency, reaching ~100%. Similar results were obtained previously by Dzmitruk et al. [31] for phosphorus dendrimers and siRNA with a scrambled sequence; however, the level of transfection was significantly lower for other types of dendrimers (~10% for PAMAM G3, ~60% for PAMAM G4, and ~30% for carbosilane dendrimers). Comparing our results with the transfection efficacy of other types of dendrimers, it can be concluded that PLL dendrimers can serve as an extremely efficient tool for the delivery of siRNA into the cells in vitro.
In summary, based on the conducted experiments, it can be concluded that the PLL dendrimers D3K2, D3R2, and D3H2 are capable of forming complexes with siRNA, and the obtained dendriplexes differ in the strength of dendrimer-siRNA interactions and binding stoichiometry, as well as the electrostatic surface potential and size. The tested dendrimers exhibited varied cytotoxicity relative to the THP-1 and U937 cell lines, with the highest toxic effect exhibited by the dendrimer with the highest surface electrostatic potential. The use of PLL dendrimers made it possible to obtain non-toxic and highly efficient siRNA delivery systems in vitro, increasing the cellular uptake of nucleic acid molecules compared to the commercially available transfection agent.
Dendrimers
PLL dendrimers of the 3rd generation (D3): D3K2 (containing two additional lysine residues (Lys-Lys) between each pair of neighboring branching points of standard lysine dendrimer of the 3rd generation), D3R2 and D3H2 (with two additional arginine (Arg-Arg), or histidine (His-His)
Fluorescence Polarization Studies
Phosphate-buffered saline (PBS, 10 mM, pH 7.4) solutions containing control siRNA with a scrambled sequence, labeled with fluorescein (FITC) (sc-36869, Santa Cruz Biotechnology, Inc., Heidelberg, Germany) at constant concentration (0.1 µM), were prepared, and their fluorescence was measured. The siRNA-FITC solutions were subsequently titrated with solutions of the tested dendrimers (D3K2, D3R2, or D3H2) at concentrations ranging from 0.002 to 5 µM (in order to achieve dendrimer:siRNA molar ratios ranging from 1:50 to 50:1). The dendrimer:siRNA mixtures were incubated at room temperature for 10 min to ensure the formation of complexes, and then fluorescence anisotropy was measured on a Perkin-Elmer LS-55 spectrofluorometer in a 1-cm path length quartz cuvettes. The excitation and emission wavelengths were 485 and 520 nm, and the excitation and emission slit widths were set to 7 and 5 nm, respectively. The cuvette holder was temperature controlled (25 • C).
Zeta Potential and Hydrodynamic Diameter Measurements
Measurements of the zeta potential and hydrodynamic diameter were performed with the use of Zetasizer Nano ZS (Malvern Instruments Ltd., Malvern, UK). All samples were placed in the low volume sizing cuvettes (ZEN0112, Malvern) for hydrodynamic diameter determination or in the folded capillary cells (DTS 1070, Malvern) for zeta potential measurements and measured at 25 • C. For zeta potential studies, the solutions of studied dendrimers and siRNA-FITC were prepared and the titrations were carried out analogously to fluorescence measurements. Additionally, the zeta potential measurements of free dendrimers in H 2 O and PBS were performed. The hydrodynamic diameter was measured at a dendrimer:siRNA molar ratio of 20:1 for D3K2 and D3G2, and 30:1 for D3H2. The data were analyzed using the Malvern software.
Preparation of Dendriplexes
The dendriplexes of previously established optimal dendrimer:siRNA molar ratios were prepared by mixing PBS solutions (for cytotoxicity studies) or Opti-MEM medium (Gibco, Thermo Fisher Scientific, Waltham, MA, USA) solutions (for transfection assays) of siRNA-FITC (0.05 µM) and D3K2 (1 µM), D3R2 (1 µM), or D3H2 (1.5 µM) macromolecules. The mixtures were stirred for 10 min at room temperature to ensure the formation of complexes. The obtained dendriplexes were used in subsequent experiments. The control complex of siRNA-FITC (0.05 µM) with Lipofectamine 2000 (Thermo Fisher Scientific, Waltham, MA, USA) was prepared according to the manufacturer's protocol.
Cytotoxicity Studies
To estimate the cytotoxicity of dendrimers and dendriplexes, the resazurin assay was performed [48]. Cells were seeded into 96-well black plates at a density of 1.5 × 10 4 cells per well, and treated with increasing concentrations of D3K2, D3R2, and D3H2 for 24 and 72 h at 37 • C in an atmosphere of 5% CO 2 . Following the incubation, resazurin was added to the culture medium to a final concentration of 12.5 µg/mL and the plates were incubated at 37 • C in darkness to allow the conversion of resazurin to resorufin. The fluorescence of the metabolized resazurin was measured after 2 h at 530 nm excitation and 590 nm emission using the PowerWave HT Microplate Spectrophotometer (BioTek, Winooski, VT, USA). The cytotoxicity of dendriplexes and Lipofectamine 2000:siRNA control complex was evaluated in an analogous manner.
Transfection
Cells were seeded into 12-well plates at a density of 1.5 × 10 5 cells per well, and treated with dendriplexes and Lipofectamine 2000:siRNA control complex for 24, 48, and 72 h at 37 • C in an atmosphere of 5% CO 2 . Following the incubation, the cells were washed with PBS, suspended in fresh medium, and transferred to flow cytometry tubes. The fluorescence was measured using a Becton Dickinson LSR II flow cytometer (BD Biosciences, San Jose, CA, USA). The green fluorescence at 485 nm excitation and 520 nm emission was measured, and the number of FITC-positive cells was expressed as a percentage of the total number of cells in the sample.
Statistics
For statistical analysis, one-way ANOVA followed by post-hoc Tukey's test was used. In all tests, p values < 0.05 were considered to be statistically significant.
Conclusions
The performed in vitro tests allowed demonstration of the differences in the cytotoxicity of the tested PLL dendrimers, as well as the high biocompatibility of dendriplexes formed by this type of polymer. Most importantly, a very high level of cellular uptake of dendrimer:siRNA complexes was shown, exceeding 90% regardless of the dendrimer structure. These studies constitute the first stage of evaluation of the possibility of the application of the studied dendrimers as carriers for siRNA and will be continued in a wider scope. Only after demonstrating that the transported nucleic acid effectively inhibits expression of the target gene will it be possible to state that PLL dendrimers are an effective method of cell transfection, and may in the future become the basis of modern gene therapy. Additionally, considering the differences in the physicochemical properties of dendriplexes formed by various types of PLL dendrimers, it is reasonable to continue the studies in the field of their characterization, in order to elucidate the role of different amino acids in the structure of the dendrimer in the interactions with siRNA. Funding: This work is based upon work from COST Action "Nano2Clinic. Cancer Nanomedicine-from the bench to the bedside" CA17140 supported by COST (European Cooperation in Science and Technology). I. M. Neelov, I. I. Tarasenko and V. V. Bezrodnyi are grateful to RSF grant 19-13-00087. | 6,820.8 | 2020-04-29T00:00:00.000 | [
"Biology",
"Chemistry"
] |
Towards in situ determination of 3 D strain and reorientation in the interpenetrating nanofibre networks of cuticle
Please note that technical editing may introduce minor changes to the text and/or graphics, which may alter content. The journal’s standard Terms & Conditions and the ethical guidelines, outlined in our author and reviewer resource centre, still apply. In no event shall the Royal Society of Chemistry be held responsible for any errors or omissions in this Accepted Manuscript or any consequences arising from the use of any information it contains. Accepted Manuscript
Introduction
In the design of advanced functional composites, a key characteristic is the assembly (either via self-organization or guided deposition) of sub-micron elements such as nanowires or nanofibres into a hierarchical and ordered system at multiple length scales between the molecular and microscopic levels. These include mineralized collagen fibrils in bone, 1 ordered calcite nanocrystals in hierarchical clay nanocomposites, 2,3 ordered 2D materials inside 3D biomineralized materials, 4 mechanically high performance polymer/nanoclay composites, 5 oriented TiO 2 nanocrystals assemblies for photocatalysis, 6 and semiconductor nanocrystals in superlattices. 7 The precise orientation, strain and structure of the nanoscale inclusions in such systems is a crucial determining factor in enabling function and influencing a diverse range of designed material properties, including mechanics, 4,8,9 catalytic performance or semiconductor performance. 7 In this regard, advances in X-ray techniques including scanning nano-diffraction, ptychography and coherent X-ray diffraction have been applied to determine the strain, shape and texture of individual nanoparticles or composite aggregates. [10][11][12] However, an implicit assumption of much current X-ray scanning microprobe and in situ methods is a neglect of the depth dimension in the analysis of 2D diffraction maps. The 2D X-ray diffraction pattern obtained is a slice through the 3D reciprocal space intensity distribution. 13 This limits the application of most such methods to simple in-plane geometries or sections or special materials such as collagen fibrils with an ordered periodic structure at the nanoscale, while in most real-life systems, the 3D morphology may have no particular symmetry or alignment to sample shape. While recent innovative methods like 3D small-angle X-ray scattering (SAXS) tomography 14 and polychromatic X-ray diffraction, 15,16 which reconstruct 3D reciprocal space intensity in a model-free manner, circumvent this 2D limitation, these methods have limitations for in situ studies. SAXS tomography can take several hours of synchrotron time per reconstruction, 14 and the polychromatic X-ray diffraction analysis requires several minutes with a specialized energy-dispersive detector, 15 or scanning the photon energy. 3D X-ray structural microscopy uses polychromatic radiation to measure grain orientation and strain in functionally graded materials and composites, but requires sample rotation. 17 Indeed, the in situ dynamics of the nanoscale inclusions can follow a complex and non-predetermined path of coupled rotation, stretching and phase transformation in 3D, and requires time-resolutions of the order of seconds or below, and do not readily allow steps such as sample-rotation or energy scanning at each step of the process. 14,18 Further, methods such as ptychography are suited for scanning with high (a few tens of nanometres) resolution to obtain structure information, but are also comparatively time consuming due to overlapping scans and are therefore not suited for in situ studies of samples in the millimetre size range. 12 There is therefore a significant need for multiscale 3D reconstruction methods for in situ nanoscale mechanics. This need is especially relevant for biological and biomimetic composites, where the hierarchical architecture leads to complex, multi-dimensional motifs. 9 A prototypical example of such a multiscale biocomposite (ESI, Fig. S1 †) is the crustacean cuticle. 19,20 At the nanoscale, the cuticle may be considered a three-phase composite of ∼3 nm diameter chitin fibrils, crosslinked amorphous proteins and biogenic mineral (calcium carbonate), along with water. The mineralized fibrils aggregate into fibres at the scale of ∼100 nm, which in turn form a characteristic continuous rotated layered plywood structure at the scale of ∼10 μm, known as the Bouligand motif. 21 A network of pore canal fibres run perpendicular to these Bouligand layers, forming an interpenetrating network of nanofibers which has been likened to a honeycomb structure. 19 This structural motif has evolved into a range of functional specializations, from impact resistant exoskeletons like the dactyl and telson in the mantis shrimp, to hyper-extensible appendages for laying eggs, 22 to specialized sensory organs in spiders. 23 In particular, the exoskeleton of the mantis shrimp has attracted considerable recent attention, due to its ability to resist high rate, repetitive loading with no structural damage serving as a template for bioinspired composites. [24][25][26][27][28] While multiscale modelling studies of the (lobster) cuticle exist, suggesting that much of the variation of mechanical properties arises due to structure at the microscale and above, 29 there is little direct experimental in situ evidence of the nanoscale and microscale mechanisms in crustacean cuticle.
In this paper, we develop and apply an in situ multiscale X-ray diffraction/modelling scheme to determine the nanoscale and microscale deformation mechanisms in crustacean cuticle. By modelling the crustacean cuticle extracellular matrix as two interpenetrating fibre-lamellate structures at the sub-micron scale, we predict the 3D X-ray diffraction intensity distributions from these fibres using an asymptotic integral approach. 30 Under mechanical load, these distributions will alter in a manner dictated by the coupled effects of strain at the nanoscale along with 3D deformation and reorientation at larger scales. We show how, by modelling the fibre-level stress and strain fields by matching lamination theory to the experimental X-ray peak shifts, 31 and subsequently accounting for larger mesoscale (>10 μm) deformations at the scale of lamellae and interpenetrating fibre distributions, we can determine the in situ nano-and microscale mechanics of crustacean cuticle with high precision. Our approachsolely relying on the existence of fibre symmetry at the molecular levelis designed to apply to in situ studies of the structural dynamics of nanoscale inclusions in advanced multiscale functional materials, provides both mechanical strain as well as structural reorientation, and can be carried out using standard 2D X-ray detectors or lab-setups.
Ultrastructural model and experimental results
2.1. Analytic 3D X-ray diffraction intensity distributions for interpenetrating nanofibre networks Fig. 1 shows the experimental protocol for in situ tensile testing during synchrotron XRD experiment, and the relation of X-ray diffraction geometry to the underlying nanofibre organization. Tergite specimens from the stomatopod (Fig. 1a) cuticle embedded in two orthogonal orientations (Fig. 1b) are deformed during synchrotron XRD (Fig. 1c), leading to the acquisition of a series of XRD patterns (for details see Materials and methods). The microstructure of cuticle consists of in-plane fibres in a twisted plywood arrangement known as Bouligand layers (green fibres, Fig. 1d), interpenetrated with perpendicularly oriented pore-canal fibres (blue fibres, Fig. 1d). The basic microstructural unit in each scattering volume element is therefore a combination of in-plane fibres (IP) (forming Bouligand plywood layers) and bundles of out-ofplane (OP) fibres (from the pore-canals) (Fig. 1d). 32 Here, we consider both micro units as variations of an underlying planar fibre distribution w(γ;γ 0 ,Δγ 0 ) ( Fig. 1e and Table S1-II †), with the Bouligand (IP-) phase corresponding to fibres equally oriented in all directions in the lamellar plane, and the porecanal (OP-) fibres oriented principally in one direction (along the pore). As the plane of the fibres in the sample may be oriented at nonzero angles to the principal coordinate axes of the lab-frame, we denote α and β (with respect to q L z and q L y axis respectively) as the Euler tilt angles of the plane with respect to the lab coordinate system (Fig. S3 †). These micro-units are themselves comprisedat the nanoscaleof chitin fibres, 29 made of α-chitin molecules arranged in a fibre-symmetric manner around the fibre axis (Fig. S1 †). As a consequence, the diffraction intensity of the (hk0) reflections (such as the equatorial (110) peak) can be represented in reciprocal space as rings, 33 and the (00l) reflections (such as the (002) peak) as paired spots. To justify the assumption of fibre symmetry, some discussion of the size of the X-ray scattering volume relative to the micro-and nanostructural build-ing blocks is needed. Specifically, cuticle fibre symmetry is believed to hold at the fibre-level (100-300 nm or 0.1-0.3 μm in diameter) and above. 19,32 The scattering volume in our experiments is given by the product of the beam crosssectional area (10 μm×1 0μm) with the sample thickness (∼500 μm), and can be seen to be much larger than the fibre dimensions, and hence the material can be considered as having fibre symmetry at the scale of the measurements. The assumption of fibre symmetry may, however, break down for very small scattering volumessmaller than single fibressuch as with nanofocus X-ray beams and submicron thick samples. To show the intensity distribution on the reciprocal space as a function of 3D orientation, a polar-sphere-like representation is used. The X-ray diffraction (XRD) intensity pattern corresponding to the model will be the 2D Ewald surface intersection with 3D volume of reciprocal space scattering intensity (Fig. S2 †). Different spheres correspond to different reflections, and the spherical intensity variation correlates to the 3D orientation distributions of IP and OP fibres. As the full 3D intensity variation on the different reciprocal spheres cannot be fully captured using a 2D detector at a single orientation, here we used two orthogonal tensile test geometries together with modelling to fully capture the deformation and reorientation information for both IP and OP fibres ( Fig. 1b and d). Both the (002) and (110) reflections can be used to calculate the axial and radial fibrillar deformation respectively as well as orientation for the chitin fibres, but in this initial work we present results only on the (002) reflection. Fig. 2a show the geometry of IP and OP fibres in the L1 configuration. Fig. 2b shows how, for the (110) reflection, constructive interference of the (hk0) rings from the IP fibres leads to peaks only at the poles perpendicular to the intersection plane between QS(110) sphere and Ewald sphere. 33,34 Therefore, the intensity variation of (110) reflection from the major fibre component (IP) is not captured by the detector. 33 Concurrently, for the (002) reflection, the paired diffraction spots from individual fibres lead to rings parallel to the q y -q z plane due to the Bouligand distribution of the IP fibres (Fig. 2c). In this study, we will use the (002) reflection to calculate the deformation and reorientation of IP fibres in the L1 configuration.
These complex distributions in reciprocal space can be represented analytically. Consider the Bouligand lamella to be oriented in the q L y − q L z plane (indicated with green fibres in Fig. 2a). For a single fibre, the intensity distribution in reciprocal space can be written as (ESI †): where the scattering vector q is given by over all possible fibre angles in the lamella, and these 3D spherical intensity distributions are plotted in Fig. 2b and c.
To obtain the intensity profile on the detector, the 3D reciprocal space distribution is transformed to 2D detector coordinates (q,χ) (transformation equations in ESI, Table V †). For a uniform fibre distribution w(γ;γ 0 ,Δγ 0 )=w 0 in the lamellar plane (which represents Bouligand lamellae with fibres in the sub-lamellae at all possible angles), by taking the asymptotic limit of small Δq (002) , it is possible to obtain a closed form of the azimuthal intensity profile: where κ = Δq (002) /q (002) is a parameter denoting the relative width of the (002) ring (q (002) is the reciprocal lattice vector corresponding to the (002) peak) and χ is the azimuthal angle with respect to q L z axis inside the intersection plane between the Ewald sphere with the QS(002) sphere. The width of the ring is a measure of both the degree of misorientation of fibrils within a fibre at the nanoscale, as well as the misorientation of fibres within a lamellar plane; fully parallel fibrils will lead to κ = 0. Due to the well-ordered parallel lamellate structure in tergite, we make the approximation in this paper that the intralamellar reorientation can be neglected, i.e. κ is a constant. For more general fibre orientation geometries, κ should be con-sidered a variable parameter like α and β. Details of the integration, transformation equations and asymptotic limit are in ESI: Tables I-III † and accompanying text. In the aligned state (where α = β = 0°) and the Bouligand plane is parallel to the lab-frame, it is clear that the intensity of the (002) ring will be constant as a function of azimuthal angle χ, with a value of: In Fig. 2d an example 2D XRD pattern is shown in the L1-orientation, with the (002) and (110) reflections indicated, whose peaks are shown on a radial profile in Fig. 2e. Azimuthally resolved intensity plots are shown for these reflections in Fig. 2f. A ring background subtraction was used to eliminate the diffuse mineral scattering background I bgr in the WAXD pattern using I bgr (χ;q 0 )=( I(χ;q 0 + Δq)+I(χ;q 0 − Δq))/2 for both (110) and (002) reflections (Δq = 0.1 nm −1 is a small increment of wavevector such that q 0 ± Δq is outside of the Bragg peak in each case). A clear angular variation of intensity is observed in both subplots, which, when taken together with Fig. 2b and c, implies slight nonzero value of the tilt angles α and β, and these tilts will be quantitatively determined in the following subsections. Shifts in the (002) peak positions (Fig. 2e) will (in an angularly resolved sense to be described in the next section) be linked to the strain along the fibre axis (ε f ) induced by the tensile loading. When the cuticle is deformed, a priori expectations are that the fibre distributions (both IP and OP) will undergo both (i) nanoscale axial deformation along the fibres and reorientation of the fibres in the Bouligand plane (changing the planar fibre distribution w(γ;γ 0 ,Δγ 0 )), as well as (ii) an overall angular movement of the Bouligand layer itself (change in α and β)a t the mesoscale. While the analytic relations given previously are applicable in the general case, for the specific case considered here, where the fibre plane is nearly aligned with the lab-principal axes, we can proceed via a simpler two-step approximation. First, given that the Euler tilt angles α and β are small to start with, the deformation of the fibres in the Bouligand plane can be obtained from the 2D XRD pattern in the same manner as would be for an un-tilted configuration. This step will provide the nanoscale strain and reorientation, and enable us to track the change in the fibre orientation distribution during the loading process, and is described in the next subsection.
Fibre mechanics in the Bouligand lamellae match laminate theory predictions at nanoscale
An averaged tensile stress-strain curves for the tergite cuticle is shown in Fig. 3a, showing a linear increase of tissue stress with strain with a slight downward curvature evident at strains >0.6-0.8%. Concurrently, the radial peak profiles for the (002) reflection show shifts; for the direction parallel to the loading direction, to smaller wavevector (Fig. 3b) implying a tensile deformation of the chitin fibres. Fig. 3c shows the schematic of the plywood lamellae. The strain in the different sublayers of the Bouligand lamellae was calculated from shifts in the angularly resolved profiles of the (002) peak, and plotted in Fig. 3d. The result shows that chitin fibres which orientated close to the tensile direction (ψ =0°-40°) exhibit a positive strain as the stress increases, while fibres orientated further away (60°-90°) from the tensile direction showed a negative strain (Fig. 3d). In the transition region (40°-60°) the chitin fibres showed no significant strain increments compared to the other regions. The experimental data appear to lie in three groups (0-40°: tension, 50-60°: no change; 70-90°: compression), rather than the continuous change in Fig. 3, but this effect is largely due to the experimental scatter in the fitted data.
The in-plane deformation and reorientation then were calculated using classical lamination theory to compare with the experimental results obtained from WAXD patterns. The plywood structured tergite sample was treated as a laminate comprising 100 Bouligand sublayers (laminae). The reinforcement (fibre) was considered to be the mineralized chitin fibre, and the surrounding interfibrillar phase (matrix) was taken to be the mineral-protein composite. The fibre orientation in different laminae rotates around the normal axis of the whole laminate to match the plywood structure of the cuticle. Using initial estimates of the chitin, mineral and protein material properties and relative volume fractions from previous work, 19,35 the deformation (Fig. 3e) of each lamina inside the whole laminate, 21,28 was calculated from an analytical formulation. More detailed information on the material property assignment and analytical formulae were described in ESI (section S3). † Even without any parameter fitting of the literature values to the data, good qualitative agreement is observed between Fig. 3d and e, although the deformation of the onaxis fibres is somewhat less in the experimental case than in the model. Fitting the model to the data as a function of the volume fraction, fibre moduli and other parameters is in principle possible in future work.
Generally, the fibre orientation distribution changes can be determined by tracking the angle-resolved I(χ) changes for the (002) reflection during tensile loading. The experimental results (Fig. S6a †) show that the normalized diffraction intensity is increasing in the angular region close to the tensile direction and decreasing in the angular region away to the tensile direction. However, the angle-resolved I(χ) changes can result both from in-plane fibre reorientation (from lamination theory) and the overall 3D tilting of the Bouligand lamellae. Therefore, the lamination model was used to factor out the inplane reorientation effect.
From the modelled deformation of each lamina, it is possible to obtain the in-plane fibre reorientation (ESI, section S3, † eqn (S25) †). Under load, the angular intensity distribution is expected to narrow in width, as the fibres reorient towards the tensile axis. To describe this analytically, on application of a perturbing stress σ, a fibre originally at γ reorients to γ σ according to the relation: where σ = σ/σ 0 is a dimensionless perturbation parameter (σ 0 = 100 MPa; as the experimentally observed ranges of stress are σ T < 100 MPa, and f (γ) ≪ 1, σf (γ) is a small parameter). The new angular distribution (under stress) is denoted w σ (γ;γ 0 ,Δγ 0 ). Using first order perturbation, conservation of fibre number, and an initially uniform fibre distribution in the cuticle lamella w 0 =1 / π, it is possible to show (ESI, section S4 †) that the changed distribution function is given by where B is a dimensionless function (obtainable from composite laminate analysis) of the cuticle material parameters. The angular change is, similarly, γ σ − γ = −σBsin(2γ) which implies zero angular shift for fibres oriented parallel (γ = π/2) and perpendicular (γ = 0) to the loading direction. Using the same model parameters as used to predict the deformation of each layer, B can be calculated and the angular reorientation plotted (Fig. 3f ). It turns out that in this particular material (cuticle) the in-plane reorientation and change in orientation function is very small (angular changes of the order of 0.01°).
In this way, by using the parameters from fitting the fibre deformation in Fig. 3c (with model results in Fig. 3d), we obtained the changed fibre orientation distribution function at a given stressas long as the stress remains below the elastic limit point of validity for laminate theory. While in the particular case of cuticle considered here the change of orientation function was negligible (Fig. S6b †), in other layered composites like armored fish scales much larger reorientations have been observed via small-angle X-ray scattering. 1 In general, the change in reorientation function will not necessarily be negli-gible in large-deformation scenarios, or in deformation of very soft materials, where the ratio between stiffness of the reinforcing fibres and the surrounding matrix is very large. 36
Mesoscale reorientation shows layer alignment to tensile direction
The stress-altered fibre reorientation function w σ (γ;γ 0 ,Δγ 0 ) can now be inserted into eqn (2) to factor out the in-plane nanoscale reorientation, enabling the mesoscale Euler tilt angles α and β to be fitted as functions of applied stress and strain (as stated in the previous section, for cuticle the change in w(γ;γ 0 ,Δγ 0 ) is negligible). To show the predicted diffraction model sensitivity to the tilt angles, Fig. 4a and d show the deviation of the 2D and 1D intensity profiles (1D for (002) only) from a straight line due to nonzero but very small α = 2°(with no change in β or in the Bouligand layer fibre orientation function). Fig. 4b and e show the diffraction intensity changes with a small β tilt while α = 0°. Fig. 4c and f show that a combination of α and β tilt can split the diffraction ring. It is clearly observed that major deviations from isotropy are observed for quite small α and β angles.
The qualitative reasoning for this sensitivity arises because there are two competing small parameters: the term 4π λ sin 2 2Θ 2 ¼ λq 2 4π in eqn (2) and width Δq (002) of the (002) ring in the q x direction. Small movements of the cuticle layer will rapidly bring the intensity of the (002) ring into and out of the Ewald intersection (Fig. 3c), resulting in a high sensitivity to angular changes. This feature, though fortuitous (it would cease to hold for large reciprocal lattice vectors q or wavelength λ), is useful in practice, as the changes in the angles themselves are expected to be quite small in linear elasticity, so having large changes in the intensity distribution for small angular changes improves fit sensitivity. Fig. 4h shows the experimental I(χ) plots, and fitted curves, for three points I-III on a typical stressstrain curve of cuticle (Fig. 4g). By fitting α and β over the whole strain range (Fig. 4i), it is observed that α (denoting the deviation from the stress axis) reduces from ∼2°to >1°on application of load, with a similar change in β of about ∼1°. Such a change in α is as expected, as under tensile load the Bouligand plane would align toward the loading direction.
Pore canal fibres compress whilst Bouligand fibres extend under loading
So far, we have considered only the deformation and reorientation of the IP fibre which is the majority phase of the interpenetrating nanofiber network. The OP fibres ( Fig. S1f and Fig. 1a4, a5 †) interpenetrating the Bouligand layer via the transversely running pore canals will also contribute intensity on the QS(110) and QS(002) spheres. In the case of L2 geometry, the regions of (110) and (002) intensity arising from IP and OP fibre contributions are all captured in the detector ( Fig. 5a and b). It is seen that the intensity peaks of (002) reflection for each phase are nearly orthogonal to each other (IP-and OP-arrows in Fig. 5c), permitting determination of peak changes in each phase individually. The 3D tilting of the lamellae plane in the L2 geometry can be directly determined using the (110) reflection and the associated model diffraction functions (ESI , Table V †). The trace intersection of the Ewald sphere with the reciprocal lattice spheres is shown for (002) and (110) in Fig. 5c. Fig. 5d indicates the allocation of peaks for IP and OP fibres in the I(χ) curves. In Fig. 5f, the strain increments for both porecanal fibre and the IP fibre within the Bouligand lamellae are plotted against tissue strain. The result show that the OP fibre also exhibits a linear compressive response up to ∼−0.15% (∼0.6% tissue strain), shortly before the level at which macroscopic yielding and failure is observed (0.8%). It is clear that this phase of the nanofibre network (the pore-canal fibres) bears load and is expected to contribute to the overall mechanical properties. The corresponding reorientation dynamics of α and β deduced from the azimuthal angle changes of (110) reflection is shown in Fig. 5e, and again, reorientation of the tilt angle α to smaller values (∼6.5°to 4.5°) is observed, upon application of load.
Discussion and conclusion
In summary, we determined the 3D deformation and reorientation of two interpenetrating nanofiber networks in crustacean (stomatopod) cuticle, by developing a mathematical model to predict the 3D reciprocal diffraction intensity changes of (110) and (002) reflections of α-chitin fibres for two orthogonal diffraction geometries, in a combined in situ synchrotron mechanical test with X-ray diffraction. Taking advantage of the fibre symmetry, the deformation and reorientation at different hierarchical levels of the crustacean cuticle including the whole Bouligand fibre lamellae and pore-canal fibre bundles (mesoscale), each sub-lamellae (microscale) can be quantitatively determined by simple experimental design with the assist of analytical formulae. As seen in Fig. 3 and 4, we find the method is highly sensitive to both strain and angular changes as induced by stress, as the X-ray azimuthal pattern changes significantly for shifts of less than one degree, and strains are typically less than 1%.
Our method clearly overcomes the limitation of 2D XRD patterns in capturing 3D diffraction intensity changes in reciprocal space through a modelling approach, whilst other structural characterization methods (reviewed in the introduction) require time-consuming sample rotations and raises concern of radiation damage to the samples. Therefore it is very suitable for in situ or in operando study in materials science, when the deformation and orientation dynamics of crystalline phase is strongly correlated to the material function. In addition, we also employed the lamination theory simulation to decouple the intensity changes due to the in-plane anisotropic strain-induced reorientation effect from changes resulting from the 3D tilt of the whole Bouligand lamellae during the tensile test (Fig. 6).
One other interesting aspect of our method is that the decoupling of strain and reorientation between 2D and 3D is potentially reversible. By this we means that by obtaining the 3D reorientation information in one specific diffraction geometry (e.g. L2), the (α,β) parameters could be determined first, and accounted for in the model for I(χ)( e q n( 2 ) ) ,w h i c hw o u l d enable the purely in-plane deformation and reorientation to be determined. Consequently, in an inverse problem approach (analytical or numerical), the results can thereby be inserted back into (for example) lamination theory simulations to deduce the material properties of different nanoscale components. This will be very helpful in identify the material properties of components in nanostructured biocomposites like amorphous mineralsorproteinswhicharedifficult to characterize individually.
A characteristic of our approach is that it is applicable to any fibre network with molecular level fibre symmetry and ( partial) crystalline order, and does not require the existence of special additional symmetries of periodicities at higher length scales (between 10-100 nm) such as in collagen. 37 As such this approach is especially suitable for fibre-based biological composites. Further, the method may also be potentially extended also to highly mineralized biocomposites with relatively little organic material, such as nacre in mollusk shells, 9 as long as the mineral phase is at least partly crystalline. By modelling the texture of the mineral diffraction rings similar to the manner presented here, if the sample scattering volume (and X-ray microfocus beam size) is large enough to ensure fibre symmetry of the mineral nanoscale inclusions, our approach can be adapted to model the XRD signal.
Indeed, both natural and synthetic composites comprising nanorods and nano-sheets can be considered, if partially crystalline. In such implementations, however, it must be noted that the current 2D lamellar fibre distribution w(γ;γ 0 ,Δγ 0 ) distribution (characteristic of the Bouligand patterns in cuticle) is a simplified case of a more general elliptical orientation distribution function in two spherical polar angles, which will be needed when considering natural composites with arbitrary 3D microstructural distribution. Hence in such cases, the twodimensional distribution with the delta-function in the diffraction kernel (eqn (1)) will simplify to a single integral, which can be solved numerically (or approximated analytically). Complementing the in situ information from our diffraction/ modelling method, for single nanorods, nanoparticles or nanosheets, methods like Bragg coherent diffraction imaging or ptychography 11,12 can be used to obtain the 3D phase and strain information.
Beyond the functional analysis of biocomposites and their graded architecture, 38 other examples of applications of the method can be to link 3D strain and orientation changes of the crystalline lattice of nanocomponents with the in situ or in operando mechanical, electrical, thermal, and optical performance. These may include the preferential orientation of the semi-crystalline polymer nanofibres and their correlation with piezoelectric response in energy conversion materials, 39 the thermal and mechanical performance with respect to the strain and texture changes of nanoplatelets in engineering alloys, 40 and the synthesis process with the resulting texture of mineral nanofibres and corresponding photocatalytic activity in environmental applications. 41,42 Regarding other methods for analysis of 3D nanoscale structure in other classes of materials, we note 3D static strain and texture determinations for metal grains in thin films using scanning nano-diffraction, 10,43 precession electron diffraction of strain in semiconductor quantum well structures and orientation of nanocrystals in biogenic calcite using XANES. 44 Indeed, where a clear hierarchy of structural levels do not exist (in contrast to biological materials), and in situ mechanics are not needed, methods like 3D X-ray structural microscopy, 18 which use sample rotation and aperture scanning, may be more appropriate. Strain evolution in nanocrystals can also be determined from coherent diffraction imaging, 11 but such methods are usually focused on single particles rather than assemblies of them. Further, the approach presented here, to determine both real-time orientation and strain changes in 3D, can be applied to more complex systems even when the deformation and reorientation is small.
The angledependent deformation of fibres, shown to be consistent with lamination theory assuming a continuous distribution of fibre orientations, sheds light on the underlying mechanisms enabling elasticity and toughness. The tensile elongation of fibres along the loading direction, transitioning to a compression perpendicular to the load, implies a strong interconnection between sublayers in the Bouligand lamellae. These interconnections are most likely the transverselyrunning pore-canal fibres, 19 which "stitch" the Bouligand fibre layers together. The smooth angular transition between rotating sublayers of the Bouligand structure (or sub-lamellae in the term used in bone) most likely accentuates the strong inter-connection and increased toughness. 24,28 Our results further highlights the mechanical importance of the pore-canal network, as a compressive strain in the pore-canal fibres, nearly equal in magnitude to the tensile strain in the Bouligand layer, is developed (Fig. 5f, reaching a maximum magnitude of ∼0.15%). These results demonstrate that the pore-canal fibres also bear load, and support the concept of an interpenetrating, mechanically interlocked double network of fibres.
The importance of the interfibrillar matrix (mineralized protein) in enabling shear transfer between fibres is shown by the differences between the tissue and the fibre strain (a ratio of ε f /ε T ∼ 0.4). Analogous interfibrillar shearing has been observed for the mineralized collagen fibres in bone with similar ratios from 0.4-0.6, 37,45 which suggests this is a generic feature of mineralized fibrillar biocomposites. Prior work has implicated mechanisms such as sliding and rotation of fluoroapatite nanorods in the cuticle of the dactyl for its high fracture resistance. 25 In contrast, our results on the chitin deformation provide information on the mechanisms of the organic fibres rather than the mineral, both of which are expected to play coupled and essential roles in determining material properties.
In relation to prior multiscale modelling work on cuticle, 19,29 such methods provide effective elastic properties at multiple length scales, from the molecular to the microscopic. Because our experimental probe reports deformation and reorientation rather than effective moduli, a one-to-one comparison with multiscale models is not straightforward. A combination of such multiscale modelling and the current experimental method (especially at the microscale and above, where the honeycomb motif is integrated into the Bouligand structure) will be needed for a comprehensive structural understanding.
We note that a weakness of the current experimental approach is that the XRD signal is an average of the patterns in both exo-and endocuticle in the L1 geometry, whose Bouligand layers have different stiffness, densities and ordering. 46 However, this is a limitation of our current samplepreparation protocol rather than the diffraction reconstruction method itself, and in future, sample preparation methods like focused ion beam milling or laser microdissection could enable isolation of distinct tissue regions. Also, as we focus on the crystalline diffraction signal from the chitin fibres, we do not separately account for the mineral phase deformation. The deformation of the fibres must therefore be interpreted as that of a mineralized chitin fibre. In L2 geometry, we observed mineral reflections (corresponding to calcite) only in the outer parts of the tergite exocuticle, consistent with prior work on lobster cuticle showing calcite to be present only in the outer 50 μm. 47 The importance of different mineral chemical structures for impact resistance (e.g. fluoroapatite versus hydroxyapatite) has been shown before, and in the future, 25 analysis of peak shifts of mineral, possibly in combination with spectroscopy (for the noncrystalline region) could shed light on the mineral phase mechanics.
In summary, we have shown the first experimental results on the in situ, multiscale deformation mechanisms in the chit-inous cuticle of crustaceans. The cuticle has attracted considerable interest as an advanced biomaterial, being the basic building block underlying several biological adaptations to sensation, 23 vision and impact resistance, 24,25 inspiring development of bioinspired composites. By showing explicitly the linkage between the diffraction intensity and the 3D multiscale deformation, both in the experimental results and the analytical formulae derived, we also provide a template to apply this nanomechanical method to understand structure-function relations in these functionally diverse specializations.
Sample preparation
Mantis shrimp (Odontodactylus scyllarus) from the tropical Indo-Pacific were purchased from a commercial supplier (Tropical Marine Centre, London) and stored at −20°C till used for sample preparation. The abdomen tergite was dissected from mantis shrimp, and the central region of the tergite was sectioned under constant irrigation using a lowspeed diamond saw (Buehler Isomet, Buehler, Duesseldorf, Germany). The sectioning is indicated schematically in Fig. 1b and provided the tensile test samples. As described earlier for bone, 48,49 the ends of the test sample were embedded in UVcurable dental cement (Filtek™ Supreme XT, 3 M ESPE, USA; Fig. 1b) to grip the samples. To orient the cuticle in multiple directions to the incident X-ray beam, the test samples were embedded in two different ways. In the first (L1) configuration, the surface (epicuticle) of the tergite was oriented such that the incident X-ray beam (10 × 10 μm 2 cross-section) was perpendicular to the cuticle surface and passed through both exoand endo-cuticle. In the second (L2) configuration, the incident X-ray beam is parallel to the tergite surface, which enabled the 10 × 10 μm 2 sized beam to focus on either the exoor endocuticle by translating the sample laterally with respect to the beam. Typical dimensions of specimens were ∼0.5 mm (thickness) × 0.6 mm (width) × 3.0 mm (length). Tergite samples from at least 3 different shrimps were used for testing.
Synchrotron tensile testing
Synchrotron XRD combined with in situ tensile testing on cuticle was carried out at the microfocus end-station at beamline I22, Diamond Light Source (DLS) (Harwell, UK). Cuticle specimens were mounted in a micro-tensile tester (Fig. 1a3 †), an adaptation of the setup previously used by us, 48 with a maximum load 110 N. Motor strain was measured from displacement of sample grips, and corrected for machine compliance in the grips by lab measurements, as described by us previously. 37,50 In the lab tests, ink-markers were placed on cuticle tensile-test samples and marker displacement tracked using a CCD camera with digital image correlation. 37 Tissue strain was calculated from the fractional increase in marker spacing. Linear regressions between the tissue strain and motor strain were calculated, and used to convert synchrotron strains from motor to tissue strain. When the correction is applied, apparent tissue moduli are in the expected range of crustacean cuticle ∼3-6GPa. 51 Strain controlled tensile tests were carried out with tissue strain rate of 0.006% s −1 . XRD patterns were acquired every 0.5% motor strain increment with a 1 second exposure time using a Pilatus 2 M detector (Dectris, Switzerland). To minimize radiation-induced damage to the tissue, the samples were moved 10 μm vertically between XRD acquisitions and a 50 μm molybdenum attenuator was used as done previously by us for bone. 49 The lateral translation will not lead to inhomogeneous regions of the sample being included in the same test. Specifically, in the L1 configuration, the material is homogenous in the plane parallel to the sample surface, comprised of the exocuticle and the endocuticle underneath, and the signal is an average of the diffraction from each region. During the translation of the sample relative to the beam, the lateral or vertical displacements of ∼10 micron are much smaller relative to the sample area (facing the X-ray) of ∼600 micron (width) × 3000 micron (length) and will thus not lead to issues with sample inhomogeneity. For the L2 configuration, the exoand endocuticle layers form two approximately parallel bands oriented vertically in the tester. Therefore, when we shift the sample vertically such the beam is always located in the same region of one plywood lamellae, the material can, in this geometry as well, also be considered as homogenous along the axis of translation. Sample to detector distance (L = 230.1 ± 1.0 mm) and beam center was determined using a silicon standard. After the mechanical tests, all fractured test specimens were air dried and coated with gold for scanning electron microscopy, to determine sample cross-sectional area (Inspect F, FEI, and Eindhoven, Netherlands).
XRD data reduction
The acquired XRD patterns were analyzed using Fit2D, 52 around the (002) crystallographic peak of chitin (between 12.15 and 12.25 nm −1 ) using the CAKE command. For the azimuthal intensity profile I (002) (χ), radial averages of intensity in a narrow ring around the (002) peak, followed by background subtraction diffuse scattering was carried out, as described previously. 49 For the radial intensity profiles at angle χ, I χ (q), the intensity was azimuthally averaged over arc-shaped sectors (angular width 7°) centered at χ (Fig. 2d). I χ (q) were fitted using the Python package lmfit 53 to a Gaussian with a linear background term, to determine peak position q (002) (χ), peak width and amplitude, and c-axis lattice spacing was obtained from d (002) (χ)=2 π/q (002) (χ). Axial fibre strain (ε f ) was calculated from fractional changes in (002) lattice spacing relative to the unstressed value.
Laminate simulation for in-plane fibre reorientation
As described in ESI, section S3, † a laminate model of the Bouligand layer, with cuticle material parameters from lobster cuticle (Nikolov et al.), 54 was constructed, and its structural response compared to the azimuthally varying fibre strain (Fig. 3d). 4 experimentally levels of tissue stress (0, 17.1, 34.1 and 51.2 MPa) were selected from the stress/strain curve of a cuticle sample. By applying these stress-levels to the laminate, the fibre-deformation and reorientation can be calculated using the laminate model equations (eqn (S21)-(S25) †). Subsequently, the modified orientation function w σ (γ) (eqn (5)) was obtained, and used in eqn (2), allowing a fit of the 3D orientation parameters (tilt angles α and β). 3D XRD intensity distributions on the reciprocal spheres were plotted using Mayavi v2.0. 55 | 9,266.6 | 2017-08-10T00:00:00.000 | [
"Materials Science"
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Automated Characterization of Cyclic Alternating Pattern Using Wavelet-Based Features and Ensemble Learning Techniques with EEG Signals
Sleep is highly essential for maintaining metabolism of the body and mental balance for increased productivity and concentration. Often, sleep is analyzed using macrostructure sleep stages which alone cannot provide information about the functional structure and stability of sleep. The cyclic alternating pattern (CAP) is a physiological recurring electroencephalogram (EEG) activity occurring in the brain during sleep and captures microstructure of the sleep and can be used to identify sleep instability. The CAP can also be associated with various sleep-related pathologies, and can be useful in identifying various sleep disorders. Conventionally, sleep is analyzed using polysomnogram (PSG) in various sleep laboratories by trained physicians and medical practitioners. However, PSG-based manual sleep analysis by trained medical practitioners is onerous, tedious and unfavourable for patients. Hence, a computerized, simple and patient convenient system is highly desirable for monitoring and analysis of sleep. In this study, we have proposed a system for automated identification of CAP phase-A and phase-B. To accomplish the task, we have utilized the openly accessible CAP sleep database. The study is performed using two single-channel EEG modalities and their combination. The model is developed using EEG signals of healthy subjects as well as patients suffering from six different sleep disorders namely nocturnal frontal lobe epilepsy (NFLE), sleep-disordered breathing (SDB), narcolepsy, periodic leg movement disorder (PLM), insomnia and rapid eye movement behavior disorder (RBD) subjects. An optimal orthogonal wavelet filter bank is used to perform the wavelet decomposition and subsequently, entropy and Hjorth parameters are extracted from the decomposed coefficients. The extracted features have been applied to different machine learning algorithms. The best performance is obtained using ensemble of bagged tress (EBagT) classifier. The proposed method has obtained the average classification accuracy of 84%, 83%, 81%, 78%, 77%, 76% and 72% for NFLE, healthy, SDB, narcolepsy, PLM, insomnia and RBD subjects, respectively in discriminating phases A and B using a balanced database. Our developed model yielded an average accuracy of 78% when all 77 subjects including healthy and sleep disordered patients are considered. Our proposed system can assist the sleep specialists in an automated and efficient analysis of sleep using sleep microstructure.
Introduction
Sleep is an important aspect of human life and it greatly affects our mental and physical health. Sleep consists of periodic repetition of unconsciousness (physical-inactivity) called non rapid eye moments (NREM)) followed by high activity called rapid eye moments (REM). The REM and NREM manifests certain important functioning of brain including memory consolidation, brain clearance from metabolites and cellular restoration. However, the entire process is yet not completely perceived and known. To distinguish sleep's macrostructure, sleep is categorized into five stages: wakefulness (W), N1, N2, N3, and REM, according to the guidelines of American Academy of Sleep Medicine (AASM) [1]. The distinction is made on the 30 s window of electroencephalogram (EEG) signal by the trained medical practitioners. The sleep stages N1, N2, and N3 form NREM part of the sleep cycle followed by REM. In literature, many studies are available on the macrostructure of sleep and researchers have developed models for automated classification of sleep stages using machine learning techniques and PSG [2][3][4][5][6][7][8][9]. Recently, deep learning-based methods have also been employed for sleep scoring [10][11][12].
However, ephemeral events such as K-complexes and transient power alterations in frequency bands are neglected by these macrostructure based sleep scoring rules. In the AASM guidelines, only the arousal definition captures the short periods of changes in cortical activation. Although, phasic events like K-complexes and delta bursts show characteristics similar to arousal, but they are not considered as arousal if there is no to short-term frequency increase in EEG [13,14]. To overcome these shortcomings of macrostructure based sleep scoring, a new microstructure based sleep scoring technique named cyclic alternating pattern (CAP) was devised, which includes such phasic events in brain activity [15] as an alternative scheme to describe NREM sleep. CAP is found to be useful in the detection of insomnia, sleep apnea syndrome, epileptic disorders and periodic limb movements [16]. Ferini-Strambi et al. have observed the impact of CAP on heart rate variability during sleep in healthy young adults [17]. They concluded that, the cardiac autonomy in normal subjects is influenced by the physiological fluctuations of EEG arousal level. Studies have found that during coma, the CAP in EEG signal is correlated with the motor activity, cardiorespiratory rate and cerebrospinal fluid pressure. These events were observed to increase during phase A and decrease during phase B [18,19]. The NREM sleep stage is observed to have alternating patterns of cerebral activation (phase A) followed by duration of deactivation (phase B), which separate two or more consecutive phase A periods [15]. The CAP phase A typically includes events like K-alpha, K-complex sequences, delta bursts, alpha waves, vertex sharp transients and arousals. The duration of these phases may vary between 2 s to 60 s. Two successive phase A events are considered as a single phase A event if the duration of separation between them is less than 2 s [20]. The combination of phase A and phase B is termed as a CAP cycle and this cycle begins with phase A and ends with phase B. Two successive CAP cycles are needed to form a CAP sequence [21]. If a phase A is not accompanied by phase B, then it is termed as an isolated phase A and is considered as non-CAP (an absence of CAP for >60 s duration). Thus, a CAP sequence contains minimum three A phases (A-B-A-B-A) followed by non-CAP period [22]. However, there is no upper limit in terms of overall duration or number of CAP cycles, and approximate mean duration of a CAP sequence in healthy young adults is around 150 s containing six CAP cycles [23]. In general, a CAP sequence always follows a continuous NREM sleep EEG pattern with a minimum duration of 60 s. CAP phase A can be detected using any EEG lead [22]. Figure 1 shows the typical image of a CAP cycle for multiple EEG channels and Figure 2 displays the typical waveforms of phase A and phase B. High amplitude slow EEG waves increases with increasing depth of sleep whereas low amplitude fast rhythms are dominantly present in REM sleep. CAP phase A is subdivided into three subtypes A1, A2, and A3 based on the duration of high amplitude slow waves and low amplitude fast rhythms. Subtype A1 is characterised by high amplitude slow waves covering >80% of entire phase A duration and low amplitude fast rhythms, if present, covers <20% of total phase A duration. Subtype A2 is characterised by a mixture of fast and slow EEG waves. Low amplitude slow waves in phase A2 covers around 20-50% of entire phase A duration. Subtype A3 is characterised by dominant low amplitude fast rhythms covering >50% of the phase A duration. CAP sequences triggered or interrupted by body movements are also distinguished as subtype A3 [22]. The CAP parameters include CAP rate, CAP time, and no of phases A1, A2 and per hour. Cap rate refers to the percentage ratio of CAP time to total NREM sleep time. CAP time refers to the total duration of all CAP sequences. CAP time increases with increase in number of CAP cycles. For healthy sleepers, CAP rate has very low variability. It is observed to vary with age. It is very low for toddlers (around 13%), gradually increases with age and peaks during peripubertal stage (around 62%), then again decreases for adults and middle age (around 37%) followed by an increase during elderly age (55%) [22].
Amplitude( V)
Thus, the detection of CAP phases and estimation of CAP parameters is essential for accurate sleep analysis. However, the CAP detection in human beings is prone to errors and a cumbersome task. In literature, few attempts have been made for identifying CAP phases automatically using computer aided systems [24][25][26][27][28]. However, the studies on the automated detection of sleep phasic events are very few. Also, the model developed using machine learning methods on the above studies have been tested on very small number (5-10) of good sleepers without considering sleep disordered patients. Further, despite using large number of discriminating features the classification performance is not very high. Hence, there is a need for a model to be tested with significant number of subjects, involving both healthy controls and sleep disordered patients which can exhibit high performance. It is also desirable that the model should employ small number of features for training and testing so that it can be implemented in real time application.
In the proposed study, we have used a large number of subjects comprising of healthy as well as sleep disordered-patients suffering from six different disorders. We have implemented an ensemble learning method by employing wavelet-based Hjorth and entropy features extracted from monopolar C4-A1 and bipolar F4-C4 EEG channels to develop an automated model for detection of CAP phases. The developed model achieved better classification performance than the existing state-of-art studies. Our developed method is simple, computationally efficient and hence it may be deployed in clinical applications.
Material Used
This study is accomplished using the public CAP sleep database, which contains nightlong sleep polysomnographic (PSG) recordings of 108 subjects logged at the Sleep Disorders Center of the Ospedale Maggiore of Parma, Italy. The database contains recordings of 16 healthy subjects and patients suffering from insomnia (9), narcolepsy (5), nocturnal frontal lobe epilepsy (40), periodic leg movement (10), REM behavious disorder (22), and sleep-disordered breathing (4). Each PSG recording contains multiple channels including EEG, electrocardiogram (ECG), electromyogram (EMG), electrooculogram (EOG), SpO2 and respiratory signals. EEG channels include traces like F4-C4, C4-A1, C4-P4, P4-O2, Fp2-F4, Fp1-F3, C3-P3, P3-O1 and other combinations of F3/F4/C3/C4/O1/O2 with reference A1/A2. The sampling frequencies of these EEG channels varies from 100 Hz to 512 Hz. Bipolar EEG channel F4-C4 and monopolar EEG channel C4-A1 are present in maximum number of sleep recordings. Based on the availability of C4-A1 and F4-C4 channels coupled with 512 Hz sampling frequency, we have taken 77 subjects for the identification of CAP phase A in this study. Terzano et al. [21] suggested that bipolar EEG leads are favourable for CAP phase detection. So we have also evaluated performance of each of the two leads (F4-C4 and C4-A1) independently and combined. We have performed CAP phase classification using EEG signals from healthy subjects as well as disordered patients individually and combined. Table 1 shows gender and age details of healthy controls and sleep disordered patients used in this study. Figure 3 represents the procedure involved in the automated identification of CAP phase A and phase B. Firstly, we collected PSG recordings of all 77 subjects then EEG recordings are extracted with sampling frequency of 512 Hz. We separated C4-A1 (monopolar) and F4-C4 (bipolar) EEG montages for this study. Both EEG channels are reprocessed via normalization and filtering operations. Subsequently, labelled A and B phases are segmented using windows of one and two seconds duration. Each EEG epoch (of lengths either 1 s or 2 s) is subjected to an optimal mean squared bandwidth minimized (OMSBM) orthogonal wavelet filter bank (OWFB) that decomposed the EEG epochs into six subbands [29]. The wavelet entropy and Hjorth parameters of each subband are computed from the decomposed subband coefficients and used as discriminating features. We have employed several machine learning classifiers to distinguish the features to choose the optimum performing classifier. Ten-fold cross-validation is performed to develop the model.
Preprocessing
EEG signals contains most of the useful information in the frequency range below 35 Hz. Hence, to remove the noise artifacts and preserve only the necessary information, EEG signals are bandpass filtered using an infinite impulse response (IIR), butterworth filter of order four [30,31]. The lower and upprer cut-off frequencies have been set to 0.5 Hz and 35 Hz, respectively as mentioned in guidelines of AASM [1]. After filtering, normalization of the signal is done to uniformly scale down the amplitude in the range of 0 to 1.
CAP sleep database contains phase A annotations scored by expert neurologists in accordance with the Terzano's reference atlas of rules [15]. With the help of the annotations, we have separated CAP phase A recording from the NREM sleep EEG signal and labelled remaining NREM signal as non-CAP recording. These phase A (CAP) and phase B (non-CAP) signals are segmented into epochs of 2 s duration each. Later, in order to develop a precise CAP scoring system, we have also obtained CAP classification results using 1 s duration epoch of each phase. All EEG epochs are balanced with respect to both phase A and phase B. For balancing we used random undersampling to reduce the number of epochs from either phase to equalize epoch count of both phases.
Orthogonal Filter Bank and Wavelet Decomposition
There are many wavelet filter banks available in the literature with wide variety of applications [32][33][34][35][36]. Among these filter banks, the orthogonal filter bank is remarkable due to its advantage of energy preservation [37][38][39]. In this study, we have used the orthogonal wavelet filter with minimum root-mean-square (RMS) bandwidth [40][41][42]. Generally, equiripple filter method and band-energy minimization method are used to achieve sharper roll-off. Although, these methods are efficient, but they do not take entire spectrum into account as they are based on edge frequency specifications. On the other hand, RMS bandwith simultaneously considers both transition band and pass/stopband, comprehensively describing a filter's frequency localization and avoiding influence of ripple amplitude specifications [43,44]. In this method, for the optimization of RMS bandwidth, either a symbolic method can directly applied [40] or constrained optimization problem that is transformable into a convex optimization problem like semidefinite programming (SDP) problem [45] can be used. The SDP includes non-negativity constraints during the optimization. We have used orthogonal filter with length 12 and 4 vanishing moments [46] in this study. The significance of this method is that, it can give more accurate and thorough results including all local and global minimum [47,48].
Five level wavelet decomposition yielded six subbands with frequency ranges 0-1 Hz, 1-2 Hz, 2-4 Hz, 4-8 Hz, 8-16 Hz, 16-32 Hz. In this work, lower frequency band (0-1 Hz) is called the approximation coefficient and remaining bands with higher frequencies are called detailed coefficients [49]. Figures 4 and 5 displays the subbands after wavelet decomposition for an epoch of phase A and phase B, respectively.
Feature Extraction
We computed wavelet entropy and three Hjorth parameters from each subband to get 48 discriminating features for CAP phase identification using two EEG channels. The size of the feature array employed is 165960 × 48. The details of discriminating features are as follows: Wavelet Entropy: Wavelet entropy is used for quantitative analysis of transient features of non-stationary physiological signals including EEG. It is able to measure the uncertainty involved in a random process and for a wavelet subband it can be defined as [50]: where, x i represents the magnitude of i th wavelet coefficient. Hjorth Parameters: Three Hjorth parameters named activity, mobility and complexity are utilized in our study along with wavelet entropy for feature extraction which are extensively used in applications related to EEG signals. These parameters mainly represent the time domain characteristics of EEG signals [51]. Table 2 provides the description of these parameters and their expression. In order to measure, discriminating abilities of each feature, we have computed the p-values and rank of each feature using Kruskal-Wallis test. Table 3 shows the p-values and ranks for all 48 features computed using Kruskal-Wallis test. From the table, it is clear that p-vales of all features are close to zero. Hence, all features are statistically significant for the classification task. Table 2. Details about Hjorth parameters used in this study [51].
Activity
Mobility (µ) Complexity Formula Description It is the variance of the signal x(t).
It represents total energy of the signal x(t).
It gives estimate of the mean frequency. It represents the proportion of standard deviation of the power spectrum.
It gives estimate of the bandwidth frequency. It represents change in frequency.
Classification and Validation
After performing feature extraction, features have been applied to several supervised machine learning (ML) classifiers. For the implementation of these algorithms and to develop the model, we have employed the Statistics and Machine Learning Toolbox of MATLAB R2020a. The obtained features are used to train various classifiers namely support vector machines (SVM), K-nearest neighbour (KNN), ensemble bagged trees (EBagT) and ensemble boosted trees (EBoosT). We developed the model using samplewise ten-fold cross-validation scheme. Initially, all classifiers are trained using a trial and error approach, because it is difficult to determine in advance which algorithm will perform better for our extracted features. Once the best classier is obtained among all, we performed hyperparameter tuning to increase the performance further. We observed that, for most of the classification tasks EBagT and EBoosT algorithms attained the best classification performance after extensive simulations, however, for few classification tasks SVM algorithm showed better results. It can be noted from Table 1 that, we have considered large number of epochs in our study and ensemble methods yielded better results compared to other algorithms. It is to be noted that we have balanced the epochs of both phases before training the classifiers. The data balancing makes the model more reliable for practical applications.
Results
The entire experimentation and training related to our study was accomplished using MATLAB R2020a installed on an Ubuntu server 18.04. The specifications of the server are: an Intel Xeon E5-2690 v3 CPU @2.6 GHz (6 cores), 56 GB RAM and a 12 GB Nvidia K80 GPU.
In this work, we have used monopolar C4-A1 and bipolar F4-C4 EEG channels for the identification of CAP phases A and B using sleep recordings of 77 subjects. The database contains recordings of healthy subjects and variety of sleep disorders like NFLE, SDB, narcolepsy, PLM, insomnia and RBD. In this work, we have extracted and analyzed CAP phase information for each type sleep disorders separately. The results are given below for both EEG montages individually and combined. The classification performance was evaluated in terms of average classification accuracy (ACA), precision (Pcn), Recall (Rcl), F1-score (F1), Cohen's Kappa (κ) value and area under curve (AUC).
We have taken six healthy subjects and extracted 9930 epochs (2 s duration) of phase A and phase B for two EEG channels. Though features have been applied to several classifiers, the optimal performance was obtained using ensemble boosted trees and bagged trees classifier to classify CAP phases. The model could attain ACA of 75.7% and 76.4% for C4-A1 and F4-C4 channels, respectively. It is evident that bipolar channnel F4-C4 channel performed better than the monopolar counter part. Combining the features extracted from both channels yielded better ACA of 83.30%. The confusion matrix corresponding to three classification tasks for good sleepers can be seen in Table 4. It can be observed from Table 4 that, for healthy sleepers both phases are detected equally well while features of both channels are classified together. The CAP sleep database contains seven EEG recordings for both montages, at sampling rate of 512 Hz with average duration of 575 min, corresponding to insomniac patients. We have classified total of 11328 epochs (2 s) into phase A and phase B. We have achieved maximum ACA of 71.4% and 72.5% for C4-A1 and F4-C4 channels, respectively. It can be seen that bipolar channel F4-C4 performed better than the monopolar channel C4-A1, individually. By combining both EEG channels, ACA increased to 76.5%. Confusion matrix and performance parameters for insomnia subjects are shown in Table 5. The CAP sleep database contains EEG recordings of five narcolepsy patients, with both montages sampled at 512 Hz frequency and an average duration of 494 min. We have taken 10086 epochs (2 s each) of phase A and phase B. The best possible ACA achieved is 77.20%. The confusion matrix for all three classification tasks can be seen in Table 6. The CAP database contains 27 EEG recordings of NFLE patients at sampling frequency of 512 Hz and an average duration of 505 min. We have classified 73236 epochs (2 s duration) into phase A and phase B. Among all classifiers, ensemble bagged trees classifier gave best performance with maximum ACA of 84%, F1-score of 0.84 and Cohen's κ coefficient of 0.68 using both channels . Confusion matrix and performance parameters corresponding to classification using C4-A1, F4-C4 and combination of both can be seen in Table 7.
The CAP database contains nine PLM patients' EEG recordings for both the montages, at sampling rate of 512 Hz and with an average duration of 431 min. The maximum ACA, F1-score and Cohen's κ obtained are 77%, 0.76 and 0.54, respectively. Table 8 shows the confusion matrix and performance parameters for patients suffering from PLM. 22 RBD patients' EEG recordings obtained from CAP sleep database were segmented into total number of 39654 epochs of 2s which contains either phase A or phase B. The average duration for each of these recordings is 514 min. For classifying the phases of RBD patients, the proposed model attained the best ACA of 72%, 70%, and 77% for F4-C4 channel, C4-A1 channel and combined channels, respectively. The F1-score and Cohen's κ of 0.71 and 0.44, respectively were obtained corresponding to the features obtained from the combined channels. Table 9 shows results obtained using RBD patients. The CAP sleep database contains one SDB patient's EEG recording for both the channels, with sampling rate of 512 Hz and 396 min duration. We segregated EEG signals into 1668 epochs (2 s each) which comprises of phases A and phase B. Using EBagT classifier on the extracted features, with C4-A1 and F4-C4 channels separately, the model attained ACA of 74.9% with 10 fold cross validation, whereas combined features from both channels produced ACA of 81.5%. We have obtained F1-score and Cohen's κ equal to 0.81 and 0.63, respectively for combined features. Confusion matrix and performance parameters obtained for SDB patients are shown in Table 10. After considering detection of phases of all sleep disordered patients and healthy controls individually, we then combined all 77 subjects with a total of 165,960 epochs corresponding to phases A and B. The model attained ACA of 71.4% and 71.0% with C4-A1 and F4-C4 channels, respectively using ensemble bagged trees classifier with 10 fold CV. On combining features obtained from both channels, ACA increased to 78.0% and F1-score and Cohen's kappa obtained are 0.77 and 0.56, respectively. It is also interesting to note that both the channels performed equally well in identifying phases when used separately. However, on combining the features from both montages there is a gain of around 7% in the ACA. It can be noticed from the results that, for narcolepsy, NFLE and PLM patients, C4-A1 channel performed better than F4-C4. F4-C4 channel performed better for healthy, insomnia and RBD patients. Both the channels performed almost the same for SDB patients. Table 11 shows the classification results when all subjects are taken together. It can be noted from Table 12 that, highest classification performance is obtained using EbagT classifier compared to other classifiers used in our work.
Discussion
In the literature, the studies on detection of micro structure CAP phasic events are sparse and limited. On the other hand, a plethora of studies are available on identification of sleep macro-structures events including sleep stage scoring and identification of sleep disorders. Moreover, these handful of studies on CAP phase identification have used only healthy controls with few exceptions of Hartmann et al. [26] and Mendonca et al. [28], which have included either NFLE or SDB patients. In this proposed study, we have performed CAP phase identification using all 77 subjects comprising six types of sleep disordered patients having NFLE, SDB, narcolepsy, PLM, insomnia and RBD along with good sleepers.
We have also conducted the whole experiment taking 1-second EEG window in addition to normal 2 s window length. It can be observed from Tables 4-11 and 13 that, the phase classification performance is better for the epochs of 2 s than 1 s. Although the performance achieved using 1 s EEG epochs is inferior but the signal processing burden gets reduced on the system. Our results reveal that for Healthy, Insomnia, and RBD subjects bipolar EEG analysis is better, which is in line with the observations made by Parrino et al. [22]. But, for Narcolepsy, NFLE and SBD subjects, monopolar EEG channel is found to be better. However, for accurate analysis, we believe that both channels are equally important. To the best of our knowledge, there is no clinical reason available regarding the superiority of channel (monopolar or bipolar). However, our results reveal that when both monopolar and bipolar EEG channel are used together, the performance of the model improved for sleep disorder as well for healthy good sleepers.
We have computed the microstructure details of subjects used in this study, like CAP rate, CAP time and NREM time (Table 14). It is evident from Table 14 that the average CAP rate is found to be 0.56 when all subjects (health+sleep disordered) are taken together. In the table, we have also mentioned the CAP rate for the six sleep disordered subjects and healthy controls when they are considered separately. It can be noticed from the table that the CAP rate of healthy subjects is lowest (0.41) and increased for sleep disordered subjects. The CAP rate for SDB patients is the highest (0.78) among all. RBD patients showed lower CAP rate (0.49) compared to other sleep disorders. Hence, CAP rate can be used as a measure to indicate the sleep quality. The CAP rate either increases or decreases sharply in sleep disorder cases. More precisely, the CAP rate increases in insomnia [52][53][54][55][56], apnea [57], PLM [58], NFLE [59], and depression [60,61]. The CAP rate decreases in conditions like narcolepsy [62], continuous positive airway pressure (CPAP) treatment in apnea [63][64][65][66] and neurodegenerative disorders, like Alzheimer's disease [67]. Table 15 shows the comparison of our proposed method with other previously performed state-of-the-art studies. Various techniques have been employed by researchers for CAP phase detection. All the studies mentioned in the table have used CAP sleep database with majority of work being performed with EEG signals of healthy subjects. Mendez et al. [25] used unbalanced data with 3963 Phase A events from only ten healthy adult subjects. They have used K-nearest neighbour (KNN) classifier and features including energy, sample entropy, standard deviation, Tsallis entropy and frequency band indices. They obtained an accuracy and sensitivity of around 80% and specificity of 70%. Navona et al. [24] have achieved an accuracy of 77% using EEG band descriptors and thresholding. Hartmann et al. [26] have used 16 healthy sleepers and 30 nocturnal frontal lobe epilepsy (NFLE) suffering subjects obtained from CAP sleep database. They achieved an accuracy of 82.42% for healthy subjects. The epoch length considered in their study is variable with a duration of 1-3 s. Dhok et al. [27] have used balanced data with 4653 occurrences of phase A and phase B each, from six healthy subjects of CAP sleep database for automated CAP phase classification. They used Wigner-Ville distribution based feature extraction and support vector machine (SVM) classifier to achieve classification accuracy of 72.35%. Mendonca et al. [28] have used time series analysis, Matrix of Lags and SVM classifier and obtained classification accuracy of 77% using ECG signals of 60 s duration. Recently, Loh et al. [68] developed a deep neural network (1D-CNN) model for CAP phase classification and obtained an accuracy of 73.64%. Mariani et al. [69] have observed that Hjorth actvity is a better descriptor for CAP A phases and helped to achieve better classification performance between phase A and phase B which is inline with the findings of our proposed study. It can be observed from the table that most of the studies have used only imbalanced data in which case the model developed may bias towards the majority class and cannot be considered as an ideal fit for a clinical application. The proposed study employed a balanced data to overcome bias, under fitting and over fitting problems. The proposed model attained ACA of 83% which is better than the most of the studies presented in Table 15.
The key attributes and benefits of our study are as follows: • We have employed openly available CAP sleep database for easy reproducibility and to make it easy for other researchers to compare their work with this study. • We have used only two EEG channels to reduce complexity and discomfort to patients. The simultaneous use of both C4-A1 and F4-C4 EEG channels improved the performance which is evident from our results. It can be noted that, although the classification task considered is binary, the task is demanding due to high level of resemblance in characteristics of phases, which is clear from the results obtained by the state-of-the-art methods available. The classification accuracy in the range of 72-83% have been achieved using various techniques including few deep learning models also as shown in Table 15. Further, to examine the discriminating abilities of wavelet based features, we have performed the experiments without using wavelet decomposition and noticed high degradation in the performance (Table 16). The proposed method has yielded high classification results due to the use of highly discriminating nature of optimal wavelet based Hjorth features used by us to train the model. Our results demonstrated that if we do not use wavelet decomposition and use the Hjorth parameters of EEG directly, then the performance decreases. Similarly, if we use the wavelet decomposition and use some statistical features other than Hjorth parameters, again the performance degrades. On the other hand, when both optimal wavelet decomposition and Hjorth parameters are employed together, the optimal performance is obtained. Presently, the CAP phases are identified by trained clinicians in sleep laboratories only. This process is cumbersome, stressful and time consuming. Hence, there is always a scope for a computer based automated approach. As discussed earlier, previous few studies have tried to develop a model for CAP characterization. Our method has achieved better performance for CAP phase identification. However, it should be tested using a large independent cohorts before implementing in a clinical application, this can be considered as one of the limitations of the proposed study. There is scope for further improvement in the results obtained using 1 s epochs. The future scope of this work includes the use of deep learning (DL) based techniques like convolutional neural network (CNN), LSTM and recurrent neural network (RNN) for an automated identification of CAP phases. Although, DL-based techniques perform better in many cases but for this problem, our proposed method worked better than rest of the reported works. Hartmann et al. [26] have already explored DL-based LSTM technique for automated detection of CAP phase A. Our results are found to be better because we have used highly discriminating wavelet-based features and optimal ensemble classifiers for the classification task. In future, it would be interesting to evaluate the performance of the proposed method for identifying sub-phases A1, A2, and A3 of the phase A.
Conclusions
The sleep-scoring is widely used in monitoring and analysis of sleep as well as identifying sleep disorders. The sleep macrostructure, represented by different sleep stages provide information regarding the neural activity and brain waves during sleep. However, the macrostructure sleep stages alone cannot provide information about the functional structure and stability of sleep. Besides, the shorter phasic events K complexes, delta-wave bursts, vertex waves, saw-tooth waves, sleep spindles and short-lasting arousals are also abundant in sleep. These events show certain patterns and represents the microstructure of sleep. CAP captures microstructure of the sleep and can be used to identify sleep instability. This paper presents an automated CAP characterization system using optimal waveletbased features extracted from EEG signals. Our study aimed to reduce the diagnosis time of sleep by specialists. The main intention of the study is to identify the CAP phases of sleep disordered patients. We have utilized the entire CAP sleep database containing both sleep disordered patients and good sleepers. Our study presented the results obtained from healthy subjects, sleep disordered patients individually as well as all subjects combined. An optimal mean squared bandwidth minimized orthogonal filter bank is employed for the decomposition. The combination of highly discriminating wavelet entropy and Hjorth parameters coupled with optimally tuned ensemble bagged trees classier yielded a promising performance. The proposed model classified A and B phases of REM sleep. The model has yielded average classification accuracy of 84%, 83%, 81%, 78%, 77%, 76% and 72% for NFLE, healthy, SDB, narcolepsy, PLM, insomnia and RBD subjects, respectively in discriminating phases A and B using a balanced database. The best accuracy of 84% has been obtained for NFLE patients. However, the proposed model requires to be tested using a diverse and large data before clinical implementation. Our developed system is simple and fully computer-based, which can reduce the challenges faced by sleep specialists in scoring of CAP phases. In future, we aim to develop a model for the identification of subtypes A1, A2 and A3 of CAP phase A using DL based techniques like CNN, LSTM and RNN.
Conflicts of Interest:
The authors declare no conflict of interest. | 7,753.2 | 2021-07-30T00:00:00.000 | [
"Computer Science"
] |
Uncovering the potential role of oxidative stress in the development of periodontitis and establishing a stable diagnostic model via combining single-cell and machine learning analysis
Background The primary pathogenic cause of tooth loss in adults is periodontitis, although few reliable diagnostic methods are available in the early stages. One pathological factor that defines periodontitis pathology has previously been believed to be the equilibrium between inflammatory defense mechanisms and oxidative stress. Therefore, it is necessary to construct a model of oxidative stress-related periodontitis diagnostic markers through machine learning and bioinformatic analysis. Methods We used LASSO, SVM-RFE, and Random Forest techniques to screen for periodontitis-related oxidative stress variables and construct a diagnostic model by logistic regression, followed by a biological approach to build a Protein-Protein interaction network (PPI) based on modelled genes while using modelled genes. Unsupervised clustering analysis was performed to screen for oxidative stress subtypes of periodontitis. we used WGCNA to explore the pathways correlated with oxidative stress in periodontitis patients. Networks. Finally, we used single-cell data to screen the cellular subpopulations with the highest correlation by scoring oxidative stress genes and performed a proposed temporal analysis of the subpopulations. Results We discovered 3 periodontitis-associated genes (CASP3, IL-1β, and TXN). A characteristic line graph based on these genes can be helpful for patients. The primary hub gene screened by the PPI was constructed, where immune-related and cellular metabolism-related pathways were significantly enriched. Consistent clustering analysis found two oxidative stress categories, with the C2 subtype showing higher immune cell infiltration and immune function ratings. Therefore, we hypothesized that the high expression of oxidative stress genes was correlated with the formation of the immune environment in patients with periodontitis. Using the WGCNA approach, we examined the co-expressed gene modules related to the various subtypes of oxidative stress. Finally, we selected monocytes for mimetic time series analysis and analyzed the expression changes of oxidative stress genes with the mimetic time series axis, in which the expression of JUN, TXN, and IL-1β differed with the change of cell status. Conclusion This study identifies a diagnostic model of 3-OSRGs from which patients can benefit and explores the importance of oxidative stress genes in building an immune environment in patients with periodontitis.
Introduction
Periodontitis is a prevalent and chronic inflammatory condition that is characterized by a destructive inflammatory response affecting the tissues surrounding the teeth, including gingivitis, periodontal pocket formation, and periodontal bone loss, ultimately leading to loss of support and loss of teeth (1). Recent research indicates that periodontitis affects approximately 50% of adults worldwide, with an estimated prevalence of severe periodontitis ranging from 10-15% (2). Several factors, including plaque, tartar, traumatic occlusion, food fillings, poor restorations, and mouth breathing, can lead to the development of periodontitis (3). Failure to treat gingivitis in a timely manner can lead to inflammation spreading from the gums to the deeper layers of the periodontium, alveolar bone, and dental bone, culminating in periodontitis (4). In the early stages of the disease, patients may not exhibit any overt symptoms, with secondary gingival bleeding or halitosis being the most common. However, by the time patients develop symptoms, the disease has progressed to a more severe stage and may lead to tooth loss, making it the primary reason for tooth loss in adults (5). Currently, periodontitis diagnosis relies on radiological examinations, probing pocket depth, bleeding on analysis, and CAL(Clinical Attachment Loss) (6). Nevertheless, these tools have limitations and may lag in identifying and diagnosing periodontitis in the early stages.
Oxidative stress (OS) is a condition characterized by an imbalance between antioxidant and oxidative actions in the body, leading to the secretion of enhanced proteases, the generation of significant amounts of oxidative intermediates, a tendency towards oxidation, inflammatory infiltration of neutrophils, and primarily reactive oxygen species (ROS) (7). Kanzaki et al. have reported that periodontitis is a pathological condition in which oxidative stress plays a direct and indirect role in tissue degradation. The balance between defense systems and oxidative stress is essential for maintaining healthy periodontal tissue (8). In patients with periodontitis, oxidative stress induced by periodontitis can promote pro-inflammatory pathways, including osteoclast production, resulting in bone loss (9). ROS can indirectly contribute to the deterioration of periodontal tissue destruction by functioning as an intracellular signaling molecule in the osteoclast pathway (10). Furthermore, plasma, saliva, and gingival sulcus oxidative stress markers are higher in individuals with periodontitis (11). The development of periodontitis is a complex process that involves multiple genes and their products, and single gene markers often do not adequately reflect the pathogenesis of periodontitis and have poor sensitivity for disease diagnosis. Therefore, there is a need to develop novel predictive models based on oxidative stress biomarkers that can be used for the early screening and diagnosis of the disease, which would be of great value in clinical practice.
Machine learning has been extensively utilized in identifying the relationship between gene expression patterns and diseases since the advent of next-generation sequencing (12,13). Artificial intelligence (AI) has emerged as a potent tool for assessing the risk and diagnosing periodontitis, ranging from its early to moderate and severe stages. By leveraging advanced machine learning and deep learning algorithms, AI can scrutinize vast amounts of clinical data (14), including a patient's oral health status, oral hygiene habits, and lifestyle, to provide precise risk assessment and disease diagnosis. Furthermore, AI can aid dentists in image analysis for diagnosis, such as assessing periodontal pocket depth and bone loss (15). This enables the early detection of moderate and severe periodontitis and facilitates the formulation of appropriate treatment plans to prevent further disease progression effectively.
Given the widespread prevalence and significant impact of periodontitis on oral health and quality of life, our research aims to elucidate the underlying molecular mechanisms and construct a precise diagnostic model by integrating transcriptome sequencing, machine learning algorithms, and single-cell sequencing technologies. Through state-of-the-art Nomogram and decision curve analysis, we have rigorously evaluated the model's performance and successfully classified periodontitis patients into two distinct subtypes, namely C1 and C2. In-depth analysis of immune infiltration in these subtypes has shed light on the differences and immune mechanisms underlying the subtypes, providing crucial insights into understanding the pathogenesis of periodontitis. Furthermore, by leveraging single-cell sequencing data, we have delved into the intricate cellular communication and modeled gene expression in the periodontitis microenvironment, revealing novel insights into the disease progression at the cellular level. The findings from our research are expected to provide robust academic support for the development of personalized treatment and management strategies for periodontitis, ultimately improving patient outcomes and enhancing oral health.
Raw data collection and processing
The flowchart summarizes the main design of the present study ( Figure 1). Raw microarray datasets GSE16134 (comprising 70 normal and 240 affected samples), GSE10334 (containing 64 normal and 183 patient samples), and GSE23586 (comprising 3 normal and 3 affected samples) were retrieved from the Gene Expression Omnibus (GEO) database for total RNA data (Supplementary Table 1). GSE16134 and GSE23586 were used to screen the model genes, and GSE10334 was used to validate the diagnostic model. In order to decrease any batch effects across or within the three cohorts, the R package "limma" with the "normalize between arrays" function was employed. The performance of the combat function was evaluated using principal component analysis (PCA). Each gene's probe ID is transformed into a gene symbol. If a gene symbol is related to multiple probe ids, the average expression value of the probe id was determined as the gene's average expression value. Single-cell data were collected from GSM5005043 of the GSE164241 cohort containing 10× scRNA-seq data from affected oral mucosa samples from patients with periodontitis and one normal mucosa sample (16). With a relevance score of ≥50, 47 oxidative stress protein domains were retrieved from the GeneCards (https:// www.genecards.org) database.
Characterization of OSRGs connected to periodontitis that is differently expressed
Through the "Linear model for microarray data" ("limma") package in R (17), Benjamini-Hochberg false discovery rate adjusted for p-values <0.05, and |log FC|> 1 as thresholds for screening differentially expressed OSRGs, differential expression analysis was carried out in GSE23586 and GSE16134 to screen for periodontitis-associated OSRGs. Heat maps were used to display these. Volcano plots demonstrate the OSRG expression patterns in diseased and healthy subjects. To assess the correlation between OSRGs, Pearson correlation coefficients were calculated for DE-OSRGs in periodontitis samples. Visualization in R using "corrplot".
FEA (functional enrichment analysis) for DE-OSRGs in patients with periodontitis
For the functional analysis of biological functions, the Kyoto Encyclopedia of Genes and Genomes (KEGG) and Gene Ontology (GO) packages0 were used. The Benjamini-Hochberg method or FDR for multiple testing corrections was used to modify the pvalue. The cutoff was established at FDR<0.05. Cellular components (CC), molecular functions (MF), and biological processes (BP) were the GO categories.
2.4 GSEA (gene set enrichment analysis) for the model gene GSEA was used to clarify the biological importance of defining genes functionally (18). The reference set used in this study was the gene set of "c2.cp.kegg.v11.0.symbols" from the Molecular Signature Database (MSigDB, http://software.broadinstitute.org/ gsea/msigdb) (15). We sorted the training cohort according to the expression of model genes and divided the samples into two categories according to the median value of expression and extracted the differential genes in different categories for analysis.Gene set permutations were performed 1,000 times to arrive at a normalized enrichment score for each analysis. Significant enrichment was defined as an FDR = 0.05 or lower.
PPI (protein-protein interaction) network construction
GeneMANIA (http://www.genemania.org) is a platform for constructing protein-protein interaction (PPI) networks that can be employed to anticipate gene function and discover genes with similar functions. The network integration algorithm uses bioinformatics techniques such as site prediction, genetic exchange, gene enrichment analysis, co-expression, colocalization, and physical interaction. This study analyzed PPI networks of model genes using GeneMANIA (19). The network's genes were analyzed for KEGG and GO enrichment using the "clusterProfiler" R tool. Significantly enriched functions or pathways were identified according to the criterion: adjusted P < 0.05 and visualized with bubble plots.
Building and validating a predictive model based on OSRG associated with periodontitis
The genes listed above were employed to identify diagnostic genes for periodontitis. Reduction of bias due to cohort imbalance by using resampling in our COX regression analysis of cohort sequencing data and machine learning screening of biomarkers. To accomplish this, a supervised machine learning technique, support vector machine recursive feature elimination (SVM-RFE), was utilized to classify and regress the genes based on a training set with labels. SVM is a supervised learning algorithm that attempts to find a hyperplane in a high-dimensional space that maximally separates the classes, reducing the risk of overfitting and improving the model's generalization performance when dealing with datasets with a small number of samples (20). The feature set was then refined by training a subset of features from various categories and identifying the most accurate characteristics. The most valuable variables were retained by performing a minimum LASSO (absolute shrinkage and selection operator) regression using the 'glmnet' package in R, which calculated and selected the linear model, LASSO is a regression analysis method that aims to reduce model complexity by shrinking the coefficients of the less important variables to zero, making it useful in dealing with datasets that have a large number of features (21). To perform LASSO classification, the variables from the binomial distribution were used in conjunction with a standard error lambda value for the minimal criterion (1-SE criterion), which had a decent performance but only 10 cross-validation factors. On the other hand, random forest is an ensemble learning method that constructs numerous decision trees The flowchart summarizes the main design of the present study. Frontiers in Immunology frontiersin.org during training and predicts the mode of the classes as the output. It is a robust and accurate method that can handle both numerical and categorical data, missing values, and noisy data (22). The genes were ranked using random forest, and those with relative values greater than 0.25 were deemed typical random causes. When used in combination, LASSO, random forest, and SVM can provide complementary insights into identifying reliable oxidative stress genes for diagnosing periodontitis. LASSO can identify the most relevant features, random forest can provide accurate and robust predictions, and SVM can improve the generalization performance of the model. However, careful design and validation of the integration process are necessary to ensure that each method's strengths are fully utilized, while minimizing potential biases and limitations. Subsequently, the rms algorithm was used to construct a nomogram model that predicted the probability of acquiring periodontitis. The predictive performance of the nomogram model was assessed using calibration curves, and the area under the curve (AUC) for scanning for distinctive genes and assessing their diagnostic value was calculated using the 'P ROC' function in the R package for the receiver operating characteristic (ROC) curve (23).
Unsupervised clustering of PD patients
We used unsupervised clustering analysis using the ConsensusClusterPlus R package (24) to group 423 samples of periodontitis patients into various clusters based on three modelled oxidative stress genes using a k-means method with 1,000 cycles. A combination of cumulative distribution function (CDF) curves, consensus matrix, and consistent clustering scores (>0.9) was used to determine the ideal number of clusters (k=2). Subsequently, principal component analysis (PCA) was used to evaluate the gene distribution of different clusters. The expression of the modelled genes was also scored with fGSEA for both subtypes. Furthermore, gene expression profiles of prognostic DE-OSRG within different clusters were evaluated using the t-test, with DE-OSRG with a P-value of less than 0.001 regarded as a distinct prognostic OSRG for periodontitis and displayed with box plots. DEGs in various clusters were screened using |log FC criterion |≥0.2 and adjusted P-values <0.05. By examining these enriched GO terms and KEGG pathway analyses using R in the " clusterProfiler" package and visualizing the differential pathways using bar charts, the enrichment pathways of DEGs in different typologies were studied and compared.
Analysis of single-sample gene set enrichment for different clusters
The single-sample Gene Set Enrichment Analysis (ssGSEA) (25) was used to compute and compare the infiltrating immune cells. Immunological pathways in periodontitis, various clusters, and box plots were used to visualize the results. Additionally, Pearson correlation coefficients were computed to assess the relationship between DE-OSRG and the immune pathways, infiltrating immune cells, and periodontitis samples. The results were visualized in R using "corrplot".
2.9 WGCNA (weighted gene co-expression network analysis) to find co-expression modules associated with oxidative stress isoforms WGCNA investigates the connections between gene networks and disease and the relationships between gene modules and clinical traits. WGCNA was performed using the R package (26) of "WGCNA" (version 1,70.3) to identify co-expression modules). In order to assure the validity of the quality outcomes, the top 5000 genes with the highest variance were applied to future WGCNA analyses. A weighted adjacency matrix was created using the best soft power and then converted into a topological overlap matrix (TOM). When the minimum module size was set to at least 200, modules were produced using a TOM dissimilarity measure (1-TOM) based on a hierarchical clustering tree technique. A random colour is selected for each module. The module eigengene represents the overall gene expression profile in each module. Dynamic tree-cutting and hierarchical clustering were used to find the module. Gene salience (GS) and module affiliation (MM) were evaluated to connect modules to clinical features. The hub module was designated with the highest Pearson affiliation correlation (MM) and an absolute p-value of 0.05. MM >0.8 and GS >0.2 indicated module connectivity height and clinical significance. Further investigation was carried out on the corresponding modules' genetic data.
scRNA-seq data subgroup processing and pseudo-time series analysis
The following steps were used to process the 10 scRNA-seq data: (1) The R program "Seurat" package was used to convert 10 scRNA-seq data to Seurat objects (27). (2) To undertake quality control (QC), low-quality cells were eliminated after determining the percentage of mitochondrial or ribosomal genes. (3) The "FindVariableFeatures" function was used to screen the top 2000 high-variability genes after QC, and UMI was carried out. (4) Gene correlation analyses were conducted to determine the data quality after the first 2,000 highly variable genes were screened using the "FindVariableFeatures" program. (5) PCA (Principal component analysis) based on 2000 genes and unified flow approximation and projection (UMAP) (28) was used for downscaling and cluster identification. The "SingleR" package (29) of R software was used to identify various cell types for cluster annotation. The inferred cell differentiation trajectories were calculated using Monocle 2 (cell trajectory reconstruction analysis employing gene counts and expression). DDRTree was used to select and downscale the DEGs in the clustering results. Cells were then binned, and trajectories were constructed. Heat maps of sorted gene expression were created following clustering analysis to visualize the top 100 driver genes and the 'target genes' expression trends in each cell cluster (30)(31)(32)(33). In order to select DE-OSRG genes and illustrate the results, the statistical method "Branch Expression Analysis Model (BEAM)" was employed to determine the contribution of genes during cell development. Using the "plot cell trajectory" feature, the association between the trajectory of gene modifications and cell differentiation was displayed.
Statistical analysis
R software version 4.1.3 was used to conduct the statistical analysis. A one-way analysis of variance (ANOVA) and t test are performed on the data to investigate whether the Oxidative stress model genes, pathway enrichment results, immune cell infiltration and immune function score differs significantly between the patient groups. p-values and false discovery rate (FDR) q-values below 0.05 were regarded as statistically significant.
Differentially expressed OSRGs in patients with periodontitis
Box-and-whisker plots were employed to normalize the data, where different data sets were represented by different colors, rows corresponded to samples, and columns represented gene expression levels within the samples (Supplementary Figures 1A, B). Before batch correction, PCA analysis was performed on several data sets, and GSE10334 and GSE16134 were found to be distinct without any overlap ( Figure 2A). The plot of PCA analysis using the sva program after batch correction is shown in Figure 2B, where the intersection of the two datasets was utilized as a batch for further evaluation. Based on the conditions of P-adjustment <0.05 and | log2 fold-change (FC) | >0.5, a total of 891 genes, including 555 upregulated genes and 247 down-regulated genes, were identified as differentially expressed genes (DEGs) (Supplementary Table 2).
Among the genes associated with oxidative stress, 52 DE-OSRGs exhibited differential expression between samples with periodontal disease and those without, as shown by the intersection of DEGs and genes associated with oxidative stress (Figures 2C, D). These 52 DE-OSRGs were subjected to correlation analysis, with GFM1 showing the strongest negative correlation with TGFB1 and HADHA exhibiting the strongest positive association with ACADVL ( Figure 2E). Furthermore, KEGG enrichment analysis and GO functional analysis were conducted to assess the biological activities and signaling pathways associated with these 52 DE-OSRGs. The significantly enriched items were selected using P<0.05 and shown in bar graphs ( Figure 2F). The BP category was mainly associated with a response to oxidative stress and stress-activated protein kinase signaling cascade, while the CC category was mainly associated with inflammasome complexes and platelet alpha particles. The MF category was enriched with antioxidant activity, cysteine-type endopeptidase activity involved in apoptosis, and NAD+ nucleotidase activity protease binding. KEGG enrichment analysis identified the top 10 pathways based on the enrichment score out of 32 significantly enriched KEGG pathways ( Figure 2G). Most enriched pathways were associated with il-17 signaling and atherosclerotic disease, including sterol hormone production, T-cell factor cytokine receptor interaction, natural killer cell-mediated cytotoxicity, and other KEGG pathways. Interestingly, the enrichment analysis results revealed a strong correlation with the immune response, which prompted us to conduct a systematic analysis of the immune status of patients with periodontitis.
Three machine learning algorithms to screen modelling genes
The SVM-RFE, random forest, and LASSO algorithms are employed to choose signature genes and assess their diagnostic effectiveness. Three algorithms were applied to screen signature genes among differentially expressed genes associated with crucial periodontitis progression and oxidative stress processes. The ideal l was determined by cross-validation to be 0.004 for the LASSO method. By comparison, we selected the minimum criteria for constructing the LASSO classifier to identify 30 feature genes ( Figures 3A, B).
When there were 9 features ( Figure 3C), the error was minimized for the SVM-RFE algorithm, and 9 relevant feature genes were, as a result, found. The top 10 genes in importance were selected by combining RandomForest feature selection and classification tree results ( Figures 3D, E). Finally, the three feature genes-IL-1b, TXN, and CASP3-common to the SVM-RFE, Random Forest, and LASSO algorithms were discovered by crossover. These genes are depicted by the VENN diagram ( Figure 3F).
Evaluate the diagnostic efficacy of OSRGs
Logistic regression modeling was employed to determine the corresponding regression coefficients, and a linear prediction model was established by weighting the coefficients based on individual genes. The logistic regression models for signature genes were combined to construct a diagnostic nomogram for periodontitis ( Figure 4A). Each gene was assigned a score in the nomogram, and the overall score was calculated by adding the scores of all the genes. This overall score reflects various periodontitis risks. Calibration curves were employed to assess the prediction power of the nomogram, and the results showed that it could accurately predict the risk of periodontitis with minimal difference between actual and predicted risks ( Figure 4B).
Furthermore, decision curve analysis (DCA) revealed that the IL-1b+TXN+CASP3 model had a higher net benefit than the reference model across the threshold range, suggesting that predictions based on this model could better reflect the patient's condition ( Figure 4C). The accuracy and area under the curve for the training set (GSE16134, GSE23586) and the test set (GSE10334) were 0.915 and 0.890, respectively, indicating "excellent" resilience of the model (Figures 4D, E). To our knowledge, after the data balancing process, the machine learning method exhibited significantly improved sensitivity and AUC. After SMOTE balancing, the AUC values reached a maximum of 0.83 for IL-1b, 0.82 for CASP3, and 0.86 for TXN ( Figures 4F-H).
Interaction analysis of model genes and enrichment analyses
Through GSEA analysis, we evaluated the signaling pathways associated with the signature genes. The results revealed that IL-1b ( Figure 5A The significance of the differences was tested using the method of wilcox.test, and the p.signif obtained was expressed as "***"<0.001, "**"<0.01, "*"<0.05. positively correlated with the OLFACTORY TRANSDUCTION pathway, while CASP3 was negatively correlated. The opposite was observed for the B CELL RECEPTOR SIGNALING PATHWAY. Furthermore, IL-1b was positively correlated with the INTESTINAL IMMUNE NETWORK FOR IGA PRODUCTION and TXN was inversely correlated with this pathway. To further investigate the function of the signature genes, we constructed a PPI network using the GeneMANIA database ( Figure 5D) and performed GO/KEGG analysis for the top 20 genes in terms of connectivity. The results showed that oxidative stress response and stress-activated pathways were relatively abundant biological processes (BP) in this dataset. The mitochondrial membrane gap in the cellular component (CC), and the outer side of the plasma membrane were significantly enriched. Additionally, cysteine-type endopeptidase activity involved in apoptotic processes and NAD+ nucleosidase activity were significantly correlated with enriched molecular functions (MF) ( Figure 5E). According to the results of KEGG analysis, the main enrichment pathways were MAPK signaling pathway, apoptosis, and Th17 cell differentiation ( Figure 5F).
Construction of periodontitis oxidative stress subtypes based on OSRGs
A total of 423 samples of periodontitis were clustered in GSE10334 and GSE16134 based on three prognostic oxidative stress-responsive genes (OSRGs). The clustering variable (k) was estimated as 2 based on the relative change in the cumulative distribution function (CDF) plot and the area under the CDF curve ( Figures 6A, B), dividing the dataset into two clusters associated with oxidative stress. Cluster 1 (C1) had 246 cases, and cluster 2 (C2) had 177 cases. Principal component analysis (PCA) revealed significant differences between the subtypes ( Figure 6C). The gene expression profiles of the two clusters were represented by the three prognostic OSRGs on the heat map ( Figure 6D). CASP3 and IL-1b were most highly expressed in C2, while TXN expression levels were highest in C1. The expression levels of oxidative stress genes in the two subtypes were compared using single-sample gene set enrichment analysis (ssGSEA). The expression of oxidative stress genes was more frequent in C2 than in C1, defining C2 as a subtype with high oxidative stress expression ( Figure 6E). Box-and-whisker plots displayed differentially expressed genes between periodontitis progression and oxidative stress-related gene subtypes ( Figure 6F). KEGG enrichment analysis of differentially expressed genes showed that with increased expression of oxidative stress genes, cellular metabolism, including unsaturated fatty acid synthesis, folate biosynthesis, and tyrosine metabolism, also became frequent. However, we found the opposite to be true for immune activity, which was enriched in the subtype "Intestinal immune network for IgA production," as well as pathways related to immune system diseases such as systemic lupus erythematosus (SLE) and autoimmune diseases ( Figure 6G). Gene Ontology (biological process) enrichment analysis was performed on subtypes, in which some immune-related biological processes were downregulated in C1, including positive regulation of interleukin 1b production, T helper 17 cell lineage commitment, mature B-cell differentiation, and positive regulation of myeloid leukocyte differentiation. We conjecture that the expression of oxidative stress genes is involved in processes related to constructing the immune microenvironment in patients with periodontitis ( Figure 6H).
Immunological cell infiltration and enrichment of immune pathways in samples with various subtypes of oxidative stress
The immune microenvironment plays a critical role in regulating the pathology of periodontitis, as evidenced by significant variations in the relative enrichment scores of immune cell infiltration, periodontitis (disease), and healthy tissue immune pathway activity in periodontal disease ( Supplementary Figures 2A, B). Immunometabolic alterations in the immune microenvironment of periodontitis tend to differ in patients with different subtypes of oxidative stress. Exploring the immune infiltration patterns of different subtypes helps to uncover the underlying mechanisms of periodontitis development. We systematically investigated the immune cell infiltration in the immune microenvironment of periodontitis with varying subtypes of oxidative stress. Using the CIBERSORT algorithm to compare 22 immune cells, we observed significant differences between high and low oxidative stress subtype groups. In the increased oxidative stress subgroup, B cells naïve, neutrophils, NK cells resting, and other immune cells exhibited high infiltration, while T cells CD8, T cells follicular helper, monocytes, and other immune cells showed low infiltration in the low oxidative stress subgroup ( Figure 7A). The different levels of infiltration of various immune cells in periodontitis tissues significantly impacted immune function, which we scored using the "ssGSEA" algorithm, revealing that the majority of immune function scores were significantly higher in the high-oxidative stress group than in the low-oxidative stress group ( Figure 7B).
We then examined the spearman correlation coefficients of the three validated biomarkers (CASP3, TXN, IL-1b) with 20 immune cells and immune functions and observed that these three biomarkers were considerably associated with most immune cells. CASP3 had the strongest positive correlation with plasma cells and the strongest negative correlation with dendritic cells resting; TXN had the strongest positive correlation with dendritic cells resting and the strongest negative correlation with plasma cells and B cells naïve, and IL-1b had the strongest positive correlation with neutrophils ( Figure 7C). Based on immune functions, we found that CASP3 and IL-1b exhibited positive correlations with all immune functions, while TXN showed significant negative correlations with most immune functions ( Figure 7D). Based on these results, we speculate that the expression profile of oxidative stress genes is a crucial factor in shaping the immune environment and promoting periodontitis development.
Analysis of weighted co-expression networks in patients with periodontitis
In this study, we aimed to investigate the gene networks associated with periodontitis oxidative stress subtypes. To accomplish this, we clustered differential gene matrices of GSE10334 and GSE16134 expression matrices of all periodontitis patients, with a total of 423 samples, to identify functional gene modules that are associated with periodontitis in different subtypes. To ensure the reliability of our results, we excluded samples with apparent abnormalities by setting a threshold ( Figure 8A). Gene coexpression similarity was determined using Pearson correlation coefficients, and weak connections were filtered out using the topological overlap matrix (TOM) during the network creation. The soft threshold was set to 9, which was consistent with the scalefree distribution and provided adequate average connectivity for the following construction of co-expression modules ( Figure 8B).
After merging the modules with strong links, five modules were identified for further analysis using the 0.55 clustering height restriction ( Figure 8C). Finally, the primers and merged modules were displayed beneath the clustering tree ( Figure 8D). The accuracy of module descriptions was demonstrated by transcriptional correlation analysis inside modules, with no significant link observed between modules (Figures 8E, F). The relationship between modules and clinical symptoms was investigated using positive correlations between ME levels and clinical characteristics. The blue-green modules showed negative correlations with C1 (r = 0.38, p = 1e-13) and positive correlations with C2 (r = -0.38, p = 1e-13) ( Figure 8G).
Furthermore, we identified therapeutically relevant modules, with the turquoise module shown to be substantially linked with typing in the typing MM versus GS scatter plot ( Figure 8H). We then extracted genes from the turquoise module for enrichment analysis, and as expected, many immune-related pathways were enriched. These include active regulation of cytokine production, functional regulation of immune responses, leukocyte migration, neutrophil degranulation, regulation of lymphocyte activation, responses to viruses, B-cell receptor signaling pathways, and responses to bacteria. Overall, our findings highlight the crucial involvement of oxidative stress events in forming the immune environment in periodontitis patients.
scRNA-seq data quality control and dimensionality reduction clustering
To investigate the gene expression profiles of individual cells, we first pre-processed the single-cell data for normalization ( Figure 9A). The quality of the cells was examined using UMI and Gene correlation analysis, which indicated a favorable correlation coefficient of r = 0.77 between nCount and nFeature, confirming the high quality of the cells ( Figure 9B). We then applied the RunPCA function in the Seurat package for principal component analysis (PCA), using the 'scaledata' function to scale selected highly variable genes, and finding anchor points by PCA downscaling. Subsequently, we selected the data of the top 10 PCs for downscaling ( Figures 9C, D). The results of the control and affected sites were visualized using umap and are presented in Figure 9E.
Next, we employed the findclusters function of the Seurat package to cluster the cells into groups and annotated the subgroups using the "singleR" package, which identified a total of 8 cell types ( Figure 9F). To further characterize the expression profiles of specific genes, we plotted the expression of "CASP3", "TXN", and "IL-1b" in the cell clusters using umap ( Figure 9G). We subsequently calculated the OSscore for each cell subpopulation by scoring each cell type with the oxidative stress gene set. Our analysis showed that the expression of oxidative stress genes was more active in monocyte in the immune cell subpopulation at the affected site compared to the control site, while the opposite was observed for Tcells ( Figure 9H).
Pseudotime series analysis
We extracted monocytes, the immune cell subpopulation with the highest score of the oxidative stress gene set ( Figure 10A), for the following analysis step-package for cell annotation of each subpopulation ( Figure 10B). The "monocle" software was used to investigate the cell trajectories, and pseudo-times of the thirteen crucial cell types found. The earlier the cell differentiation, the darker the blue colour, demonstrating that monocytes differentiate from left to right over time. There are three different nodes of differentiation for monocytes, with nodes followed by cells indicating other states, And it was observed that memory B cells, CD16-monocytes, and NK cells were clustered at one end of the trajectory and distributed among the affected sites in patients with periodontitis ( Figures 10C, D).
Then, we used the branching expression analysis model (BEAM) to find thirteen regulatory genes differentially expressed in different cell subpopulations, screened essential genes with qval (corrected P), and took intersections with the set of genes for oxidative stress. The distributed expression of oxidative stress genes with the proposed time series was obtained. Finally, we created a heat map using these 13 genes ( Figure 10E). And the temporal expressions of the genes "JUN", "IL-1b", and "TXN" in the normal and diseased groups, respectively, were selected and shown. The results showed significant differences in the expression of most of the oxidative stress genes as the proposed time series progressed ( Figure 10F). This is consistent with our prediction.
Discussion
Periodontitis is a common bacterial-induced inflammatory disease of the oral cavity that can destroy the connective tissue and bone of the periodontium. Approximately 1.1 billion people suffer from severe periodontitis. In the early stages of periodontitis, most patients do not seek medical attention due to the lack of subjective or mild symptoms (34). If periodontitis is not treated in a timely manner, it can cause teeth to loosen or even fall out, affecting a person's ability to chew. Furthermore, periodontitis can lead to other systemic diseases such as cardiovascular disease. The bacterial load from oral infections may cause bacterial endocarditis and subsequent heart valve destruction, increasing the risk of ischemic heart disease mortality. For rheumatoid arthritis, periodontal anaerobic bacteria may penetrate the synovial fluid of patients with rheumatoid arthritis and promote chondrocyte apoptosis.
Regarding respiratory system diseases, enzymes secreted by periodontal bacteria may modify the mucosal surface of the oral pharynx and promote the adhesion of respiratory pathogens. Additionally, periodontal cells secrete a mixture of cytokines and other biologically active factors into saliva, which could stimulate respiratory epithelial cells to release other cytokines and attract inflammation cells to that site. These inflammatory cells secrete proteases that destroy epithelial cells, making them more susceptible to colonization by respiratory pathogens. In summary, periodontitis is no longer an isolated disease but is associated with a large number of systemic diseases (35-37).
Although several diagnostic methods are available, such as bleeding on probing (BOP) and probing pocket depth (PPD), CAL all of these methods require a particular stage of periodontitis development before they can play a diagnostic role, which is not conducive to improving patients' quality of life as soon as possible (38). Therefore, developing biomarkers that can diagnose periodontitis early can help patients and dentists understand periodontal health earlier (34). The function of oxidative stress in periodontitis has received much attention in recent years. Usually, immune cells respond by producing ROC for defence (39, 40). However, neutrophils activate purine degradation pathways during the bacterial invasion of periodontal tissues, producing large amounts of ROS, ultimately creating an inflammatory environment that causes periodontal tissue destruction (41).
In addition, ROS can interfere with the cell cycle of gingival fibroblasts and cause apoptosis while inducing matrix proteases to degrade the matrix, thereby altering the inflammatory environment (42,43). Despite the importance of oxidative stress in periodontitis, there is a lack of diagnostic models based on oxidative stress-based diagnostic models for the diagnosis of periodontitis is lacking. Therefore, in this study, based on GSE10334, GSE16334 GSE23586, we screened key genes using SVM, Lasso and random forest, respectively and took the intersection of the three, thus creating a multigene diagnostic model of 3OSRgs that can identify periodontitis patients early and accurately and therefore stop disease progression.
It is clear that cystathionine 3 (CASP3), a member of the interleukin-1b-converting enzyme family, induces apoptosis by affecting the TNF and p53 pathways and is therefore considered a critical link in the apoptotic signalling pathway (44,45). Another study showed that expression of the apoptotic marker CASP3 in the gingiva of patients with periodontitis levels was higher than in normal gingival tissue, indicating high apoptotic activity at the site of periodontitis (46). Furthermore, in all severities of periodontitis, IL-1b levels in gingival sulcus fluid were more significant than in the control group and are thus considered a disease characteristic of periodontitis (47). TXN can reduce ROS-producing oxidative proteins and thus regulate cellular redox status (48). Unfortunately, TXN has been little studied in periodontitis.
Based on the diagnostic model, we classified patients into C1 and C2 types using three modelled genes to differentiate patients more closely to provide precision treatment. The expression of oxidative stress genes in patients in C1 and C2 was then scored and visualized using ssGSEA, whereby C2 was defined as a high oxidative stress type and C1 as a low oxidative stress type.
It has been demonstrated that while the process leading to chronic periodontitis is initially associated with bacterial biofilms, tissue destruction occurs primarily due to an increased immune response in the individual. Among the immune system cells involved in this process, monocytes/macrophages produce and secrete high levels of metalloproteinases, reactive oxygen species (ROS), tumor necrosis factor (TNF), interleukin-1 (IL-1), interleukin-6 (IL-6), and nuclear factor kappa-b ligand (RANK-L), which amplify the inflammatory response to control bacterial growth while leading to destruction of periodontal tissue (49). Moreover, the interaction between microbial ecological dysregulation and the inflammatory environment has emerged as the most important pathogenesis of periodontal disease (50), and anti-inflammatory therapies targeting the immune microenvironment can promote cell homing and tissue formation, thus facilitating immune regulation and tissue repair (51). Therefore, differentiating patients with periodontitis with different immune profiles and implementing personalized immunotherapy accordingly may obtain better efficacy and have greater clinical application value. In addition, the presence of type 1 cytokines in the gingival sulcus fluid of periodontitis patients has been proposed to be the main cause of Porphyromonas gingivalis-specific IgG2 production, while Porphyromonas gingivalis-dendritic cell-NK cell interaction can produce IFN-g and type 1 cytokines in a short period of time (52). In addition, pathogens can stimulate monocytes to secrete large amounts of ROS, TNF-a, IL-1b and other cytokines to limit bacterial multiplication and lead to periodontal destruction (53-57). Macrophages play critical roles in periodontitis's destruction and repair phases (51), most likely because macrophages polarize towards M1, release matrix-degrading enzymes and pro-inflammatory mediators, and enhance osteoclast activity in periodontitis (58, 59). Neutrophils have been extensively studied in periodontitis. Activating neutrophils by MIP-1a, CXCL8, and ROS initiates phagocytosis based on complement and antibodies, thereby causing tissue damage (60-63). It has also been concluded that the main reason for the healing effect of conventional mechanical therapy is the normalization of dysfunctional phagocytes (64) In addition, vitamin C can treat periodontitis by reducing oxidative substances produced by neutrophils (65). Meanwhile, based on the P38/MAPK pathway, 1,25-dihydroxy vitamin-D3 promotes neutrophil apoptosis in type 2 diabetic periodontitis tissue to reduce periodontitis (66). Single-cell technology shows excellent advantages in analyzing the immune microenvironment in diseased tissues at the cellular level (67). In addition, based on single-cell sequencing data, reconstruct pseudo-time-series and mimic real-time trajectories (68) as closely as possible, thus reflecting changes in gene expression and cell differentiation during disease progression. Dentists can then target the use of immune drugs according to the patient's oxidative stress gene expression and immune infiltration, potentially leading to better outcomes.
Conclusion
OS signature is a novel predictive biomarker and a possible therapeutic target for patients with PD, as we have shown for the first time. Additionally, OS signature can characterize the immunological milieu of PD patients and appropriately estimate the prognosis of PD patients, which can assist doctors in identifying certain patient subgroups that may benefit from immunotherapy and chemotherapy for individualized treatment.
Data availability statement
The original contributions presented in the study are included in the article/Supplementary Material. Further inquiries can be directed to the corresponding authors. | 9,223.2 | 2023-07-05T00:00:00.000 | [
"Biology"
] |
Brevinin-1GHd, A Novel Hylarana guentheri Skin Secretion-Derived Brevinin-1 Type Peptide with Antimicrobial and Anticancer Therapeutic Potential.
Abstract Host-defense antimicrobial peptides (AMPs) from amphibians are usually considered as one of the most promising next-generation antibiotics because of their excellent antimicrobial properties and low cytotoxicity. In the present study, one novel Brevinin-1 type peptide, Brevinin-1GHd, was isolated and characterized from the skin secretion of the frog, Hylarana guentheri. Brevinin-1GHd was found to possess a wide range of antimicrobial activity through penetrating the bacterial membrane within a short time while showing low hemolysis at bactericidal concentrations, even against the resistant strains. It also inhibited and eradicated biofilms that are thought to be closely related to the rise in resistance. Meanwhile, Brevinin-1GHd exhibited wide-spectrum anti-proliferation activity toward human cancer lines. Taken together, these results indicate that Brevinin-1GHd with its excellent antimicrobial and anticancer activities is a promising candidate for a novel antibiotic agent, and study of its structure–activity relationships also provided a rational template for further research and peptide analog design.
Introduction
The growing problems of antibiotic-resistance have stressed the urgent demand for alternative and potent anti-infection agents [1,2]. As a fundamental constituent of innate immunity and defense systems, antimicrobial peptides (AMPs) from amphibian skin secretions have gradually become the focus of researchers. These skin-derived bioactive peptides were reported to have potent and broad-spectrum antimicrobial activity [3]. Compared with conventional antibiotics, AMPs are less likely to lead to resistance problems and can kill antibiotic-resistant bacteria within in a short time while showing low cytotoxicity to normal eukaryotic host cell lines, which makes them one of the most promising of alternative antibiotic agents [4].
Nowadays, more than 600 AMPs belonging to more than 30 families have been identified from amphibians [5]. Brevinins are a significant group of AMPs from the skin secretions of Rana frogs with potent antimicrobial activities and hemolytic actions. Generally, they have been divided into two subfamilies, Brevinin-1 and Brevinin-2, based on their primary structural characteristics. Brevinin-1 was first isolated from a skin extract of Rana brevipoda porsa, which is an Oriental pond frog [6]. They typically adopt an extended alpha-helix secondary structure and contain 24 amino acid residues and a heptapeptide ring known as a "Rana-Box" formed by a disulfide bond at the C-terminus [7]. Brevinin-1 family peptides exhibit a broad-spectrum antimicrobial activity including against some drug-resistant strains of pathogenic bacteria [8]. In addition to their excellent antibacterial activities, they also show strong anti-proliferation activity against a range of human tumor cells. However, their significant hemolytic activity would impede their further development as therapeutics [9].
In order to further study features of AMPs and find promising next-generation antibiotics, the work of our research group in isolating and characterizing novel bioactive peptides from frog skin secretions has continued. In this report, a novel AMP named Brevinin-1GHd was discovered in and isolated from the skin secretion of Hylarana guentheri. Through a 'shotgun' cloning strategy and structural confirmation by mass spectrum (MS/MS) fragmentation sequencing, the primary structure of Brevinin-1GHd was unequivocally established. A variety of biological and biophysical assays were subsequently applied to further evaluate the antimicrobial activity of Brevinin-1GHd on several common and drug-resistant micro-organisms and anti-proliferation activity against several common human cancer cells and cytotoxicity to horse red blood cells and normal human cells were also studied. The kinetics of bacterial killing and antibiofilm assays were also performed.
Experimental section Specimen biodata and secretion acquisition
Specimens of the broad-folded Frog, Hylarana guentheri (n = 3), were obtained in the field in southern China. All frogs were adults of undetermined sex and secretion harvesting was performed in the field after which the frogs were released. Skin secretion was obtained by gentle transdermal electrical stimulation of the dorsal skin, as previously described [10]. Stimulated secretion was maintained at 4 • C prior to being snap-frozen in liquid nitrogen, lyophilized and stored at −20 • C prior to analyses. The procedure of secretion acquisition had been overseen by the Institutional Animal Care and Use Committee (IACUC) of Queen's University Belfast, and approved on 1 March 2011. It was carried out under the U.K. animal (Scientific Procedures) Act 1986, Project license PPL 2694, which was issued by the Department of Health, Social Services and Public Safety, Northern Ireland.
"Shotgun" cloning of cDNAs encoding novel peptide biosynthetic precursors
Lyophilized Hylarana guentheri skin secretion was dissolved (5 mg/ml) in cell Lysis/mRNA stabilization buffer (Dynal Biotech, U.K.). Polyadenylated mRNA was isolated by magnetic oligo-dT beads as described by the manufacturer (Dynal Biotech, U.K.) and subjected to 3 -RACE procedures to obtain full-length nucleic acid sequence encoding biosynthetic precursor using a SMART-RACE kit (Clontech, U.K.) essentially as described by the manufacturer. Briefly, the 3 -RACE reactions employed a Nested Universal Primer (supplied with the kit) and a degenerate sense primer (S1: 5 -GAWYYAYYHRAGCCYAAADATGTTCA-3 ) that was designed to a highly conserved domain of the 5 -untranslated regions of previously characterized antimicrobial peptide precursor cDNAs from closely related Rana species. The PCR cycling procedure was as follows-initial denaturation step: 60 s at 94 • C; 35 cycles: denaturation 30 s at 94 • C, primer annealing for 30 s at 61 • C; extension for 180 s at 72 • C. PCR products were gel-purified, cloned using a pGEM-T vector system (Promega Corporation) and sequenced using an ABI 3100 automated capillary sequencer.
Analyses of Brevinin-1GHd primary and secondary structure
Reverse-phase HPLC (RP-HPLC) and mass spectrometry were used to elucidate the primary structure of Brevinin-1GHd. A further 5 mg of lyophilized Hylarana guentheri skin secretion were analyzed as in a previous study [11]. An analytical RP-HPLC column (Phenomenex C-5, 0.46 cm × 25 cm) and Cecil CE4200 Adept (Cambridge, U.K.) gradient RP-HPLC system (from 0.05/99.95 (v/v) trifluoroacetic acid (TFA)/water to 0.05/19.95/80.00 (v/v/v) TFA/water/acetonitrile in 80 min) were employed to isolate peptides from skin secretion. Thereafter, the primary structure of the novel peptide was established by a matrix-assisted laser desorption ionization, time-of-flight mass spectrometry (MALDI-TOF MS) (Voyager DE, Perspective Biosystems, Foster City, CA, U.S.A.) and an LCQ-Fleet electrospray ion-trap mass spectrometer (Thermo Fisher Scientific, San Jose, CA, U.S.A.).
Bioinformatics techniques were used to analyze the acquired sequence. An online tool, NCBI-BLAST (https://blast. ncbi.nlm.nih.gov/Blast.cgi), was used to compare this sequence with all the sequences that are recorded in GenBank, and then generated related peptide sequences based on identities ranging from high to low. The helical structure and structural parameters were analyzed by HeliQuest (http://heliquest.ipmc.cnrs.fr/) and I-TASSER online server.
The secondary structure of Brevinin-1GHd was determined with the JASCO J-815 circular dichroism (CD) spectrometer (Jasco, Essex, U.K.). About 50 μM of peptide solutions were prepared in precision quartz cell (Hellma Analytics, Essex, U.K.) with 10 mM ammonium acetate (NH 4 AC) and 50% trifluoroehanol (TFE) in 10 mM NH 4 AC buffer, respectively. The sample was analyzed at 20 • C with scan range of 190-250 nm, scanning speed of 100 nm/min, 1 nm bandwidth and 0.5 nm data pitch.
Peptide synthesis and purification
The peptide was synthesized by a solid phase peptide synthesis method using a synthesizer (Protein Technologies, U.S.A.) along with standard Fmoc-chemistry. The primary peptide product was cleaved from the resin and deprotected for at least 8 h, precipitated in ether over 3 days, and then washed three times with ether and dried for more than 24 h. After this, the peptide was re-dissolved and rapidly frozen in liquid nitrogen and lyophilized in a freeze dryer. After freeze drying, the peptide was purified by RP-HPLC.
Kinetic time-killing assay
To evaluate the antimicrobial properties, the kill-time curve assay was performed against the Gram-negative bacterium, E. coli, the drug resistant Gram-negative bacterium, P. aeruginosa, the Gram-positive bacterium, S. aureus and MRSA. Cell cultures containing various concentrations (0.5 ×, 1 ×, 2 × MIC) of peptide and 32 μM of ampicillin were diluted with phosphate-buffered saline (PBS) and spread over MHA plates after incubation for 0, 5, 10, 20, 30, 60 and 120 min. The bacterial colonies were counted after overnight incubation.
Minimum biofilm inhibitory concentration (MBIC) and minimum biofilm eradication concentration (MBEC) assays
MBIC and MBEC were performed as previously described [11]. In MBIC assay, bacteria culture (5 × 10 5 CFU/ml) was incubated with different concentrations of Brevinin-1GHd (ranging from 521 to 1 μM) at 37 • C for 24 h. In MBEC assay, 100 μl of bacteria medium was seeded to a 96-wells plate and incubated at 37 • C for 48 h until the appearance of mature biofilm. Then, the plate was washed with sterile PBS twice and treated with different concentrations of Brevinin-1GHd at 37 • C for 24 h. The plate was then washed with PBS for twice and stained with Crystal Violet solution (Sigma-Aldrich, U.K.), and further dissolved with 30% of acetic acid (Sigma-Aldrich, U.K.). The absorbance was measured at 595 nm with a Synergy HT plate reader (Biotech, Minneapolis, MN, U.S.A.).
SYTOX green assay
The SYTOX green assay was performed as previously reported to analyze the effect of peptide on membrane integrity [11]. Briefly, bacterial strains were incubated to the exponential phase and collected after centrifuging at 1000 × g for 10 min. Then, the bacterial pellet was washed with 5% TSB (dissolved in 0.85% NaCl solution) twice and resuspended at a density of 10 8 CFU/ml. Peptide at concentrations of 1× MIC, 2 × MIC and 4 × MIC were incubated with bacterial suspension at 37 • C for 2 h and then mixed with SYTOX Green nucleic acid stain (Thermo Fisher Scientific, U.S.A.) at 37 • C for 10 min on the shaking incubator. The changes of fluorescence were monitored by use of a Synergy HT plate reader at excitation/emission wavelengths of 485/528 nm.
Hemolysis and cytotoxicity assays
The hemolysis assay used horse erythrocytes (2% suspension) (TCS Biosciences Ltd., Buckingham, U.K.) as reported previously [11]. Serial concentrations of peptide were incubated with horse blood cell suspension at 37 • C for 2 h. 1% Triton X-100 was used as positive control to calculate hemolysis of test peptide and PBS was served as the negative control. After that, the mixtures were centrifuged at 1000 × g for 5 min and lysis of red cells was determined by measuring of the OD values at 550 nm.
Human cancer cell MTT assay
The anticancer activity of peptide on four kinds of cancer cell lines: H157 (ATCC-CRL-5802), U251MG (ECACC-09063001), MDA-MB-435s (ATCC-HTB-129) and PC3 (ATCC-CRL-1435) were measured by the MTT assay. Cell lines were seeded into 96-well plates at a concentration of 5 × 10 3 cells per well in the corresponding culture medium with serum for 24 h. The next day, the culture medium was replaced with 100 μl of serum-free medium. After 4 h, Brevinin-1GHd solutions, in concentrations ranging from 0.1 nM to 0.1 mM in serum-free medium, were added to replace the culture medium. After 24 h of treatment, 10 μl of MTT reagent (5 mg/ml) were added to each sample. The cells were incubated for 4 h and mixtures in each well were then removed and replaced with 100 μl of DMSO. Finally, the absorbance of each sample at 570 nm was determined using an ELISA plate reader.
Statistical analysis
Statistical analyses of all bioactivity assays were performed using Prism 6 (GraphPad Software, U.S.A.). The statistical significance of difference was analyzed by a one-way ANOVA. Data points represent the average of three independent experiments with error bars presenting the SEM.
"Shotgun" cloning of Brevinin-1GHd from the skin secretion of Hylarana guentheri
A biosynthetic precursor encoding Brevinin-1GHd cDNA was consistently cloned from the skin secretion cDNA library of Hylarana guentheri. The open reading frame consisted of 71 amino acid residues. The N-terminal 22 amino acid residues encoded a putative signal peptide, followed by an acidic amino acid residue-rich spacer domain that terminated in a typical -Lys-Arg-(-KR-) propeptide convertase processing site, followed immediately by the mature AMP at the C-terminal end (Figure 1). The average molecular mass of the putative mature peptide from the cloned precursor was calculated as 2495.14 Da. The Brevinin-1GHd biosynthetic precursor-encoding cDNA has been deposited in the NCBI Database (accession code; MN817129).
Brevinin-1GHd primary and secondary structure
The putative mature peptide, Brevinin-1GHd, was identified by RP-HPLC through analyzing the lyophilized crude skin secretion of Hylarana guentheri. All collected fractions were then analyzed by MALDI-TOF MS and a single fraction containing a peptide corresponding to the theoretical molecular mass was identified (Figure 2A,B). The primary structure of Brevinin-1GHd was further analyzed by MS/MS fragmentation sequencing ( Figure 2C).
To further study putative secondary structure and structural parameters, Heliquest and I-TASSER were used in analysis ( Figure 3B,C). The results demonstrated that Brevinin-1GHd adopted an alpha-helix secondary structure ( Figure 3D) with a hydrophobic face consisting of A, A, L, I, V ( Table 1).
The results of CD spectroscopy revealed that Brevinin-1GHd adopt a random coil structure in an aqueous environment, while forming an alpha-helix structure in a membrane-mimetic environment.
MIC and MBC
Brevinin-1GHd was found to be active against the yeast, C. albicans, with an MIC of 4 μM and was even more potent against the Gram-positive bacteria, S. aureus and MRSA, with MICs of 2 and 4 μM, respectively (Table 2). However, this peptide was less potent against the Gram-negative bacteria, E. coli and P. aeruginosa, with an MICs of 8 and 32 μM. Notably, the antimicrobial activities of Brevinin-1GHd against P. aeruginosa were comparable to Ampicillin.
Time-killing assay for Brevinin-1GHd against E. coli, S. aureus, P. aeruginosa and MRSA
The time-killing assay is widely used for in vitro investigations of novel AMPs. In the present work, two common bacteria, E. coli ( Figure 4A) and S. aureus ( Figure 4B), and two drug-resistant bacteria, P. aeruginosa ( Figure 4C) and MRSA ( Figure 4D), were subjected to kinetic study. The novel peptide displayed rapid bactericidal activity against all test strains, showing a higher efficiency compared to Ampicillin after 1 h exposure (Figure 4).
Anti-biofilm activity of Brevinin-1GHd
Brevinin-1GHd was found to inhibit biofilm formation of S. aureus and MRSA at concentrations of 2 and 4 μM, respectively. Brevinin-1GHd also eradicated established biofilms at concentrations of 2 and 16 μM.
Discussion
The skins of amphibians play an essential role in their survival and their ability to thrive in complex environments. Gene-encoding AMPs are one of the most important components of amphibian innate immunity and defense system against infection by micro-organisms. In the present paper, one novel AMP was isolated and characterized from skin secretion of Hylarana guentheri. As the NCBI-BLAST alignment suggested, this novel peptide shared similar properties with most peptides in the Brevinin-1 subfamily. Among these, Brevinin-1GHd is 83% identical with Brevinin-1GHa and 71% identical with Gaegurin-5 [13,14].
Antimicrobial activity
As with most peptides of the Brevinin-1 family, Brevinin-1GHd adopted an alpha-helical structure and exhibited a wide range of antimicrobial activity, even against resistant strains such as MRSA and P. aeruginosa. Among these, Brevinin-1GHd presented a higher potency against the typical Gram-positive bacterium, S. aureus, when compared with the classical Gram-negative bacterium, E. coli, and this phenomenon is quite commonly observed for many other peptides. The fact that Brevinin-1GHd showed stronger activity against S. aureus than against E. coli, could be explained by the differences in structures of their cell envelopes. Gram-positive bacteria have a thicker peptidoglycan layer consisting of anionic teichoic acid. In contrast, in Gram-negative bacteria, the peptidoglycan layer is thinner and less cross-linked. Also, Gram-negative bacteria have a thick lipopolysaccharide (LPS) layer outside the peptidoglycan layer [15]. When the AMPs attack Gram-positive bacteria, they only need to diffuse across the layer of peptidoglycan first and then disrupt the cytoplasmic membrane. However, in the case of Gram-negative bacteria, AMPs must permeabilize a thick LPS layer before they reach and disrupt the inner cytoplasmic membrane [16]. The result of time-killing kinetic assays and SYTOX green assays, revealed that Brevinin-1GHd killed the bacteria within a short time mainly through permeating and disrupting their membranes.
Anticancer activity
Brevinin-1GHd showed cytotoxicity on normal human cells HMEC-1 and HaCaT with IC 50 values of 15.62 and 29.69 μM, respectively; however, IC 50 values of Brevinin-1GHd toward test cancer cells were relatively lower (Table 3), demonstrating, at working concentrations, Brevinin-1GHd could inhibit the growth of test cancer cells without causing huge damage on normal cells. Therefore, the further development of Brevinin-1GHd in anticancer study will be still promising. According to previous studies, Brevinin-1 type peptides were reported to inhibit the growth of a wide range of cancer cells [9]. However, the exact mechanism of AMP action is still not clear yet [17]. It is generally accepted that cancer cell membranes, unlike those of normal cells, display a negatively charged surface. The cationic AMPs could thus combine with the cancer cell membrane through electrostatic interaction [17]. When the AMPs accumulate on the bacterial outer membrane to reach a certain concentration, AMPs can penetrate the membrane, causing leakage of the cellular contents leading to cell death. This mechanism may explain the action of Brevinin-1GHd since Brevinin-1GHd contained four net charges, which may allow the peptide to interact with the anionic membrane.
Hemolysis and cytotoxicity
Although Brevinin-1GHd showed considerable hemolysis at high concentration, it did not possess significant hemolytic activity at the lowest MIC concentration. Hemolytic activity is a common characteristic for most amphibian-derived AMPs, and this factor can impede the further therapeutic development of most AMPs [18]. However, through rational design and structural modification, this problem can be solved to some extent and the application of these AMPs could still be promising. Meanwhile, although Brevinin-1GHd showed significant cytotoxicity on normal human cells at 10 −4 M, this side-effect was greatly reduced at the concentration of 10 −5 M under which the growth of cancer cells was still inhibited. Therefore, the further development of this peptide is still promising. In our previous study, one novel Brevinin-1 type peptide, Brevinin-1GHa, was first found in Hylarana guentheri and two analogs, Brevinin-1GHb and Brevinin-1GHc, were designed to further study the relationships between structure and activity. The study of Brevinin-1GHa and its two analogs revealed that the deletion or removal of the "Rana-Box" decreased its antimicrobial activity while reducing hemolytic activity [13]. Through comparing differences of structure and activity between Brevinin-1GHa and its analogs, the hypothesis was established that the hemolytic activity was determined both by the hydrophobicity and hydrophobic face since the lack and decrease in hydrophobicity of Brevinin-1GHb and Brevinin-1GHc showed lower hemolytic activity than Brevinin-1GHa [13]. Interestingly, although Brevinin-1GHd had the same hydrophobic face, higher hydrophobicity and similar length of alpha-helix structure as Brevinin-1GHa, its hemolytic activity was slightly lower than Brevinin-1GHa ( Figure 8). By further comparing their structural parameters (Table 4), we decided to supplement the hypothesis that besides the effects of hydrophobicity and hydrophobic face on peptide hemolytic performance, the role of net charge also needs to be considered. Since fungal membranes are similar with those of other eukaryotic cells, the trend of anti-fungal activity may be similar with that of hemolytic activity [19]. Compared with Brevinin-1GHa, the net charge of Brevinin-1GHd was slightly lower, which may explain the different antimicrobial activity against C. albicans. Normally, the hemolysis of eukaryotic cells requires peptide to insert into the cell membrane and form a channel-like structure as in the "barrel-stave" model. The higher net charge the peptides contain, the easier they bind to the cell membrane [20]. Therefore, although Brevinin-1GHd had higher hydrophobicity, similar length of alpha-helix and same hydrophobic face, it showed relative lower cytotoxicity toward red blood cells than Brevinin-1GHa.
The role of the "Rana-Box"
The "Rana-Box" is a unique structure and appears in many AMPs originating from frogs. This contains an intermolecular disulfide bridge at the C-terminus of the peptide and seven to nine amino acid residues [21]. According to previous studies, the roles of the "Rana-Box" could be briefly summarized in several points: (1) The "Rana-Box" stabilizes the alpha-helix structure, complementing a stable activity; (2) The cyclic structure provides a stable structure for the peptide to resist the hydrolysis of proteases such as carboxypeptidase; (3) The "Rana-Box" favors peptide to induce membrane conductance in planar lipid layers and the efflux of K + from bacteria; (4) For some peptides, the "Rana-Box" provides the source of net positive charge [22]. In the past decades, a large number of studies have been carried on the "Rana-Box". Some studies emphasized the importance of this structure since elimination of the C-terminal cysteine residue impeded antimicrobial performance [14]. Other studies, however, dismissed its role as replacing cysteine residues with serine, deletion of disulfide bond or resetting the position of the "Rana-Box" produced no effect on peptide antimicrobial activity, even helping to reduce hemolysis [22][23][24][25]. In a previous study, we also characterized and designed Brevinin-1GHa and its two analogs to further study the relationship of the "Rana-Box" structure and its effect on antimicrobial activity. However, neither truncating the C-terminal cyclic structure nor removing the "Rana-Box" to the middle part of the peptide, greatly decreased antimicrobial activity [13]. The actual role of the "Rana-Box" in antimicrobial performance is still ambiguous and more factors need to be considered. In fact, no matter what changes in this cyclic structure were made, these would always come with some variations on structural parameters or secondary structure. For example, truncating the "Rana-Box" greatly increased the helicity of Nigrocin-HL analog, which may explain why the antimicrobial activity of Nigrocin-HLD was better [12]. However, the elimination of cyclic structure made the putative length of the alpha-helix of Brevinin-1GHb shorter than Brevinin-1GHa, which was in accordance with the decrease of antimicrobial activity. Also, the motif of the cyclic structure was quite different between different families, even for the peptides in the same family. The variations in residues may lead to differences in structural parameters, which may further influence the working model of the peptide. Therefore, analyzing the relationship of the "Rana-Box" structure and activity needs to be carried out on the case-by-case basis.
In order to further characterize this cyclic structure in the Brevinin-1 family, we collected and aligned all Brevinin-1 peptides from the UNIPORT database (https://www.uniprot.org/). In the Brevinin-1 family, most peptides contained seven amino acids within their "Rana-Box". For each heptapeptide-ring containing Brevinin-1 family peptide, the sequence of each loop segment was extracted and submitted to WebLogo (URL: http://weblogo.threeplusone.com) to generate a logo graphic (Figure 9).
Residue preferences identified in Figure 9 revealed the molecular diversity and residue specificity. The most prevalent residue at each position was also the most tolerated residue in naturally occurring Brevinin-1 heptapeptide rings. In heptapeptide ring containing Brevinin-1 type peptides, the residue at P5 was preferentially lysine or arginine. The most prevalent P2 and P6 residue were also the lysine. Therefore, for most Brevinin-1 family peptides, the "Rana-Box" provides at least two net charges. They may play a significant role in the electrostatic interactions between cationic peptide and anionic cancer or bacterial membranes. The specific membrane binding model of Brevinin-1 family peptides may be the same as the previous model in which the helical kink leads to a diagonal binding of the N-terminal hydrophobic residues in the concave of the helix deeply combined with the membrane core and cationic clusters of "Rana-Box" in the convex of the helix being exposed on the membrane surface [26].
Conclusion
Brevinin-1GHd is a novel Brevinin-1 family peptide isolated from the skin secretion of Hylarana guentheri. Brevinin-1GHd exhibited potent bactericidal activity toward common and drug-resistant bacteria strains and significant anti-proliferation activity against a range of human cancer cells. Furthermore, Brevinin-1GHd displayed rapid bacterial-killing kinetics and considerable capacity in eradicating S. aureus and MRSA biofilms. It showed negligible cytotoxicity toward horse red blood cells at MIC concentrations. Brevinin-1GHd also provided a valuable template to further study the relationship of structural parameters and hemolysis of Brevinin-1 type peptides and clues for design of potential alternative antibiotics. | 5,510.4 | 2020-04-29T00:00:00.000 | [
"Biology",
"Chemistry"
] |
Decoding the Spatial Configuration of the Ottoman Palace “Khdewedj El Amia” in Algiers (Algeria) through Space Syntax
Palaces of the Ottoman era, the Golden age of Islamic civilization, bear witness to a prestigious know-how, drawing its rules from a way of life governed by the Islamic Sharia, the socio-cultural context of the Berber-Arab population and the climate-physical environment. The palace of Khdewedj El Amia is one of the majestic palaces located at the Casbah of Algiers and constitutes the subject of this article whose objective is to decode its genome in order to understand the social logic of a space inhabited and designed by a princess who lost her sight. Hence the name El Amia, which means blind in Arabic. The decoding of this building used the space syntax approach via a visibility graph analysis (VGA) performed by the Depthmap tool and a quantitative analysis of the graph justified by the Agraph tool. It is about taking into account the way in which vernacular architecture can stimulate the direct perception of space and participate in the construction of the user’s path. It was found that the palace is made up of two entities; one is of public order highlighting the resident/alien interface, and another intended for the private apartments, the harem of the princess, isolated from the outside world.
Decoding the Spatial Configuration of the Ottoman Palace "Khdewedj El Amia" in Algiers (Algeria) through Space Syntax architectural heritage Ottoman palace "Khdewedj El Amia", Algiers, Algeria spatial integration space perception visibility graph analysis Palaces of the Ottoman era, the Golden age of Islamic civilization, bear witness to a prestigious know-how, drawing its rules from a way of life governed by the Islamic Sharia, the socio-cultural context of the Berber-Arab population and the climate-physical environment. The palace of Khdewedj El Amia is one of the majestic palaces located at the Casbah of Algiers and constitutes the subject of this article whose objective is to decode its genome in order to understand the social logic of a space inhabited and designed by a princess who lost her sight. Hence the name El Amia, which means blind in Arabic. The<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>decoding of this building used the space syntax approach via a visibility graph analysis (VGA) performed by the Depthmap tool and a quantitative analysis of the graph justified by the Agraph tool. It is about taking into account the way in which vernacular architecture can stimulate the direct perception of space and participate in the construction of the user's path. It was found that the palace is made up of two entities; one is of public order highlighting the resident/alien interface, and another intended for the private apartments, the harem of the princess, isolated from the outside world.
introduction
Ot toman architecture in Algeria features a great diversity, essentially composed of three typologies: religious, military, and civil architecture, including the palaces which are architectural masterpieces. The Casbah of Algiers is an illustrative example of the presence of these three types of architecture that remain a living lesson in the vernacular architecture dating from medieval times. The palaces and residences of Algiers from the Ottoman era, considered to be architectural gems, can be found amidst the ruins of the Casbah, but are unfortunately disused and converted into museums or administrative headquarters. These palaces served as residences of notables or as high places of the exercise of political power during the Ottoman regency. 1 Dar Khdewedj El Amia is one of them. It is a 16 th -century house built in 1575 by a naval officer, Rais Yahia, on a disused zaouia of Sidi Ahmed Abdellah ez-zouaoui. 2 In 1789, Hassan, then Khaznadji (Minister of Finance) of the Dey Mohamed Ben Othmane, acquired it to house his blind daughter Khdaoudj, a princess who lost her sight. Hence, the name El Amia, which means blind in Arabic. After the French invasion in 1830, the palace was assigned to the deputy director of the interior and the attorney general. In 1909, it became the private hotel of the first president of the Court of Appeal. Since the independence (1962), the Palace has been the museum of popular arts and traditions.
This architectural heritage, formed by three centuries of Ottoman rule, received little attention from the colonial authorities. Neglected and little considered in the heritage directories of the French period 3 or independent Algeria, it has been insufficiently studied and evaluated (Cherif, 2015). Vernacular space has long been characterized as residual, it sits on the spatial and temporal margins of human settlements, it is not clearly appropriate and does not have a character of permanence. In fact, the vestiges inherited from ancient civilizations should not remain static, dead and locked in tradition (Besse, 2003). A place of the moment, of duration, of rooting and of feeling, this architecture expresses messages, the ways that individuals and groups distinguish themselves, express their identity and their most common ways of hidden thinking (Chiva, 1987).
Nevertheless, this heritage has aroused the interest of several researchers, who have all emphasized its architectural and urban richness (Cherif, 2009;Hadjilah, 2020;Piaton, 2018;Kameche, 2013;Golvin, 1988; Boutabba, 2018), but did not address the social logic behind the design and spatial arrangement of this palace designed for the attention of a person who has lost her sight. From this perspective, we wonder if the building has been rearranged vis-à-vis this infirmity to provide an intelligible space, which is easily identifiable by a blind person so that the spaces used by the blind are in the most integrated parts of the palace.
The visual memory of space helps in the recognition of space, but this fact is possible only for sighted people. For the blind, the perception of space requires other sensory dimensions such as smell, hearing, and touch. Knowing the particular modes of the path of a specific person is a heuristic way of approaching the complexity of space and the conduct of accessing it (Deac & Ticala, 2017). Yvette Hatwell has concluded that the spatial knowledge acquired by the blind is exactly the same as that of the sighted. Blindness can cause a delay in the acquisition of spatial skills, but the errors observed and the order in which the acquisitions are made are exactly the same in the blind and the sighted. The cognitive space of the blind is therefore no different from that of the sighted (Hatwell, 2017).
Recent research has focused on the apprehension of space through perception, which consists of organizing and associating infor- 1 Under the Ottoman Regency (1516-1830) the medieval city of Algiers went from being a simple village to an urban center.
2 Religious school where students are accommodated who receive teaching in doctrine and grammar given by master Sidi Ahmed Abdellah ez-zouaoui. mation drawn from the place that mobilizes the body and the user's sensory acuity through the sensory system. It is about considering the way in which vernacular architecture can stimulate the direct perception of space and participate in the construction of the user's path (Thomas, 1999;Simonnet, 2004;Mouzoune, 2005).
Properly diagnosing and studying this palace quickly placed us at the intersection of perceptual, social and spatial senses. This has led us to systematically use the analysis protocol developed by the "space syntax" approach. We pay spatial attention to the social context within the perceptual in order to offer a theoretical platform that can be relied on to make rational decisions about how the heritage space was designed for any category of people suffering from any disability. The spatial organization and morphology reflect a form of society organization, as well as the representations and values that operate in this society (Besse, 2003).
materiaL and method
"Space syntax" is a set of theories and tools used to analyse spaces in the built environment. Its aim is based on the fact that spatial morphology influences the distribution of the use of spaces, and that the resulting dynamics in turn condition the social interactions, uses and occupations that develop there. The first publications by Bill Hillier and Julienne Hanson (1984) bring together the basic notions of this theory. The theory has enabled many researchers to develop and broaden the field of its use (Jiang, Claramunt & Klaqvist, 2000). This model directly enters the characterization of historic buildings and the field of archaeology. The work of Quentin Letesson (2009) applies it to the study of Minoan cities of the Bronze Age, Hamouda et al. (2021) apply it to Domus in north Africa, Peter Eeckhout (2013) applies it to the complexes of the cities of the pre-Hispanic Andes, and Eric Duprè-Moretti (2019) extends the concept onto a more global notion, which is that of the anthropization of a mountain according to the movement or dynamic response to the rules emanating from a community.
In terms of architecture, it is a matter of creating a justified graph that can be created by Agraph and which brings out the existence of zones of occupation and of hierarchical movement effects between them. This hierar-chy refers to control, freedom, tightness or permeability between different kinds of users. The method can be approached by VGA (visibility graph analysis) that is "the analysis of the set of isovists of a spatial system" (Turner, Doxa, O'Sullivan & Penn, 2000), which has had its source in the work of Benedikt (1979). Through Depthmap, this analysis allows (Turner, 2004) to calculate several configurational properties (connectivity, integration, depth, and control…) and presents the different components of the space on a plan, with shades of colours ranging from blue for low values to red for high values. The strong point of this analysis is the possibility of correlating the visual access of an environment with human preferences in reality (Hillier, 2007) by transforming them into numerical values that make it possible to deduce the social representations of the spaces studied (Hillier & Vaughan, 2007). The configurational properties provide various measures which provide information on the degree of intelligibility of the spaces studied, in order to properly orient and guide the user in his movement in an urban or inhabited space according to these morphological and spatial characteristics (Turner & Penn, 2002).
Integration is a static aggregate measure that measures the ease of reaching that space from any other space in the overall spatial arrangement. It is also an indicator of co-presence which promotes social interactions. From then on, integrated spatial systems generate evolution in social relations by allowing new encounters, while segregated systems are used in conservative modes responsible for structuring and reproducing pre-existing social statuses (Arab & Mazouz, 2018).
Connectivity is a static local metric that indicates the number of connections a space has in relation to other surrounding spaces (Jiang & Claramunt, 2002).
Control is a measure allowing the evaluation of the spatial control potential that a cell exerts locally over the surrounding spaces (Letesson, 2009). Mean depth provides information on the depth or shallowness of each cell by counting how many steps separate it from the initial space. It is used to calculate the number of steps in the space system (Assassi & Mebarki, 2021).
The basic models of a justified graph refer to the symmetry/asymmetry variables relating to the form of integration, and to the distributivity/non-distributivity variables relating to the form of control. 4 The shape of the graph varies according to the four types of representation to highlight a circulation system in the studied set and to identify the distribution and symmetry, or non-distribution and asymmetry, of the structures or cells contained in this set: a-type: single bond or dead-end-space; b-type: multiple links serving type a, which denotes a strong round trip flow control through the same point; c-type: multiple links on a single ringy path with therefore a different choice of return path; dtype: multiple links comprising at least two rings indicating a less controlled flow with a large choice of outward or return routes and the topological depth of the different elements (Duprey-Moretti, 2019).
Space syntax theory makes the connection between the physical form of space and its social significance through two parameters: perception and action, which are the basis of human behaviour, and especially in the social aspect, environmental and cognitive.
case study
The palace of Khdewedj El Amia is located in the centre of the city of Algiers (capital of Algeria) in the district of the lower Kasbah (Figs. 2-3).
The first space to be introduced upon entering in this palace is the space locally called "sqifa" (Fig. 1), decorated with a fountain once used for ablutions of guests. This entrance is majestic with its marbled, twisted columns, decorated with an acanthus leaf and opening onto a second "sqifa", bordered by a series of benches. "This is where people waited before being introduced to the Dey." We also notice a huge silo, "the mekhzen", where wheat and grains were stored at the time. The floors open onto the sun-drenched patio "waste'dar". Marbled and twisted col-umns, walls covered with earthenware in the colours of ochre yellow, emerald green and Egyptian blue. Stairs lead to the different floors with four bedrooms each, where we discover the ballroom, the most spacious in the palace. Under colonial administration, the space underwent transformation such as the laying of parquet floors, the installation of French windows and a fireplace. The stucco lace ceiling and openwork domes covered with glass roofs are additions (Mouffok, 2018).
The plan is formed by two wings (Fig. 4), each organized around a patio, probably revealing that the palace is the result of the twinning of two contiguous buildings and that the two entities have undergone several transformations to give the current form.
resuLts
The spatial organization of buildings is strongly correlated with the model of use and occupation of different spaces. It directs the flow of movement and orientation of individuals within a physical environment (Cuisenier, 1991; Hillier et al, 1993;Turner & Penn, 2006). The simulation results of the spatial analysis made on the basis of the modelled plans of the palace, using DEPTHMAP and AGRAPH, shall be studied according to the degree of depth of connectivity, integration and control.
Visual analysis
• Visual integration -The syntactic map of integration of the ground floor of the Kh- • Visual connectivity -Through the reading of the visual connectivity map corresponding to the VGA analysis, a strong correspondence between the maximum results obtained in the integration map of the first level, peaks in the degree of connectivity scattered over the gallery considered to be the main space (Fig. 6). The spaces that represent the highest connectivity values are the open spaces located on the lateral sides of the patios, as well as the terrace of the second floor which does not observe any obstacles and therefore has one of the best connectivity in the plan. The second level connectivity map shows values that do not have the same distribution of integration values, the most connected space coincides with the first gallery which welcomes upon the arrival of a person rising from the stairs. The more you move from the patio to the surrounding rooms, the more the connectivity of the spaces decreases. For the third level, the ballroom is the most connected space. The value is also important at the level of the gallery which borders this same clearly privileged space. As for the two other floors, the less connected spaces are the deepest ones, which puts them in hiding in relation to the visual field of the users. Spaces with the highest connectivity values are expected to be more accessible from different directions and may offer more possibility of orientation choice for users, so these spaces are expected to be used more often than others.
• Visual control -The palace control chart presents results very similar to those ob-dewedj El Amia palace shows maximum values of integration at the level of the gallery and the "Sqifa", which is a static functional space. The degree of integration is clearly repeated at two levels ( Fig. 5), going towards the extension that the original palate underwent. The gallery which connects these spaces seems to be strategic because it both allows having a distant view from the entrance and gives access to many important spaces. The spaces that exhibit the most segregated values of integration are located at all the ends of the palace and correspond with the interior of the rooms as well as the storage spaces. For the second level, a single room offers a considerable degree of integration in its heart. This space is clearly a privileged room (living space) as its dimensions are larger than the rest of the rooms and its spatial characteristics allow the visibility only once inside.
The integration map obtained from the third level VGA analysis shows two considerable integration peaks occupying the two sides of the room transformed into the ballroom during the French occupation. It was the living space of the first floor. This space seems to be remarkably strategic by: the absence of physical obstacles and its opening onto the gallery which opens onto the patio on the lower level, as well as by the dimensions of this room in relation to the rest. At the same time, other spaces with an additional function are segregated and they are characterized by the impermeability responding to their social character of intimacy. tained in the two previous analyses (Fig. 7). The most integrated spaces of the building's spatial system are most connected and at the same time those with the highest values of control. These spaces are clearly located at the level of sqifas, circulation spaces, and at the intersections of passages. For the assimilation of the degree of control, we wish to underline that for the three floors the spaces which have the highest values are the spaces controlling the spatial system. These are in parallel the most integrated and visually connected with respect to the other spaces having minimal degrees of controls. These characteristics mean that each locally connected space can be globally integrated into the entire spatial system, which means that these spaces are most passed through, travelled, chosen, and used by users, and are meant to be the places that facilitate all tasks relating to orientation.
QuantitatiVe analysis
To refine the analysis, Agraph software was used to give more detailed results for each convex space constituting the system. Each level was translated into a justified graph from which the numerical values of the depth, integration and control of each space were highlighted. The justified graph is more complex compared to those of other levels, it is an amalgamation of tree and ring configurations; symmetric, asymmetric, distributed and non-distributed with a distributive index of (0.91) and a symmetry index of (1.1). These are very low values and the asymmetric non-distributed configuration wins out.
Two access points inside, probably a main entrance and a secondary service entrance offering quite a lot of flexibility in terms of traffic and consequently losing control potential. From the main entrance, a sequence of b-type spaces (sqifas) is deployed in a distributed asymmetric system attesting to the existence of a subtle and complex management of circulation to differentiate the interface between residents and between residents and visitors. The distribution is local and manifests itself at the level of the bedrooms and the kitchen with a local effect and accentuating the segregation of these spaces.
External ringy configuration is an annularity that only exists with regard to the relationship between interior and exterior and is often considered a powerful interpretive vector, especially with regard to the relationships between residents and visitors. This ring is notably made up of sqifas (first space of access to the interior in the Arab Muslim culture) and galleries as spaces of transitions and they are the most important spaces in terms of the me-diation between the two internal and external spheres and it is an important pivot of circulation within the building (Hillier & Hanson: 1984, Letesson: 2009). An annular system can have two essential functions overall: it can offer various choices of movement to people living there, but it is also used to ''register within the building the different circulation models of the different user groups (Hanson, 1998). The service access is controlled by the sqifa while the main access is controlled by the succession of two elbow-shaped sqifas, emphasizing the desire to establish a clear line between the inside and outside and an enormous concern for control. From the first sqifa to the second gallery, the control value increases exponentially (Fig. 8 and Table I).
The gallery 1 is the most integrated space and illustrates the concept of spatial solidarity, it articulates the circulation to the other rooms and by its layout offers a framework particularly suited to meetings between residents, but especially to the reception of visitors who are much more controlled by gallery 2, which shows the highest control rate of (4.36) and serves the upper levels probably occupied by the blind princess.
The second level displays a tree-justified, non-distributed and symmetric graph at each depth level with a very high distributive index of around 17 and a very low symmetry index of around 1.42. B-type spaces exert a certain potential for control; first are the stairs, then the gallery on a global scale and then the rooms on a local scale (Table II).
First floor Second floor
Third floor Fourth floor The symmetrical tree structure means that there is a tendency to integrate social categories which target the relationship between residents and non-distribution indicates a trend towards a super-ordered unitary control. It is the domain of the inhabitants with very strong sanctions against the penetration of visitors. Within such a structure the circulation options are minimal.
Access to this level is via the stairs which display the highest control value followed by the gallery (Fig. 9). This transition space, being a generator of symmetry, helps to isolate the cells constituting the floor, without blocking communication between them by being a pole of convergence. Four main rooms are served by the gallery, each occupies one side of the square, three of which have a succession of spaces in a "Russian doll" type model, which allows extraordinary mastery of the degree of control authorized in each room of the palace and thus master the connectivity desired for each type of visitor. In the first level, galleries, sqifas and courtyards display the highest degree of integration (i) and control (CV) and lowest degree of depth (MDn), compared to rooms and other additional spaces. The third level of the palace has less spaces and displays a non-distributed asymmetric justified graph with a tree structure at the fourth level of depth (Table III), showing a symmetry whose pole of convergence is the gallery which overlooks the central courtyard and which has the highest control value (Fig. 10). Generator of symmetry, this space helps to isolate certain activities from one another, but by being a powerful vector of circulation. The global configuration can immediately be referred to through the concept of trans spatial solidarity, i.e. a form of solidarity achieved through the control of categories in isolation rather than the interpenetration of categories through spatial contiguity and random movement (Hillier & Hanson, 1984). The rooms evolve asymmetrically just like the second level with the presence of a trivial ring with local effect connecting two rooms between them. According to Fig. 10, the circulation spaces are the best integrated ones in the system and ensure the highest controllability effect, while other spaces display balanced degrees of depth integration and control, forming occupancy spaces with local movements according to the configuration of the space giving a more private aspect to these spaces.
The terrace, on the fourth level, as an openair space, has a privileged location in the spatial distribution of the palace, at its level, it is superficial, very well integrated and exerts strong control over the movements that lend themselves to it (Fig. 11). The justified graph (Table IV) is strongly asymmetric and nondistributed. Cell organization with simple linear sequencing of b-type spaces is a way of configuring a building for the sake of maintaining a certain distance from the outside world and compared to other levels of the palace.
discussion
According to the justified graphs of different floors, the one on the ground floor stands out from the others by its annular configuration which is used to give the user the choice of movement and the possibility of a freer exploration of the interior of the building (Han-son: 1998). Namely, an annular system is a distributed system, that is to say, it is a set of spaces through which the visitor can pass, subject to more or less extensive control (Hillier & Hanson: 1984). This gives it the public character of the fact that it favours the residents / visitors interface. At the higher levels, the privacy prevails and is illustrated by the asymmetric tree configuration of the justified graphs and the sequential movement which refers more directly to the sphere of relations between residents (Hanson: 1998) and the strict control of movement.
The first observation relates to the role that intimacy and the social framework play in the spatial configuration and the characterization of its integrative properties. The spatial configuration of the terraces rejects it to integrate with the rest of the house, but all very well controlled from the inside of the building.
For the bedrooms, the result in relation to this space mainly relates to the role that the transparency of the gallery overlooking the patio of the palace plays in improving the configurational properties of the space. The situation of a hardly visible space, and little connected, integrated or more controlled by the rest, gives a hidden spatial image. In the background it can be intended for a function requiring these needs for depth and intimacy.
According to Rachel Thomas, locomotion without vision follows the following modes of movement: crossing, avoiding obstacles, entering or leaving a space, ensuring its positioning and the straightness of movement. In this sense, it should be understood that the tree-like organization, strongly adopted from the second level, is a relatively elementary way of configuring a building for the sake of maintaining a certain distance from the external world, as well as for the sake of establishing a clear architectural framework, easy to read and less ambiguous to use, especially for the blind. In the case of the tree like system, the poles of convergence are generally formed by a symmetrical arrangement of subordinate cells with an occupational character of a-type to b-type pivot space (gallery; Letesson, 2009). Being of public use the first level, the annular configurations of the first level multiply and highlight the resident-visitor interface. The resident of the palace, in this case Khdewedj El Amia, should probably use the upper floors which are easily understood, compared to the first level which is used by the staff working in the palace. This study was carried out with the main objective of revealing the sensitive dimension of the palace architecture dating from the 16 th century and intended for a blind person in order to compensate for this lack through a pleasant space to live in. Another objective was to show how an ordinary perception reveals the vernacular space in its constructed and sensitive qualities.
Indeed, all you have to do is put your foot in it to confirm the feeling of a real living space providing total pleasure, preventing a sighted or blind user from falling into a feeling of insecurity or disorientation. The way in which the spaces were distributed according to the social logic of the era affected the human sensory as well as bodily experience. The succession of the baffled "sqifa" spaces facilitates the gradual control of movement within the palace, by allowing visitors to enter the space while preventing them from going further inside and reaching the private spaces. The transparency of the courtyard ensures the second degree of control. In fact, the galleries which surround it are very well connected to the private spaces with the right angles and affecting a bedroom at each side of the square of the patio. The bedrooms themselves exercise the third degree of control over the niches: spaces annexed to the bedrooms which should have more intimate functions.
The methodological process adopted is an approach that seems most appropriate and that has quickly made it possible to extract the configurational characteristics of a building with a specific destination. The syntactic analysis with Depthmap and Agraph gave the opportunity to know the tendencies of a user in terms of movement in a space and the choice of route in relation to the spatial connectivity offered to him. The characteristics and properties of static spaces with a degree of control, integration, and high connectivity, must be exploited to provide a space that is easy to decipher and less ambiguous to use. | 6,729.8 | 2021-01-01T00:00:00.000 | [
"Linguistics",
"History"
] |
Measurement of Groomed Jet Substructure Observables in \pp Collisions at $\sqrt{s} = 200$ GeV with STAR
In this letter, a comprehensive suite of jet substructure measurements via the SoftDrop algorithm, including the shared momentum fraction ($z_{\rm{g}}$) and the groomed jet radius ($R_{\rm{g}}$), are reported in \pp collisions at $\sqrt{s} = 200$ GeV collected by the STAR experiment. These substructure observables are differentially measured for jets of varying resolution parameters from $R = 0.2$ to $R = 0.6$ and transverse momentum range $15<p_{\rm{T, jet}}<60$ GeV$/c$. These studies show that, at RHIC kinematics with increasing jet resolution parameter and jet energy, the $z_{\rm{g}}$ distribution asymptotically converges to the DGLAP splitting kernel. The groomed jet radius measurements reflect a momentum-dependent narrowing of the jet structure for jets of a given resolution parameter, i.e., the larger the $p_{\rm{T, jet}}$, the narrower the first split. For the first time, these fully corrected measurements are compared to leading order Monte Carlo generators and to state-of-the-art theoretical calculations at next-to-leading-log accuracy. We observe that RHIC-tuned PYTHIA 6 is able to quantitatively reproduce data whereas the LHC-tuned event generators, PYTHIA 8 and HERWIG 7, are unable to provide a simultaneous description of both the $z_{\rm{g}}$ and $R_{\rm{g}}$, resulting in opportunities for fine parameter tuning of these models in \pp collisions at varying collision energies. We also find that the theoretical calculations without non-perturbative corrections are able to qualitatively describe the trend in data for jets of large resolution parameters at high $p_{\rm{T, jet}}$, but fail at small jet resolution parameters and low jet momenta.
Abstract
In this letter, a comprehensive suite of jet substructure measurements via the Soft-Drop algorithm, including the shared momentum fraction (z g ) and the groomed jet radius (R g ), are reported in p+p collisions at √ s = 200 GeV collected by the STAR experiment. These substructure observables are differentially measured for jets of varying resolution parameters from R = 0.2 to R = 0.6 and transverse momentum range 15 < p T,jet < 60 GeV/c. These studies show that, at RHIC kinematics with increasing jet resolution parameter and jet energy, the z g distribution asymptotically converges to the DGLAP splitting kernel. The groomed jet radius measurements reflect a momentum-dependent narrowing of the jet structure for jets of a given resolution parameter, i.e., the larger the p T,jet , the narrower the first split. For the first time, these fully corrected measurements are compared to leading order Monte Carlo generators and to state-of-the-art theoretical calculations at next-to-leading-log accuracy. We observe that RHIC-tuned PYTHIA 6 is able to quantitatively reproduce data whereas the LHC-tuned event generators, PYTHIA 8 and HERWIG 7, are unable to provide a simultaneous description of both the z g and R g , resulting in opportunities for fine parameter tuning of these models in p+p collisions at varying collision energies. We also find that the theoretical calculations without non-perturbative corrections are able to qualitatively describe the trend in data for jets of large resolution parameters at high p T,jet , but fail at small jet resolution parameters and low jet momenta.
Introduction
Jets are well-established signals of partons, i.e., quarks and gluons, created in the hard scatterings during high energy hadron collisions [1]. Jets have played a prominent role as an internal probe of partonic energy loss mechanisms in the quark-gluon plasma created in heavy-ion collisions. Refer to [2] and [3] for recent reviews of the experimental measurements and theoretical calculations on jet quenching. An important prerequisite of such studies is a quantitative understanding of jet properties related to its production, evolution and hadronization. The production of hard scattered partons is governed by 2 → 2 quantum chromodynamics (QCD) scattering at leading order (LO) and 2 → 3 at next-to-leading order (NLO), and is calculable using Parton Distribution Functions (PDFs) [4], which are extracted with fits to experimental measurements, including but not limited to jet cross-sections at various kinematics. Given a hard scattered parton, the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) splitting kernels [5,6,7] describe its evolution and fragmentation based on perturbative quantum chromodynamics (pQCD). At LO, the DGLAP splitting functions of a parton in vacuum are dependent on the momentum fraction of the radiated gluon and the corresponding angle of emission. The most efficient way for a highly virtual/off-shell parton to lose its virtuality is via consecutive radiation/splitting (for example q → q+g), resulting in a parton shower. Due to the double logarithmic structure of the splitting kernels and color coherence in the QCD, the evolution is expected to follow an angular or virtuality ordered shower. Such an ordering implies that the earliest splits are soft and wide in angle with the harder (referring to a high momentum radiated gluon) collinear splits happening later during jet evolution. Therefore, this process can be described by two natural scales: the split's momentum fraction and its angle with respect to the parton direction which, in turn, describe jet structure in vacuum. The primary focus of this letter is to study QCD and parton evolution in p+p collisions at RHIC. We establish a quantitative description of jet substructure that can serve as a reference for comparison to similar measurements in heavy-ion collisions where jet properties are expected to be modified due to jet quenching effects.
In this letter, we present fully corrected measurements of the SoftDrop groomed momentum fraction (z g ) and the groomed jet radius (R g ) in p+p collisions at centerof-mass energy √ s = 200 GeV. They allow a direct measurement of the DGLAP splitting functions during jet evolution. These measurements emerge as a "by-product" of the modified mass drop tagger or SoftDrop [8,9,10] grooming algorithm, used to remove soft, wide-angle radiation from sequentially clustered jets. This is achieved by recursively de-clustering the jet's angular-ordered branching history via the Cambridge/Aachen (C/A) clustering algorithm [11,12], which sequentially combines nearest constituents, i.e., those located closest in angle. Subjets are discarded until the transverse momenta, p T,1 and p T,2 , of the subjets from the current splitting fulfill the where R g is the groomed jet radius or a measure of the distance as defined in pseudorapidity-azimuthal angle (η − φ) space between the two surviving subjets and R is the jet resolution parameter. This analysis sets β = 0 and a momentum fraction cut of z cut = 0.1 [9] to determine if a subjet at a given clustering step survives the grooming procedure. The z cut parameter is set to reduce sensitivity to non-perturbative effects arising from the underlying event and hadronization [9,13]. It has been shown that for such a choice of z cut and β, along with the usage of the C/A algorithm for de-clustering, the distribution of the resulting z g converges to the vacuum DGLAP splitting functions for z > z cut in a "Sudakov-safe" manner [10], i.e., independent of the strong coupling constant (α s ) in the ultraviolet (UV) limit and under the fixed coupling approximation. Since the splitting kernels are defined to be independent of the momenta of initial partons, the UV limit corresponds to a jet of infinite momentum.
The SoftDrop z g was first measured by the CMS collaboration in p+p and Pb+Pb collisions at √ s NN = 5.02 TeV at the LHC for highly energetic jets with p T,jet > 140 GeV/c [14]. As the measurements are not corrected for smearing due to detector effects and resolution in Pb+Pb, the Monte Carlo (MC) generators, such as PYTHIA 6 [15], PYTHIA 8 [16] and HERWIG++ [17,18], are smeared instead to make meaningful comparisons. Due to the granularity of the CMS calorimeter, a R g > 0.1 threshold was enforced which consequently introduced a bias towards wider jets in the study [19]. It was shown that event generators at the LHC generally reproduce the trend in p+p collisions, but individually, neither PYTHIA 8 nor HERWIG 7 were able to quantitatively describe the measurements within systematic uncertainties. The large center-of-mass energies at the LHC increases NLO effects in jet production and fragmentation along with an increased sensitivity to multi-parton interactions and pileup. On the other hand, due to their large jet p T , the measurements are less sensitive to the hadronization process and higher-order power corrections [20,21] due to a small α s .
The p+p collisions at RHIC provide a complementary environment to study the jet structure and parton evolution. Due to the reduced center-of-mass energy (200 GeV as compared to 5.02 TeV), the study offers further insights regarding jet evolution by exploring different contributions of NLO effects and hadronization. For example, the higher-order effects in jet production at RHIC are suppressed compared to the LHC, while jets at RHIC are more susceptible to non-perturbative effects such as multi-parton interactions, the underlying event and hadronization effects by virtue of their kinematics at lower energies. Some of these effects are negated by the SoftDrop grooming procedure [20]. Jets used in this analysis are minimally biased since no additional selections are applied to the angular threshold. The measurements are fully corrected for detector response via a two-dimensional unfolding procedure. Thus in this letter, for the first time we present fully corrected jet substructure measurements at RHIC that are complementary to the LHC measurements. Additionally, they serve as a crucial baseline for tuning event generators, validating state-of-the-art theoretical calculations of jet functions, and for using similar measurements in heavy-ion collisions to extract medium-modified parton dynamics.
Experimental Setup and Jet Reconstruction
The data analyzed in this letter were collected by the STAR experiment [22] in jets that pass the SoftDrop criteria are then considered for the study.
Detector Simulation and Unfolding
In order to study the response of the STAR detector to jet substructure observables, p+p events at √ s = 200 GeV are generated using the PYTHIA 6.4.28 [15] event generator with the Perugia 2012 tune and CTEQ6L PDFs [26]. The PYTHIA 6 used in this analysis was further tuned to match the underlying event characteristics as measured by STAR in a recent publication [27]. These generated events are then passed through a GEANT3 [28] simulation of the STAR detector and embedded into zero-bias data from the same p+p run period. With the GEANT simulated PYTHIA 6 events, identical analysis procedures including event and jet selection criteria mentioned in Sect. 2 are implemented. Jets that are found from PYTHIA 6 simulations before and after the embedding procedures are hereafter referred to as particle-level and detector-level jets, respectively. The long-lived weak-decaying particles, which are not included in the jet finding at the particle level, are simulated in the event generation, and their decay prod- ucts are included in the detector-level jets as in real data analysis. The STAR detector response to a jet is estimated by comparing the properties of a PYTHIA 6 particle-level jet with its geometrically matched detector-level jet based on the following matching criterion, (∆η) 2 + (∆φ) 2 < R, where the ∆ refers to the difference between the detector-and particle-level jets in the same event and R is the jet resolution parameter.
With our jet quality selections, we have about 2% of detector-level jets with p det T,jet > 15 GeV/c that cannot be matched to particle-level jets. On the other hand, the jet finding efficiency for particle-level jets varies within 80-94% for 15 < p part T,jet < 60 GeV/c. The two dimensional p T,jet response matrix for R = 0.4 jets is shown in Fig. 1, in which the filled markers represent the average detector-level p det T,jet for a given particle-level p part T,jet . In comparison to the dashed diagonal line in Fig. 1, we find the mean p det T,jet to be smaller than the corresponding p part T,jet primarily due to tracking inefficiency. For the jet substructure observables, the detector response is shown in Fig. 2, plotted as the ratio of detector-level jet quantity to the matched particle-level jet quantity for a variety of p det for detector effects via a two-dimensional (e.g., p T,jet and z g ) unfolding procedure. Fig. 3 for z g on the left and R g on the right. The bottom panels show the ratio of simulation to data where we observe a good agreement. In comparing the particle-level and detector-level PYTHIA 6 distributions, we see small but statistically significant differences due to the detector response which we correct for via an unfolding method described below.
The SoftDrop z g and R g distributions in this analysis are unfolded to the particle level to correct for detector effects including smearing and bin-by-bin migration. The fact that the detector response peaks at unity and is independent of p T,jet , as shown in Fig. 2, generates a more diagonal unfolding matrix in 4 dimensions (i.e., detector-and particle-level p T,jet and z g or p T,jet and R g ). Two-dimensional Bayesian unfolding [29] is done using the tools available in the RooUnfold package [30] with four iterations to take into account non-diagonal bin-to-bin migrations both in jet p T and SoftDrop observables. As a consequence of the detector simulation reproducing the uncorrected data as shown in Fig. 3, the unfolding procedure converges and is numerically stable.
The priors in the unfolding procedure are taken from the PYTHIA 6 simulation and their variations are studied as a source of systematic uncertainty.
Systematic uncertainties
There are two main categories of systematic uncertainties considered in this analysis. The first is related to the reconstruction performance of the STAR detector, including the uncertainty on the tower gain calibration (3.8%) and the absolute tracking efficiency (4%). The other source of systematic uncertainty is due to the analysis procedure, i.e., the use of hadronic correction (as described in Sec. 2) and the unfolding procedure. The correction to the tower energy, based on the matched tracks' momenta, is varied by subtracting half of the matched tracks' momenta from their corresponding tower E T . With regards to the unfolding procedure, the uncertainties include the variation of the iteration parameter from 2-6 with 4 as the nominal value, and a variation of the input prior shape for z g , R g and p T individually by using PYTHIA 8 and HERWIG 7. We estimated the effect of different sources on the final results by varying the detector simulation, following the same unfolding procedure and comparing to the nominal result. Since we are reporting self-normalized distributions, the luminosity uncertainty with respect to the data-taking is not considered. The total systematic uncertainties for the z g and R g measurements, calculated by adding individual sources in quadrature, are presented in Tab. 1 and 2 for R = 0.4 jets in 20 < p T,jet < 25 GeV/c range. For both measurements, the largest systematic uncertainty results from the unfolding procedure.
The total systematic uncertainties for these softdrop observables decrease slightly as the jet resolution parameter increases.
Results
The fully corrected z g and R g measurements are compared to leading order event generators, PYTHIA 6, PYTHIA 8 and HERWIG 7. Since our PYTHIA 6 events do not include weak decays at the particle level, we generate PYTHIA 8 and HERWIG 7 events with the same requirement. We note that for the observables discussed in this letter, we do not observe a significant effect due to weak decays. The parton shower implementations are varied amongst the models, with PYTHIA 6 and PYTHIA 8 featuring virtuality ordered shower in contrast to HERWIG 7 with angular ordering. The description of the underlying event in PYTHIA 6 is based on the Perugia 2012 tune [31] and further tuned to match data from RHIC whereas PYTHIA 8 uses the Monash 2013 tune which was based on the LHC data [32]. The HERWIG 7 calculations use the EE4C underlying event tune [33] appropriately scaled for the collision energy at RHIC.
The fully corrected z g measurements for jets of varying p T,jet are compared to MC predictions as shown in Fig. 4. In addition, we show the symmetrized DGLAP splitting function at leading order for a quark emitting a gluon as the red dashed lines. The different panels represent jets with low p T,jet in the top middle and high p T,jet in the bottom right. We observe a more symmetric splitting (larger mean z g or, consequently, a flatter shape) function at lower p T,jet that gradually tends towards more asymmetric (smaller mean z g ) at higher p T,jet . The measurements also indicate a p T,jet -independent z g shape slightly steeper than the theoretical limit around p T,jet > 30 GeV/c within our kinematic range. With symmetric splitting functions, the probability to radiate a high-z gluon (where z is defined as the radiated object's energy fraction with respect to the original parton) is enhanced as opposed to an asymmetric splitting function dominated by low-z emissions. This evolution from a symmetric to asymmetric splitting function with increasing p T,jet is consistent with pQCD expectation wherein, a high-momentum parton has an enhanced probability to radiate a soft gluon. Such behavior is captured by both angular and virtuality ordered parton shower models. With default hadronization turned on, PYTHIA 6, PYTHIA 8 and HERWIG 7 describe the qualitative shape as observed in these measurements. To compare more quantitatively, the bottom panels show the ratio of the model calculations to data, and the shaded red region represents the total systematic uncertainty in data. Both PYTHIA versions are able to describe the z g measurements. However, HERWIG 7 seems to prefer more symmetric splits, especially at larger p T,jet .
The SoftDrop R g for R = 0.4 jets are presented in Fig. 5. The R g shows a momentumdependent narrowing of the jet structure as reflected in a shift to smaller values as the jet momentum increases. The measured R g distributions are qualitatively reproduced by all event generators. In contrast to the observations from the z g measurement, HER- WIG 7 shows a slight tendency towards smaller R g , while PYTHIA 8 prefers a systematically wider R g distribution. For R = 0.4 jets, PYTHIA 6 is able to quantitatively describe data, whilst neither PYTHIA 8 nor HERWIG 7 is able to explain both z g and R g observables simultaneously within the experimental systematic uncertainties.
We further measured the splitting by varying the jet resolution parameter R as shown in Fig. 6 and Fig. 7 for the z g and R g , respectively. The left, middle and right panels represent R = 0.2, 0.4 and 0.6 jets. The top row is for jets with 15 < p T,jet < 20 GeV/c and the bottom row for jets with 30 < p T,jet < 40 GeV/c. Jets with smaller resolution parameters and at lower p T,jet display stronger z g shape modification with respect to the ideal DGLAP splitting and do not reproduce the characteristic 1/z shape seen at higher p T,jet . The narrowing of the R g with increasing p T,jet becomes more significant for jets of larger resolution parameters. The flattening of the z g shape for jets with R = 0.2 and low p T,jet are due to the stringent kinematic constraints on the phase space available. This observation is evident by the R g ranges seen in the top left panel in Fig. 7, for the splitting that is a direct consequence of virtuality/angular ordering.
The dashed black curve shows the z g and R g distribution from PYTHIA 8 events without hadronization (parton jets). We find that hadronization, as described in PYTHIA 8, tends to create softer z g or more asymmetric splits. In contrast, we observe the apparent robustness of the R g observable against hadronization effects.
Due to recent advances in theoretical calculations regarding jets of small resolution parameters and low momenta [34,35], we can now compare our fully corrected data to predictions at next-to-leading-log accuracy in Fig. 8 for z g (left panels) and R g (right panels). The systematic uncertainty in the theoretical calculations (gray shaded band) arises from QCD scale variations, including the p T -hard scale, the jet scale (p T,jet · R) and the scales associated with the substructure observables mentioned here [34]. We note that the systematic uncertainties for the calculations are large for the kinematic range studied in this measurement. These predictions are for jets at the parton level without non-perturbative corrections. This is one possible reason why the comparison to data at low jet momenta and small jet resolution parameter exhibits large deviations in the z g . On the other hand the predictions for the R g observable show large discrep- ancies with the data for all of the jet resolution parameters and kinematics except the largest resolution parameter and highest p T,jet where the shape gets close to the data.
These comparisons highlight the need for more realistic calculations, including corrections arising from non-perturbative effects and higher-order corrections to further understand jet substructure more quantitatively.
Summary
In summary, we presented the first fully corrected SoftDrop z g and R g measurements of inclusive jets of varying resolution parameters with 15 < p T,jet < 60 GeV/c in p+p collisions at √ s = 200 GeV. The z g distribution converges towards an approximately p T,jet -independent shape above 30 GeV/c which is slightly more asymmetric than the idealized UV limit. On the other hand, the R g reflects a momentum-dependent narrowing of the jet structure. We observe that lower momentum jets are more likely to have a wider jet structure with more symmetric splitting within the jet. This behavior reverses for higher p T,jet jets wherein they are narrower and dominated by asymmetric splits. We also note that at small jet resolution parameters and low p T,jet , the z g is sensitive to hadronization effects resulting in a significant enhancement of asymmetric splitting, whereas for larger resolution parameters, 0.4 and 0.6, the effect is moderate and only results in a minor (shape) change towards more asymmetric splitting. The SoftDrop R g is observed to be less sensitive to hadronization. For both the measurements presented in this letter, we observe that the RHIC-tuned PYTHIA 6 is able to reproduce data whereas PYTHIA 8 and HERWIG 7 are unable to simultaneously describe both scales of the jet evolution. We also showed comparisons to theoretical calculations that extend the predictive power of pQCD at jet scales closer to the fundamental QCD scale, i.e., for jets with small momenta and resolution parameters. Such comparisons to data highlight the need for continued theoretical studies into the exact interplay between measured hadronic jet substructure observables and the underlying partonic splitting at RHIC energies. These studies offer a unique opportunity to further tune MC event generators and for understanding higher order effects on jet evolution at RHIC kinematics. | 5,303.2 | 2020-03-04T00:00:00.000 | [
"Physics"
] |
Predicting single-cell cellular responses to perturbations using cycle consistency learning
Abstract Summary Phenotype-based drug screening emerges as a powerful approach for identifying compounds that actively interact with cells. Transcriptional and proteomic profiling of cell lines and individual cells provide insights into the cellular state alterations that occur at the molecular level in response to external perturbations, such as drugs or genetic manipulations. In this paper, we propose cycleCDR, a novel deep learning framework to predict cellular response to external perturbations. We leverage the autoencoder to map the unperturbed cellular states to a latent space, in which we postulate the effects of drug perturbations on cellular states follow a linear additive model. Next, we introduce the cycle consistency constraints to ensure that unperturbed cellular state subjected to drug perturbation in the latent space would produces the perturbed cellular state through the decoder. Conversely, removal of perturbations from the perturbed cellular states can restore the unperturbed cellular state. The cycle consistency constraints and linear modeling in the latent space enable to learn transferable representations of external perturbations, so that our model can generalize well to unseen drugs during training stage. We validate our model on four different types of datasets, including bulk transcriptional responses, bulk proteomic responses, and single-cell transcriptional responses to drug/gene perturbations. The experimental results demonstrate that our model consistently outperforms existing state-of-the-art methods, indicating our method is highly versatile and applicable to a wide range of scenarios. Availability and implementation The source code is available at: https://github.com/hliulab/cycleCDR.
• Training set: there are 73,222 samples in total, including 6,309 drugs and 42 cell lines.
• Validation set: there are 9,152 samples, including 3,003 drugs and 37 cell lines.This set served as an intermediate evaluation tool during training, facilitating parameter adjustments and mitigating the risk of overfitting.
• Test set: there are 9,152 samples, including 2,954 drugs and 40 cell lines.This set was employed to assess the final performance of the trained model.
S2 Proteomic response to drug
The RPPA dataset include 3520 samples in total, covering 156 unique drugs and 363 cell lines.We identified the cell lines exhibiting significant protein level changes compared to unperturbed cell lines, and randomly partitioned these cell lines to validation and test sets in 1:1 ratio.The remaining samples consists of the training set.Finally, we obtained the training, validation and test set as below: • The training set comprises 2816 samples involving 52 drugs and 121 cell lines.
• The validation set consists of 352 samples regarding 52 drugs and 121 cell lines.
• The test set includes 352 samples, spanning 52 drugs and 121 cell lines.
S3 Single-cell transcriptional response to drug
The sci-Plex3 dataset comprises 218,086 samples (drug-cell pairs), spanning 187 drugs and 3 cell lines.We followed a similar approach to chemCPA by allocating all cells treated with 9 drugs exclusively to the test set, ensuring that there is no overlap of these drugs between the training and test sets.This allows us to evaluate the model's ability to generalize to novel drugs.We identified the cells exhibiting significant gene expression changes compared to unperturbed cells, and randomly partitioned these cells to validation and test sets in 1:1 ratio.The remaining samples consists of the training set.Following data partition, we obtained the training, validation and test set as below: • The training set includes 195,558 samples , covering 178 drugs and all 3 cell lines.
• The validation set contains 14,634 samples, covering 178 drugs and all 3 cell lines.
• The test set consists of 7,894 samples, focuses exclusively on the 9 held-out drugs across all 3 cell lines.
The sci-Plex4 includes a total of 11,042 samples (drug-cell pairs), encompassing 17 unique drugs and 3 distinct cell lines.Similarly, we identified the cells exhibiting significant gene expression changes compared to unperturbed cells, and randomly partitioned these cells to validation and test sets in 1:1 ratio.The remaining samples consists of the training set.Following data partition, we obtained the training, validation and test set as below: • The training set includes 8,140 samples , covering 12 drugs and all 3 cell lines.
• The validation set contains 1,436 samples, covering 5 drugs and all 3 cell lines.
• The test set consists of 1,466 samples, focuses exclusively on the 5 held-out drugs across all 3 cell lines.
S4 Single-cell transcriptional response to gene perturbation
The Replogle et al. release the single-cell transcriptional responses to singlegene and multigene perturbations on K562 and RPE-1 cell lines.In our study, we consider only the single-gene perturbation data.Since most cells have limited response to gene perturbation, namely, most genes do not exhibit significant change in thier expression levels.To evaluate our model to capture the real response to gene perbutation, we identified the cells exhibiting significant gene expression changes compared to unperturbed cells, and randomly partitioned these cells to validation and test sets in 1:1 ratio.The remaining samples consists of the training set.The K562 dataset include a total of 116,050 samples (drug-cell pairs), encompassing 412 unique single-gene perturbation on one cell lines.Following data partition, the K562 dataset yield the training, validation and test set as below: • The training set includes 111,392 samples, covering 397 gene perturbations on one cell lines.
• The validation set contains 2,294 samples, covering 15 gene perturbations and one cell lines.
• The test set consists of 2,264 samples, focuses exclusively on the 15 held-out gene perturbations on one cell lines.
The RPE-1 dataset include a total of 129,608 samples (drug-cell pairs), encompassing 651 unique single-gene perturbation on one cell lines.Following data partition, the K562 dataset yield the training, validation and test set as below: • The training set includes 126,024 samples, covering 618 gene perturbations on one cell lines.
• The validation set contains 1,828 samples, covering 33 gene perturbations and one cell lines.
• The test set consists of 1,756 samples, focuses exclusively on the 33 held-out gene perturbations on one cell lines.
S5 Exploration of drug similarity influence on predictive performance
To explore the differences in prediction accuracy across different samples, we examined the similarity between training and test samples in the sci-plex4 dataset.Specifically, we considered each drug-cell line pair as a sample and calculated the similarity based on the induced gene expression profiles.We firstly computed the average values of the expression profiles across all cells of one type of cell line treated by a specific drug.The averaged profiles served as the representative for the drug-cell line sample.Subsequently, we calculated the cosine similarity.Figure 2a illustrates the similarity heatmap between the training samples (x-axis) and test samples (y-axis).Next, we employed the RDKit's Tanimoto algorithm to compute the chemical structure similarity between drugs.Figure 2b depicts the similarity heatmap for drugs in the training set (x-axis) versus those in the test set (y-axis).
Figure S4a clearly illustrated that the cell lines treated with Tucidinostat and Tacedinaline in the test set (denoted by green box) exhibited low similarity with the samples from the training set.In line with this observation, Figure S4b showed significant discrepancy in the chemical structures of these two drugs with those present in the training set (denoted by green box).The results imply a tendency for chemically similar drugs to induce similar gene expression profiles across the three cell lines studied.
We further check the model performance on these two drugs.Figure S4c presents the prediction results for the test set samples, with the x-axis representing cell linedrug samples and the y-axis denoting the r2 scores.Notably, the predictions for the samples associated with Tucidinostat and Tacedinaline are significantly lower than those for other samples.
Based on these observations, we hypothesize that the model is more accurate in predicting the effects of drugs with "seen" pharmacological properties during training stage.This discovery underscores the importance of incorporating drug diversity to enhance the predictive accuracy.Such findings offers a new perspective on understanding model prediction biases and provides valuable guidance for future model improvements.
Figure S1 :Figure S2 :
FigureS1: Performance evaluation on sci-plex4 single-cell transctiptional response dataset in the terms of r 2 and explained variance (EV) metrics.
Figure S3 :
FigureS3: The boxplots of r2 scores computed for individual genes across samples on sci-plex4 dataset.
Figure S4 :
Figure S4: Performance evaluation of sciplex4 single-cell transduction response data divided by drug combination.(a)illustrated the similarity heatmap between the training samples (x-axis) and test samples (y-axis).(b) depicted the similarity heatmap for drugs in the training set (x-axis) versus those in the test set (y-axis).
Table 1 :
Performance evaluation of sciplex4 single-cell transduction response data divided by cellular drug combinations. | 1,968.4 | 2024-06-28T00:00:00.000 | [
"Computer Science",
"Biology"
] |
Measurement of the Rheological Properties of High Performance Concrete: State of the Art Report
The rheological or flow properties of concrete in general and of high performance concrete (HPC) in particular, are important because many factors such as ease of placement, consolidation, durability, and strength depend on the flow properties. Concrete that is not properly consolidated may have defects, such as honeycombs, air voids, and aggregate segregation. Such an important performance attribute has triggered the design of numerous test methods. Generally, the flow behavior of concrete approximates that of a Bingham fluid. Therefore, at least two parameters, yield stress and viscosity, are necessary to characterize the flow. Nevertheless, most methods measure only one parameter. Predictions of the flow properties of concrete from its composition or from the properties of its components are not easy. No general model exists, although some attempts have been made. This paper gives an overview of the flow properties of a fluid or a suspension, followed by a critical review of the most commonly used concrete rheology tests. Particular attention is given to tests that could be used for HPC. Tentative definitions of terms such as workability, consistency, and rheological parameters are provided. An overview of the most promising tests and models for cement paste is given.
The rheological or flow properties of concrete in general and of high performance concrete (HPC) in particular, are important because many factors such as ease of placement, consolidation, durability, and strength depend on the flow properties. Concrete that is not properly consolidated may have defects, such as honeycombs, air voids, and aggregate segregation. Such an important performance attribute has triggered the design of numerous test methods. Generally, the flow behavior of concrete approximates that of a Bingham fluid. Therefore, at least two parameters, yield stress and viscosity, are necessary to characterize the flow. Nevertheless, most methods measure only one parameter. Predictions of the flow properties of concrete from its composition or from the properties of its components are not easy. No general model exists, although some attempts have been made. This paper gives an overview of the flow properties of a fluid or a suspension, followed by a critical review of the most commonly used concrete rheology tests. Particular attention is given to tests that could be used for HPC. Tentative definitions of terms such as workability, consistency, and rheological parameters are provided. An overview of the most promising tests and models for cement paste is given.
Introduction
The rheological (flow) properties of concrete are important for the construction industry because concrete is usually put into place in its plastic form. This importance can be attested to by the large body of literature existing on concrete rheology [1,2,3,4]. Unfortunately, due to the complex composition of the material, no definite method for predicting the flow of concrete from its components exists. Even measurements of the rheological parameters are not easily performed due to the large range of particle sizes found in concrete (from 1 m cement grains to 10 mm coarse aggregates or even larger (100 mm) as found in a dam). Therefore, the flow of a given concrete is usually measured using one of the many standard tests 1 available that only partially measure the intrinsic flow properties of the material. Flow tests are of limited value unless they measure the intrinsic rheological properties of concrete. A better understanding of the flow properties of concrete is needed to be able to predict the flow of concrete from the properties of the components.
The purpose of this paper is to assess the state of the art in measurements of flow properties of concrete. A critical review of the tests available is given with special emphasis given to tests for high performance concrete (HPC). Definitions of terms commonly used in the field and their link to material properties are provided.
Fluid And Suspension Rheology
Concrete and mortar are composite materials, with aggregates, cement, and water as the main components. Concrete is really a concentrated suspension of solid particles (aggregates) in a viscous liquid (cement paste). Cement paste is not a homogeneous fluid and is itself composed of particles (cement grains) in a liquid (water).
Because concrete, on a macroscopic scale, flows as a liquid, equation (1) is applicable. If a shear force is applied to a liquid as shown in Fig. 1, a velocity gradient is induced in the liquid. The proportionality factor between the force and the gradient is called the viscosity. The velocity gradient is equal to the shear rate ␥ . A liquid that obeys this equation is called Newtonian [1].
where = viscosity ␥ = shear rate = dv /dy (see Fig. 1) = shear stress = F /A F = shear force A = area of plane parallel to force. Most of the equations used for concentrated suspensions, such as concrete, try to relate the suspension concentration to the viscosity or the shear stress to the shear rate, thus assuming that there is only one value for the viscosity of the whole system. Table 1 and Table 2 give the most commonly used equations in the two approaches. Equations from Table 1 are used to describe the flow of cement paste [5], but they are not applicable to concrete due to the complexity of the suspension (aggregates in a suspension (cement paste)). Table 2 gives equations commonly used for concrete.
It should be noted that quite a few of the equations described in Table 2 incorporates a second factor, the Power equation [7] = A ␥ n n = 1 Newtonian flow n > 1 shear thickening n < 1 shear thinning Eyring [7] = a ␥ + B sinh -1 (␥ /C ) Atzeni et al. [9] yield stress. The physical interpretation of this factor is that the yield stress is the stress needed to be applied to a material to initiate flow. For a liquid, the yield stress equal to the intersection point on the stress axis and the plastic viscosity is the slope of the shear stress-shear rate plot (see Fig. 2). A liquid that follows this linear curve is called a Bingham liquid. Figure 3 shows some of the idealized types of curves that can be obtained when shear stress is plotted against shear rate. All the curves depicted can be described by one of the equations of Table 2. Liquids following the power law are also called pseudo-plastic fluids.
Atzeni et al. [7] have compared the various equations and proposed a modification of the Eyring equation as the best fit for concentrated suspensions such as cement paste. Unfortunately, the parameters of the Eyring equations are not physical values, but fit variables. Therefore, these parameters cannot be measured independently or modeled, but are calculated by a best-fit routine.
The main conclusion that can be deduced from studying the proposed equations is that all (with the exclusion of the Newtonian liquid) use at least two parameters to describe the flow. In the case of a concentrated suspension such as concrete, it has been shown [4,5] that a yield stress exists. The equations that have a physical basis include at least two parameters, with one being the yield stress, are the Herschel-Bulkley and Bingham equations. The Herschel-Bulkley equation contains three parameters, one of which, n , does not represent a physical entity. It has been shown [10] that in certain concretes, such as self-consolidating concretes, this is the equation that best describes their behavior. Nevertheless, the most commonly used equation today is the Bingham equation, because the parameters used are factors that can be measured independently (Fig. 2) and because the flow of real concrete seems to follow this equation fairly well [4] in most cases.
Concrete Rheology
In the construction field, terms like workability, flowability, and cohesion are used, sometimes interchangeably, to describe the behavior of concrete under flow. The definitions of these terms are very subjective. Table 3 [14] lists some of the major definitions of workability given by professional societies. Tattersall's [4] interpretation of workability is "the ability of concrete to flow in a mold or formwork, perhaps through congested reinforcement, the ability to be compacted to a minimum volume, perhaps the ability to perform satisfactorily in some transporting operation or forming process, and maybe other requirements as well". Kosmatka et al. [11] mention the following three terms while referring to concrete rheology: workability, consistency and plasticity. The definitions given are: • "Workability is a measure of how easy or difficult it is to place, consolidate, and finish concrete" • "Consistency is the ability of freshly mixed concrete to flow" • "Plasticity determines concrete's ease of molding".
It is clear that the definitions are descriptive and no agreement can be found. In the field, the situation is often worse because these terms are used differently by the various persons involved. From the previous list, all the terms used are defined according to the feelings of the person and are not based from the physical behavior of the material. Richtie [12] attempted to define the flow of concrete by linking it to various effects such as bleeding, sedimentation, and density. He distinguishes three properties: stability, compactibility, and mobility. The stability is linked to bleeding and segregation. The compactibility is equivalent to density, while mobility is linked to internal friction angle, bonding force, and viscosity. These descriptions, at least, link commonly used words with physical factors that can be measured. However, we believe that this is not enough. All these terms should be discarded in favor of physically measurable parameters. For instance, we could say that a concrete has a higher viscosity, instead of referring to a lower workability. Tattersall [4] summarizes very clearly the concrete workability terminology by classifying it into three classes: qualitative, quantitative empirical, and quantitative fundamental. The following items fall in the three classes.
• Class I: qualitative Workability, flowability, compactibility, stability, finishability, pumpability, consistency, etc. To be used only in a general descriptive way without any attempt to quantify. • Class II: quantitative empirical Slump, compacting factor, Ve-be, etc. To be used as a simple quantitative statement of behavior in a particular set of circumstances. • Class III: quantitative fundamental Viscosity, yield stress, etc. To be used in conformity with the British Standard Glossary [13]. Association of That property of freshly mixed concrete or mortar which Concrete Engineers, determines the ease with which it can be mixed, placed and Japan compacted due to its consistency, the homogeneity with which it can be made into concrete, and the degree with which it can resist separation of materials As stated in Sec. 2.2, the properties that could be used to describe the concrete flow are the yield stress and the viscosity. Any test that describes the flow behavior of concrete should at least measure these two properties. Unfortunately, most existing tests measure only one factor, either related to the yield stress or to the viscosity. Descriptions of these tests are given in Sec. 3.1. Tests measuring both parameters exist but are neither cheap nor easy to carry out, so they are not widely used. Section 3.2 describes these tests.
Aside from measuring the flow of concrete, rheology is concerned with the prediction of the flow from the properties of the components (i.e., cement paste, mortar) or from the mix design (i.e., w/c ratio, aggregate content, type of cement and admixture dosage). No attempt to develop a prediction model has yet been successful. One difficulty comes from the fact that the size range of the particles is very wide (micrometers to tens of millimeters). Also, the factors influencing the flow properties of concrete are more than the factors influencing the rheology of the parts (cement paste and aggregates). There is no linear relationship between the rheological parameters of cement paste and those of concrete. The main reason being the gap between the aggregates which varies with the concrete cement paste volume content. Ferraris et al. [15] showed that cement paste has a different rheological behavior depending on the gap between the plates of a rheometer that simulate the distance between the aggregates. The distance between the aggregate depends on the cement paste volume content. Also, the rheological behavior of a material depends on the conditions of the experiment such as shear rates, temperature, mixing energy. Therefore, it is important that the cement paste be measured in the same conditions that it will experience in concrete. This approach was followed by Yang et al. [16] to determine the influence of mixing methods on the flow properties of cement paste. Martys [17] is currently attempting to develop a simulation of the flow of concrete using a computerized model with the mix design and the cement paste rheology measured under the same conditions as in concrete as input variables. De Larrard [18] developed a model based on optimization of mixture design, linking maximum close packing with concrete properties. Further description of these models is beyond the scope of this paper.
It should be kept in mind that all the models or methodologies given here assume that the concrete is formed of particles but no interparticle forces are directly considered. The only reference to particle interaction is the acknowledgment that all properties are timedependent, implying that phenomena, such as flocculation of the cement particles and hydration, are continually taking place.
In summary, concrete is a suspension, including particles that may range from less than 1 m to over 10 mm. The flow properties of such a suspension can often be described approximately using a Bingham model, defined by two factors, plastic viscosity and yield stress. Most of the widely used tests are unsatisfactory in that they measure only one parameter, which does not fully characterize the concrete rheology. Figure 4 shows how two concretes could have one identical parameter and a very different second parameter. These concretes may be very different in their flow behaviors. Therefore, it is important to use a test that will describe the concrete flow, by measuring (at least) both factors.
High Performance Concrete
High performance concrete (HPC) is defined by ACI [19] as follows: "HPC is a concrete meeting special combinations of performance and uniformity requirements that cannot always be achieved routinely using conventional constituents and normal mixing". The rheological property of HPC should be: "HPC places and compacts easier" [20]. In a detailed characterization of HPC, given by Goodspeed et al. [21], the reference to rheology is: "Ease of placement and consolidation without affecting strength".
To achieve this property special precautions need to be taken. According to Malier [22], a more workable HPC can be obtained in two ways: either by reducing the flocculation of cement grains or by widening the range of grain sizes. Examining Malier's method, it is apparent that the first approach relates uniquely to the cement paste, while the second approach relates to the aggregate's size distribution as well as the influence of fillers. The aggregate's size distribution is at the base of the computerized calculation of concrete mixture design developed by Shilstone [23].
Aitcin [24] has raised several questions on the production of a more workable HPC: • "How to evaluate simply rheological performance of portland cement and its compatibility with given superplasticizers? • How to evaluate simply in the laboratory and in the field, the workability of a concrete having a very low water/cement ratio by means other than the slump test? • How is diminished the rheological performance of a given portland cement in the domain of low water/cement ratio? • How to optimize the use of supplementary cementitious materials when making low water/cement ratio concrete?" Today, the workability of HPC is evaluated using the same tests as used for normal concrete. However, the specific characteristics of HPC hinder the correct interpretation of current tests. This situation is demonstrated when the yield stress, as measured by a slump cone, is in the range desired but the viscosity (not measured in a slump cone test) may be so high that the mix is labeled "sticky" and is difficult to place in the molds even with vibration.
Therefore, new tests are being designed specifically for HPC, as will be described in Sec. 3.2.3.
Test Methods
Test methods for flow properties of concrete can be divided into two groups in regard to whether the output of the experiment gives one or two parameters. As was discussed in Sec. 2.2, to correctly define the rheology of concrete both the yield stress and the viscosity need to be measured.
One-Factor Tests
Most currently used tests measure only one rheological value or factor. The relationship between the factor measured and either of the two fundamental rheological parameters is not obvious. In most cases, the fundamental parameter cannot be calculated from the factor measured, but can only be assumed to be related. The tests that are discussed here are (all references will be given in the sections where the tests are discussed): Tests 1 through 3 are related to the yield stress because they measure the ability of concrete to start flowing. Tests 4 to 10 are related to the viscosity because they measure the ability of concrete to flow after the stress exceeds the yield stress. The stress applied is either by vibration (tests 4-6) or by gravity (tests 7-10).
Slump Test
A truncated metal cone, open at both ends and sitting on a horizontal surface, is filled with concrete, and lifted quickly. The slump of the concrete is measured as shown in Fig. 5. This measurement is widely used due to its simplicity. In this test, the stress is composed of the weight of the concrete per unit area. The concrete will slump or move only if the yield stress is exceeded and will stop when the stress (or weight of the concrete/area) is below the yield stress. Therefore, the slump test is related to the yield stress [25]. Some researchers have tried to simulate the slump test [26] using the finite element method. Assuming that concrete follows the Bingham equation, they were able to produce pictures of the concrete slump versus time (Fig. 6), but no prediction from the concrete composition was possible because no material properties for the components (cement paste, aggregates) were used.
The variability in the slump measurements is attributed mainly to the operator and to variations in mixture proportions. This test is a useful quality control tool because it can help detect changes in the composition of concrete delivered, e.g., changes in the amount of mixing water. This test is a standard in the United States (ASTM C143) [27] and is used in other countries as well.
A modification of the slump test, used for concretes with very high slump (as high as 305 mm (12 in) minus the coarser aggregate diameter), is to measure the spread instead of the height drop. This measurement is rarely reported and is not a standard. A second modification of the slump cone (see Fig. 7) is the test used in Germany (DIN 1045) [28]. The slump cone is placed on a special metal sheet. After the cone is lifted, the metal sheet is lifted and dropped a predetermined number of times. The spread of the concrete is measured. This version of the slump cone test is related to the viscosity and not to the yield stress because dropping the metal sheet subjects the concrete to a stress that is greater than the yield stress. Therefore, the measurement is related to the flow of concrete when the yield stress is exceeded. If the concrete does not slump or spread, than this measurement is not useful because the yield stress was not exceeded and the concrete did not flow. This statement can be applied also to the measurement of the standard slump of the concrete.
Recently, the slump cone test procedure was modified to allow the estimation of both the yield stress and the viscosity [29,30]. As the modified slump cone test is classified as a test for two parameters, it will be described in Sec. 3.2.
Penetrating Rod: Kelly Ball, Vicat, and Wigmore Tests
The principle of these tests is that the depth of penetration of an object will depend on the yield stress of the concrete. The mass or the force applied on the penetrating object will measure the yield stress of the concrete. Usually, the mass or the force is pre-established, i.e., it does not vary depending on the sample. Therefore, these tests really measure whether the applied stress is higher or lower than the yield stress of the concrete. Similar to the slump test, these tests are useful mainly on work sites as quality control tools to determine if the composition (mainly the water content) has been changed. These tests are also frequently used to determine the setting time of concrete. Figures 8 and 9 show two of the most known configurations. Other test descriptions can be found in ASTM C 403 [31] or, for the Vicat needle, in ASTM C 953 [32].
It should be noted that the Kelly Ball described in ASTM C360 [33] was up for reapproval in 1998. It failed to pass, due to lack of use, therefore it will likely be withdrawn as a ASTM standard.
Turning Tube Viscometer
The turning tube viscometer consists of a tube (60 mm in diameter and 800 mm long) that can be filled with the material to be measured [34]. A ball is then dropped in the fluid and its velocity measured between two points 370 mm apart [the two inductance coils will detect the ball passing (Fig. 10)]. The ball sizes are 12.7 mm, 15.9 mm, and 24.9 mm. Using the Stokes equation, the viscosity is calculated. This instrument has been used to measure the viscosity of cement paste. It is not recommended for concrete, because the diameter of the ball should be significantly larger than that of the aggregates. Otherwise, the concrete cannot be considered to be a uniform medium in which the ball is freely falling. Also, the diameter of the tube needs to be large enough to insure that the coarser aggregates do not interlock and stop the ball's descent.
K-Slump Test [35,36]
This test was widely used [35] before it became an ASTM standard in 1997 [36]. The test is described in the ASTM book [36] as a "rapid assessment of consistency and flow as well as the uniformity and the change with time of freshly mixed concrete." The schematic design of the probe is shown in Fig. 11. The probe is inserted in the concrete to be tested so that the collar floater is on the concrete surface. A portion of the concrete flows into the hollow center of the probe through the perforated exterior tube. A floater or measuring rod, placed inside the perforated tube, measures how much concrete was able to flow into the probe. A higher volume corresponds to a higher ease of placement of the concrete. Nasser et al. [35] assume that the concrete flows freely into the inner tube. In reference of the two fundamental parameters (yield stress and viscosity) characterizing the rheology of concrete, this test will give a value related to the yield stress of the concrete, because the concrete will not move into the probe unless the yield stress is overcome. The stress is applied by the weight of the surrounding material. This test is suitable only for a material with low yield stress because the probe is not inserted very deeply in the concrete; therefore the stress applied by the material around the probe is not very high. It should be consid-ered that a concrete with coarse aggregates larger than the slots in the external tube, i.e., 9.4 mm (3/8 in) in diameter, will not flow into the tube. In this case, only the mortar will flow in the device and the device will only measure the ability of the concrete to segregate.
Nasser et al. [35] showed that the values obtained with this test correlate with slump test results, although the scatter of the data is relatively high. The standard deviation is Ϯ8 % for a single operator using the same device [36].
Ve-be Time And Remolding Tests (Powers Apparatus)
These tests measure the capability of the concrete to change shape under vibration [38]. In both tests, concrete is placed in an open-ended truncated cone (Fig. 12). The time it takes the concrete to remold itself into a cylinder under vibration, after the cone is lifted away, is the output of these tests. Due to the vibrations, the concrete starts flowing after the yield stress has been overcome. Therefore, these tests can be assumed to be related to the plastic viscosity. Nevertheless, the relationship is not direct. The advantage of remolding tests is that they simulate placement of concrete under vibration, related to the field usage of concrete.
LCL Apparatus
The LCL [37] apparatus was developed in France, and like the remolding test, determines the time it takes for concrete to flow into a new form (Fig. 13). The main difference from the previous two tests is the geometry. The concrete is poured into a prismatic mold behind a wedge. The wedge is removed and the mold is vibrated. The operator can change the amplitude while the vibrator used determines the frequency. The time for the concrete to flow and occupy the whole prism is considered a measure of the workability. The yield stress is likely overcome by the vibration, therefore the measurement is related to the plastic viscosity of the material. If the amplitude of the vibration is slowly raised until the concrete starts flowing, a value related to the yield stress can be obtained.
Vibration Testing Apparatus and Settling Curve, Fritsch Test [38]
The Fritsch test measures the ability of concrete to be remolded or consolidated. Figure 14a shows a schematic drawing of the apparatus. A concrete sample is placed in a container with a vibrator. The time to obtain full consolidation, i.e., time when the lid is not descending anymore, is measured. The concrete is tested under vibration, thus the shear stress is likely to be higher than the yield stress. These experimental conditions can lead to the assumption that this test will give an indication on the plastic viscosity of the concrete. But, as previously, the viscosity cannot be calculated from this value. A compaction factor can be calculated. A settling curve (Fig. 14b) is determined by plotting the height of the lid versus the time of vibration. The height after vibration, h f , is represented by the asymptote of the settling curve.
Flow Cone
The flow cone [39] is widely used for oil well cement slurries and has been adapted for use with concrete. It consists of a funnel that is 615 mm long with a 150 mm Vibration testing apparatus after Fritsch [38]; h0 is the height of the lid at the beginning of the experiment and hf is the height at the end or at full consolidation. hc is the asymptote for the height versus time.
long outlet. The upper diameter is 230 mm and the orifice diameter is 75 mm. The slope of the funnel is wall is 6:1. The amount of concrete needed is 10 L and the maximum aggregate diameter is 20 mm. The time for a given volume of concrete to pass through the orifice is measured. If the concrete starts moving through the orifice, it means that the stress is higher than the yield stress, therefore, this test measures a value that is related to the viscosity. If the concrete does not move, it shows that the yield stress is greater than the weight of the volume used. An equivalent test using smaller funnels (orifice of only 5 mm) is used for cement paste as an empirical test to determine the effect of admixtures on the flow of cement pastes. Correlation of cement paste measurements with the concrete flow was attempted with no conclusive results [40].
Filling Ability
Two slightly different tests exist to measure the filling capacity of concrete, i.e., the capability of concrete to flow into a form (Figs. 15 and 16). In the first test (Fig. 15 [41]), the concrete is "pushed" through an opening partially obstructed by reinforcing bars, by applying a static pressure of about 2400 Pa. In the second test ( Fig. 16 [37]), the concrete is dropped into the mold through a funnel. In both cases, the yield stress of the concrete is exceeded; therefore the value measured here is related to the viscosity. If the stress applied is lower than the yield stress, no measurement is obtained.
Orimet Apparatus [1]
This instrument consists of a 600 mm long tube, closed at the bottom by an openable trap. The time for the concrete to flow through the long tube is recorded. The test method of the Orimet is similar to the flow cone. This test has been used for underwater concrete. The instrument is more flexible than the flow cone because the orifice or diameter of the tube can be selected to accommodate different aggregate sizes.
Two Factor Tests
We now examine the tests whose output gives two parameters. The values measured by these tests do not necessarily allow a direct calculation of the viscosity and yield stress. The factors measured are often indirectly related to the two fundamental parameters in a nontrivial way. The difficulty in designing correct rheological tests, tests that allow direct measurement of the fundamental parameters, is largely due to the size of the coarse aggregates, the tendency of segregation, and to the time effects. The most common fluid rheometer geometry is coaxial cylinders. In this geometry, having aggregates with a size of 10 mm or greater would force the dimensions of the instrument to be huge because these dimensions are dictated by the desirability of having a linear flow gradient between the shearing surfaces. A good approximation of this linear flow gradient can be achieved if the difference between the inner and outer radii is at least five times the diameter of the maximum size aggregate and if the ratio between the radii is held between 1 and 1.10. Therefore, the minimal dimensions, with a maximum aggregate size of 10 mm, will be 0.5 m for the radius of the inner cylinder and 0.55 m for the outer cylinder radius. These are relatively large dimensions for a relatively small maximum size aggregate.
Tattersal Two-Point Test [4]
This is the first and most widely known instrument for measuring the flow properties of concrete. The apparatus (Fig. 17) consists of a bucket containing the concrete to be tested. A vane of special geometry, or impeller, is lowered into the sample. The impeller starts rotating and the resistance on the impeller due to the material, i.e. torque, is measured. As the speed of rotation of the impeller is increased a curve of the torque versus the speed is recorded. The graph obtained is linear, therefore the stress is extrapolated to the torque at zero speed to give the yield stress and the plastic viscosity is related to the slope of the curve. Tattersall [4] designed the first instrument, but others, Gjorv [42], Wallevick [43] and Beaupré [44,46] have improved and commercialized it. The main improvement was to automate the instrument. The torque and the speed are automatically recorded using a computer. The instrument is now available as the BML viscometer [42] or the IBB Concrete Rheometer [46] (Fig. 18). The impeller shape is not always the same, i.e., BML has a type of serrated cylinder while IBB uses an "H"-shaped impeller. The impeller of the IBB rheometer has a planetary motion in addition to an axial rotation. In both cases, the plot of torque measured versus the speed of the rotor is recorded and results in a linear relationship. The slope, h , and the intercept at zero speed, g , are related to the plastic viscosity and the yield stress, respectively. Assuming that the effective average shear rate is proportional to the speed of the impeller, Tattersall [4] gave the following equation: where: T = torque G = constant obtained by calibration with Newtonian fluids K = constant obtained by calibration with non-Newtonian fluids N = speed of the impeller 0 = yield stress = viscosity Therefore, 0 = g /(G /K ) and = h /G , where g and h are the two values measured. Unfortunately, the entities G and K are almost impossible to obtain for three main reasons: Fig. 18. IBB Concrete Rheometer [46].
• The flow pattern in the instrument is too complicated and not linear (or turbulent flow) to allow a calculation of G and K . • The specimen container is too large to be able to use a standard oil to calibrate the rheometer (although some tentative calibrations were made by Tattersall [45]). We believe that the impellers will not be able to shear the whole volume of material when no aggregates are present, leading to nonvalid calibration. • No standard granular material exists with which to calibrate the instrument.
Bertta Apparatus [47]
This test apparatus was developed at the Technical Research Centre of Finland. Concrete is placed between two concentric cylinders of 480 mm and 330 mm diameters. The outer cylinder rotates in a oscillatory mode. The operator selects the frequency and amplitude. The torque induced by the movement is measured in the inner cylinder. This configuration allows the operator to calculate the viscosity and the yield stress of the concrete as a function of frequency. The advantage of this instrument is that is allows the operator to calculate the intrinsic rheological parameters of the materials and not only two related values, such as g and h (Tattersall device). Two issues that remain are: • The maximum aggregate size should be limited to 13 mm (0.5 in), calculated as being 1/5 of the gap between the cylinders. • The ratio between the radii of the two cylinders radii is 1.45. This is considered too high to have a linear flow gradient, raising the question as to whether the calculation of the rheological parameters is correct.
This instrument is not commercially available.
The BTRHEOM Rheometer
The rheometer, BTRHEOM, was developed at the Laboratoire Central des Ponts et Chaussées (LCPC), France by de Larrard et al. [48]. It consists of a bucket with a serrated bottom, and a rotating top wheel (Fig. 19) resting on the concrete. The shear stress distribution (Fig. 20) allows direct calculation of the viscosity and yield stress according to the following equations based on the assumption that the concrete is a Bingham fluid. If this assumption is not correct, another set of equations will need to be established using the correct relationship between the shear rate and shear stress. Due to the linear pattern of flow gradient, a shear rate and shear stress can always be calculated analytically in this geometry.
where: 0 = shear yield stress = viscosity R 1 and R 2 = inside and outside radii of the apparatus h = height of the sheared part of the sample ⌫ = torque applied to the sample ⍀ = angular velocity of the rotating part ⌫ 0 and Ѩ⌫ /Ѩ⍀ = ordinate at origin and slope of the experimental straight line ⌫ (⍀ ).
The instrument was used to collect data on shear stress versus shear rate. The results confirmed that the assumption of concrete being a Bingham fluid is correct if it had certain characteristics-These being a relatively fluid or soft concrete (typically a slump higher than 80 mm) with shear rates ranging between 0.5 s -1 and 8 s -1 . De Larrard et al. [10] found that, over a wider range of shear rates, concrete behaves more like a coarse granular suspension following the Herschel-Bulkley equation (see Table 2). This apparatus permits measurements to be done under vibration. Therefore, the yield stress and the viscosity of the material can be obtained under a variety of situations. The limitations of this instrument are the range of plastic viscosity and yield stress that can be attained, i.e., high yield stress or high plastic viscosity concretes cannot be sheared. There is always a possibility of segregation during the test especially under vibration.
Modified Slump Cone Test [25,29]
Recently, a modification of the slump cone was developed to allow the measurement of viscosity. As mentioned in Sec. 3.1.1, the standard slump test can only be correlated with the yield stress. The modification consists in measuring not only the final slump height but also the speed at which the concrete slumped. There are two methods to measure the speed at which the concrete slumped (Fig. 21): • The original method consists of measuring the time for a plate resting on the top of the concrete to slide down with the concrete (Fig. 22) a distance of 100 mm • Researchers at Sherbrooke University [49] eliminated the plate and shortened the central rod so that its top was 100 mm below the full slump cone height. Then the test consisted of measuring the time for the concrete to slump to the height where the rod becomes visible.
The second method has the advantage that there is no risk of the plate getting stuck, but has the disadvantage that it may be difficult to see the appearance of the rod. Fig. 21. Schematics of the modified slump cone test. T is the "slump time" [25]. The yield stress, 0 , can be calculated from the final slump, using the following empirical equation: 0 = 347 (300 Ϫ S ) + 212 (4) where is the density expressed in kg/m 3 , and S is the final slump in mm. The viscosity can be determined from the 100 mm slump time using an empirical equation that was determined by de Larrard et al. [25,30]. The equation used is: = T и 1.08 ϫ 10 -3 (S Ϫ 175) for 200 mm < S < 260 mm (5) = 25 ϫ 10 -3 T for S < 200 mm where is the viscosity in Paиs and T is the slumping time in seconds. To facilitate the interpretation of the results, these equations can be represented in a graphic form as shown in Fig. 23.
Conclusions
Concrete flow properties need to be characterized by more than one parameter because concrete is a non-Newtonian fluid. The most commonly-used model is the Bingham equation that requires two parameters, i.e., yield stress and the plastic viscosity. The yield stress determines the stress above which the material becomes a fluid. The plastic viscosity is a measure of how easily the material will flow, once the yield stress is overcome. Other models for special concretes, such as self-leveling or self-compacting, require a more complex model, such as the Herschley-Bulkley equation.
Most of the common tests for measuring the flow properties of concrete yield only one parameter that is related either to plastic viscosity or to yield stress, or to some ill-defined combination of both. Most of these tests try to simulate field conditions and the results cannot easily be related to fundamental rheological properties. Their usage should be limited to quality control, or to check that mixture proportions have not been changed between batches. Of course, combining two tests, one related to yield stress and one related to viscosity, should give a better description of the concrete flow.
Recently, tentative steps have been made to develop tests that can measure both parameters, possibly in fundamental units. These tests are the rheometers (BTRHEOM, IBB, BML) that allow shearing at various rates, or the modified slump cone test.
This paper review has pointed out that most of the available tests are empirical. This is not a satisfactory situation for two reasons: • It is hard, if not impossible, to relate results obtained with different tests • The factors measured are not linked to independently measurable factors, that can be defined in fundamental physical units.
The author would like to emphasize that more research, novel tests, and models should be developed to better characterize the rheology of concrete in general and HPC in particular. | 9,352 | 1999-10-01T00:00:00.000 | [
"Engineering"
] |
Glucosyltransferase Activity of Clostridium difficile Toxin B Triggers Autophagy-mediated Cell Growth Arrest
Autophagy is a bulk cell-degradation process that occurs through the lysosomal machinery, and many reports have shown that it participates in microbial pathogenicity. However, the role of autophagy in Clostridium difficile infection (CDI), the leading cause of antibiotics-associated diarrhea, pseudomembranous colitis and even death in severe cases, is not clear. Here we report that the major virulent factor toxin B (TcdB) of Clostridium difficile elicits a strong autophagy response in host cells through its glucosyltransferase activity. Using a variety of autophagy-deficient cell lines, i.e. HeLa/ATG7 −/−, MEF/atg7 −/−, MEF/tsc2 −/−, we demonstrate that toxin-triggered autophagy inhibits host cell proliferation, which contributes to TcdB-caused cytopathic biological effects. We further show that both the PI3K complex and mTOR pathway play important roles in this autophagy induction process and consequent cytopathic event. Although the glucosyltransferase activity of TcdB is responsible for inducing both cell rounding and autophagy, there is no evidence suggesting the causal relationship between these two events. Taken together, our data demonstrate for the first time that the glucosyltransferase enzymatic activity of a pathogenic bacteria is responsible for host autophagy induction and the following cell growth arrest, providing a new paradigm for the role of autophagy in host defense mechanisms upon pathogenic infection.
Clostridium difficile (C. difficile) infections (CDIs) are the major cause of antibiotic-associated pseudomembranous colitis, and lead to severe diarrhea, ruptured colon, perforated bowels, kidney failure and death [25][26][27] . There has been a dramatic increase in CDIs over the past decade, largely due to the excessive use of antibiotics and the emergence of more virulent strains, such as strain B-1470. C. difficile has become the leading cause of healthcare-associated infections 27,28 . As a gram-positive anaerobe bacterium, C. difficile exerts its pathogenic effects mainly by producing two virulent factors, enterotoxin A (TcdA) and cytotoxin B (TcdB) [29][30][31] . Both toxins enter cells via receptor-mediated endocytosis [32][33][34] . Their glucosyltransferase (GT) domains are subsequently released into the cytoplasm where they mono-glucosylate small GTPases of the Rho subfamily 35,36 , such as RhoA, Rac1, Cdc42, and TC10, by using the UDP-glucoses as co-substrates [37][38][39][40][41][42][43][44] . These reactions lead to actin condensation and consequently cell-rounding, membrane blebbing, and eventually cell death [45][46][47][48][49][50] . While both toxins are glucosyltransferases with similar structures that act on a variety of cell types, TcdB exhibits a 100-fold higher rate of enzymatic activity than TcdA 51,52 . A mutant study in a hamster disease model provided evidence that TcdB, but not TcdA, was essential for virulence 53 . However, another study suggested that both toxins were needed for the virulence of C. difficile 54 . Despite this controversy, the role of TcdB in CDIs is indispensable. The cytotoxin of TcdB elicits its biological effects by inhibiting cell proliferation 55 and even inducing both apoptotic response 56,57 and necrotic cell death 58 in a variety of human cells. It remains to be understood how exactly TcdB exerts its cytopathic and cytotoxic effects.
In this study, we provide evidence that host autophagy, triggered by TcdB from C. difficile through its glucosyltransferase activity, is critical for TcdB to inhibit host cell proliferation which plays as an important role in the biologic effects of TcdB 55 .
Results
TcdB Triggers Autophagy Induction in Host Cells. To investigate the role of host autophagy in C. difficile toxin B (TcdB) infection process, we first set out to determine whether and how TcdB affects the cellular autophagy level. By assessing the dynamics of LC3 as indicated by the appearance of the autophagosome-specific marker lipidated LC3 (LC3-II) converted from its unconjugated form (LC3-I) 59, 60 , we could monitor the autophagy activity over the course of toxin exposure. HeLa cells stably expressing GFP-LC3 were incubated with TcdB of various concentrations over different time periods. Aside from the expected cell-rounding phenotype, TcdBintoxicated cells showed an increase in the number of autophagosomes (Fig. 1A). The statistical average number of LC3 puncta in each cell further confirmed that the accumulation of autophagosomes correlated positively with toxin-exposure time at a fixed TcdB dose (5 ng/ml) (Fig. 1B). The immunoblotting analysis showed more LC3-II accumulated with longer toxin-exposure time (Fig. 1C), which also indicated the increase of autophagosomes by TcdB. Moreover, the increase of autophagosomes correlated with the amount of toxin when the exposure time was fixed (8 h) (Fig. 1D). Statistically, it showed clearly that the average number of LC3 puncta in each cell increased with the amount of toxin added (Fig. 1E). Consistently, more LC3-II accumulated under higher dosage of TcdB, shown in the immunoblotting assay (Fig. 1F). Interestingly, cells were sensitive to TcdB exposure such that as low as 0.5 pg/ml of toxin was sufficient to induce autophagosome formation ( Supplementary Fig. S1A). We also found that TcdA, another key virulent factor of C. difficile [29][30][31] , leads to autophagosome formation and induces autophagy in HeLa cells ( Supplementary Fig. S1B,C). In agreement with the results from HeLa cells, TcdB also triggered autophagosome accumulation in the human intestinal cells HT-29 ( Fig. 1G and H), the natural host targets of TcdB.
Considering that autophagy is a dynamic process, and autophagosomes are intermediate structures, their accumulation could result from either de novo induction of autophagy or inhibition of autophagosome degradation. In order to monitor the autophagy flux under TcdB treatment, we used the lysosomal inhibitor, chloroquine (CQ), to block autophagosome degradation 60,61 . The accumulation of LC3-II triggered by TcdB was significantly enhanced in the presence of CQ for both 12 and 24 h toxin exposure (Fig. 1I), similar to the effects of the serum starvation (SS) treatment, the physiological inducer of autophagy. The quantification results further showed that the turnover rate of LC3-I to LC3-II with CQ is almost 4 times of that without CQ under TcdB treatment, which is greatly higher than the mock control and SS treatment (Fig. 1I). These data indicated that TcdB indeed increased the autophagy flux. In fact, the TcdB-triggered Rac1 glycosylation was delayed by 0.5 h with the addition of CQ, suggesting that CQ slightly inhibits the endocytosis of TcdB ( Supplementary Fig. S2). It rules out the possibility that CQ helps the endocytosis of TcdB to promote the autophagy response. Altogether, these results suggested that the autophagosome accumulation results mainly from the TcdB-mediated induction of autophagy rather than its inhibition of autophagosome degradation. of (D). For each time point, the average number of LC3 puncta per cell were counted from over 50 cells. (F) Cells were analyzed by immunoblotting on the levels of endogenous LC3-I and LC3-II with the treatment of TcdB of different concentration for 8 h. All bands were calculated by Image J for this and other figures. (G) Autophagosome accumulation with TcdB treatment in HT-29 cells. Cells transiently transfected with GFP-LC3 were treated by 5 ng/ml of TcdB and analyzed for GFP-LC3-positive autophagosome signals. Scale bar = 7.5 μm.
(H) Cells were analyzed by immunoblotting on the levels of endogenous LC3-I and LC3-II with the treatment of TcdB (5 ng/ml) under different time points. (Full-length blots are presented in Supplementary Fig. S10) (I). Assay of TcdB-triggered autophagy flux. HeLa cells were treated by 50 pg/ml of TcdB, or serum starvation (SS) for 12 or 24 h, with or without the lysosomal inhibitor chloroquine (CQ, 7 μM), and cell lysates were analyzed by immunoblotting for levels of endogenous LC3-I and LC3-II (Top). Each band was normalized with mock control treated by CQ. (Full-length blots are presented in Supplementary Fig. S11). Supplementary Fig. S12A). (B) Effects of ATG7 deficiency on TcdB-induced Rac1 glucosylation in HeLa cells. Wild type and ATG7 −/− HeLa cells were exposed to TcdB (5 ng/ml) for indicated period, before lysed for immunoblotting assay to detect the total and non-glucosylated Rac1 protein level. (Full-length blots are presented in Supplementary Fig. S12B). (C) Effect of ATG7 deficiency on TcdBtriggered cell viability changes in HeLa cells. Cell viability assay was performed to determine the cytopathic effect of TcdB on wild type and ATG7 deficient HeLa cells. The values shown represent the mean ± standard deviation (n = 6), as defined by error bars in this and other figures. (D) Effect of ATG7 deficiency on TcdBtriggered cell death in HeLa cells. The cells were incubated with TcdB toxin for 48 h before the LDH assay as described in the Experimental Procedures. The values shown represent the mean ± standard deviation (n = 3). (E) Effect of ATG7 deficiency on TcdB-triggered cell viability changes in MEFs. The MTT assay was performed as described in the Experimental Procedures. The values shown represent the mean ± standard deviation (n = 6). (F) Effect of ATG7 deficiency on TcdB-triggered cytotoxicity in MEFs. The LDH assay was performed to determine the killing effect of TcdB on the wild type and MEF/atg7 −/− . The cells were incubated with TcdB toxin for 48 h before the LDH assay. The values shown represent the mean ± standard deviation (n = 6). Autophagy Induction Facilitates TcdB-Caused Cell Proliferation Inhibition. Given that TcdB induced a dramatic autophagy response in host cells, we wanted to know next whether the induced autophagy plays a role in TcdB-mediated cytotoxic or cytopathic effects. To answer this, we generated ATG7 knockout HeLa cells, since ATG7 is essential for the early steps of autophagosome formation. Cells lacking this protein are deficient in conventional autophagy, as demonstrated by the loss of LC3 lipidation 62 . Indeed, HeLa cells with complete loss of ATG7 expression failed to respond to either SS ( Supplementary Fig. S3) or TcdB exposure as there was no LC3-I conversion to LC3-II ( Fig. 2A). Besides, knockout of ATG7 had little effect in delaying the Rac1 glycosylation that indicates the TcdB endocytosis process (Fig. 2B). From the results of the MTT and LDH assays, it showed that HeLa/ATG7 −/− cells were more resistant to TcdB in terms of the inhibition of cell proliferation (Fig. 2C), since the killing activity of TcdB was marginal under this concentration (Fig. 2D), and it was observed that cell growth was highly inhibited after TcdB treatment ( Supplementary Fig. S4). The cell viability shown in the MTT analysis started to drop sharply when TcdB dosage exceeded 1ng/ml (Fig. 2C), correlating well with the occurrence of cell death as shown in the lactate dehydrogenase (LDH) assay (Fig. 2D). Consistently, the cell viability and the LDH assays in MEF/atg7 −/− showed that the lack of ATG7, an essential gene for autophagosome formation and autophagy induction 62 , led to an increase in cell viability upon TcdB exposure (Fig. 2E). This was due to less inhibition of cell proliferation rather than reduced cell death when the toxin concentration is below 1 ng/ml (Fig. 2F). These data suggested that the ATG7-dependent induction of autophagy plays a critical role in TcdB-mediated cell-growth inhibition.
In addition to the genetic cell models, we also found that the addition of 3-methyladenine (3-MA), an autophagy inhibitor by blocking PI3K function 63 , resulted in increased cell viability in HeLa cells treated with TcdB, while serum starvation could reverse this phenotype caused by 3-MA and made cells more sensitive to TcdB (Fig. 2G,H). Our data indicated that the autophagy pathway is required for TcdB-mediated inhibition of cell proliferation, one of the major cytopathic effects caused by TcdB 55 .
Besides cell growth arrest, our data also showed that TcdB triggered cell death under higher concentrations ( Fig. 2D,F), consistent with previous reports demonstrating that high concentrations of TcdB lead to cell death, which has been defined as necrosis 58 . To investigate the role of autophagy in TcdB-triggered cell death, we monitored both cell viability and cell death under the treatment of low or high concentrations of TcdB in autophagy-deficient HeLa and NRK cells. When exposed to low concentrations of TcdB, as expected, both knockout cell lines behaved more resistant to TcdB-caused cell proliferation inhibition. However, under higher concentrations of TcdB, which started to kill host cells, both autophagy-deficient cells became more sensitive to TcdB-caused cell death ( Supplementary Fig. S5). These data suggested that autophagy might play a protective role in TcdB-triggered cytotoxicity under higher dosage.
Glucosyltransferase Activity of TcdB Is Required for Autophagy Induction. As it is well-known
that TcdB induces strong autophagy to hinder host cell proliferation, we set out to identify the responsible domain(s) of this toxin. The primary structure of TcdB is divided into the glucosyltransferase (GT) domain, the cysteine protease domain (CPD), and the delivery/receptor-binding domains 64 . Although detailed analyses of the regions outside the enzymatic domain are not clear, it has been established that the GT domain (GTD) consists of the first 543 amino-acids, including a conserved DXD motif that is essential for its glucosyltransferase activity 65 .
To clarify whether the GT domain of TcdB and/or its enzymatic activity is involved in the autophagy induction, we expressed and purified a mutant TcdB (TcdB*) protein harboring three point mutations (Y284A and D286/288 N) ( Fig. 3A; Supplementary Fig. S6A) that completely abolished the toxin's glucosyltransferase activity 66 . As shown by both immunoblotting analysis and fluorescence microscopy, TcdB*, unlike its wild type counterpart, failed to induce autophagy response as indicated by GFP-LC3 puncta accumulation and increased endogenous LC3-II level (Fig. 3B,C; Supplementary Fig. S6B). This suggests that the glucosyltransferase activity of TcdB is required for triggering autophagy. As predicted, TcdB* also lost the capability of eliciting the cell-rounding phenotype (Fig. 3C,D), consistent with previous studies 65 .
To further verify whether this enzymatic domain is sufficient to trigger autophagy, plasmids expressing only the GT domain or its corresponding mutant were constructed (Fig. 3A) and introduced into HeLa cells. The autophagosome accumulation and the increase of LC3-II levels were only found in cells expressing the wild type GT domain, but not the mutant GT* (Fig. 3E,F). To confirm that the observed autophagy induction is indeed due to the GT domain expression, we co-transfected the GFP-expressing plasmid with GT-or GT*-expressing plasmid at 1:1 ratio. Twenty-four hours after co-transfection, cells that became rounded were exclusively those expressing GFP and GT, rather than GFP and GT* (Fig. 3G). This result suggested that the glucosyltransferase activity of the GT domain, which is reported to be responsible for the disruption of the cytoskeleton in host cells 65 , is necessary and sufficient to induce autophagy upon TcdB exposure.
TcdB-induced Autophagy and Cell-rounding Are Not Interdependent. Since the glucosyltransferase activity is responsible for both TcdB-triggered autophagy and cell-rounding, and it has been reported that extracellular matrix (ECM) detachment can induce autophagy 67 , we investigated whether there is a causal relationship between autophagy induction and cell-rounding. TcdB causes cell rounding through its glucosyltransferase activity by inactivating small GTPases of the Rho family 39,65,68 . To address this question, we conducted a detailed fluorescence microscopic assay to investigate the dynamic changes of cell morphology and autophagy induction with exposure to a series of TcdB doses. Interestingly, the autophagy induction, indicated by the increased GFP-LC3 signals, occurred earlier than the appearance of cell-rounding when cells were exposed to relatively high concentrations of toxin ( Fig. 4A; Supplementary Fig. S7C,D). This was further confirmed by the statistical analysis of the average number of LC3 puncta in each cell, which showed that the LC3-labelled autophagosomes increased significantly at 0.5 h under the treatment of 5 ng/ml TcdB while most cells did not show the rounded morphology (Fig. 4B). On the contrary, the autophagy induction occurred later than the cell-rounding SCIenTIfIC REPoRTs | 7: 10532 | DOI:10.1038/s41598-017-11336-4 appearance when cells were incubated in relatively low concentrations of toxin ( Fig. 4A; Supplementary Fig. S7A,B). This was proved by the statistical analysis of LC3 puncta in each cell under 0.05 ng/ml TcdB treatment (Fig. 4C). These data ruled out the possibility that cell-rounding is a prerequisite for autophagy induction. Furthermore, TcdB was able to trigger cell-rounding morphology in autophagy-deficient MEF/atg7 −/− cells as efficiently as in wild type cells (Fig. 4D), as well as inducing similar glucosylation rates of the Rac1 substrate (Fig. 4E). Thus, we concluded that TcdB-triggered cell-rounding and autophagy are not interdependent.
Both the mTOR Pathway and PI3K Complex Are Involved in the TcdB-induced Autophagy
Process. Based on the role of autophagy in the TcdB-triggered cytopathic process, the next step was to determine the key factors or signaling pathways of the autophagy process responsible for this functional phenotype. Wild type and atg7 −/− MEF cells were treated by TcdB (1 ng/ml) or SS (serum starvation) for 8 h, before lysed for immunoblotting analysis (left); Wild type and atg7 −/− MEF cells were exposed to TcdB (5 ng/ml) for indicated period, before lysed for immunoblotting assay to detect the total and non-glucosylated Rac1 protein level (right). (Full-length blots are presented in Supplementary Fig. S14).
SCIenTIfIC REPoRTs | 7: 10532 | DOI:10.1038/s41598-017-11336-4 The mammalian target of rapamycin, mTOR, a serine/threonine kinase, is a potent suppressor of autophagy, mediating a variety of stimuli to regulate the autophagic process 4, 5, 60 . As a negative upstream regulator of mTOR, TSC2 is responsible for sensing the cellular amino acid contents indirectly, and inhibiting mTOR signaling 6,7 . To demonstrate whether mTOR participates in TcdB-induced autophagy, wild type and tsc2 −/− MEFs were used to assess the effects of TcdB exposure. Upon treatment of 5 ng/ml TcdB in MEFs, most of Rac1, one of the glucosyltransferase substrates, was converted to glycosylated form within 30 min. The suppression of mTOR occurred after 4-8 h, as indicated by the reduced phosphorylation of S6K and 4EBP1, two surrogate makers for mTOR kinase activity 69 , and lipidated LC3-II also appeared (Fig. 5A left). In MEF/tsc2 −/− (Fig. 5A right), TcdB no longer caused the reduction of the phosphorylation of S6K and 4EBP1, suggesting that TcdB-triggered mTOR inactivation observed in the wild type MEFs was conducted through TSC2. However, the conversion of LC3-I to LC3-II still occurred in MEF/tsc2 −/− . TcdB was still able to glycosylate Rac1 in MEF/tsc2 −/− , although this process was delayed by 0.5-1 h.
Similar results were obtained in HeLa cells, with the TcdB-triggered inhibition of mTOR activity occurring after 8 h as indicated by the decrease of p70-S6K (Fig. 5B), although there was an increase at 4 h. This phenomenon occurred in HeLa cells that were exposed to all three concentrations of TcdB, 5 ng/ml (Fig. 5B), 0.05 ng/ml ( Supplementary Fig. S8A) and 0.5 ng/ml ( Supplementary Fig. S8B), with a transient fluctuation ( Supplementary Fig. S8C). Consistent with MEF/atg7 −/− , MEF/tsc2 −/− also had a higher resistance to TcdB-triggered cell growth inhibition than wild type (Fig. 5C). These data demonstrated that the TSC2-mTOR pathway is involved in TcdB-induced autophagy and cytopathic effects, although it's not indispensable for the TcdB-induced autophagy process.
Besides the role of mTOR in the regulation of autophagy, we also wanted to know if the toxin triggers this process through the class III PI3K complex, a key complex for autophagy initiation 70 . The typical PI3K complex contains VPS34, VPS15, BECN1, and ATG14L or UVRAG 8,71 . To verify whether the PI3K complex is involved in TcdB-mediated autophagy induction, we studied the effects of TcdB on the protein-protein interaction amongst components of the PI3K complex. After co-introduction into HeLa cells, Flag-tagged VPS34 specifically precipitated with Myc-tagged ATG14L and UVRAG, confirming that VPS34 was able to bind to these two proteins 71,72 . Interestingly, TcdB treatment significantly increased the amount of Myc-tagged ATG14L and UVRAG precipitated by Flag-tagged VPS34 (2-3 folds' increase) in the co-immunoprecipitation assay (Fig. 6A). These results showed that TcdB enhances the PI3K complex formation, which includes at least VPS34, and ATG14L or UVRAG. In agreement with the above results, the addition of VPS34 inhibitors, 3-methyladenine (3-MA) and wortmannin 73 , inhibited TcdB-induced cell proliferation inhibition (Fig. 6B,C). Similar results were obtained from HT-29 and Caco-2 cells. 3-MA treatment provided cell resistance to TcdB-triggered cell proliferation inhibition (Fig. 6D,E), further supporting a universal role of the PI3K complex in TcdB-induced autophagy and consequently cell growth inhibition. These data indicated that both the mTOR pathway and the PI3K complex play important roles in TcdB-induced autophagy and consequently cytopathic effects through cell growth inhibition. The protein-protein interaction between VPS34 and ATG14L or UVRAG with or without TcdB treatment. HeLa cells were cotransfected with the plasmids encoding VPS34-Flag and myc-ATG14L/myc-UVRAG. 24 h after transfection, cells were treated with or without TcdB (1 ng/ml) for 3 h, before lysed by NP40 lysis buffer. Cell lysates were immunoprecipitated with anti-Flag mAb and immunoblotted using anti-myc mAb or anti-Flag mAb. The amount of β-tubulin in the whole cell lysate (WCL) was assayed as the loading control. The intensity of the blotting signal was quantified with ImageJ (http://rsbweb.nih.gov/ij/), and the relative intensity was labeled below the images. (Full-length blots are presented in Supplementary Fig. S17)
Discussion
Autophagy is an important self-eating process involved in microbial pathogenicity. Here we report for the first time that host autophagy can be triggered by C. difficile cytotoxin B through its glucosyltransferase activity. The autophagy response affects TcdB's cytopathic effects by facilitating TcdB-caused cell proliferation inhibition. Our mechanistic studies indicate that the glucosyltransferase activity-related cell-rounding process has no causal relationship with TcdB-triggered autophagy induction, while the mTOR pathway and PI3K complex are involved in this induction process. Based on these results, we provide a working model for host autophagy in the pathogenesis of a glucosyltransferase bacterial toxin (Fig. 7).
The glucosyltransferase activity of TcdB was found necessary and sufficient for TcdB-induced host autophagy (Fig. 2). Thus we speculated that the substrates of TcdB might be responsible for the autophagy induction process. The glucosyltransferation of Rho family proteins by TcdB leads to their irreversible inactivation, which causes cytoskeletal disruption and cell-rounding morphology 39 . However, cell-rounding, which has been reported to be a trigger of autophagy in other cases 67 , is proven not to be the reason of autophagy induction in this case because autophagosome accumulation could occur before cell-rounding under high dosage of TcdB exposure (Fig. 4A,B; Supplementary Fig. S7C,D). It's still an open question whether the TcdB glucosyltransferased-Rho family proteins directly trigger host autophagy.
It is also possible that other substrates or the overall glucosyltransferased-modification pattern of all substrates of the GTD are recognized by certain autophagy receptors. One of the autophagy receptor candidates is galectin 8. It recognizes and binds to host glycans when exposed to damaged bacteria vacuoles, resulting in the recruitment of NDP52, and the subsequent induction of autophagy through LC3 74 . To investigate the linkage mechanism between TcdB and these proteins, we have tested the interaction and function of some autophagy adaptors (such as NDP52 and SQSTM1/p62) for TcdB-induced autophagy, but none of them gave us a positive result. The modification of these small GTPases by the GTD of TcdB using UDP-glucoses as co-substrates 39 , is uncommon in host cells 75 . Therefore it is still an open question if this unique modification could be recognized by the host as a sign of danger, and in turn inducing autophagy as a self-defense mechanism. How the glucosylation activity of TcdB contributes to these downstream processes remains to be determined.
Once host autophagy is triggered through GT activity, TcdB could maintain the autophagy activity of host cells at a relatively high level (Fig. 1A), a quite different pattern from the case of starvation stimulation, where the autophagy activity fluctuates like a sine wave due to the feedback signaling pathway 1,76,77 . mTOR is known to serve as a sensor to monitor the intracellular levels of nutrients 4, 5 , excessive levels of which can activate mTOR to suppress autophagy, providing a negative feedback loop to prevent cell death from excessive autophagy induction 78 . Our results show that the activity of mTOR was gradually decreased by TcdB treatment, with an increase at 0.5 h and 4 h ( Fig. 5B; Supplementary Fig. S8). It could be speculated that the transient up-regulation of mTOR activity during the fluctuation cycle may be a result of the feedback mechanism, and it is eventually overpowered by the inhibition mediated by TcdB. This suggests that the feedback signaling pathway was somehow turned off by TcdB at a later stage.
In many infection cases, the host autophagy interacts with the pathogen endocytosis process. For instance, autophagy facilitates the cytoplasmic delivery of ANTXR2-associated LF during endocytosis 79 . In the case of TcdB exposure, however, the induction of host autophagy seems to be unrelated to endocytosis of the toxin, based on the following evidence: (1) the mutant TcdB without its glucosyltransferase activity 65,66 failed to elicit a autophagy response (Fig. 3A-C; Supplementary Fig. S6B); (2) the efficiency of TcdB in glucosylating the substrate Rac1, and causing the cell-rounding phenotype were similar in both wild type and autophagy-null mutants (atg7 −/− ) MEFs (Fig. 4D,E); (3) the intracellular expression of the GT domain of TcdB through plasmid transfection was sufficient to up-regulate autophagy (Fig. 3E,F). As in the innate defense mechanism, autophagy also functions as a cellular defense mechanism against infection, such as in the case of Vibrio cholera cytolysin (VCC) intoxication or anthrax infection, demonstrating a cellular defense role of autophagy against secreted bacterial toxins 21,[80][81][82] . In addition, the induction of autophagy can overcome the blockade of mycobacterial phagosome maturation, and inhibit the survival of intracellular Mycobacterium tuberculosis 83 . In order to evade autophagy-mediated defense mechanisms, many microbial pathogens or their virulence factors have evolved a myriad of strategies. For instance, Listeria monocytogenes uses a variety of mechanisms to evade destruction by the host autophagy system in order to colonize the cytosol of macrophages 84 . Also, cAMP-elevating toxins suppress immune responses, and modulate host cell physiology by inhibiting host autophagy 85 . The case we have presented here shows that autophagy induction facilitates TcdB-induced cell proliferation inhibition under the exposure of low-dosage TcdB, while it blocks cell death triggered by a high-dosage of TcdB ( Fig. 2; Supplementary Fig. S5). There are two explanations to interpret this phenotype: 1) Autophagy plays as an accomplice of the toxin to facilitate its inhibition of cell proliferation, which might cause some pathogenic effects such as inflammation. This process could be beneficial for the bacteria in terms of the convenience in spreading and acquiring host nutrients. 2) Autophagy plays a protective role by inhibiting cell death, so as to fight against TcdB-induced pathogenic effects upon high concentrations of TcdB exposure. The physiological concentrations of C. difficile toxin B around local tissue cells, however, still remain a controversial question 58,[86][87][88] . We believe that autophagy participates in the pathogenesis of C.difficile infection as either an "accomplice" or a "protector" to influence TcdB-triggered pathogenic effects.
Fluorescence microscopy. HeLa and HT-29 cells were grown onto glass coverslips in 6-well plates. After toxin exposure, cells were washed by PBS twice, fixed by 4% (wt./vol.) paraformaldehyde in PBS for 10 min, and permeabilized in 0.2% Triton X-100 in PBS for 10 min. The coverslips were mounted onto slides using mounting medium containing DAPI solution (Vector Laboratories, Vectashield), and the cells were examined by either LSM 510 laser-scanning confocal microscope (Zeiss) or TCS SP2 spectral confocal system (Leica).
Cell viability assay. HeLa, HT-29 or Caco-2 cells were seeded in 96-well plates 1 day before the addition of serially diluted TcdB toxin. MTT staining and detection were performed as described 91 . The starting concentration of cells used was 5 × 10 4 /ml for HeLa, 1 × 10 5 /ml for both HT-29 and Caco-2 cells. The cells were incubated with TcdB toxin for 48 h at 37 °C before the MTT assay. The spectrophotometer readings at 570 nm were determined using a Multi-Detection Reader (TECAN, Infinite M200). Cell viability was normalized to wells with mock treatment. Each data point and related error bar shown in figures for MTT assays represent the average results from six wells. LDH cytotoxicity assay. HeLa, MEF cells were seeded in 96-well plates 8 hours before the addition of serially diluted TcdB toxin. LDH staining and detection were performed as described in product instructions (G1780, Promega). The starting concentration of cells used was 5,000 cells per well and the cells were incubated with TcdB toxin as indicated time at 37 °C before the LDH assay. The spectrophotometer readings at 490 nm were determined using a Multi-Detection Reader (TECAN, Infinite M200). The death signal represented by the amount of LDH release was normalized to wells with maximum LDH activity of total lysed cells. Each data point and related error bars shown in figures for LDH assays represent the average results from three repeats.
Immunoblotting analysis and co-immunoprecipitation (Co-IP).
For immunoblotting, cells were treated by TcdB, serum starvation treatment (SS), or H 2 O 2 with or without chloroquine (CQ) for different time periods, and then lysed for immunoblotting analysis according to standard protocol. For Co-IP assay, plasmids were transfected into HeLa cells prior to different treatment, and the cells were subjected for immunoprecipitation analysis according to manufacturer's protocol of Sigma anti-Flag M2 affinity gel (#A2220, Sigma). Quantitative analysis was performed using ImageJ (http://rsbweb.nih.gov/ij/).
Construction of stable knockout cell lines using TALENs technique. The design and assembly of the two pairs of TALENs constructs used for ATG7 gene-knockout were based on our own ULtiMATE protocol 92 . More specifically, the two targeting sequences for ATG7 loci are 5′-CCTGGACTCTCTAAA-3′ for TALEN L (ATG7) and 5′-CCAAGGCACTACTAA-3′ for TALEN R (ATG7), with a spacer sequence (5′-ctgcagtttgcccctt-3′). The identification and verification of gene knockout events were based on both sequencing analysis of genome PCR fragments of targeting loci and immunoblotting analysis using antibodies specifically against ATG7. | 6,867 | 2017-09-05T00:00:00.000 | [
"Biology",
"Medicine"
] |
CNTCB-YOLOv7: An Effective Forest Fire Detection Model Based on ConvNeXtV2 and CBAM
: In the context of large-scale fire areas and complex forest environments, the task of identifying the subtle features and aspects of fire can pose a significant challenge for the deep learning model. As a result, to enhance the model’s ability to represent features and its precision in detection, this study initially introduces ConvNeXtV2 and Conv2Former to the You Only Look Once version 7 (YOLOv7) algorithm, separately, and then compares the results with the original YOLOv7 algorithm through experiments. After comprehensive comparison, the proposed ConvNeXtV2-YOLOv7 based on ConvNeXtV2 exhibits a superior performance in detecting forest fires. Additionally, in order to further focus the network on the crucial information in the task of detecting forest fires and minimize irrelevant background interference, the efficient layer aggregation network (ELAN) structure in the backbone network is enhanced by adding four attention mechanisms: the normalization-based attention module (NAM), simple attention mechanism (SimAM), global attention mechanism (GAM), and convolutional block attention module (CBAM). The experimental results, which demonstrate the suitability of ELAN combined with the CBAM module for forest fire detection, lead to the proposal of a new method for forest fire detection called CNTCB-YOLOv7. The CNTCB-YOLOv7 algorithm outperforms the YOLOv7 algorithm, with an increase in accuracy of 2.39%, recall rate of 0.73%, and average precision (AP) of 1.14%.
Introduction
Forests are a vital component of the Earth's ecosystem, providing rich biodiversity and habitats for numerous plants and animals.Their presence contributes to maintaining ecological balance, promoting species interactions, and ensuring the stability of ecosystems [1,2].However, forest fires devastate habitats and biodiversity.They are categorized by location into ground, surface, and crown fires, differing in behavior and impact.Their size, measured by the area burned or heat release rate (HRR), evolving from growth to decay phases, is influenced by environmental conditions and management.They can swiftly engulf vegetation and trees, leaving many wildlife species without their homes.Additionally, the significant carbon emissions released by forest fires exacerbate global climate change [3,4].This climate change, in turn, further increases the risk of forest fires, creating a vicious cycle.
The early detection of forest fires allows for prompt action and emergency response.This helps in quickly controlling the fire and reducing the damage and loss caused by the fire [5][6][7][8].At present, there are many ways to detect forest fires.Observation towers are a common way to see if forest fires are happening [9,10].With the development of satellite remote sensing technology, people begin to observe forest fires by satellite [11,12].The deployment of sensors to detect forest fires is also one of the common ways that real-time forest environment detection can quickly discover the fire situation.Deep learning models can perform real-time processing and analysis, enabling rapid detection and response to forest fires [13][14][15].This is crucial for emergency rescue and fire control, as it reduces the response time and helps minimize the damage caused by fires to some extent [16][17][18][19].As a deep-learning-based object detection algorithm, YOLOv7 offers a high detection accuracy and inference speed.It is currently widely applied in the field of forest fire detection.
In order to address the limitations of traditional methods and reduce false alarms and complexity, Yar et al. proposed an improved YOLOv5s model that integrates a Stem module in the backbone of YOLOv5, replaces the larger kernel with a smaller kernel in the neck, and adds a P6 module in the head.Their model outperforms 12 other detection models and contributes a medium-scale annotated fire dataset for future research [20].Al-Smadi et al. proposed a new framework that reduces the sensitivity of various YOLO detection models.Different yolo models, such as YOLOv5 and YOLOv7, are compared with Fast R-CNN (Region-based Convolutional Neural Network) and Faster R-CNN in detection performance and speed.The results show that the proposed method achieves significantly better results than the most advanced target detection algorithms while maintaining a satisfactory level of performance under challenging environmental conditions [21].Zhou et al., based on the overall structure of YOLOv5 and MobileNetV3 as the backbone network, used semi-supervised knowledge extraction (SSLD) for training, which improved the convergence speed and accuracy of the model [22].Dilli et al. used the target detection library YOLO model based on DL to carry out early wildfire detection on UAV thermal images, and used the significance graph integrated with thermal images to solve the shortcomings of using thermal images.The proposed approach is considered capable of providing technical support for night monitoring to reduce the catastrophic loss of forest resources and human and animal life in the early stages of wild forest fires [23].Zhang et al. proposed a multi-scale convergent coordinated pyramid network with mixed attention and fast Robust NMS (MMFNet) for the rapid detection of forest fire smoke [24].Jin et al. designed an enveloping self-focusing mechanism to solve the problem of identifying bad fire sources, focusing on the characteristics of the channel and spatial direction, and collecting contextual information as accurately as possible.In addition, a new feature extraction module is constructed to improve the detection efficiency while preserving the feature information [25].In summary, these studies share a common focus on improving fire detection performance using various modifications and enhancements to YOLO-based models.They explore different techniques, such as integrating new modules, comparing YOLO models with other detection algorithms, utilizing semi-supervised learning, and incorporating attention mechanisms.Despite their promising results, these studies may still face challenges in addressing specific issues, such as sensitivity to environmental conditions, identification of bad fire sources, and efficient feature extraction.Further research and development are needed to optimize these models and address their limitations.
With the continuous advancement of the YOLO series algorithms, YOLOv7 has emerged as a remarkable innovation, offering improved accuracy and faster processing speeds compared to its predecessor, YOLOv5.The application of YOLOv7 in forest fire detection holds great potential for enhancing the effectiveness of such detection efforts.However, the task of detecting forest fires poses certain challenges, particularly in scenarios where the fire area is extensive and the forest background is complex.In such cases, the model may struggle to capture the intricate details and distinguishing features of the fire.
To address these challenges and bolster the applicability of the YOLOv7 algorithm in forest fire detection, this research focuses on augmenting the model's capabilities by incorporating ConvNextV2 and ConvFormer networks.ConvNeXtV2 integrates self-supervised learning techniques along with Fully Convolutional Masked AutoEncoder (FCMAE) and Global Response Normalization (GRN) layers, enhancing the model's performance in various recognition tasks.Conv2Former employs a simple convolutional modulation layer instead of the self-attention mechanism, and compared with residual modules, the convolutional modulation operation in Conv2Former can also adapt to the content of the input.Moreover, to enhance the model's ability to discern crucial information amidst complex forest backgrounds, an attention mechanism is introduced through the ELAN-CBAM module, building upon the ELAN structure.This culmination of efforts gives rise to the CNTCB-YOLOv7 algorithm for forest fire detection.
Compared with the standard YOLOv7 algorithm, the CNTCB-YOLOv7 algorithm places greater emphasis on global information, effectively reducing false detection and elevating both the detection accuracy and AP.Leveraging these improvements, the research contributes to the study of forest fire behavior and the identification of key characteristics that aid in the understanding and prediction of forest fire propagation.This, in turn, facilitates more proactive and targeted firefighting strategies, ultimately leading to improved forest fire management and mitigation efforts.In addition, real-time monitoring and analysis of forest fire situations can collect a large amount of fire data, which is helpful for studying the spread patterns and characteristics of forest fires under different environments and conditions, such as the rate of fire spread.The improved model performance can also support the establishment of more accurate forest fire risk prediction models, enhancing the ability for early warning and forecasting.In conclusion, the proposed method in this study provides technical support for in-depth research on forest fire behavior and forest fire management.
Hyperparameter Settings
The hyperparameter settings in the experiments include the image size, epochs, batch size, initial learning rate (Lr0), and optimizer.Image size determines the input size of the model, usually measured in pixels, set to 640 × 640 pixels in our experiments.Epochs determine the number of iterations the model goes through the entire dataset during the training process, with 200 epochs set for this study.Batch size refers to the number of samples used to update the model weights each time, and here it is set to 8. Initial learning rate (Lr0) determines the initial learning speed of the model, which is set at 0.01 in our case.The optimizer determines the optimization method used by the model to find local optimal solutions, and in this study, stochastic gradient descent (SGD) is used as the optimization method.
The aforementioned settings, which contribute to enhancing the training process and the performance of the models, are derived from experimental trials and empirical assessments.The optimal configurations of these hyperparameters are influenced by the characteristics of the datasets and the architecture of the models.It is crucial to adjust these values when conducting different experiments to ensure the best possible outcomes.
Dataset
In order to obtain forest fire images required by model training, we employed various data collection methods.Firstly, we downloaded traditional forest fire images and nonforest fire images using web crawler technology.Secondly, we extracted a series of frames from downloaded forest fire videos to serve as additional forest fire images.Moreover, we utilized publicly available fire datasets, such as the BoWFireDataset [26].The combined use of these data sources contributes to enhancing the quality and effectiveness of the model training.A total of 2590 images were obtained.Among the collected images, 2058 images were positive sample images with forest fire, while the remaining 532 images were negative sample images without forest fire.To ensure the compatibility of the input data with our model's requirements, all images were uniformly resized to a resolution of 640 × 640 pixels.This standardization is crucial for maintaining consistency across the dataset and facilitating efficient processing by the models employed in our study.Furthermore, considering the specific context of detecting large-scale fires within complex forest environments, certain images underwent cropping, aimed at enhancing the proportional representation of fire within these images.Finally, the prepared forest fire dataset was divided into the training set and verification set according to the ratio of 8:2. Figure 1 shows some fire and non-fire images included in the dataset.
Model Performance Evaluation Index
In this paper, the task of forest fire detection is classified as a binary problem, that is, it is judged as fire or non-fire.For the forest fire category, fire is a positive sample and non-fire is a negative sample.In the binary classification problem of forest fire, the following four situations usually occur in the data sample, which are True Positive (TP), the result predicted by the model is positive sample, and the actual number of samples is positive sample, that is, the fire is predicted by the model, and the real picture is also fire, respectively.If the example is True Negative (TN), the result predicted by the model is negative samples, and the actual number of samples is negative samples; that is, it is predicted by the model as non-fire, and the real picture is also non-fire.In the case of False Positive (FP), the predicted result of the model is positive samples, but it is actually the number of samples of negative samples, that is, the number of samples that are misjudged as fire without fire.False Negative example (FN): The result predicted by the model is negative samples, but it is actually the number of samples of positive samples; that is, the number of samples that misjudge the fire as non-fire [27].
Precision is the proportion of true positive samples out of all the samples predicted as positive by the model.The calculation method is shown as Equation (1) [28].
Recall is the proportion of true positive samples that are accurately predicted as positive by the model, out of all the true positive samples.The calculation method is shown as Equation ( 2) [29].
Average precision (AP) is a metric that measures the average precision.It is obtained by calculating the area under the Precision-Recall (P-R) curve generated by plotting precision (P) on the x-axis and recall (R) on the y-axis.The calculation formula for AP is shown as Equation (3) [30].
When calculating AP, the average precision values for different classes are weighted and averaged to obtain the mean average precision (mAP) [31].The calculation formula is shown as Equation ( 4), where n represents the total number of classes and AP i represents the AP value for the i-th class.
mAP is commonly used to evaluate object detection algorithms.In this paper, we focus on forest fire detection, a single class, so we use the AP metric with a 50% Intersection Over Union (IOU) threshold, referred to as AP50 [32].
YOLOv7 Algorithm Structure
YOLOv7 is an object detection model known for its high accuracy, ease of training, and deployment capabilities [33].It has a faster network speed compared with the YOLOv5 model and achieves better results on the MS COCO (Microsoft Common Objects in Context) dataset.The overall network structure of YOLOv7 is shown in Figure 2, which shares similarities with the network structure of YOLOv5, with the main difference being the internal network modules.At the input end, YOLOv7 uses the same Mosaic data augmentation method as YOLOv5, as well as adaptive anchor box calculation and adaptive image scaling.The main backbone network of YOLOv7 incorporates the Extended Efficient Layer Aggregation Networks (E-ELAN) and Max Pooling (MP) modules, merging the model's Neck and Head layers into a unified Head layer.In Figure 2, MP1 and MP2 are two separate MP modules used in the YOLOv7 backbone network.
As shown in the diagram, the CBS (Convolution-BatchNorm-Silu) module consists of three components: a convolutional layer, a Batch Normalization layer, and a Silu (Sigmoid Linear Unit) activation function.The ELAN (Effective Layer Aggregation Network) module is an effective hierarchical aggregation network that employs a feature fusion technique to enhance the model's feature extraction capability and obtain stronger feature representations.The ELAN module has two main branches.One branch adjusts the number of channels using a 1 × 1 convolutional kernel, while the other branch adjusts the number of channels with a 1 × 1 convolutional kernel and then performs feature extraction using four consecutive 1 × 1 convolutional kernels.The outputs of the four branches are then concatenated to obtain the final output.The Efficient Layer Aggregation Networks-Higher (ELAN-H) module is similar to the ELAN module in structure, but it differs in the number of selected output features to be concatenated in the second branch, which is higher.
The MP module also consists of two main branches, as shown in Figure 3, and its main purpose is to perform downsampling operations on the feature maps.One branch uses max pooling followed by a 1 × 1 convolutional layer with a stride of 1 to adjust the number of channels.The other branch adjusts the number of channels with a 1 × 1 convolutional layer and then performs downsampling using a 3 × 3 convolutional layer with a stride of 2. The outputs of the two branches are concatenated to obtain the final downsampling output.
The SPPCSPC module, as a component of the YOLOv7 structure, effectively extracts image features and improves the detection accuracy of the model.The SPPCSPC module consists of two parts: SPP (Spatial Pyramid Pooling) and CSP (Cross Stage Partial).The SPP part is primarily responsible for performing feature pooling at different scales to extract features of varying sizes.The CSP part aims to reduce the number of parameters and further enhance the feature extraction capabilities.The structure of the SPPCSPC module is shown in Figure 4, featuring multiple branches of max pooling.Each max pooling branch operates at a different scale.The pooling operations at different scales have different receptive fields, allowing the model to better handle objects of varying sizes and ensuring the effectiveness of the detection process.
Conv2Former
The self-attention mechanism in transformers can model global pairwise dependencies and provide a more efficient way of encoding spatial information.However, when processing high-resolution images, self-attention can be computationally expensive.Con-vNext, by borrowing the design and training approach from transformers, achieves a better performance than some common transformers.To date, how to effectively construct more powerful models using convolutions remains a hot research topic.
In Conv2Former, when processing high-resolution input images, a simple convolutional modulation layer is used instead of self-attention, which can save memory consumption compared with self-attention.Moreover, compared with residual modules, the convolutional modulation operation in Conv2Former can also adapt to the content of the input [36].As shown in Figure 6, on the left is the self-attention operation, where the output of each pixel is obtained by taking the weighted sum of all the positions.Similarly, this process can be simulated by the convolutional modulation operation on the right side of the figure, which calculates the output of a large kernel convolution and performs a Hadamard product with the value representation.The results show that using convolution to obtain the weight matrix can also achieve good results.
Improved Strategy for YOLOv7
In order to improve feature extraction and information fusion for forest fire detection in larger and more complex scenarios, and to enhance the detection accuracy of the YOLOv7 algorithm, this study modifies the backbone network and the Head layer of the YOLOv7 algorithm.Specifically, high-performance ConvNeXtV2, Transformer-style Conv2Former, introduced in the previous chapter, are used to replace the first and last ELAN modules in the backbone network, as well as all ELAN-H modules in the head layer.As a result, multiple improved versions of the YOLOv7 algorithm are obtained, namely ConNeXtV2-YOLOv7 and ConvFormer-YOLOv7.As the overall network architecture is similar, this study only presents the network structure of ConNeXtV2-YOLOv7, as shown in the Figure 7.
Backbone and Head Improvement
To enhance the performance of convolutional neural network(CNN) models, a common approach is to introduce attention mechanisms.Attention mechanisms can suppress irrelevant noise information and allow CNN models to focus more on useful information, thereby improving the model's expressive power to handle different visual tasks.Additionally, attention mechanisms can select and compress feature maps, suppressing non-essential information and reducing the dimensionality of feature maps, thereby reducing computational complexity.Attention mechanisms can improve the model's robustness to factors such as occlusion and noise, making the model more robust.Furthermore, the introduction of attention mechanisms provides interpretability and visualizability, making the model's outputs more intuitive and understandable.To further improve the performance of the YOLOv7 algorithm and make the network pay more attention to important information in the current forest fire detection task, attention mechanisms are introduced to aggregate local information of feature maps.Specifically, improvements are made to the remaining ELAN module in the backbone network, as indicated by the "Attention" label in Figure 8. Four types of attention mechanisms are experimented with individually.
ELAN Structures That Introduce Attention Mechanisms
Normality-based Attention Module (NAM), as a lightweight and efficient attention module based on normalization , is often used in image classification and target detection tasks in deep learning.NAM proposed an attentional calculation method that can be weighted for input feature graphs [37].The importance of weights is expressed by the normalized scaling factor, so as to suppress irrelevant channels and pixel information in images.In this way, differences between input values can be better distinguished, allowing the network to focus more on the features that are most useful for the task at hand.
Attention mechanisms are commonly used in various computer vision tasks to improve model performance and have received widespread attention.However, the importance of preserving both channel and spatial information for enhancing cross-dimensional interactions is often overlooked.Therefore, a Global Attention Mechanism (GAM) is proposed, which aims to improve the performance of deep neural networks by reducing information redundancy and amplifying global interaction representations [38].GAM draws inspiration from the sequential channel attention mechanism of CBAM and redesigns the sub-modules.To maintain crossdimensional information, the channel attention sub-module in GAM uses a 3D arrangement and employs a multi-layer perceptron to amplify spatial dependencies across dimensions.Additionally, in the spatial attention sub-module, the concentration of spatial information is achieved through the use of two convolutional layers.Experimental results on image classification tasks such as CIFAR-100 and ImageNet-1k demonstrate that this attention mechanism exhibits an excellent performance in models like ResNet and MobileNet.
The Convolutional Block Attention Module (CBAM) is an attention mechanism that combines both spatial and channel attention to aggregate the local information of feature maps.The channel attention module and spatial attention module are two independent submodules of CBAM, allowing the network to focus more strongly on important information and perform weighted attention on both spatial and channel dimensions, achieving a plug-and-play effect [39].When a feature map is input to CBAM, it first goes through the channel attention module.In the channel attention module, the feature map undergoes two parallel operations: max pooling and average pooling, which compress the feature map into two one-dimensional feature vectors.These vectors are then passed through a shared fully connected layer, and the results are added together.Finally, the sigmoid activation function is applied to obtain the channel attention features.The channel attention features are multiplied with the input features to obtain the input features for the spatial attention module.This process also includes max pooling and average pooling operations.After pooling, the results are concatenated based on channels and passed through a convolutional layer to adjust the channels to 1.The sigmoid activation function is applied to obtain the spatial attention feature map.The spatial attention feature map is multiplied with the input of this module to obtain the final generated feature map.
Currently, attention modules usually suffer from two problems.First, they can only refine features along the channel or spatial dimension, thus limiting the flexibility of learning their attention weights across channels as well as spatial variations.In addition, their structures such as pooling need to be composed of a complex set of elements.Therefore, based on neuroscience theory, the SimAM module is proposed for solving these problems.After considering the spatial and channel dimensions, the 3D weights are inferred from the current neurons, and then the neurons are refined, allowing the network to learn more discriminative neurons.SimAM, as a conceptually simple but effective attention module , is able to infer feature maps in a layer without adding parameters to the original network compared with common spatial as well as channel attention module 3D weights [40].In addition, an optimized energy function is proposed so as to derive the importance of each neuron.On the CIFAR-10 and CIFAR-100 datasets, the SimAM module has a better performance in terms of accuracy compared with common attention modules such as SE and ECA.
Comparison of Multiple Model Results
In this section, we consider applying various structures to the YOLOv7 algorithm and compare the performance of the models to find a better model for forest fire detection.Table 1 shows a comparison of the experimental results for different models.Conv2Former has a better performance than traditional CNN-based models [36], and in order to further improve the model's performance, the Conv2Former-YOLOv7 algorithm was proposed.However, according to the results, applying Conv2Former-YOLOv7 to forest fire detection did not achieve the expected performance in terms of accuracy, recall rate, and AP.ConvNeXtV2 can enhance channel-wise feature competition and has shown a superior performance in various visual tasks by using fully convolutional mask autoencoders and global response normalization techniques.Therefore, the ConvNeXtV2-YOLOv7 algorithm was proposed.The experimental results showed that compared with the YOLOv7 algorithm, the ConvNeXtV2-YOLOv7 algorithm achieved an accuracy of 85.81% and an increase of 2.02%.It also improved the recall rate by 0.59% and the AP by 0.61%.After comprehensive comparison of overall performance, the ConvNeXtV2-YOLOv7 algorithm is more suitable for forest fire detection.
An Experimental Comparison of Attentional Mechanisms
In order to further enhance the model's generalization ability, suppress irrelevant features and pixel information in forest fire images, and better distinguish the differences between input values, the network should pay more attention to the most useful features for the current task.Therefore, in this section of the experiment, based on the performance of the ConNeXtV2-YOLOv7 algorithm, attempts were made to embed NAM, SimAM, GAM, and CBAM modules in the ELAN structure of its backbone network.In order to verify the feasibility of the method, comparative experiments were conducted between the attentionmechanism-integrated ConvNeXtV2-YOLOv7 algorithm and YOLOv7 and ConvNeXtV2-YOLOv7 algorithms.As shown in Table 2, it can be observed that compared with the ConNeXtV2-YOLOv7 algorithm, the introduction of SimAM and GAM attention modules did not effectively improve the model's performance; instead, there was a slight decline.However, by introducing the NAM and CBAM attention modules, there was a certain improvement in accuracy.Specifically, the introduction of the NAM attention module led to a decrease of 3.81% in the recall rate, while the introduction of the CBAM attention module showed a slight improvement.Additionally, both models showed varying degrees of improvement in AP, with the introduction of the CBAM attention module showing a more significant improvement.In terms of parameter count, the introduction of the GAM attention module increased the parameter count to 50.1 million (M), while the algorithms incorporating the NAM, SimAM, and CBAM modules all showed a decrease in parameter count compared with the YOLOv7 algorithm, and the parameter count was relatively close.Through comprehensive comparison, the performance of the ConNeXtV2-YOLOv7 algorithm was improved by incorporating the CBAM attention mechanism, leading to the proposal of the CNTCB-YOLOv7 forest fire detection method.Building upon the ConNeXtV2-YOLOv7 algorithm, embedding the CBAM module in the ELAN structure of the backbone network effectively improved the model's accuracy.Figure 9 illustrates the structure of ELAN-CBAM, which enhances global interactions while preserving channel and spatial information, thereby improving the performance and detection effectiveness of the network model.
Furthermore, as shown in Table 3, compared with the YOLOv7 algorithm, the CNTCB-YOLOv7 algorithm achieved an accuracy of 86.18%, an improvement of 2.39%.The recall rate and AP were also improved by 0.73% and 1.14%, respectively.Additionally, in terms of model lightweightness, the CNTCB-YOLOv7 algorithm only requires 33.73 M, a reduction of 3.47 M compared with the YOLOv7 algorithm.This reduction in computational resource usage helps improve the inference speed of the model.In addition, the YOLOv7 algorithm and the proposed CNTCB-YOLOv7 algorithm were tested on a dataset of test images, and partial test results are shown in Figures 10 and 11.
Figure 10 shows the test results for large-scale forest fires.In Figure 10a,c, we can see the test results of the YOLOv7 algorithm, while Figure 10b,d show the test results of the CNTCB-YOLOv7 algorithm.From Figure 10a,b, it can be observed that when the forest fire image represents a large-scale crown fire, the CNTCB-YOLOv7 algorithm performs better in terms of detection compared with the YOLOv7 algorithm.Furthermore, from Figure 10c,d, it can be seen that when the forest fire image represents a large-scale surface fire, the YOLOv7 algorithm only detects a portion of the fire area in the image, while the CNTCB-YOLOv7 algorithm is able to detect all fire areas in the image.The CNTCB-YOLOv7 algorithm pays more attention to the global information of forest fires compared with the YOLOv7 algorithm, resulting in a better detection performance.Figure 11 show the test results for complex forest backgrounds.In Figure 11a,c, we can see the test results of the YOLOv7 algorithm, while Figure 11b,d show the test results of the CNTCB-YOLOv7 algorithm.From Figure 11a,b, it can be observed that when there is background interference similar to the color of the fire in the image, both the YOLOv7 and CNTCB-YOLOv7 algorithms did not produce false detections.Additionally, the detection performance of the CNTCB-YOLOv7 algorithm is superior to that of the YOLOv7 algorithm.Furthermore, as shown in Figure 11c,d, when there are images with colors and textures similar to the fire, the YOLOv7 algorithm might have result in false detections, while the CNTCB-YOLOv7 algorithm did not lead to such occurrences.
Discussion
In order to improve the feature representation capability and detection accuracy of the model, and to make the network pay more attention to the most useful features for the current task, further enhancing the model's generalization ability, we made corresponding improvements to the YOLOv7 algorithm.The experimental results show that the proposed CNTCB-YOLOv7 algorithm surpassed the YOLOv7 algorithm in terms of precision, recall, and mean average precision, and it had a lower parameter count and faster inference speed.We first introduced the ConvNeXtV2 and Conv2Former network structures, replacing parts of the ELAN modules in the YOLOv7 algorithm to enhance the model's feature representation ability and detection accuracy.Comparative experiments revealed that the ConvNeXtV2-YOLOv7 algorithm was more suited for forest fire detection tasks, thus it was chosen as the base model for further improvements.On this foundation, we introduced an attention mechanism by embedding the CBAM module within the backbone network's ELAN structure, achieving the aggregation of local information in feature maps.This enabled the network to focus more on critical information in forest fire detection tasks, leading to the development of the CNTCB-YOLOv7 algorithm.The introduction of the CBAM module significantly improved the model performance, while reducing the parameter count, which is advantageous for enhancing the inference speed.This methodology offers technical support for in-depth research on forest fire behavior and management.Early high-precision detection can shorten response times, helping to quickly controlling the spread of fires and mitigate losses.Real-time monitoring and analysis of forest fires can collect extensive fire data, aiding in the study of fire spread patterns and characteristics under different environments and conditions, such as the rate of fire spread.The improved model performance also supports the development of more accurate forest fire risk prediction models, enhancing early warning and forecasting capabilities.
The CNTCB-YOLOv7 algorithm, characterized by a superior detection accuracy, can contribute significantly to an enhanced comprehension of fire behavior.This, in turn, facilitates the implementation of more proactive firefighting strategies, thereby bolstering the overall management and mitigation of forest fires.
However, there may be potential limitations in the model's generalization ability to different environments and conditions, which could be addressed in future work by exploring more diverse datasets and incorporating additional attention mechanisms.While our model demonstrates performance improvements over YOLOv7, it lacks comparative analysis with other prevalent models like Faster R-CNN, SSD, or RetinaNet.
In current study, the evaluation of our model primarily relied on metrics such as Precision, Recall, AP, and mAP.These metrics were selected due to their direct relevance to the performance goals of our classification task, especially in the context of our uniquely self-collected dataset.However, our analysis lacks crucial statistical measures that are essential for understanding the variability and reliability of the model's performance across different scenarios.This absence might limit the depth of our findings in terms of statistical consistency and reliability.
In future work, we plan to enhance our model through further refinement by incorporating additional attention mechanisms, conducting comprehensive comparisons with other prevalent models, and expanding our evaluation criteria.This expansion includes introducing standard deviations and confidence intervals in our analysis to provide a more comprehensive statistical understanding of our model's performance.Additionally, we aim to test and validate our model on a broader range of datasets.This expansion will not only enhance the generalizability of our findings, but also allow us to assess the model's performance under different scenarios and conditions.In addition, we will explore the applicability of our model in diverse domains by considering additional data types, such as LiDAR (Light detection and ranging) data [41,42].This broader range of datasets will enable us to thoroughly test and validate the robustness and versatility of our model across various fields.
Furthermore, future research could focus on optimizing the model's inference speed and reducing computational resource utilization, making it more suitable for real-time monitoring and analysis of forest fires.Furthermore, we plan to investigate how the enhanced model could support more accurate forest fire risk prediction models, thereby aiding in forest fire management and mitigation efforts.
Conclusions
This article presents a forest fire detection model based on ConvNeXtV2 and CBAM, named CNTCB-YOLOv7, designed to enhance the feature extraction and information fusion capabilities of the YOLOv7 algorithm to address challenges in large-scale fire areas and complex forest backgrounds.Firstly, we introduced networks such as ConvNeXtV2 and Conv2Former into the structure of YOLOv7 to find the best-performing network model.Then, we improved the ELAN structure in the backbone network using attention mechanisms and proposed the ELAN-CBAM structure.Based on the comparison of experimental results, we proposed a CNTCB-YOLOv7 Forest fire detection method.Compared with the YOLOv7 algorithm, the CNTCB-YOLOv7 algorithm achieved a 2.39% improvement in accuracy, and the recall rate and AP were improved by 0.73% and 1.14%, respectively.Additionally, the parameter count of CNTCB-YOLOv7 decreased by 3.47 M compared with the YOLOv7 algorithm, reducing the utilization of computational resources and helping to improve the model's inference speed.
Our future work includes refining the model with additional attention mechanisms, conducting thorough comparisons, and expanding the evaluation criteria.We aim to validate its performance on diverse datasets, optimize inference speed for real-time monitoring of forest fires, and explore its potential to support risk prediction models for better forest management.
Figure 4 .
Figure 4. SPPCSPC module.2.3.Improving the Network Used by the YOLO7 Algorithm 2.3.1.ConvNeXtV2The ConvNeXt model was proposed by leveraging the network structure of the Swin Transformer and using the ResNet-50 architecture as a base, as described in[34].The performance of the ConvNeXt model on COCO detection and ADE20K surpasses
Figure 5 .
Figure 5. Block structures of ConvNeXt V1 and ConvNeXt V2.In ConvNeXt V2, the GRN layer (in green) was added after the dimension-expansion MLP layer and the LayerScale (in red) was dropped.
Figure 6 .
Figure 6.Self attention mechanism and convolutional modulation operation.
Figure 8 .
Figure 8.The structure of introducing the attention mechanism for ELAN.
Figure 10 .
Figure 10.Test image results with a large range of forest fires: (a,c) YOLOv7 algorithm; and (b,d) CNTCB-YOLOv7 algorithm.
Table 1 .
Comparison of experimental results of different models.
Table 2 .
Experimental comparison of adding different attention mechanisms. | 7,772.8 | 2024-02-12T00:00:00.000 | [
"Environmental Science",
"Computer Science"
] |
Sudden large-volume detachments of low-angle mountain glaciers – 2 more frequent than thought ? 4
The detachment of large parts of low-angle mountain glaciers, resulting in massive ice-rock avalanches, have so far been 26 believed to be a unique type of event, made known to the global scientific community first for the 2002 Kolka Glacier detachment, Caucasus Mountains, and then for the 2016 collapses of two glaciers in the Aru range, Tibet. Since 2016, several 28 so-far unrecognized low-angle glacier detachments have been recognized and described, and new ones have occurred. In the current contribution, we compile, compare and discuss 20 actual or suspected large-volume detachments of low-angle 30 mountain glaciers at ten different sites in the Caucasus, the Pamirs, Tibet, Altai, Alaska’s St. Elias mountains, and the Southern Andes. Many of the detachments reached volumes in the order of 10–100 million m. The similarities and differences between 32 the presented cases suggest that glacier detachments often involve a coincidental combination of factors related to lowering of basal friction, high or increasing driving stresses, concentration of shear stress, or low resistance to exceed stability thresholds 34
period of mass-wasting activity, the glacier changed in unusual ways: it bulged and became heavily crevassed (Fig. 4), it developed a scarp at the location of the later detachment, and supraglacial ponds formed (Kotlyakov et al., 2004;Evans et al., 220 2009b;Kotlyakov et al., 2010b). Unusually high geothermal heat fluxes underneath the glacier (fumaroles and sulphur smell were reported in the glacier bed shortly after detachment), the impact energy of a large rock/ice fall, and successive loss of 222 shear stress due to excess water pressure have been proposed as possible factors and ultimate triggers of the 2002 detachment (Kotlyakov et al., 2004;Evans et al., 2009b;Kotlyakov et al., 2010b). Similarly, the additional loading of Kolka Glacier from 224 the rock and ice falls has more recently been proposed to have increased the basal shear stress until it exceeded a frictional threshold given by the glacier bed material, topography, and hydraulic conditions (Kääb et al., 2018). After the detachment, 226 lakes were visible on the Kolka Glacier bed, pointing to the involvement of large amounts of subglacial water in the detachment. The high mean avalanche velocities of 50-80 m/s (Huggel et al., 2005) suggest availability of large amounts of To roughly estimate the event volume we derive the ice thickness along the center flow line of the glacier based on an estimated 262 basal shear assuming a driving stress of 1.2 10 5 Pa as suggested for mountain glaciers, a slope of 16°, and a form factor of 0.8, which then results in a thickness of around 60 m (Cuffey and Patterson, 2010). Multiplying half of this depth (i.e. assuming a 264 triangular cross-section) with the detached area (ca. 200,000 m 2 ) gives a first volume estimate of roughly 6 10 6 m 3 . Whereas satellite images after detachment suggest that much of the glacier bed might actually have a triangular cross-section, it may 266 have been more shallow in the lowermost and uppermost parts. As an order of magnitude, we suggest a detachment volume of 5 10 6 m 3 and assign a conservative error of ±1 10 6 m 3 to this estimate.
268
The cirque from which the 2017 event originated was also the source of other slope instabilities over recent years. Another (much smaller) ice-rock avalanche from a neighbouring glacier occurred between 15 and 24 July 2016 (dates from Planet This glacier also showed increased sliding speeds and crevassing around the later detachment area for at least 2-3 weeks before the failure. For the end of July 2019 we found surface speeds of roughly 2.5 m/day, a marked increase compared to roughly < surge-like advance. This condition is still visible in Landsat data 5-6 years later, though less certain due to the lower resolution of Landsat data (no other data is available to us between 2007 and 2015). Landsat data also suggest that the glacier experienced 288 a similar advance in the early 1990s. Under the limitation of the reduced spatial resolution of the Landsat data, however, we do not find signs of a large detachment event or large ice-rock avalanche. Nevertheless, we draw attention to a surprisingly 290 vegetation-free landform visible downstream of the 2019 detachment in pre-event imagery (Fig. 8). The lack of vegetation, the streamlined microtopography, and zones of rough and chaotic microtopography that resemble avalanche or debris flow Very-high resolution satellite images over the Peter the First Range suggest abundance of weak bedrock and fine sediments.
298
All over the range, signs after large debris flows, rock avalanches or ice-rock avalanches are visible in high resolution satellite images (Maxar, CNES/Airbus, Planet; Leinss et al, 2020). The Pamirs in general are known to be geomorphologically very 300 active, with a number of associated hazards (Mergili et al., 2012;Gruber and Mergili, 2013;Strom and Abdrakhmatov, 2018) and a cluster of surge-type glaciers (Kotlyakov et al., 2008;Kotlyakov et al., 2010a;Gardelle et al., 2013; Even if not documented in detail in an internationally accessible format so far, to our best knowledge, both the 2017 and 2019 detachments and their downstream effects were very likely noted by the local communities as the lowermost ice/rock deposits 310 stopped not far from settlements, agricultural fields, and pastures, and very-high resolution images (Maxar) show that flooding happened close to houses and two irrigation channel bridges were partially destroyed. County, China) in the western Tibetan Plateau (termed Aru-1). The fragmented ice mass ran out 6 km beyond the glacier terminus, killing nine herders and hundreds of their animals, and reached the Aru Co lake (Tian et al., 2017;Kääb et al., 2018).
336
The ice debris covered 8-9 km 2 and a volume of the detached glacier part of 68 10 6 m 3 was calculated. On 21 September 2016, a second glacier (Aru-2) detached just a few km south of Aru-1 ( Fig. 9). Similar to the July event, the glacier ice fragmented (Gilbert et al., 2018). It showed that the two glaciers were close to their steady state geometry with no/little sliding until 2010. Thereafter, decreasing friction under the whole detachment area of Aru-1 and in more localized zones of Aru-2 356 started to trigger the surge-like mass transfer. Modelling the glaciers' thermal regimes revealed that the frictional changes likely occurred in temperate areas of the two glaciers and that stress concentration occurred on the cold-ice margins (Gilbert 358 et al., 2018). The surge-like changes of basal friction under the Aru glaciers were thus likely not associated with a change of the glaciers' thermal regimes but rather with a change in friction due to increasing water pressure in the already temperate (Wenying, 1983). The first ice-rock avalanche happened between 26 January and 3 February 2004, 384 and the involved volume was estimated to be 20-25 10 6 m 3 , perhaps up to 36 10 6 m 3 according to a local information signboard (Paul, 2019). Three years later, between 23 September and 2 November 2007, a second detachment followed a surge- The event seems to have had a severe impact on Sedongpu Glacier. We generated two elevation models from 13 Nov 2015 428 Spot6 and 30 Dec 2018 Pleiades tri-stereo data that produced robust results despite the extreme topographic conditions. Differencing the two DEMs indicates that the October 2017 rock avalanche removed around 17 and 33 10 6 m 3 of material 430 from two close-by but separated areas, respectively (Fig. 11c). If both failures happened as part of the same event, the total volume of 50 10 6 m 3 makes this one of the larger rock avalanches detected in recent decades. Based on visual inspection of 432 satellite data, we consider it very likely that the avalanche also involved small glaciers from the west wall of Gyala Peri and incorporated ice from the surface of the glaciers lower down, as it ran over them. The Chinese seismic database registered two Jacquemart et al. (2020) found that the water availability during the exceptionally warm summer of 2013 was primarily melt driven and up to 4.8 standard deviations (σ) above the long term mean . No detachments were detected in 2014, 544 when water availability was below average (-0.5 σ). Water availability was again higher in 2015 (+ 1 σ), when the second detachment occurred.
566
The volume of the deposit was estimated at 8.1 10 6 m 3 (Marangunic, 1980). Five mountaineers witnessed the event and noted https://doi.org/10.5194/tc-2020-243 Preprint. Discussion started: 22 October 2020 c Author(s) 2020. CC BY 4.0 License. several supraglacial ponds and 2-3 cm of wet snow on the surface of the glacier (Marangunic, 1980). These observations 568 suggest that the triggering mechanism of the glacier detachment likely involved an extreme reduction of the basal drag due to high water saturation of the glacier bed. Aparejo glacier appears to sit on a glacier bed composed primarily of weak subglacial 570 till , and the slope on the lower two thirds of the glacier averages 7°. Snowmelt infiltration and warm precipitation due to a sudden increase of the zero-degree isotherm elevation could have provided the main source of infiltrated water, leading to 572 enhanced water pressure at the glacier bed. During a field inspection on 12 March 1980, Marangunic (1980) found that the nearby debris-covered glacier to the east, glacier no 51 according to the Chilean glacier inventory at the time (Fig. 14), also 574 showed significant signs of surge-like instability, such as a heavily crevassed front and patches of freshly exposed ice along its entire length. The prominent terminal moraine of this glacier may have contained its detachment, though.
576
The Aparejo glacier is situated in a region of complex geology with a number of weak rock formations, including sandstones and fine-grained conglomerate in the immediate vicinity of the glacier. (Ugalde, 2016). Ugalde (2016) sampled the grain size 578 distribution of the remains of the lower ice-rock avalanche deposits and did not find them to contain more fines that a typical moraine, but notes that spatial variability was high and that the 35 years since the detachment mav have depleted the deposits 580 of fine particles. In the former avalanche path, modern satellite images show streamlined striations similar to those reported from several other detachments in this contribution. Remarkably, similar striations are also visible in Hycon airphotos from 582 1956. Interestingly, the geomorphology of the deposit area is similar between the 1956 airphotos and the post 1980-event highresolution satellite images. One possible interpretation of this is that large mass flows had already originated from the Aparejo 584 cirque at earlier times. A detailed field investigation would be required to determine whether the striations consist of glacial flutes formed under a previous glacier extent or stem from a catastrophic detachment.
586
In 2015, the glacier had around 15% of its pre-detachment volume, covering much of the original area, and with a surface slope of around 20° (Ugalde, 2016). The current glacier terminus lies at around 3400 m a.s.l., slightly below the lower regional The role of basal water pressure in the detachments is difficult to examine in detail, but most detachments could have involved severe reduction in friction due to high basal water pressure (likely at least for Kolka 2002, Aru, Flat Creek, Sedongpu, 738 Aparejo). Ways to rapidly increase basal water pressure include: an increase in water input (e.g., large high-altitude rain events (Kääb et al., 2018) or increased surface snow/ice melt) into a subglacial drainage system not capable of adjusting fast enough; 740 inefficiencies or blockages of this drainage system; or increased permeability of the glacier through enhanced crevassing (Dunse et al., 2015). Sudden weakening of the strength of subglacial till under high pore water pressure and over large parts 742 of the glacier bed was shown to be a key process leading to the Aru detachments (Gilbert et al., 2018). Ongoing surge-like activity may enhance sensitivity to water input (Flowers et al., 2016).
744
In Figure 18 we attempt to summarize the main drivers of the glacier detachments described here. We define a detachment's disposition as the sum of long-term factors that might promote glacier detachments and refer to triggers to describe short-term 746 factors that might suddenly tip the scale toward a catastrophic failure. Fundamentally, it seems that different combinations of dispositions and triggers are able to produce instability. Aside from the commonalities mentioned above, the observed and planning. The particularly low friction coefficients (H/L) involved in the detachments enable them to travel over low slopes (where other types of ice-rock avalanches would stall) and to cover large distances. The detachment events seem very 802 rare, but their large volumes, fast evolution, and the exceptionally long reaches and high speeds hold the potential for severe impacts even far away from the source. Our compilation of all (so far) known cases shows that low-angle glacier detachments 804 might have, though rare, more frequently occurred than thought. The differences between the events suggest that there is no straightforward way to predict where they might occur, but the following list of the most common conditions might support a 806 more systematic assessment. high driving stresses, the resulting concentration of high shear stresses, and the lack of sufficient resistance develop fastly, or are combined fastly, preventing the glacier to adjust to changing forces in a steady way. Several of the factors 838 potentially involved in the detachment are subsequently also able to strongly reduce basal friction of the resulting icerock avalanche and lead thus to particularly low angles of reach. Boxes in the figure indicate main physical conditions, 840 grey italic text indicates different actual processes that can fulfil these conditions, sorted from long-term (left) to shortterm (right) variability.
Conclusions
In this contribution we describe around a dozen ice-rock avalanche events that we characterize as sudden large-volume 844 detachments of low-angle glaciers. Overall, these events seem to be more frequent than previously thought. The detached volumes ranged from a few up to more than 100 10 6 m 3 . We described one new event in the same size-class as the 2002 Kolka 846 https://doi.org/10.5194/tc-2020-243 Preprint. Discussion started: 22 October 2020 c Author(s) 2020. CC BY 4.0 License.
• Repeated events or geomorphological imprints of potential earlier collapses or other violent ice-rock mass flows can 878 be further investigated, but events can also happen without historical precedence through shifts in the array of failure conditions.
880
• Several of the glaciers investigated here showed abnormal crevassing and enhanced precursory surface speeds in the days to weeks before detachment.
882
• The surface slopes found in this study for the detached glaciers ranged between roughly 10° and 20°.
Due to the large amounts of snow and ice involved in glacier detachments, the high chance of lubrication and of liquefaction 884 of glacier ice and subglacial sediments, and smooth geometries of glacial valleys, avalanche friction is typically greatly reduced. This results in the particularly high mobility of the ice-rock avalanches resulting from low-angle glacier detachments 886 and can lead to substantial damage far from the source. Between the large runout distances and the varying factors that can impact a glacier's detachment probability, high-mountain hazard management will, after the first general assessment provided 888 in this study, benefit from more detailed investigations of glacier detachments, the conditions that lead to them and the mechanics that drive them. | 3,588.2 | 2021-04-12T00:00:00.000 | [
"Geology"
] |
Learning Discriminative Projection With Visual Semantic Alignment for Generalized Zero Shot Learning
Zero Shot Learning (ZSL) aims to solve the classification problem with no training sample, and it is realized by transferring knowledge from source classes to target classes through the semantic embeddings bridging. Generalized ZSL (GZSL) enlarges the search scope of ZSL from only the seen classes to all classes. A large number of methods are proposed for these two settings, and achieve competing performance. However, most of them still suffer from the domain shift problem due to the existence of the domain gap between the seen classes and unseen classes. In this article, we propose a novel method to learn discriminative features with visual-semantic alignment for GZSL. We define a latent space, where the visual features and semantic attributes are aligned, and assume that each prototype is the linear combination of others, where the coefficients are constrained to be the same in all three spaces. To make the latent space more discriminative, a linear discriminative analysis strategy is employed to learn the projection matrix from visual space to latent space. Five popular datasets are exploited to evaluate the proposed method, and the results demonstrate the superiority of our approach compared with the state-of-the-art methods. Beside, extensive ablation studies also show the effectiveness of each module in our method.
I. INTRODUCTION
With the development of deep learning technique, the task of image classification has been transfered to large scale datasets, such as ImageNet [1], and achieved the level of human-beings [2]. Does it mean that we are already to solve large-scale classification problems? Two questions should be answered: 1) Can we collect enough samples of all the classes appeared all over the world for training? 2) Can the trained model with limited classes be transfered to other classes without retraining? The first question cannot be given an affirmative answer because there are 8.7 million classes only in animal species [3] and over 1000 new classes are emerging everyday. Therefore, many researchers moved their focus to the second question by employing transfer learning [4], [5] and Zero-shot Learning (ZSL) [6].
ZSL tries to recognize the classes that have no labeled data available during training, and is usually implemented by The associate editor coordinating the review of this manuscript and approving it for publication was Gang Li . employing auxiliary semantic information, such as semantic attributes [7] or word embeddings [8], which is similar to the process of human recognition of new categories. For example, a child who has not seen a ''zebra'' before but knows that a ''zebra'' looks like a ''horse'' and has ''white and black stripes'', will be able to recognize a ''zebra'' very easily when he/she actually sees a zebra.
Since the concept of ZSL was first proposed [9], many ZSL methods have been proposed and most of them try to solve the inherent domain shift problem [10]- [13], which is caused by the domain gap between the seen classes and unseen classes. Although these methods can alleviate the domain shift problem and achieve certain effect, their performance are limited due to their negligence of unseen classes. To fully solve the domain shift problem, Fu et al. [14] assumed that the labeled seen samples and the unlabeled unseen samples can be both utilized during training, which is often called transductive learning. This type of method can significantly alleviate the domain shift problem and achieve the state-of-the-art performance [15]- [17], but the unlabeled VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ unseen data usually is inaccessible during training in realistic scenarios.
In addition, conventional inductive learning often assumes that the upcoming test data belongs to the unseen classes, which is also unreasonable in reality because we cannot have the knowledge of the ascription of the future data in advance. Therefore, Chao et al. suggested to enlarge the search scope for test data form only the unseen classes to all classes [18], including both seen and unseen categories, which is illustrated in Fig. 1. To better solve the domain shift problem on the more realistic GZSL setting, many synthetic based methods have been proposed [19]- [22]. They often train a deep generative network to synthesize unseen data from its corresponding attribute by applying the frameworks of Generative Adversarial Network (GAN) [23] or Variational Auto-Encoder (VAE) [24], and then the synthesized data and the labeled seen data are combined to train a supervised close-set classification model. The synthetic based methods can also achieve state-of-the-art performance, but there is a serious problem that when a totally new object emerges the trained model will inevitably fail unless new synthetic samples are generated and retrained with previous samples. To solve the above mentioned problems, in this article, we proposed a novel method to learn discriminative projections with visual semantic alignment in a latent space for GZSL, and the proposed framework is illustrated in Fig. 2. In this framework, to solve the domain shift problem, we define a latent space to align the visual and semantic prototypes, which is realized by assuming that each prototype is a linear combination of others, including both seen and unseen ones. With this constraint, the seen and unseen categories are combined together and thus can reduce the domain gap between them. Besides, to make the latent space more discriminative, a Linear Discriminative Analysis (LDA) strategy is employed to learn the projection matrix from visual space to latent space, which can significantly reduce the within class variance and enlarge the between class variance. At last, we conduct experiments on five popular datasets to evaluate the proposed method. The contributions of our method is summarized as follows, 1) We proposed a novel method to solve the domain shift problem by learning discriminative projections with visual semantic alignment in latent space; 2) A linear discriminative analysis strategy is employed to learn the projection from visual space to latent space, which can make the projected features in the latent space more discriminative; 3) We assume that each prototype in all three spaces, including visual, latent and semantic, is a linear sparse combination of other prototypes, and the sparse coefficients for all three spaces are the same. This strategy can establish a link between seen classes and unseen classes, reduce the domain gap between them and eventually solve the domain shift problem; 4) Extensive experiments are conducted on five popular datasets, and the result shows the superiority of our method. Besides, detailed ablation studies also show that the proposed method is reasonable. The main content of this article is organized as follows: In section II we briefly introduce some related existing methods for GZSL. Section III describes the proposed method in detail, and Section IV gives the experimental results and makes comparison with some existing state-of-the-art methods on several metrics. Finally in section V, we conclude this article.
II. RELATED WORKS
In this section, we will briefly review some related ZSL and GZSL works for the domain shift problem.
A. COMPATIBLE METHODS
Starting from the proposed ZSL concept [9], many ZSL methods have been emerging in recent several years. Due to the existence of the gap between the seen and unseen classes, an inherent problem, called domain shift problem, limits the performance of ZSL. These methods often project a visual sample into semantic space, where Nearest Neighbor Search (NNS) is conducted to find the nearest semantic prototype and its label is assigned to the test sample. Kodirov et al. tried to use an autoencoder structure to preserve the semantic meaning from visual features, and thus to solve the domain shift problem [13]. Zhang et al. exploited a triple verification, including an orthogonal constraint and two reconstruction constraints, to solve the problem and achieved a significant improvement. Akata et al. proposed to view attribute-based image classification as a label-embedding problem that each class is embedded in the space of attribute vectors [25], they employed pair-wise training strategy that the projected positive pair in the attribute space should have shorter distance than that of negative pair. However, the performance of these method are limited due to their negligence of unseen classes during training.
In addition, conventional ZSL assumes that the upcoming test sample belongs to the target classes, which is often unreasonable in realistic scenarios. Therefore, Chao et al. extended the search scope from only unseen classes to all classes, including both seen and unseen categories [18]. Furthermore, Xian et al. re-segmented the five popular benchmark datasets to avoid the unseen classes from overlapping with the categories in ImageNet [26]. Beside, they also proposed a new harmonic metric to evaluate the performance of GZSL, and release the performance of some state-of-the-art method on the new metric and datasets. From then on, many methods have been proposed on this more realistic setting. For example, Zhang et al. proposed a probabilistic approach to solve the problem within the NNS strategy [27]. Liu et al. designed a Deep Calibration Network (DCN) to enable simultaneous calibration of deep networks on the confidence of source classes and uncertainty of target classes [28]. Pseudo distribution of seen samples on unseen classes is also employed to solve the domain shift problem on GZSL [29]. Besides, there are many other methods developed for this more realistic setting [30], [31].
B. SYNTHETIC BASED METHODS
To solve the domain shift problem, synthetic based methods have attracted wide interest among researchers since they can obtain very significant improvement compared with traditional compatible methods.
Long et al. [32] firstly tried to utilize the unseen attribute to synthesize its corresponding visual features, and then train a fully supervised model by combining both the seen data and the synthesized unseen features. Since then, more and more synthetic based methods have being proposed [8], [30], [31], [33], and most of them are based on GAN [23] or VAE [24] because adversarial learning and VAE can facilitate the networks to generate more realistic samples [34], [35]. CVAE-ZSL [36] exploits a conditional VAE (cVAE) to realize the generation of unseen samples. Xian et al. proposed a f-CLSWGAN method to generate sufficiently discriminative CNN features by training a Wasserstein GAN with a classification loss [19]. Huang et al. [37] tried to learn a visual generative network for unseen classes by training three component to evaluate the closeness of an image feature and a class embedding, under the combination of cyclic consistency loss and dual adversarial loss. Dual Adversarial Semantics-Consistent Network (DASCN) [20] learns two GANs, namely primal GAN and dual GAN, in a unified framework, where the primal GAN learns to synthesize semantics-preserving and inter-class discriminative visual features and the dual GAN enforces the synthesized visual features to represent prior semantic knowledge via semantics-consistent adversarial learning.
Although these synthetic based methods can achieve excellent performance, they all suffer from a common serious problem that when an object of a new category emerges, the model should be retrained with the new synthesized samples of the new category. Different from these GAN or VAE based synthetic methods, our approach is a compatible one, which does not have the previous mentioned problem, and it can still accept new category without retraining even though there will be a little performance degradation.
C. TRANSDUCTIVE METHODS
Fu et al. tried to include the unlabeled unseen data in training, which is often called transductive learning, to solve the domain shift problem and achieved a surprising improvement [14]. Unsupervised Domain Adaptation (UDA) [38] formulates a regularized sparse coding framework, which utilizes the unseen class labels' projections in the semantic space, to regularize the learned unseen classes projection thus effectively overcoming the projection domain shift problem. QFSL [15] maps the labeled source images to several fixed points specified by the source categories in the semantic embedding space, and the unlabeled target images are forced to be mapped to other points specified by the target categories. Zhang et al.proposed a explainable Deep Transductive Network (DTN) by training on both labeled seen data and unlabeled unseen data, the proposed network exploits a KL Divergence constraint to iteratively refine the probability of classifying unlabeled instances by learning from their high VOLUME 8, 2020 confidence assignments with the assistance of an auxiliary target distribution [17]. Although these transductive methods can achieve significant performance and outperform most of conventional inductive ZSL methods, the target unseen samples are usually inaccessible in realistic scenarios.
III. METHODOLOGY A. PROBLEM DEFINITION
Let Y = {y 1 , · · · , y s } and Z = {z 1 , · · · , z u } denote a set of s seen and u unseen class labels, and they are disjoint Y ∩Z = ∅. Similarly, let A Y = {a y1 , · · · , a ys } ∈ R l×s and A Z = {a z1 , · · · , a zu } ∈ R l×u denote the corresponding s seen and u unseen attributes respectively. Given the training data in 3-tuple of N seen samples: (x 1 , a 1 , y 1 from N seen images. When testing, the preliminary knowledge is u pairs of attributes and labels:( a 1 , z 1 ), · · · , ( a u , z u ) ⊆ A Z × Z. Zero-shot Learning aims to learn a classification function f : X u → Z to predict the label of the input image from unseen classes, where x i ∈ X u is totally unavailable during training.
B. OBJECTIVE
In this subsection, we try to propose an novel idea to learn discriminative projection with visual semantic alignment for generalized zero shot learning, the whole architecture is illustrated in Fig. 2.
1) SAMPLING FROM PROTOTYPES
Suppose we have already know the prototypes of seen classes, the seen features should be sampled from these prototypes, so we can have the following constraint, where, P s is the prototypes of seen categories, Y s is the one-hot labels of seen samples, and · 2 F denotes for the Frobenius norm.
2) PROTOTYPE SYNTHESIS
Here we think each class prototype can be described as the linear combination of other ones with corresponding reconstruction coefficients. The reconstruction coefficients are sparse because the class is only related with certain classes. Moreover, to make the combination more flexible, we define another latent space, and construct a sparse graph in all three space as, where, H is the coefficient matrix; P = [P s , P u ], P s and P u are visual prototypes of seen classes and unseen classes respectively; C = [C s , C u ], C s and C u are the prototypes of seen classes and unseen classes respectively in latent , α and β are the balancing parameters. We apply diag(H) = 0 to avoid the trivial solution.
3) VISUAL-SEMANTIC ALIGNMENT
In the latent space, the prototypes are the projections from both visual space and semantic space, so the alignment can be represented as, where, W 1 and W 2 are the projection matrices from visual space and semantic space respectively.
4) LINEAR DISCRIMINATIVE PROJECTION
In visual space, the features might not be discriminative, which is illustrated in Fig. 2, so the direct strategy is to cluster them within class and scatter them between classes. Linear Discriminative Analysis is the proper choice and we can maximize the following function to achieve such purpose, where, S B and S W are the between-class scatter matrix and within-class scatter matrix respectively.
C. SOLUTION
Since we have already defined the loss function for each constraint, we can combine them and obtain the final objective as follows, where γ , κ and λ are the balancing coefficients.
1) INITIALIZATION
Since Eq. 5 is not joint convex over all variables, there is no close-form solution simultaneously. Thus, we propose an iterative optimization strategy to update a single unresolved variable each time. Because proper initialization parameters can not only improve the model performance but also increase the convergence speed, we further split the solution into two sub problems, i.e., initializing the parameters with reduced constraints, and iterative optimizing them with the full constraints.
Initializing H: Since A is known in advance, we initialize H first with the last term of Eq. 2. We exploit the following formulation as the loss function for H, To solve the constraint diag(H) = 0, we calculate H once per column, where H i is the i th column of H and the i th entry of H i is also removed, A \i is the matrix of A excluding the ith column.
Initializing P s : We use Eq. 1 to initialize P s , and the closed-form solution can be obtained as follows, Initializing P u : Since there is no training data for unseen classes, we cannot use the similar initialization strategy as P s to initialize P u . However, we have already get H with Eq. 7 in advance, it is easy to utilize P s and H to calculate P u . The simplified loss function can be formulated as follows, By computing the derivative of Eq. 10 with respected to P u and setting it to zero, we can obtain the following solution, Since C is unknown till now, we cannot calculate W 1 withe Eq. 3. The only way for W 1 is to optimize Eq. 4, from which we can deduce the following formulation, If we define = τ , then W 1 can be solved by obtaining the eigenvector of S −1 W S B . Initializing C: Since W 1 and P are already known, it is easy to initialize C with the first item of Eq. 3, and the solution is, Initializing W 2 : By employing the second item of Eq. 3, W 2 can be solved with following formulation,
2) OPTIMIZATION
Since the initialized value of each variable has already been obtained, the optimization of them can be executed iteratively by fixing others.
Updating H: Similar as that for initializing H, we can obtain H once per column with the following loss function, By taking the derivative of L H i with respect to H i , and setting the result to 0, we can obtain the solution of H i as follows, Updating P s : By fixing other variables except P s , we can obtain the following loss function from Eq. 5, which can be expanded as, Eq. 17 can be simplified to AP s + P s B = C, which is a well-known Sylvester equation and can be solved efficiently by the Bartels-Stewart algorithm [39]. Therefore, Eq. 17 can be implemented with a single line of code P s = sylvester( A, B, C) in MATLAB.
Updating P u : Similar as that for P s , we fix other variables except P u , and obtain, By taking the derivative of L P u with respect to P u , and set the result to 0, we can obtain the following equation, Similarly, if we set can be simplified to AP u + P u B = C, which can also be solved efficiently with P u = sylvester( A, B, C) in MATLAB.
Updating C: If we only let C variable and make others fixed, Eq. 5 can be reduced as, By taking the derivative of L C with respect to C, and set the result to 0, we can obtain the solution of C as follows, Updating W 2 : As for W 2 , Eq. 5 can be simplified as, By taking the derivative of L W 2 with respect to W 2 , and set the result to 0, we can obtain the solution of W 2 as follows, Updating W 1 : Similar as W 2 for W 1 , Eq. 5 can be reduced as, Due to the direct derivative of Eq. 22 will cause the negative order of W 1 , we rewrite it as follows, where, η is a coefficient and set as the maximum eigenvalue of S −1 W S B here. By taking the derivative of L W 1 with respect to W 1 , and set the result to 0, we can obtain the solution of W 1 as follows, After these steps, the test sample can be classified by projecting it into the latent space and finding the nearest neighbor of it from C. The algorithm of the proposed method is described in Alg. 1.
IV. EXPERIMENTS
In this section, we first briefly review some datasets applied in our experiments, then some settings for the experiments are given, and at last we show the experiment results and ablation study to demonstrate the performance of the proposed method.
A. DATASETS
In this experiment, we utilize five popular datasets to evaluate our method, i.e., SUN (SUN attribute) [40], CUB (Caltech-UCSD-Birds 200-2011) [41], AWA1 (Animals with Attributes) [42], AWA2 [42] and aPY (attribute Pascal and Yahoo) [43]. Among them, SUN and CUB are fine-grained datasets while AWA1/2 and aPY are coarse-grained ones. The detailed information of the datasets is summarized in Tab. 1, where ''SS'' denotes the number of Seen Samples for training, ''TS'' and ''TR'' refer to the numbers of unseen class samples and seen class samples respectively for testing. The set of visual features of seen classes: X s ; The set of one-hot labels of X s : Y s ; the set of semantic attributes, including both seen and unseen classes: A; The number of iterative time for optimization: iter; The hyper-parameters: α, β, γ , λ, κ and θ ; Output: The projection matrices: W 1 and W 2 ; The visual prototypes of both seen and unseen classes: P s and P u ; The latent prototypes of both seen and unseen classes: C s and C u ; 1: Initializing H with Eq. 7 once per clolumn; 2: Initializing P s and P u with Eq. 8 and Eq. 10 respectively; 3: Initializing W 1 with the eigenvectors of S −1 W S B from Eq. 11; 4: Initializing C with Eq. 12; 5: for k = 1 → iter do 6: Update H with Eq. 15 once per column; 7: Update P s with Eq. 17 by applying P s = sylvester ( A, B, C); 8: Update P u with Eq. 19 by applying P u = sylvester ( A, B, C); 9: Update C with Eq. 21; 10: Update W 2 with Eq. 23; 11: Update W 1 with Eq. 26; 12: end for 13: return W 1 , W 2 , P s , P u and C.
Moreover, we use the same split setting, which is proposed by Xian et al. in [26], for all the comparisons with the stateof-the-art methods listed in Tab. 2.
B. EXPERIMENTAL SETTING
We exploit the extracted features with ResNet [2] as our training and testing samples, which are released by Xian et al. [26], and all the the settings, including both attributes and classes split, are also the same as those in [26]. In addition, there are six hyper-parameters α, β, γ , λ, κ and θ . Since θ is only used to control the regularization terms, we set it with a small value 1 × 10 −4 . As for other five parameters, due to the fact that different dataset usually performs well with different parameters, thus we choose our hyper-parameters from the set of {0.001, 0.01, 0.1, 1, 10, 100, 1000} by adopting a cross validation strategy. To be specific, we hereby compare the difference of ZSL cross-validation to conventional cross-validation for machine learning approaches. Compared to inner-splits of training samples within each class, ZSL problem requires inter splits by in turn regarding part of seen classes as unseen, for example, 20% of the seen classes are selected as the validational unseen classes in our experiments, and the parameters of best average performance of 5 executions are selected as the final optimal parameters for each dataset. It should be noted that the parameters may not be the most suitable for the test set, because the labels of test data are strictly inaccessible during training.
C. COMPARISON WITH BASELINES
In this subsection, we conduct experiments to compare our method with some baselines methods. In addition to the methods evaluated in [26], we also compare our method with some newly proposed frameworks, such as GFZSL [50], LAGO [51], PSEUDO [52], KERNEL [53], TRIPLE [54], LESAE [55], LESD [56] and VZSL [22]. To be specific, we directly cite the results from [26] or from their own papers if it is feasible, otherwise we re-implement them according to the methods described in their own papers. We exploit the harmonic mean H to evaluate our model under the GZSL setting, and it is defined as, where, acc tr and acc ts are the accuracies of test samples from seen classes and unseen categories respectively, and we adopt the average per-class top-1 accuracy as the final result. Since our method utilizes both seen and unseen semantic attributes and focuses on the more realistic GZSL setting, we do not report the result on conventional ZSL setting. The results of our method and the compared method are recorded in Tab. 2, and the best result of each column is highlighted with bold font. From this table, we can clearly discover that our method can outperform the state-of-the-art methods on both ts and H . Concretely, our method can improve ts by 0.8% on SUN, 4.0% on CUB, 6.5% on AWA1, 5.7% on AWA2 and 5.2% on APY, and enhance H by 0.6% on SUN, 0.2% on CUB, 9.8% on AWA1, 7.7% on AWA2 and 8.0% on APY respectively compared with the best methods LESAE and TRIPLE. Besides, compared to those existing methods that have high tr but low ts and H , such as DAP and CONSE, our method can achieve more balanced performance on ts and tr and eventually obtain a significant improvement on H . We ascribe this improvement to the discriminative projection with LDA and the prototype synthesis with both seen and unseen classes, because the first one can make the projected features from same class cluster and from different classes disperse, and the second one combines both seen and unseen classes into a unified framework to alleviate the domain shift problem.
D. ABLATION STUDY 1) EFFECT OF LATENT SPACE
In our method, we utilize the latent space as the intermediate space for both visual and semantic features and we have claimed that this space can obtain more discriminative projection and alleviate the domain shift problem. Therefore, it is necessary to verify whether this space can achieve such statement. In this subsection, we remove the latent prototypes from Eq. 2 and Eq. 3, modify the discriminative projection item with LDA, and redefine the three loss functions as follows, We replace the three items L syn , L eqnarray and L LDA in Eq. 5 and re-optimize it, the performance with the new loss function is illustrated in Fig. 3, form which it can be clearly seen that the accuracies with the latent space are higher than those without the latent space on all five datasets. To be specific, we can obtain more improvement on SUN and CUB than on AWA and APY, especially on the metric ts. We attribute this phenomenon to that the learned vectors in latent space can preserve more discriminative characteristic, and the employment of unified synthesis framework on both seen and unseen classes can well alleviate the domain shift problem.
2) EFFECT OF LDA
In our method, we utilize the LDA strategy to project visual features into latent space to make them more discriminative, so it is necessary to find how much this mechanism can improve the final performance. In this experiment, we remove the loss item L LDA from Eq. 5, and conduct the evaluation on the five popular datasets. The experimental results are illustrated in Fig. 4, from which it can be clearly observed that the method with LDA can significantly outperform that without LDA constraint. This phenomenon reveals that the LDA constraint plays a very important role in improving the performance due to its powerful ability of learning discriminative features in latent space. Moreover, to more intuitively display the improvement of our method, we also show the distributions of unseen samples on AWA1 with and without LDA in latent space with t-SNE [57]. The results are illustrated in Fig. 5, from which it can be discovered that the distribution with LDA is more compact than that without LDA in each class, especially those classes at the bottom of the figure. This situation further prove that LDA is necessary for our method to learn discriminative features in latent space.
3) DIFFERENT DIMENSION OF LATENT SPACE
Since we apply latent space in our method, It is necessary to discuss the effect of the dimension of the latent space on the final performance. In our experiment, we take AWA1 as an example and change the dimension of the latent space from 5 to 60 to show the performance change. The performance curves are recorded in Fig. 6, from which it can be clearly seen that the curves monotonically increase for both ts and H , and nearly stop increase when the dimension is larger than 50. This phenomenon reveals that we can obtain better performance when we have larger dimension in latent space, but this increasing will stop when it reaches the number of classes.
E. ZERO SHOT IMAGE RETRIEVAL
In this subsection, we conduct experiments to show zero shot retrieval performance of our proposed method. In this task, we apply the semantic attributes of each unseen category as the query vector, and compute the mean Average Precision (mAP) of the returned images. MAP is a popular metric for evaluating the retrieval performance, it comprehensively evaluates the accuracy and ranking of returned results, and defined as, where, r i is the number of returned correct images from the dataset corresponding to the ith query attribute, p i (j) represents the position of the jth retrieved correct image among all the returned images according to the ith query attribute. In this experiment, the number of returned images equals the number of the samples in unseen classes. For the convenience of comparison, we employ the standard split of the four datasets, including SUN, CUB, AWA1 and aPY, which can be found in [26], and the results are shown in Tab. 3. The values of the baseline methods listed in Tab. 3 are directly cited from [58]. The results show that our method can outperform the baselines on all four datasets, especially on the coarse-grained dataset AWA1, which reveals that our method can make the prototypes in latent space more discriminative.
V. CONCLUSION
In this article, we have proposed a novel method to learn discriminative features with visual-semantic alignment for generalized zero shot learning. in this method, we defined a latent space, where the visual features and semantic attributes are aligned. We assumed that each prototype is the linear combination of others and the coefficients are the same in all three spaces, including visual, latent and semantic. To make the latent space more discriminative, a linear discriminative analysis strategy was employed to learn the projection matrix from visual space to latent space. Five popular datasets were exploited to evaluate the proposed method, and the results demonstrated the superiority compared with the stateof-the-art methods. Beside, extensive ablation studies also showed the effectiveness of each module of the proposed method.
PENGZHEN DU received the Ph.D. degree from the Nanjing University of Science and Technology, in 2015. He is currently an Assistant Professor with the School of Computer Science and Engineering, Nanjing University of Science and Technology. His research interests include computer vision, evolutionary computation, robotics, and deep learning.
HAOFENG ZHANG received the B.Eng. and Ph.D. degrees from the School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China, in 2003 and 2007, respectively. From December 2016 to December 2017, he was an Academic Visitor with the University of East Anglia, Norwich, U.K. He is currently a Professor with the School of Computer Science and Engineering, Nanjing University of Science and Technology. His research interests include computer vision and robotics.
JIANFENG LU (Member, IEEE) received the B.S. degree in computer software and the M.S. and Ph.D. degrees in pattern recognition and intelligent system from the Nanjing University of Science and Technology, Nanjing, China, in 1991, 1994, and 2000, respectively. He is currently a Professor and the Vice Dean of the School of Computer Science and Engineering, Nanjing University of Science and Technology. His research interests include image processing, pattern recognition, and data mining. | 7,637 | 2020-01-01T00:00:00.000 | [
"Computer Science"
] |
Current-Voltage Modeling of the Enzymatic Glucose Fuel Cells
Enzymatic fuel cells produce electrical power by oxidation of renewable energy sources. An enzymatic glucose biofuel cell uses glucose as fuel and enzymes as biocatalyst, to convert biochemical energy into electrical energy. The applications which need low electrical voltages and low currents have much of the interest in developing enzymatic fuel cells. An analytical modelling of an enzymatic fuel cell should be used, while developing fuel cell, to estimate its various parameters, to attain the highest power value. In this paper an analytical model for enzymatic glucose membraneless fuel cell with direct electron transfer was developed. The adequacy of the model was estimated by comparison with fuel cells parameters. The electrical characteristics of fuel cells are interpreted using this model, based on theoretical consideration of ions transportation in solution. The influence of the hydrogen ions, glucose and enzyme concentration and also a thickness of enzyme layer on electrical parameters of a fuel cell were investigated. The electrical parameters such as a current, a voltage, a power were calculated by the model, for various parameters of the fuel cells. The model aimed to predict a hydrogen ions current, an electrical voltage and an electrical power in enzymatic fuel cell with direct electron transfer. The model reveals that increasing the rates of hydrogen ions generation and consumption leads to higher value of current, voltage and power.
Introduction
The glucose fuel cells use glucose as a fuel to produce electrical energy [1]- [5], and they use enzymes as biocatalyst to convert directly chemical or biochemical energy into electrical energy [6]- [9].Enzymatic catalysts for glucose fuel cells have excellent selectivity and can generate power densities of the order of several mW•cm −2 [10] [11].Finally, in glucose enzymatic fuel cells enzymes convert the glucose into water and carbon dioxide.Modelling biofuel cells play important role in understanding and developing new devices.The enzymatic fuel cells mathematical models are based on a system of non-linear equations, including reaction kinetics, transport phenomena [12] [13], statistical analysis [14], metabolic analysis [15].There is a single channel [12] for flow of each anolyte and catholyte streams.An exponential decay in the availability of oxygen from the cathode side was observed [16] [17].Various authors have used theoretical numerical and experimental methods for estimating the fuel cell performance [18]- [21].Majority of modelling are numerical and based on mediator electron transfer mechanism and membrane used fuel cells [7] [21] [22].The focus of this paper is to develop a theoretical analytical model for enzymatic membraneless glucose fuelled fuel cell, with direct electron transfer and enzymes are immobilized on an electrode surface.The present study aimed to predict a hydrogen ions current, an electrical voltage and an electrical power in enzymatic fuel cells, based on basic chemical and electro physical principles.
Theory
In general, biofuel cells transfer electrons to an electrode either directly (direct electron transfer) or through mediator molecules (mediated electron transfer) [23].The model presented here bases on experimental results with direct electron transfer fuel cell that were reported at [8].The model includes two parallels plane each other electrodes.Electrodes are separated by a membraneless reservoir, between electrodes, containing an electrolyte (phosphate buffer) solution, enables ions movement between the electrodes.The fuel reservoir with a glucose solution is positioned left to the anode.The electrodes consisted of carbon cloth with gold or silver.The enzymes (glucose oxidase) are immobilized to an anode.The electrochemical reaction is the oxidation of glucose to gluconic acid gives two electrons and two protons [24].Hydrogen ions generated on the anode and move from the anode to the cathode through the liquid bulk.The cathode is exposed to air and the porous cathode allows oxygen to pass.On the cathode, oxygen reacts chemically with the electrons from the external circuit and with the hydrogen ions from the electrolyte to yield water [8].Michaelis-Menten equation [25] for rate of a volume hydrogen ions generationg 01 was adapted [8] to surface g 1S (Equation (1)) hydrogen ions generation It gives the surface reaction rate g 1S as a function of glucose concentration [G] and a surface enzyme concentration [E S ] .Here the kinetic enzyme reaction rates are k cat and K M .Note, that a connection between [E S ] and volume enzyme concentration [E T ] can be taken as where L is a thickness of an enzyme layer.
Mathematical Model
Enzymatic anode.The model is assumed to be in steady state in regards to proton production and consumption.Enzymes are immobilized homogeneously and can be directly oxidized on the electrode surface.An enzyme layer has a uniform thickness.A buffer solution is assumed to be electrically neutral.Hydrogen ions, generated on an anode, are moving towards a cathode, were they are consumed.A current density is assumed here to be one dimensional along the x-axis.The axis x is normal to both of electrodes.The point x = 0 on an axis x represents the surface between the enzymatic anode and a glucose reservoir, x = L is the boundary between the enzymatic anode and the buffer solution, x = d is the boundary between the buffer solution and the cathode.The thickness of the cathode doesn't take into consideration in this paper.The kinetics and mass transport in the enzyme layer (0 < x < L) can be represented as follow differential equations for hydrogen ions (Equation (2)), that describes concentration changes as a function of the distance: and for glucose where D G , H D + are diffusion coefficients of glucose and hydrogen ions respectively, H c + is hydrogen ions concentration
Bulk Solution
In the bulk (L < x < d) the mass conservation equation of solute species in a steady state conditions for the current density of hydrogen ions Here e signed electron ionic charge, E is an electrical field, F-Faraday constant, R-universal gas constant, T-temperature.
H j + is a current density of ions present in the solution during the fuel cell operations.The total current den- sity j is made up of contribution from all species.
Outside the enzyme layer in the bulk (L < x < d) the hydrogen ions behaviour if the only diffusion takes place can be expressed by the Equation ( 5).
The solution these Equations (2) (3) (5) gives hydrogen concentration along axis x which finally uses to calculate a voltage and a power of a fuel cell.
Boundary Conditions
The boundary conditions between two regions mean the equal species fluxes through the same surface and conditions of a continuity for concentrations.The diffusion coefficients of hydrogen ions are different in these two regions.Equations (6) (7) describe the following boundary conditions between the anode and the bulk where x = L for hydrogen ions: where bH D + are diffusion coefficients of hydrogen ions in the bulk solution.The concentration of the hydrogen ions at the anode surface where x = 0 was taken where c 0 is the hydrogen ions concentration between the glucose reservoir and an anode.The concentration of glucose at an anode surface (x = 0) was taken as: where [ ] 0 G is the glucose concentration in the glucose reservoir.The current density is proportional to rate of an electrochemical reaction of a unit surface electrode.An amount of charge is proportional to the amount of material passed through the interface.This yields for another boundary condition [ ] Here z expressed the number of elementary ionic charges.Boundary conditions for cathode at a point x = d defined as: where c d is the hydrogen ions concentration between the electrolyte reservoir and cathode, g 2S is a rate of surface hydrogen ions consumption on a cathode surface.
Current
The current is the flux at the electrode surface, that is a current density of a fuel cell yields Since a flux at the electrode surface where x = 0 caused by the rate g 1S of hydrogen ions generation from an anode surface per unit of time the appropriate equation for gradient can be written as: x g zD Substituting Equations (1) (17) into Equation ( 16) yields The Equation ( 18) reveals that a current density is proportional to a rate of electrochemical reactions k cat in a fuel cell, enzyme concentrations and a thickness of enzyme layer.In case of direct electron transfer increases number of electrons involved in reactions linearly increases a current density.It means that electrical characteristics of fuel cells can be significantly improved by using some types of enzyme catalyst that diverted more than two electrons to the electrode.
Actually, the current can be computed as well from the hydrogen ions concentration (Equation ( 14)): When a value of glucose concentration [G] is much greater than k M both Equations (18) ( 19) reduce (with 0.5 This yields the same value of a calculated current in both cases.These equations suggest clear ways to achieve increasing a current density and as a consequence an electrical power density: increase k cat , thickness of an enzymatic layer L and a total enzyme concentration [E T ].
Electrical Power
In general a power P, for an electrical circuit with an external load resistance R L and with electrical source V ∆ , which has an internal electrolyte resistance r O resistance between electrodes, can be expressed as where I is the current that equals to ( ) Difference potentials of electrical source V ∆ for high hydrogen ions concentration estimated by Equations (4) (15) lead to d ln The result is similar to [8].Here c L is the hydrogen ions concentration at the point x = L between the anode and electrolyte reservoir.Many factors are affecting losses in a fuel cell: mass transfer, electron transfer, chemical reactions, surface reactions etc. [26].If take into consideration these factors and Equations ( 21)-( 23) an power density P of a fuel cell can be expressed in a follow form: where A is an anode area, r i [Ohm] represents resistances of losses in a fuel cell like electrode reaction resistances, mass transfer, charge transfer etc.This expression shows, as expected, that minimizing the electrolyte resistance and the others resistance of losses in a fuel cell is essential way to increase a power.The maximal power density P can be estimated by using Equations ( 19) and (23), that is:
Model Parameters
The system of equations that described above was solved using the program Mathematica 8.The parameters are using to validate this model (except the Section 3.3) were measured by [8]: the temperature 23˚C, the distance between electrodes d was 0.003 -0.004 m.The thickness of an enzyme layer L was estimated 0.001 -0.0005 m, the glucose concentration [G] = 1 M, [E T ] = 10 −6 -10 −5 M, k M = 0.019 M, k cat = 10 3 sec −1 , the hydrogen ion diffusion coefficient in water was taken as between diffusion coefficients H D + in an area 0 < x < L and bH D + in a bulk L < x < d varies.There is 0.5, 0.8,1
Hydrogen Ions Concentration
Generated hydrogen ions are moving towards cathode and consuming there.During this process a gradient of hydrogen ions exists between the electrodes in a region L < x < d.A voltage, a current density and an electrical power of fuel cells depend on concentrations and a gradient of hydrogen ions.Therefore it is important to evaluate concentrations and a gradient of hydrogen ions in a fuel cell.The hydrogen ions concentration in the region 0 < x < L was calculated by Equation (14).The concentrations as a function of the distance x, when 0 < x < L (Figure 1) are plotted for different diffusion coefficients of hydrogen ions and different values of total enzyme concentrations.
Figure 1: The concentration of hydrogen ions (M) in a region (0 < x < L) (Equation ( 14)) is plotted against x for different total enzyme concentrations [E T ]. hydrogen ions diffusion coefficients.The hydrogen ions concentration increases with this ratio and a total enzyme concentration.A thickness of enzyme layer and an enzyme concentration influences on the boundary concentration c L and as a consequences on a voltage and a power.The hydrogen ions concentration in a bulk L < x < d was calculated by Equation (15).The hydrogen ions concentrations in a bulk as a function of the distance x, when L < x < d (Figure 2), are plotted for different ratio of diffusion coefficients and different values of a total enzyme concentration.total enzyme concentration, a thickness of enzyme layer and basic kinetic parameters.As a result, they determine an electrical power of a fuel cell.
Current Density and Electrical Power
Glucose fuel cell with glucose oxidase enzymatic filter paper was described in [6] ([G] = 10 mM, buffer phate, obtained typical current density range (5 -20) µA/cm 2 and open circuit voltage around 0.18 V).Carbon nanotubes serve to promote conduction and help immobilize the enzymes.Design was simplified by removing membrane.We think the represented here model can explain these experimental results.The dependence current density on enzyme concentration and an enzyme layer thickness was obtained from expression (19) (Figure 3).The effect of enzyme concentration and an enzyme layer thickness is linear with a current density, hence increasing either enzyme concentration and enzyme layer thickness has an important effect on the fuel cell.Lines from top to the bottom glucose concentration [G] = 0.1 M, 0.01 M, 0.001 M respectively, total enzyme concentration E T = 10 −5 M, 0.5 × 10 −5 M, 10 −6 M respectively.Calculations reveal that current density increases with a glucose concentration.For very low glucose concentration below 0.01M changing of a current density is almost linear with glucose concentration.
Eventually, according to Equation ( 19), a saturated value of a current density is independent of further increasing in glucose concentration.The maximal power density P was calculated by Equation ( 25) when j = (5 -20) µA/cm 2 and voltage around 0.18 V.This gives range about 0.9 -4 µW/cm 2 .Calculated values of a current density and a power density have a good agreement with measurements [6].Power density P decreases, after achieved a max value, with rising an external resistance and as consequence of a current reduction (Figure 4).
Lines from top to the bottom a relation is , 50 respectively.Because a fuel cell [6] has a very small current, V ∆ is orders of magnitude higher than the most of the other losses.If an external resistance increases hence a current declines, current is reciprocal to resistance. Figure 4 demonstrates the plots corresponding to the examined power density.
Conclusion
In this paper an analytical model for enzymatic membraneless fuel cell with direct electron transfer was developed.The adequacy of the model was estimated by comparison with fuel cells parameters.The calculated voltage, current and power density of this model were compared with the experimental parameters.The results reveal the dependence electrical power on hydrogen ions boundary concentrations and as consequences on the rate of hydrogens ions generation and consumption, thickness of enzyme layer, enzyme concentrations, and kinetics
Figure 1
demonstrates that the hydrogen ions concentration depends of a ratio
Figure 2 :
The concentration of hydrogen ions (M) in a bulk (region L < x < d) (Equation (15)) is plotted against x for different total enzyme concentrations [E T ].
Figure 2 Figure 1 .
Figure 1.The concentration of hydrogen ions (M) in a region (0 < x < L) (Equation (14)) is plotted against x for different total enzyme concentrations [E T ].
Figure 2 .
Figure 2. The concentration of hydrogen ions (M) in a bulk (region L < x < d) (Equation (15)) is plotted against x for different total enzyme concentrations [E T ].
Figure 4 .
Figure 4. Power density (axis y) (Equation (24)) is plotted against external resistance R L (axis x) when 0.01 Ohm < R L .< 1 Ohm, r 0 = 0.16 Ohm, anode area A = 4 cm 2 .Lines from top to the bottom relation is c L /c d = 5 × 10 3 , 50 respectively.reactionrate coefficients.Hence, power can be increased with rising electrode surface.It can be achieved by increasing a porosity of electrode.Utilizing carbon nanotubes, metallic nanoparticles electrodes can significantly improve porosity.Efficient electrical communication by increasing the catalytic power of enzyme increases the rate of hydrogen ions generation and consumption, and leads to higher values of electrical parameters of fuel cell.The developed model can be used as framework for an analytic examination and an investigation of the effects of various parameters of the fuel cell to optimize a membraneless fuel cell with direct electron transfer. | 3,836 | 2015-03-04T00:00:00.000 | [
"Engineering",
"Environmental Science"
] |
Thermal Perturbations in Supersonic Transition
defined as (cid:5) τ w / ρ w , where τ w is wall stress. The detailed formulation of the transformed velocity u vd may be found in Smits and Dussauge (Smits & Dussauge, 2006).
Introduction
In recent years, there has been considerable interest in the study of bump-based methods to modulate the stability of boundary layers (Breuer & Haritonidis, 1990;Breuer & Landahl, 1990;Fischer & Choudhari, 2004;Gaster et al., 1994;Joslin & Grosch, 1995;Rizzetta & Visbal, 2006;Tumin & Reshotko, 2005;White et al., 2005;Worner et al., 2003). These studies are mostly focused on the incompressible regime and have revealed several interesting aspects of bump modulated flows. Surface roughness can influence the location of laminar-turbulent transition by two potential mechanisms. First, they can convert external large-scale disturbances into small-scale boundary layer perturbations, and become possible sources of receptivity. Second, they may generate new disturbances to stabilize or destabilize the boundary layer. Breuer and Haritonidis (Breuer & Haritonidis, 1990) and Breuer and Landahl (Breuer & Landahl, 1990) performed numerical and experimental simulations to study the transient growth of localized weak and strong disturbances in a laminar boundary layer. They demonstrated that the three-dimensionality in the evolution of localized disturbances may be seen at any stage of the transition process and is not necessarily confined to the nonlinear regime of the flow development. For weak disturbances, the initial evolution of the disturbances resulted in the rapid formation of an inclined shear layer, which was in good agreement with inviscid calculations. For strong disturbances, however, transient growth gives rise to distinct nonlinear effects, and it was found that resulting perturbation depends primarily on the initial distribution of vertical velocity. Gaster et al. (Gaster et al., 1994) reported measurements on the velocity field created by a shallow oscillating bump in a boundary layer. They found that the disturbance was entirely confined to the boundary layer, and the spanwise profile of the disturbance field near the bump differed dramatically from that far downstream. Joslin and Grosch (Joslin & Grosch, 1995) performed a Direct Numerical Simulation (DNS) to duplicate the experimental results by Gaster et al. (Gaster et al., 1994). Far downstream, the bump generated a pair of counter-rotating streamwise vortices just above the wall and on either side of the bump location, which significantly affected the near-wall flow structures. Worner et al. (Worner et al., 2003) numerically studied the effect of a localized hump on Tollmien-Schlichting waves traveling across it in a two-dimensional laminar boundary layer. They observed that the destabilization by a localized hump was much stronger when its height was increased as opposed to its width. Further, a rounded shape was less destabilizing than a rectangular shape.
Researchers have also studied the effect of surface roughness on transient growth. White et al.(White et al., 2005) described experiments to explore the receptivity of transient disturbances to surface roughness. The initial disturbances were generated by a spanwise-periodic array of roughness elements. The results indicated that the streamwise flow was decelerated near the protuberances, but that farther downstream the streamwise flow included both accelerated and decelerated regions. Some of the disturbances produced by the spanwise roughness array underwent a period of transient growth. Fischer and Choudhari (Fischer & Choudhari, 2004) presented a numerical study to examine the roughness-induced transient growth in a laminar boundary layer. The results showed that the ratio of roughness size relative to array spacing was a primary control variable in roughness-induced transient growth. Tumin and Reshotko (Tumin & Reshotko, 2005) solved the receptivity of boundary layer flow to a three dimensional hump with the help of an expansion of the linearized solution of the Navier-Stokes equations into the biorthogonal eigenfunction system. They observed that two counter-rotating streamwise vortices behind the hump entrained the high-speed fluid towards the surface boundary layer. Rizzetta and Visbal (Rizzetta & Visbal, 2006) used DNS to study the effect of an array of spanwise periodic cylindrical roughness elements on flow instability. A pair of co-rotating horseshoe vortices was observed, which did not influence the transition process, while the breakdown of an unstable shear layer formed above the element surface played a strong role in the initiation of transition.
Although the effect of physical bumps on flow instabilities has been studied extensively, far fewer studies have explored the impact of thermal bumps. A thermal bump may be particularly effective at supersonic and hypersonic speeds. One approach to introduce the bump is through an electromagnetic discharge in which motion is induced by collisional momentum transfer from charged to neutral particles through the action of a Lorentz force (Adelgren et al., 2005;Enloe et al., 2004;Leonov et al., 2001;Roth et al., 2000;Shang, 2002;Shang et al., 2005). Another approach is through a high-frequency electric discharge (Samimy et al., 2007). Joule heating is a natural outcome of such interactions, and is assumed to be the primary influence of the notional electric discharge plasma employed here to influence flow stability.
For supersonic and hypersonic flows, heat injection for control have considered numerous mechanisms, including DC discharges (Shang et al., 2005), microwave discharges (Leonov et al., 2001) and lasers (Adelgren et al., 2005). Recently however, Samimy et al. (Samimy et al., 2007) have employed Localized Arc Filament Plasma Actuators in a fundamentally unsteady manner to influence flow stability. The technique consists of an arc filament initiated between electrodes embedded on the surface to generate rapid (on the time scale of a few microseconds) local heating. Samimy et al. (Samimy et al., 2007) employed this method in the control of high speed and high Reynolds number jets. The results showed that forcing the jet with m = ±1 mode at the preferred column mode frequency provided the maximum mixing enhancement, while significantly reducing the jet potential core length and increasing the jet centerline velocity decay rate beyond the end of the potential core.
Yan et al. (Yan et al., 2007; studied the steady heating effect on a Mach 1.5 laminar boundary layer. Far downstream of the heating, a series of counter-rotating streamwise vortex pairs were observed above the wall on the each side of the heating element. This implies that the main mechanism of the thermal bump displays some degree of similarity to that of the physical bump. This finding motivates the further study on thermal bumps since they have several advantages over physical bumps. These include the ability to switch on and off on-demand, and to pulse at any desired frequency combination. Yan and Gaitonde (Yan & Gaitonde, 2010) studied both the steady and pulsed thermal rectangular bumps in supersonic boundary layer. For the steady bump, the velocity fluctuation profile across the span bore some similarity to the physical bump in an overall sense. The disturbance decayed 140 Low Reynolds Number Aerodynamics and Transition www.intechopen.com Thermal Perturbations in Supersonic Transition 3 downstream, suggesting that the linear stability theory applies. For pulsed heating, non-linear dynamic vortex interactions caused disturbances to grow dramatically downstream. Yan and Gaitonde (Yan & Gaitonde, 2011) assessed the effect of the geometry of the thermal bump and the pulsing properties. It was shown that the rectangular element was more effective than the circular counterpart. The smaller width of the rectangular element produced higher disturbance energy, while the full-span heating indicated delayed growth of the disturbances. The disturbance energy increased with the initial temperature variation, and the lower frequency produced lesser disturbance energy.
This chapter summarizes some of the key findings in thermal perturbation induced supersonic flow transition in our research group. The chapter is organized as follows. The flow configuration, setup and numerical components are described first. The effect of the pulsed heating is then explored in the context of disturbance energy growth, and correlated with linear stability analysis. Subsequently, the phenomenology of the non-linear dynamics between the vortices produced by the pulsed bump and the compressible boundary layer is examined with emphasis on later stages of the boundary layer transition.
Flow configuration
A Mach 1.5 flat plate flow is considered with the total temperature and pressure of 325 K and 3.7 × 10 5 Pa, respectively. The thermal bump is imposed as a surface heating element and centered in the spanwise direction as shown schematically in Fig. 1. For some simulations, the nominally two-dimensional case is considered where the bump extends cross the entire span of the plate. Even for this case, the three-dimensional domain is discretized since the primary disturbance growth is three-dimensional. The heating effect is modeled as a time-dependent step surface temperature rise ∆T w with a monochromatic pulsing frequency ( f ) and duty cycle as shown in Fig. 2, where the pulsing time period T t = 1/ f . The subscript w denotes the value at the wall. For simplicity, it is assumed that ∆T w = T w − T w0 , where T w and T w0 are wall temperature inside and outside of the heating region, respectively, and T w0 is fixed at the adiabatic temperature (T ad ) as shown in Fig. 1.
In all perturbed simulations, the heating element is placed immediately upstream of the first neutral point in the stability neutral curve for an adiabatic flat plate boundary layer with the freestream Mach number (M ∞ ) of 1.5. The stability diagram, shown in Fig. 3, is obtained from the Langley Stability and Transition Analysis Codes (LASTRAC) (Chang, 2004). LASTRAC performs linear calculations and transition correlation by using the N-factor method based on linear stability theory, where the N factor is defined by N = s 1 s 0 γds, and s 0 is the point at which the disturbance first begins to grow, s 1 is the end point of the integration, which may be at upstream or downstream of where transition is correlated and γ is the characteristic growth rate of the disturbance. For disturbances at f = 100 kHz, the first neutral point is located at the Reynolds number of Re = 610 based on the similarity boundary-layer length scale (η) defined as = √ ν ∞ x/u ∞ , where ν ∞ and u ∞ are the freestream kinematic viscosity and streamwise velocity, respectively and is shown as the solid rectangle in Fig. 3. The local Reynolds number based on the running distance from the leading edge of the plate 1 is defined by Re x = Re 2 . Thus, the distance from the leading edge of the plate to the leading edge of the heating element is 7.65 mm (i.e. corresponding to Re = 610). The nominal spanwise distance between bumps is determined from the most unstable mode, which for the present Mach number is oblique. The N factor profile, shown in Fig. 4 for different spanwise wave lengths (λ)atM ∞ =1.5 and f = 100 kHz, indicates that λ = 2 mm is the most unstable mode. Thus, the nominal distance between two adjacent heating elements is set to 2 mm to excite the most unstable wave. This is accomplished by choosing a spanwise periodic condition on a domain of 2 mm, at the center of which a bump is enforced.
Numerical model
The governing equations are the full compressible 3-D Navier-Stokes equations. The Roe scheme (Roe, 1981) is employed together with the Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) (Van Leer, 1979) to obtain up to nominal third order accuracy in space. Solution monotonicity is imposed with the harmonic limiter described by Van Leer (Van Leer, 1979). Given the stringent time-step-size limitation of explicit schemes, an implicit approximately factored second-order time integration method with a sub-iteration strategy is implemented to reduce computing cost. The time step is fixed at 4.2 × 10 −8 s for all the cases.
The Cartesian coordinate system is adopted with x, y and z in the streamwise, wall-normal and spanwise direction, respectively. The x axis is placed through the center of the plate with the origin placed at the leading edge of the plate. The computational domain is L x =38 mm long, L y =20 mm high and L z =2 mm wide for case 1, and L x =76 mm long, L y =51 mm high and Lz =2 mm wide for cases 2 and 3. This is determined by taking two factors into consideration. In the streamwise direction, the domain is long enough to capture three-dimensional effects induced by heating and to eliminate the non-physical effects at the outflow boundary. Based on this constraint, the Reynolds number at the trailing edge of the plate is Re L = 1.80 × 10 6 for case 1, and 3.68 × 10 6 for cases 2 and 3. In the wall-normal direction, the domain is high enough to avoid the reflection of leading edge shock onto the surface. The upper boundary is positioned at 86δ L above the wall for case 1, and 220δ L for cases 2 and 3, where δ L is the boundary layer thickness at the trailing edge of the plate. The velocity, pressure and density in the figures shown in Section Results and analyses are normalized by u ∞ , p ∞ and ρ ∞ , respectively. The vorticity is normalized by u ∞ /L x , where u ∞ = 450 m/s and L x =0.038 m.
The grid is refined near the leading edge of the flat plate and near the heating element.
Approximately 150 grid points are employed inside the boundary layer at the leading edge of 143 Thermal Perturbations in Supersonic Transition www.intechopen.com the heating element to resolve the viscous layer and capture the heat release process. Previous results indicated that this is fine enough to capture the near-field effect of the thermal perturbation. The grid sizes are 477 × 277 × 81 in the x, y and z direction, respectively for case 1, and 854 × 297 × 81 for cases 2 and 3.
For boundary conditions, the stagnation temperature and pressure and Mach number are fixed at the inflow. The no-slip condition with a fixed wall temperature is used on the wall. The pulse is imposed as a sudden jump as shown in Fig. 2. The symmetry condition is enforced at the spanwise boundary to simulate spanwise periodic series of heating elements spaced L z apart in the finite-span bump cases. This boundary condition is also suitable to mimic two-dimensional perturbation in the full-span bump case. First-order extrapolation is applied at the outflow and upper boundaries.
Results and analyses
The study is comprised of two parts. The first part studies the effects of the pulsed bump whose properties are listed in case 1 in Table 1. The pulsed bump introduces the disturbance at f = 100 kHz, and is located at Re 0 = 610 2 = 0.3721 × 10 6 , immediately upstream of the first neutral point (Re=610) for this particular frequency, where the subscript 0 denotes the streamwise location of the thermal bump. The Reynolds number at the trailing edge of the plate is Re L = 1341 2 = 1.80 × 10 6 , which corresponds to the location immediately downstream of the second neutral point (Re =1300) as shown in Fig. 3. The rectangular bump is considered with spanwise width (w) of 1 mm and its streamwise length (l) is arbitrarily set to 0.2 mm. The second part examines the breakdown process at later stages of flow evolvement. To this end, the plate is extended far downstream of the second neutral point to Re = 1918 (Re L = 3.68 × 10 6 ) as shown in Fig. 3. Both 3D and 2D thermal bumps are considered. The cases are denoted as cases 2 and 3 in Table 1.
Unperturbed flow (basic state)
The basic or unperturbed state is a Mach 1.5 adiabatic flat plate boundary layer with Reynolds number at the trailing edge of the plate of Re L = 1.80 × 10 6 . Figs. 5 and 6 show the streamwise and wall-normal velocity profiles along the y direction at Re x = 1.4 × 10 6 at the spanwise center and side of the plate. The y coordinate is normalized with the local theoretical boundary layer thickness (δ). Both boundary layer thickness and velocity profiles are predicted correctly compared to the compressible boundary layer theory. In particular, the wall-normal velocity, which is of much smaller order v ∼ u ∞ / √ Re x , is captured correctly as well. The fact that the profiles on the center and side of the plate collapse demonstrates flow two-dimensionality as expected.
Perturbed flow by pulsed bump
A pulsed thermal bump at a frequency of 100 kHz is turned on to introduce the disturbance after the basic state is obtained. Recall that the bump is placed immediately upstream of the first neutral point (where Re = 610) for disturbances at frequency of 100 kHz. Instantaneous ω x contours on the wall (case 1) are plotted after the flow reaches an asymptotic state, the vortex pattern is formed by the dynamic vortex interaction from numerous heating pulses. When the bump is pulsed, a complex vortex shedding and dynamic interaction process results in a vortical pattern with the alternating sign in the streamwise direction. These structures are constrained in the spanwise direction, but move away from the surface, which will be shown in the time-mean values. Smaller eddies are observed at about Re x = 1.25 × 10 6 near the central region and intensified downstream of Re x = 1.5 × 10 6 .
The effect of pulsing on the time-mean streamwise vorticity is shown in Fig. 8. The spanwise-varying streaky structures are formed downstream with concentration in the central Fig. 8. Time-mean ω x contours on the wall (case 1) region and intensified after Re x = 1.5 × 10 6 . These results bear some similarity to free shear flow control with tabs. For example, Zaman et al. (Zaman et al., 1994) demonstrated with a comprehensive experimental study that the pressure variation induced by the tabs installed on the nozzle wall generated streamwise vorticity, which significantly enhanced the mixing downstream of the nozzle exit.
The vortex interaction and penetration can be seen on the cross sections in Fig. 9. The first cross section ( Fig. 9(a)) is cut immediately downstream of the bump, therefore the top pair www.intechopen.com of vortices above the wall possesses the same sign as that at the leading edge of the bump shown in Fig. 8 (positive at z = 0.5w and negative at z = −0.5w). As they move downstream, they are lifted away from the wall and induce additional vortices near the wall to satisfy the noslip condition as well on the sides where periodic conditions apply. The original pairs form a double pattern as indicated in Fig. 9(b). As they move downstream, vortices are stretched and intensified as shown in Fig. 9(c). At Re x = 1.25 × 10 6 ( Fig. 9(d)), the vortex pattern is distorted and the vortices break into smaller eddies. This leads to the complex vortex dynamic interaction downstream at Re x = 1.5 × 10 6 ( Fig. 9(e)), which completely distorts the double pattern and results in a vortex trace that appears to move towards the center region. At the last station ( Fig. 9(f)), the vorticity is intensified around the center region.
The accumulated effect of the streamwise vorticity distorts the basic state in nonlinear fashion. Fig. 10 shows the streamwise perturbation velocity contours on the downstream cross sections. The quantity plotted isū − u b , whereū is the time-mean value of the pulsed case. Please note change in contour levels between Figs. 9 and 10. Immediately downstream of the bump ( Fig. 10(a)), a velocity excess region is formed above the wall due to flow expansion. Proceeding downstream, a velocity deficit is generated downstream of the center of the heating element, while an excess is observed on both sides of the bump ( Fig. 10(b)). This behavior is similar to the observation in the flow over a shallow bump studied by Joslin and Grosch (Joslin & Grosch, 1995) and the steady heating case discussed earlier. The intensity of the excess region is at the same level as that in the steady heating (compare Fig. 10(a) with Fig. 9(a)). Proceeding downstream, the pulsed bump behaves differently from the steady one.
The velocity distortion is amplified as seen in Figs. 10(c) and (d). The velocity excess regions grow in the region near the wall across the entire span of the domain (Figs. 10(e) and (f)) as the streamwise vortices bring the high-momentum fluid from the freestream towards the wall.
The above observations are further explored in Fig. 11, which plotsū and u ′ =ū − u b along the y direction at z=0 and z=-0.5w (i.e., at the spanwise edge of the bump). The intensity of the velocity excess in the near-wall region increases along the downstream and reaches about 20% of u ∞ at Re x = 1.75 × 10 6 , while in the outer region, a velocity deficit is observed. This results in an inflection point in the mean flow near the centerline (Fig. 11(a)), giving rise to the rapid breakdown observed in Fig. 9. On the edges of the bump, the flow is accelerated cross the entire boundary layer and no inflection points are observed ( Fig. 11(b)).
The strength of disturbance energy growth for the compressible flow is measured by the energy norm proposed by Tumin and Reshotko (Tumin & Reshotko, 2001) as where q and A are the perturbation amplitude vector and diagonal matrix, respectively, and are expressed as The first three terms represent the components of the kinetic disturbance energy denoted as E u , E v and E w , respectively and the last two represent the thermodynamic disturbance energy as E ρ and E T . The spanwise-averaged disturbance energy is plotted in Fig. 12. The initial growth rate of the total disturbance energy is small and becomes larger as the disturbances are amplified in the region of 0.9 × 10 6 < Re x < 1.4 × 10 6 . The disturbances then saturate and reach finite amplitude shown as a plateau in Fig. 12(a). At this stage, the flow reaches (a) Re x = 0.38 × 10 6 (b) Re x = 0.5 × 10 6 (c) Re x = 1.0 × 10 6 (d) Re x = 1.25 × 10 6 (e) Re x = 1.5 × 10 6 (f) Re x = 1.75 × 10 6 (Schmid & Henningson, 2001). The new basic state is represented by the appearance of the inflection point at Re x = 1.5 × 10 6 in the left plot of Fig. 11(a). The disturbances grow more rapidly after Re x = 1.5 × 10 6 because the secondary instability susceptible to high frequency disturbances usually grows more rapidly than the primary instabilities. The thermodynamic disturbance energy (E ρ and E T ) in Fig. 12 (b) shows a similar trend except for a spike in the vicinity of the thermal bump as expected. However the thermodynamic components are four orders of magnitude lower than the E u , indicating that the primary disturbance quickly develops a vortical nature.
(a) at z = 0 (b) at z = −0.5w more. Thus, the dynamic vortex non-linear interaction plays an important role in the later development of the sustained disturbance growth, and will be discussed in the following section.
Analyses of breakdown process
This section explores the phenomenology of the non-linear dynamics between the vortices produced by the bump and the compressible boundary layer. To this end, the domain size is extended in both streamwise and normal directions relative to the case 1, but the spanwise width remains unchanged. The Reynolds number at the end of the plate is Re L = 3.68 × 10 6 . Two cases (cases 2 and 3 in Table 1) are examined; the first considers a three-dimensional perturbation associated with a finite-span thermal bump, and the second is comprised of full-span disturbances. In both cases, the bump is positioned at the same streamwise location as in the case 1 with the same pulsing frequency and magnitude shown in Table 1.
A new basic state (no perturbation) is obtained for the cases with the extended domain. In the absence of imposed perturbations, no tendency is observed towards transition even at the higher Reynolds number. Figs. 13 and 14 show the streamwise and wall-normal velocity profiles along the y direction at Re x = 3.5 × 10 6 . The comparisons with the compressible theoretical profiles are good and the fact that the profiles on the center and side of the plate collapse demonstrates flow two-dimensionality as expected.
The heating element is turned on after the basic state is obtained. For the finite-span case, a series of counter-rotating streamwise vortices are generated at the edges of the thermal bump by heating induced surface pressure variation as discussed earlier. These vortices shed from their origins when the element is switched off, forming a traveling vortical pattern with an alternating sign in the streamwise direction up to Re x = 1.25 × 10 6 as shown in Fig. 15(a), where the instantaneous streamwise vorticity contours are plotted on the wall. Further downstream, small organized alternating structures appear near the center region at Re x = 1.5 × 10 6 . Up to this point, the perturbed flow structures are similar to case 1 as expected. Subsequently, the vortices are intensified at about Re x = 2.0 × 10 6 due to vortex stretching 151 Thermal Perturbations in Supersonic Transition www.intechopen.com and interaction, which is described in more detail later. After Re x = 2.5 × 10 6 , the flow tends to relax to a relatively universal stage. The full-span case shows a different development as shown in Fig. 15(b). The counter-rotating vortices are not observed immediately downstream of the bump. Rather, an asymmetric instantaneous vortical pattern is initiated with small successive structures starting at about Re x = 1.25 × 10 6 , which are concentrated on the lower half of the domain. The fact that these small structures occur at the same location for both cases suggests that they are unlikely to be related to the original counter-rotating vortices, and an inherent stability mechanism that stimulates their appearance.
The vortex development is examined in a three-dimensional fashion in Fig. 16 which shows the iso-surface of the non-dimensionalized vorticity magnitude at |ω| = 100 colored with (a) finite span (b) full span Fig. 16. Iso-surface of instantaneous vorticity magnitude at |ω| = 100, x : y = 1 : 10, x : z = 1 : 10 (cases 2 and 3) the distance from the wall. This iso-level is chosen to reveal the near-wall structures. For visualization purpose, the y and z axes are equally stretched with a ratio to the x axis of 10. The same length unit is used for these three axes and Reynolds numbers are only marked for discussion purpose. Thus the structures are closer to the wall and more elongated in the streamwise direction than they appear in the plot. In the finite-span case shown in Fig. 16(a), a sheet of vorticity is generated by the wall shear and rolls up into three rows of hairpin-like vortices across the span at about Re x = 1.5 × 10 6 . The vortices are then slightly lifted away from the wall at about Re x = 2.0 × 10 6 . Correspondingly, the vortices are stretched in the streamwise direction in the wall region, resulting in the intensification of streamwise 153 Thermal Perturbations in Supersonic Transition www.intechopen.com vorticity as previously shown in Fig. 15(a). The vortices become weaker as the flow relaxes further downstream. As shown in Fig. 16(b), hairpin-like structures are also observed for the full-span case, but they develop in an asymmetric fashion. Similar to the full-span case, vortex stretching in the lifting process induces strong streamwise vorticity in the wall region.
The hairpin structures are better displayed by lowering the iso-levels to |ω| = 25 as shown in Fig. 17. The hairpin-like vortices are initiated across the span at about Re x = 2.0 × 10 6 .
(a) finite span (b) full span Fig. 17. Iso-surface of instantaneous vorticity magnitude at |ω| = 25, x : y = 1 : 10, x : z = 1 : 10 (cases 2 and 3) The legs of the hairpin constitute a pair of counter-rotating vortices oriented in the streamwise direction in the wall region. They are mainly comprised of ω x and can be difficult to discern in the total vorticity iso-surface plot since the spanwise vorticity ω z is dominant in the boundary layer. On the other hand, the heads, mainly comprised of ω z , can be easily identified in the total vorticity variable because they penetrate into the boundary layer about 2.24δ and 2.35δ at Re x = 2.5 × 10 6 and 3.5 × 10 5 , respectively, where δ is the local unperturbed laminar boundary layer thickness. It is also observed that for the full-span case, the hairpin vortices are tilted higher in the boundary layer than in the finite-span case. The fact that hairpin vortices appear in the full-span case confirms that the initial counter-rotating streamwise vortices are not a necessity in generating the hairpin vortices.
The vorticity concentration can be viewed through vorticity deviation from the basic state as shown in Fig. 18. Looking downstream, close examination reveals that the right leg rotates with positive ω x and the head with negative ω z . Three hairpin vortices are annotated on the plot. The legs can be more clearly seen in the iso-surface of ω x difference in Fig. 19 and the head in the iso-surface of ω z difference in Fig. 20. Since the value of ω changes, the structures appear to be broken, but other values confirm the coherence of the structures. The hairpin vortices are aligned in the streamwise direction, forming a pattern similar to K-type breakdown, which results from fundamental modes (Klebanoff et al., 1962). In addition, they appear to be highly asymmetric for both cases. Robinson (Robinson, 1991) pointed out that in a turbulent boundary layer, the symmetry of vortex was predominantly distorted, yielding structures designated "one-legged hairpins". Fig. 21 shows a hairpin vortex schematically. Low-momentum fluid is lifted away from the wall between the legs while high-momentum fluid from the freestream is brought down to the wall outside the legs.
The above described motion of the hairpin vortices alters the velocity distribution in the wall region. In the finite-span case, the passage of the counter-rotating vortices generates velocity (u) contours at the first grid point above the wall (i.e. y = δ 0 /200). The central low-speed region is intensified and concentrated towards the center between 1.5 × 10 6 < Re x < 2.0 × 10 6 , resulting in a strong growth of the boundary layer as shown in Fig. 22(b), which depicts the velocity contours on the symmetry plane passing through the center of the domain. At Re x = 2.0 × 10 6 which is just downstream of the second neutral point, the flow pattern changes dramatically. The low-speed streaks weaken in the wall region and the near-wall low-momentum region becomes thinner as the hairpin vortices pump the low-momentum fluid away from the wall. Strong three-dimensional fluctuations are observed in the upper portion of the boundary layer where the hairpin vortices interact with the high-momentum fluid, leading to the boundary layer distortion.
In the full-span case, the initial spanwise structures are almost two-dimensional in nature. Subsequently, the low-speed streaks are formed at about the location where the hairpin vortices start to appear as shown in Fig. 23(a). This indicates that the low-speed streaks are the footprints of the hairpin vortices. The boundary layer growth is not as strong as that in the finite-span case between 1.5 × 10 6 < Re x < 2.0 × 10 6 (compare Figs. 23(b) and 22(b)). However, downstream of Re x = 2.0 × 10 6 , strong three-dimensional fluctuations are observed, similar to the finite-span case. It suggests that the non-linear disturbance growth becomes dominant and the initial disturbance form becomes less important. This is confirmed in the disturbance energy growth in Fig. 24, which plots the spanwise-averaged Fig. 24. Spanwise-averaged time-mean total disturbance energy along the x direction (cases 2 and 3) time-mean total disturbance energy for both finite-and full-span cases. The energy growth in the 2-D perturbations is much weaker than that in the 3-D ones near the bump. However, as the non-linear stability mechanism becomes dominant after about Re x = 2.0 × 10 6 , the disturbance energy growth in both cases becomes comparable.
The accumulated effect of high-frequency pulsing is now described by the time-mean quantities. Only the finite-span results are shown unless otherwise specified. The time-mean pressure (p) contours are shown on the center plane in Fig. 25. A series of expansion waves is formed at about Re x = 2.0 × 10 6 and propagates outside the boundary layer. This is caused by the strong boundary layer distortion as shown in the time-mean streamwse velocity contours on the center plane in Fig. 26. The momentum thickness at Re x = 2.0 × 10 6 is increased by a factor of 1.7 compared to that in laminar flow, indicating that the boundary layer is highly energized downstream of Re x = 2.0 × 10 6 and shows signs of transition to turbulence. The expansion waves in the downstream location are also partially observed in case 1, in which the outlet boundary is set at Re L = 1.80 × 10 6 .
The boundary layer distortion can be assessed by the variation of shape factor H obtained from the mean velocity profile as shown in Fig. 27. The shape factor for the basic state, shown for comparison, reaches an asymptotic value of 2.6 as the flow becomes fully-developed laminar ( Fig. 27(a)). With heating, the mean flow is strongly distorted, causing the shape factor to oscillate taking values of 2.85 and 1.35 between Re x = 1.5 × 10 6 and 2.0 × 10 6 , respectively as shown in Fig. 27(a). A lower shape factor indicates a fuller velocity profile.
After Re x = 2.0 × 10 6 the shape factor decreases rapidly, indicating an increase of the flow momentum in the boundary layer, and starts to level off around Re x = 3.0 × 10 6 . Strong spanwise non-uniformity is observed at Re x = 1.5 × 10 6 and 2.0 × 10 6 as shown in Fig. 27(b), while in later stages, only mild distortion is observed and the shape factor reduces to around 1.5, which is close to the turbulent value.
Features of the turbulence statistics are examined through the transformed velocity and Reynolds stresses. Fig. 28 shows the transformed velocity profiles at different downstream locations along the center line (z=0) and the side line of the bump (z=-0.5w). In the viscous sublayer of a compressible turbulent boundary layer where y + < 5, the turbulent stresses are negligible compared to viscous stress and the velocity near the wall grows linearly with the distance from the wall as u + = y + , where u + is defined as u vd /u τ , and y + as yu τ /ν w . The friction velocity u τ is defined as τ w /ρ w , where τ w is wall stress. The detailed formulation of the transformed velocity u vd may be found in Smits and Dussauge (Smits & Dussauge, 2006). Good agreement is found with the theory at different Reynolds numbers at both center and side locations. The turbulent stresses become large between y + > 30 and y/δ 1 where the log law holds with u + = 1 κ ln(y + )+C with κ = 0.4 and C = 5.1 (Smits & Dussauge, 2006). It is shown in Fig. 28 that the logarithmic region gradually forms with increasing Reynolds number and the velocity slope approaches the log law. However, a large discrepancy remains between the velocity profile at the end of the plate (Re x = 3.5 × 10 6 ) and the log law, indicating that the perturbed flow has not reached fully-developed turbulence.
The Reynolds stress profiles are shown to further examine the evolution of the flow. Fig. 29 shows the streamwise Reynolds stress (ρu ′ u ′ ) and Reynolds shear stress (ρu ′ v ′ ) normalized by the local wall stress (τ w )atRe x = 3.5 × 10 6 . Note that the local boundary layer thickness δ varies across the span. Experimental and numerical results by other researchers (Johnson 159 Thermal Perturbations in Supersonic Transition , 1975;Konrad, 1993;Konrad & Smits, 1998;Muck et al., 1984;Yan et al., 2002;Zheltovodov et al., 1990) are plotted for comparison. The predicted streamwise Reynolds stress presents a similar trend to the experiments and other numerical data. It reaches the peak at about y = 0.05δ-0.1δ and decays rapidly between 0.1δ < y < 0.3δ. A large spanwise variation of the peak value is observed with the value at z = 0 being 1.8 times that at z = −0.5w. The same observation holds for the Reynolds shear stress as shown in Fig. 29(b), which is a main source of turbulence production in the wall-bounded flows. The largely scattered data implies that the flow is still in transitional stage, where the strong non-linear disturbances continue to extract energy from the mean flow to maintain their mobility before the energy redistribution equilibrates and the flow exhibits some features of fully-developed turbulence. This is also consistent with that the mean velocity profile being located above the log law in Fig. 28.
Overall, the effect of the disturbance introduced by thermal bumps is observed to follow classical stability theory in the linear growth region. For the parameters considered, the gross features of transitional flow appear near the second neutral point. These features consist of hairpin vortex structures which are non-staggered and resemble K-type transition. Comparison of 3-D (finite span) with 2-D (full span) perturbations effects indicate that although the near field consequences of the bump are profoundly different, the development further downstream is relatively similar, suggesting a common non-linear mechanism associated with the interaction of the disturbance with the boundary layer vorticity.
Concluding remarks
This chapter explores the stability mechanism of a thermally perturbed Mach 1.5 flat plate boundary layer. With pulsed heating at frequency of 100 kHz immediately upstream of the first neutral point, non-linear dynamic vortex interactions cause disturbances to grow dramatically downstream and the maximum velocity fluctuation reaches about 20% of u ∞ . The inflectional velocity profile makes the flow highly susceptible to the secondary instabilities. The dynamic vortex interaction at later stages of the boundary layer development is studied by extending the flat plate further downstream. Hairpin structures, considered as one kind of the basic structures in turbulence, are observed and serve to increase the momentum in the wall region. The fact that the hairpin vortices are observed in the full-span case suggests that the initial counter-rotating vortices generated by the finite-span bump might not be directly associated with the formation of hairpin structures. The boundary layer is observed to grow noticeably downstream relative to the unperturbed case. The Reynolds stresses and shape factor profiles suggest that the boundary layer is approaching turbulence, but remains transitional at the end of the computational domain. These results suggest that pulsed heating can be used as an effective mechanism to modulate the supersonic laminar-turbulence transition. One effective way to generate pulsed heating is through plasma actuator where Joule heating and electrode heating are effectively assumed as surface heating. | 9,294.6 | 2012-04-04T00:00:00.000 | [
"Physics",
"Engineering"
] |
Chitinase-Like (CTL) and Cellulose Synthase (CESA) Gene Expression in Gelatinous-Type Cellulosic Walls of Flax (Linum usitatissimum L.) Bast Fibers
Plant chitinases (EC 3.2.1.14) and chitinase-like (CTL) proteins have diverse functions including cell wall biosynthesis and disease resistance. We analyzed the expression of 34 chitinase and chitinase-like genes of flax (collectively referred to as LusCTLs), belonging to glycoside hydrolase family 19 (GH19). Analysis of the transcript expression patterns of LusCTLs in the stem and other tissues identified three transcripts (LusCTL19, LusCTL20, LusCTL21) that were highly enriched in developing bast fibers, which form cellulose-rich gelatinous-type cell walls. The same three genes had low relative expression in tissues with primary cell walls and in xylem, which forms a xylan type of secondary cell wall. Phylogenetic analysis of the LusCTLs identified a flax-specific sub-group that was not represented in any of other genomes queried. To provide further context for the gene expression analysis, we also conducted phylogenetic and expression analysis of the cellulose synthase (CESA) family genes of flax, and found that expression of secondary wall-type LusCESAs (LusCESA4, LusCESA7 and LusCESA8) was correlated with the expression of two LusCTLs (LusCTL1, LusCTL2) that were the most highly enriched in xylem. The expression of LusCTL19, LusCTL20, and LusCTL21 was not correlated with that of any CESA subgroup. These results defined a distinct type of CTLs that may have novel functions specific to the development of the gelatinous (G-type) cellulosic walls.
Introduction
Flax (Linum usitatissimum L.) phloem fibers are a valuable industrial feedstock and are also a convenient model system for studying secondary cell wall formation. The mechanical properties of bast fibers are largely dependent on the composition of their secondary walls. Bast fibers have gelatinous-type walls, which are rich in cellulose (up to 90%) and lack detectable xylan and lignin. Gelatinous fibers are widespread in various land plant taxa, but have been studied primarily in angiosperms. Depending on the species, either phloem or xylem (of either primary or secondary origin) can produce gelatinous fibers in various organs including stems, roots, tendrils, vines, and peduncles [1,2]. The mechanisms of gelatinous cell wall development in these fibers remain largely unclear. However, some genes implicated in gelatinous cell wall development have been identified. The list includes fasciclin-like arabinogalactan proteins (FLAs) [3][4][5][6], b-galactosidases [7,8], and lipid transfer proteins [6]. A role for b-galactosidases in G-type wall development has been demonstrated functionally [8].
Transcripts of genes encoding chitinase-like proteins are reportedly enriched in fibers, particularly during the cell wall thickening stage of flax phloem cellulosic fiber development [6]. Expression of CTLs during primary or secondary cell wall deposition has also been reported in species other than flax [9,10]. Plant chitinase-like proteins have been identified in a wide range of organelles and tissues, including the apoplast and vacuole [11].
Chitinase-like proteins belong to a large gene family that includes genuine chitinases (i.e. proteins with proven chitinase activity) and other homologous proteins, which may not have chitinase activity [12][13][14][15]. Here, we refer to both genuine chitinases and their homologs collectively as chitinase-like proteins (CTLs).
Chitinases catalyze cleavage of b-1,4-glycoside bonds of chitin and are organized in five classes (Classes I-V), which can be distinguished on the basis of sequence similarity [11,16,17]. Classes I, II, and IV belong to glycoside hydrolase family 19 (GH19), found primarily in plants, whereas Classes III and V belong to glycoside hydrolase family 18 (GH18) present in various types of organisms [18][19][20]. The Class I chitinases are found in both monocots and dicots, while classes II and IV are found mainly in dicots [21]. Class I and IV chitinases contain a highlyconserved cysteine-rich domain -the chitin binding domain (CBD) -at the N-terminal region [21,22], but there are two characteristic deletions in the main catalytic domain in Class IV chitinases [21]. Because chitin is the major component of fungal cell walls, chitinases are classic pathogenesis-related proteins involved in non-host-specific defense [23,24].
Plants also contain chitinase-like proteins that are not induced by pathogens or stresses. In many cases, these chitinase-like proteins have been shown to lack detectable chitinase activity. Chitinase-like proteins may play an important role during normal plant growth and development [13,15,25]. For example, AtCTL1 is constitutively expressed in many organs of Arabidopsis. Mutations of AtCTL1 lead to ectopic deposition of lignin in the secondary cell wall, reduction of root and hypocotyl lengths, and increased numbers of root hairs [15]. It was suggested that this gene could be involved in root expansion, cellulose biosynthesis, and responses to several environmental stimuli [13,26,27]. In particular, coexpression of some CTLs with secondary cell wall cellulose synthases (CESAs) was reported [28]. It has been suggested that these chitinase-like proteins could take part in cellulose biosynthesis and play a key role in establishing interactions between cellulose microfibrils and hemicelluloses [14].
The xylan-type secondary wall is the most common secondary wall in land plants and is characteristically rich in cellulose, xylan, and lignin [2]. Compared to typical xylan-type secondary walls, gelatinous layers are enriched in cellulose, have a higher degree of cellulose crystallinity, larger crystallites, and a distinctive set of matrix polysaccharides (see [2] and references therein). Presumably, cellulose synthase genes have a significant role in gelatinous cell wall formation, but the expression patterns of the complete flax CESA family has not been described to date. It is known that at least three isoforms of CESAs comprise the cellulose synthase rosette: CESA1, CESA3, and CESA6 are required for cellulose biosynthesis in primary cell walls [29], whereas CESA4, CESA7, and CESA8 are required for cellulose biosynthesis during secondary wall deposition [30].
Flax is a useful model for comparative studies of cell wall development: different parts of the flax stem form a primary cell wall, xylan type secondary cell wall, or gelatinous cell wall; these stem parts may be separated and analyzed by diverse approaches, including functional genomics. Furthermore, the publication of a flax whole genome assembly [31] facilitates a thorough study of key gene families.
In the present study, we measured expression of all predicted LusCTL genes of the GH19 family in various tissues including those that produce gelatinous-type and xylan-type cell walls. We also described the LusCESA gene family and measured expression of its transcripts in comparison to LusCTLs. Phylogenetic analysis of LusCTL and LusCESA genes identified distinct groups of LusCTL genes that were expressed preferentially at specific stages of bast fiber gelatinous cell wall development. 2 + C material was sampled with respect to the location of the snap point, which is a mechanically defined stem position in which fibers undergo transition from elongation to secondary cell wall formation [32]. The following seven samples were collected (Table 1, Figure 1): 1. ''Apex'' -the apical part of stem (1 cm of length). 2. ''TOP'' -the following ''apex'' segment of stem above the snap point with phloem fibers in the process of elongation. 3. ''MID'' -the stem segment (5 cm of length) below the snap point which contained fibers at early stages of secondary cell wall thickening. 10 cm of the stem downwards from ''MID'' was divided into Peel (4), which contained epidermis, parenchyma cells, phloem fiber bundles and sieve elements and Xylem (5), which contained parenchyma cells, xylem vessels and xylem fibers. 6. ''Fibers'' -i.e. isolated phloem fibers were obtained by washing Peels in 80% ethanol in a mortar several times and gently pressing the fiber-bearing tissues with a pestle to release the fibers. 7. Roots. The number of biological replicates was three, with five plants in each replicate.
Sequence Alignment and Phylogenetic Analysis
Predicted amino acid and nucleotide sequences of CTLs (Pfam domain: PF00182) and CESAs (PF03552) were obtained from the Phytozome database v.9.0 (Linum usitatissimum, Populus trichocarpa, Arabidopsis thaliana). CESAs of poplar (PtiCESAs) were renamed according to Kumar et al. [33]. A list of various well-characterized CTLs from different plant species was obtained from previously published works [10,21]. Sequences were aligned using MUSCLE with default parameters, and a phylogenetic tree was constructed using MEGA5 based on the Maximum Likelihood and Neighbor-Joining methods [34], bootstrapping 1000 replicates [35], model WAG+G or JTT+G. Signal peptides for protein sequences were predicted using SignalP (http://www.cbs.dtu.dk/services/SignalP/ ), molecular weights, isoelectric points of the proteins were analyzed by ProtParam (http://web.expasy.org/protparam/).
Reverse Transcription Quantitative Real Time PCR
Total RNA from all plant samples was isolated using a Trizolextraction method combined with an RNeasy Plant Mini Kit (Qiagen) according to the manufacturer's instructions. RNA quality was evaluated by electrophoresis using a BioAnalyzer (Agilent), and no degradation of RNA was evident. Residual DNA was eliminated by treatment with DNAse I using the DNA-free kit (Ambion). Gene specific primers for CTL and CesA genes were designed using Universal ProbeLibrary Assay Design Center (http://www.roche-applied-science.com/shop/CategoryDisplay? catalogId = 10001&tab = &identifier = Universal+Probe+Library) (File S1). One microgram of total RNA was reverse-transcribed using RevertAid H Minus First Strand cDNA Synthesis Kit (Thermo Scientific). The cDNAs were diluted 1:32 with nuclease free water. Real-time PCR was performed in a 7900 HT Fast realtime PCR system (Applied Biosystems, USA). Each 10 mL realtime PCR cocktail contained 2.5 mL of 0.4 mM concentrations of both forward and reverse gene-specific primers, and 2.5 mL of cDNA, 5 mL of 26Dynamite qPCR mastermix (Molecular Biology Service Unit -University of Alberta) which included SYBR green (Molecular Probes) and Platinum Taq (Invitrogen). The thermal cycling conditions were 95uC for 5 minutes, 40 cycles of 95uC for 15 seconds, and 60uC for 1 minute. A 60-95uC melting curve was performed to confirm the specificity of the products. Threshold cycles (CT) were determined using 7900 Fast Software. C T values were normalized using eukaryotic translation initiation factors 1A, 5A (LusETIF1, LusETIF5A) and glyceraldehyde 3-phosphate dehydrogenase (LusGAPDH) gene from flax (File S1) [36]. From each of three biologically independent cDNA samples, two independent technical replications were performed and averaged Table 2. Cont. for further calculations. DDCT values were generated using the apex sample as a reference. Relative transcript abundance calculations were performed using comparative C T (DC T ) method as previously described [37] for flax tissues (TOP/Apex, MID/ Apex, Peel/Apex, Xylem/Apex, Fiber/Apex, Root/Apex). Heat maps of expression levels of some genes were then created with MeV v4.8 (Multi Experiment Viewer, http://www.tm4.org/mev.) using the means of DC T.
LusCTL Phylogenetic Characterization
We searched within the flax genome assembly (version 1.0) for predicted genes with homology to Pfam domain PF00182, which is characteristic of chitinases of the glycosyl hydrolase family 19 (GH 19) family [31,38]. This search identified 37 predicted chitinase or chitinase-like genes (referred to here collectively as LusCTLs) ( Table 2). However, only three of the predicted proteins (LusCTL8, LusCTL10, and LusCTL15) contained a conserved chitin-binding domain (CBD), suggesting that not all of the LusCTLs use chitinase as a substrate. The mean predicted protein size of the 37 LusCTLs was 246.5 aa (or 27 kDa), and the majority (30/37) were predicted to be secreted ( Table 2).
The labels assigned to the 37 predicted LusCTLs are shown in Table 2. LusCTL1 and LusCTL2 were so named because they encoded proteins that were most similar to CTL1 and CTL2, respectively, which have been characterized in other species (e.g. A. thaliana [14] and G. hirsutum [10]) ( Table 2). The gene LusCTL37 was predicted to encode only a protein of 69 aa, which is much shorter than the rest of the LusCTLs (Table 2), and so it was not used in further analyses.
The LusCTLs and their inferred phylogenetic relationships are shown in Figure 2. Based on this dendrogram, the predicted LusCTLs were divided into three groups: Group A included LusCTL1-6, Group B included LusCTL7-14, and Group C included LusCTL15-36 ( Figure 2, Table 2). The flax-specific tree shown in Figure 2 was expanded by the addition of representative GH19 CTLs from other species (Figure 3). In this multispecies tree, LusCTLs of Group A, which includes LusCTL1 and LusCTL2, were part of the same clade as the well-characterized AtCTL2 of A. thaliana and GhCTL1, GhCTL2, GhCTLVII of G. hirsutum, The Group B LusCTLs (LusCTL7-14) were in the same clade as the previously defined Classes I, II, III, GH19 chitinases [10,21]. Most of group B was in the same sub-clade as Class II, although none of the previously defined Classes I-III were monophyletic in our analysis. Finally, our Group C LusCTLs (LusCTL15-36) formed a monophyletic clade with representatives of the previously defined Class IV GH19 chitinases.
LusCTL Transcript Expression
Quantitative real-time reverse-transcription PCR (qRT-PCR) was performed to study LusCTL expression patterns of L. usitatissimum genes of chitinase-like proteins in various tissues and stages of development (Table 1). These tissues and their names as used here are equivalent to the names used in previous studies [6,32,39,40]. Only 34 sets of primers were used in this assay, because members of each of two pairs of LuCTLs could not be distinguished by unique primers: LusCTL28 and LusCTL29 (95.6% aa and 96.3% nt identity), and LusCTL33 and LusCTL34 (99.6% aa and 98.8% nt identity). Thus a common set of primers was used for each of these pairs. We observed that transcripts of LusCTL1 showed enriched levels of expression (compared to the apical part of stem) in tissues in which cell walls were undergoing thickening ( Figure 4) in xylem and in phloem fibers. Transcripts for this gene were enriched 57-fold in xylem, 28-fold in the MID region, and 20-fold in fiber. Another predicted CTL, LusCTL2, showed a similar pattern of enrichment in secondary-wall bearing tissues (8.3, 4.5 and 1.4-fold higher in xylem, MID and fiber, respectively, compared to the apex), although the magnitude of its enrichment was not as strong as LusCTL1. These two LusCTLs had high sequence similarity to each other (91.9% amino acid identity) and had similar patterns of expression as compared to each other in the various flax tissues.
LusCESA Phylogenetic and Expression Characterization
To provide context for the expression patterns of LusCTLs, and to test whether the expression pattern of cellulose synthase (LusCESA) genes differed between gelatinous fibers and cells with a xylan type of secondary cell wall, expression of LusCESAs in different flax tissues was analyzed. We identified 14 predicted LusCESAs in the flax whole genome assembly by searching predicted proteins for the conserved cellulose synthase domain (Pfam PF03552). No putative LusCESA7 genes were found in the original published genome published (v1.0, [31]). However, though BLAST alignment of the CDS of Arabidopsis and poplar CESA7 sequences, two scaffolds (scaffold_57 and scaffold_464) of the flax genome assembly were identified as encoding CESA7 homologs, and these were annotated using the Augustus server (http://bioinf.uni-greifswald.de/augustus/). Thus, all 16 predicted LusCESAs were aligned with well-characterized AtCESAs from A. thaliana and PtiCESAs from P. trichocarpa ( Figure 5). This alignment was used to construct a phylogenetic tree and annotate the LusCESAs, which were named according to the established A. thaliana [41] and P. trichocarpa nomenclature systems (Table 3, [33]). The number of LusCESAs and PtiCESAs isoforms identified for each of the eight major types of CESAs was similar except in the case of CESA3, where one more gene was identified in P. trichocarpa than in L. usitatissimum ( Figure 5, Table 3). The LusCESA appeared to be typical of other genes in this family in that they were large integral membrane proteins with eight predicted transmembrane domains, a hydrophilic domain that faces the cytosol, and a zinc finger domain at the N-terminus of proteins with the characteristic amino acid motif ''CxxC'' (specific for CESAs only [42]).
Relative differential expression of LusCESA genes in different tissues of the flax stem was estimated ( Figure 6). LusCESA4, LusCESA8-A, LusCESA8-B, LusCESA7-A, LusCESA7-B had high expression in tissue that produce secondary walls (TOP, MID, Xylem, Fiber, Root). Transcripts of these LusCESA isoforms were the most enriched in Xylem, which contained cells with xylan-type cell walls, and in roots, where secondary vascular tissue (xylem) was also well-developed. These secondary cell wall type LusCESAs had also high relative expression in cellulosic fibers, although it was not as strong as for xylem.
Changes in expression of the LusCESA4, 7, 8 isoforms and ''xylem-specific'' LusCTL1 and LusCTL2 were well-correlated in different flax tissues ( Figure 7A). This group of genes was highly expressed in tissues with secondary cell walls (MID, Xylem and Roots). In contrast, the ''fiber-specific'' LusCTLs had very different patterns of expression in the same tissues ( Figure 7B): these had low level of expression in xylem, but high level of relative expression in tissues with gelatinous fibers (peel and fiber).
Discussion
Certain fibers of many plant species form G-type cell walls, which are rich in crystalline cellulose [1]. Expression of CTLs has been previously reported to be enriched during development of Gtype cell walls, along with specific FLAs [4,6,7], LTPs [6] and BGALs [6][7][8]. In this work, we analyzed expression of all LusCTL genes of GH 19 in different flax tissues and compared this expression with LusCESAs and to their inferred phylogenies. In the flax genome, 16 predicted LusCESAs were identified (Table 3). Previously only partial sequences of some flax CESAs were published [43]. All 16 flax CESAs could be placed in discrete clades with Arabidopsis and Populus CESA homologs ( Figure 5). We generally numbered LusCESAs in a way that reflects the association of each flax gene with its nearest relative in the Arabidopsis genome, as was done for CESAs of Populus [33]. Following this pattern, the LusCESA6A-F genes we named as a group, similar to PtiCESA6A-F and were not distinguished as CESA2/9/5/6 as in Arabidopsis clade (Table 3) [44]. Most of the flax and Populus CESA genes are present as pairs of paralogs in their respective genomes, although there were three LusCESA3 genes (LusCESA3A-C) for only two Populus genes and one Arabidopsis gene. AtCESA1 and AtCESA10 were represented by only one pair of genes (LusCESA1A, B) in flax.
It is well established that proteins encoded by different sets of three CESA genes (CESA1, 3,6 and CESA4,7,8) are required for cellulose synthesis during primary and secondary wall formation, respectively [44][45][46]. The functional relationships of the various paralogs of LusCESAs (except LusCESA4, Table 3) are presently unclear. According to the data obtained here, secondary cell wall LusCESA4, LusCESA7-A, B and LusCESA8-A, B were highly expressed both in the xylem cells with lignified cell walls (i.e. xylan type) and in the phloem fibers with thick gelatinous cell wall. This suggests that phloem fibers and xylem may use similar, rather than specialized rosettes. This is consistent with observations from poplar showing only minor differences in expression of cellulose biosynthetic genes in tension wood as compared to normal wood [3]. The different properties of gelatinous and xylan type cell walls are therefore likely determined not by CESAs, but by other proteins associated with cellulose synthesis, which could include specific CTLs.
We observed two LusCTLs that were expressed more strongly in xylem tissue than in any other tissue surveyed (Figure 3, LusCTL1, LusCTL2). The co-expression of certain isoforms of LusCTL1, LusCTL2 and the secondary wall LusCESAs (CESA4, 7, 8) suggested a role for these LusCTLs in secondary cell wall development ( Figure 7). As noted above, LusCTL1 and 2 are highly similar to AtCTL2 of A. thaliana and GhCTL1, GhCTL2, of G. hirsutum. The role of CTL2, and its close homolog CTL1, in cell wall biosynthesis is especially intriguing since associations between CTLs and primary or secondary cell wall synthesis have been reported in different plant species [10]. CTL2 is strongly upregulated during secondary wall formation in interfascicular fibers in A. thaliana. Reduction in crystalline cellulose content in ctl1 ctl2 mutants was demonstrated, leading to the to the suggestion that AtCTLs are involved in cellulose assembly. Furthermore, in P. trichocarpa, expression of chitinase genes related to AtCTL1, AtCTL2, and GhCTLVII are highly correlated with secondary wall formation of xylem [47]. It has therefore been proposed that CTL1 and CTL2 work in conjunction with primary-and secondary-cell wall CESAs, respectively [14]. One of the hypotheses for CTL1/2 function is regulation of cellulose assembly and of interaction with hemicelluloses via binding to emerging cellulose microfibrils [14]. However, the mechanism of CTL action in cell wall biosynthesis as well as substrates of catalytic activity (if any) remains unknown. It was suggested that the likely substrates of plant chitinases may be arabinogalactan proteins, chitooligosaccharides and other GlcNAc-containing glycoproteins or glycolipids [13,15,48,49] and the mechanism by which CTLs act is more likely to involve binding of chitin oligosaccharides than catalysis. Also, it is assumed that chitinases may participate in the generation of such signal molecules that regulate the organogenesis process [50].
Although relative expression of LusCESA (4,7,8) and LusCTL1, LusCTL2 in xylem tissue was higher compared with phloem fibers, we cannot exclude involvement of these LusCTLs in phloem fiber cell wall development. At the same time, a distinct group of LusCTLs (LusCTL19, LusCTL20, LusCTL21) had very high enrichment in samples with phloem fibers (MID, peel, fiber) with a low level of expression in xylem. According to the phylogenetic tree, these LusCTLs (group C) were most similar to the previously defined Class IV chitinases (Figure 4). High constitutive expression of Class IV (along with Class I) in most organs of A. thaliana under normal growth conditions has been previously noted [51]. Detailed bioinformatic characterization of genes of LusCTL distinct group should be conducted in future. Probably LusCTLs that are highly expressed in fibers may be specific to the gelatinous cell wall, while LusCTL1 and LusCTL2 are essential for wall thickening in general.
Conclusion
High expression of specific LusCTLs was observed in different types of thick cell wall producing tissues. LusCTL1 and LusCTL2 were preferentially expressed during secondary wall deposition of xylem and were coexpressed with secondary cell wall CESAs (4,7,8). Another group of LusCTLs, (especially LusCTL19, LusCTL20, LusCTL21) were highly expressed in bast fibers, which have cellulose-rich, gelatinous walls. The group of fiber-enriched LusCTLs was expanded in flax compared to species that do not produce bast fibers, suggesting that these genes might play a unique role during gelatinous cell wall development in general and cellulose synthesis in particular. It is possible that the presence of fiber-specific LusCTLs, along with other key participants, determines differences in mechanisms of xylan and gelatinous cell wall formation. To establish the functions of these LusCTLs further characterization, including analysis of enzyme activity and structure, is necessary. Chitinase-like proteins remain one the most mysterious proteins in the plant cell wall. This study provides further evidence of their involvement in the process, and distinguishes between groups of CTLs involved in different type of cell wall development.
Supporting Information
File S1 LusCTL gene sequences. | 5,202.4 | 2014-06-11T00:00:00.000 | [
"Biology"
] |
Comparative Dosimetric Study in Chest Computed Tomography Using Phantoms
The dissemination of Computed Tomography (CT) scan has promoted a significant increase in the absorbed dose by patients due to the diagnosis. Therefore, it is indispensable to improve protocols, seeking smaller doses, without impairing the diagnostic quality of the image. The risks of stochastic effects are greater for children due to tissue radiosensitivity coupled with longer life expectancy. In this work, a cylindrical phantom made of polymethylmethacrylate was used representing an adult chest, and a second phantom made of the same material was designed in an oblong shape, including axillary region, based on the dimensions of an eight-year-old pediatric patient. A comparative study was performed between chest scans formulated in two CT scanners in different radiodiagnostic services. The central slice of the both phantoms was irradiated successively, using a pencil ionization chamber, for the measurements in five different spots of each phantom. From the measurements, we obtained values of weighted and volumetric Dose Index (Cvol). The scans were performed with the routine chest acquisition protocols of the radiodiagnostic services, both for a voltage of 120 kV X-ray tube supply voltage. This work allowed to compare the dose between patients with variable chest volumes and the dose variation in patients between two CT scanners used for image generation with the same diagnostic objective.
INTRODUCTION
Computed tomography scanners currently installed in radiodiagnostic services present wide technological variations, either in the speed of acquisition or in the protocols used for the acquisition of images that are dependent on available technology.Thus, images generated with the same diagnostic objective in different devices can result in different doses to patient, very different, either by the technological difference or the acquisition protocol used [1].
The X-rays used for diagnosis is the artificial source that contributes most to the exposure dose of the population due to the large number of X-ray examinations performed per year.The ionizing radiation originated from the X-rays used for diagnosis is the artificial source that contributes most to the exposure dose of the population due to the large number of X-ray examinations performed per year.CT scans accounted for 5% of all radiological exams and resulted in 34% of deposited dose in the world population in the year 2000 [2].
In 2006 the contribution of medical exposures in the composition of the effective population in the USA corresponded to 48%, with 24% due to CT examinations.The other 52% are derived from other sources such as Radon (37%), spatial origin (5%), terrestrial (3%) and internal (5%).
Considering this data, it can be estimated that currently this population receives practically twice the dose received by the population before the discovery of X-rays [2,3].
The increase in the use of imaging methods that make use of ionizing radiation, and especially of CT scans is responsible for the sharp increase in the annual mean individual radiation dose.With this, there is a growing concern of the medical community, manufacturers and even patients regarding the control of the radiation dose determined by the various tests that use ionizing radiation.In addition to occupational radiological protection, clinical practice uses the principle known as ALARA (As Low As Reasonably Achievable) to guide the rational use of this technology [4].
Several factors contribute to the increased demand for CT scans, including the constant technological evolution of the equipment; the speed of the data acquisition and the reduction of the examination time; as well as the increase in the number of indications for its accomplishment, associated to greater availability and a relative tendency to decrease exam costs [5].
The risk associated with a radiological examination can be considered quite low compared to the risk due to natural radiation.However, any additional risk, no matter how small, is unacceptable if it does not benefit the patient.The knowledge of the dose distribution deposited in children is important when it is thought to change the acquisition parameters aiming at dose reduction.The risks of stochastic effects increase in the child due to the tissue radiosensitivity allied to the long life expectancy [6].
The CT scans result in absorbed doses to organs in the range of 10 to 100 mGy, usually below the lower limit considered for the occurrence of deterministic effects [Image Gently, 2014].
However, all procedures involving ionizing radiation can lead to stochastic effects, such as tumor induction.ICRP 87 (2000) advocates actions for dose reduction, such as the use of 270° partial tube rotation, selection of suitable reconstruction protocols, use of multi-channel Z filters, which would be actions to be incorporated into the technology of CT scanners.Several actions were introduced by the manufacturers, for example: specific protocols for pediatric patients, current modulation in the organ-based tube and interactive reconstruction [7].
The objective of this study is to find the differences in dose values deposited in adult and pediatric chest phantoms using the same acquisition protocols and calculate the CT dose index for the phantoms.
Computer Tomography Scanners
The experiments for the observation and comparison of the CT air kerma index and CT dose on the chest phantoms were carried out on two multislice CT scanners, one made by GE and another by Philips.The routine chest protocols and optimized pediatric chest scan protocols were used.
Table 1 shows the main characteristics of the CT scanners used.
Phantoms
Two chest phantoms were constructed by the research team of the Centro de Engenharia Biomédica (CENEB) of the Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG), being a representative of an adult and a pediatric patient's chest.The adult patient chest phantom is a cylinder made of PMMA, 32 cm in diameter and 15 cm in length.This phantom is considered the default for the dose reference in chest CT scans.Thus, all chest CT scans performed are accompanied by a report that presents a volumetric CT dose index estimated by scanner (CTDI vol ) based on the scanning of this phantom.
The pediatric chest phantom made of PMMA is oblong, with dimensions of 14 x 29 cm 2 , representing the dimensions of the chest of an eight-year-old pediatric patient, including the axillary region and 15 cm in length.
The phantom has openings for positioning of dosimeters, one central being representative of the mediastinum and four peripheral positions 3 and 9 axillary regions and 6 and 12 thoracic spine and mediastinum, which from the anatomical point of view, whose purpose will be to study the distribution of doses absorbed in these involved organs and tissues.The four peripheral openings are 90° out of phase, the center of which is 10 mm from the edge of the phantom.Figure 1 shows an illustration with the dimensions of the adult and pediatric phantoms.In order to carry out the scans on the CT devices, the phantoms were positioned in the isocenter of the gantry, and the peripheral openings were identified according to the hours of the analog clock, as: 3, 6, 9 and 12.These apertures are used as reference to position the phantom in the isocenter of the gantry with the aid of lateral side and up lasers.
The openings of the phantoms are filled with PMMA rods which must be removed one by one for the positioning of the pencil chamber, targeting the dose measurements in the five regions.Thus, while the ionization chamber is positioned in one opening, the others were filled with PMMA rods holding the phantom as a PMMA solid structure.Figure 2 shows the positioning of the adult phantom in the isocenter of the gantry.The CT air kerma index measurements were performed using a pencil chamber with the routine chest scan protocol used by the radiological services and other protocols were proposed.The measurements were recorded with the gantry at zero-degree angulation and with the phantom positioned in the isocenter.
The pencil chamber was positioned alternately in the openings of the adult chest phantom and later in the pediatric phantom.For each chamber positioning, five measurements were performed, making a minimum of 25 measurements for each protocol and for each phantom.The central slice irradiations were performed in the two phantoms, in axial mode, with a voltage supply of the X-ray tube of 120 kV in the both CT scanners.
Scanning protocols
The definition of the protocol parameters for the central slice irradiation has been performed through the operating terminal of the scanner.In the examination room, the adult phantom and later the pediatric phantom have been placed on the table and, with the aid of lasers, they were oriented so that their central axis passed through the isocenter of the gantry during the displacement of the table.Table 2 shows the protocol parameters used to irradiate the central slice of the two phantoms in axial mode, for scanners A and B, respectively.Both scanners have automatic exposure control for dose reduction through current modulation (mA).Thus, the pediatric phantom was scanned with the automatic current control system, and the typical currents generated in the scans of the phantom were obtained.
Dose index values obtained
The values of air kerma in PMMA (C k,PMMA,100 ) were obtained by reading the values recorded on the electrometer duly calibrated by the influence of temperature and pressure through the calibration factor of the ionization chamber.In order to obtain the CT Dose Index (CTDI) values from the air kerma values, an air/PMMA conversion factor of 1.0412 was used, considering the 120 kV beam [8,9].
Measurements of C k,PMMA,100
The irradiation of the central slice of the adult phantom was done using the parameters defined in Table 1.The mean values obtained for each position and the standard deviation (SD) of the measurement are presented in the Table 4. Observing the mean values recorded in the five positions, it is verified that, among the values of air kerma in the peripheral PMMA, the highest recorded value was 12.52 ± 0.34 mGy, and it occurred in position 12, and the lowest was 10.50 ± 0.03 mGy in position 6, which is an effect of filtering the beam by the table when the X-ray tube radiates the object from the bottom to the top.As the contribution in the composition of the registered value of point 6 is greater at that moment, due to the proximity of the beam focus, the total value of air kerma in that position becomes normally smaller.For these measurements, the standard deviation (SD) ranged from 0.29% to 2.72% of the average value.The proximity between the doses in points 3 and 9 indicates the good positioning of the object in the isocenter of the gantry, since if the object is displaced to the right, there would be a greater dose deposition in point 3 and, consequently, smaller in point 9.The average value obtained at the central point was the lowest, 5.73 ± 0.02 mGy, corresponding to approximately 48.52% of the mean peripheral values.It should be noted that the dose recorded in points 3 and 9 are of paramount importance, since there are located axillary lymphatic chains that are radiosensitive.
The average values of air kerma in the PMMA C k,PMMA,100 calculated allow us to verify that the highest recorded value was 19.12 ± 0.10 mGy and occurs at position 12; and the lowest was 13.92 ± 0.04 mGy at position 3.The dose values at positions 3, center and 9 are very close and smaller than the values recorded in positions 6 and 12.For these measurements the standard deviation varied between 0.29% and 1.16% of the average value.Figure 3 shows graphs of Ck,PMMA,100 values for adult and pediatric phantoms on A and B scanners.
For the measurements of the adult chest phantom in the CT scanner B it was verified that, among the values of air kerma in PMMA in the peripheral openings according to Table 5, the highest recorded value was 9.11 ± 0.43 mGy, and occurs in the position 12, and the lowest was 8.14 ± 0.25 mGy in the position 6, which is an effect of filtering the beam by the table when the tube irradiates the object from the bottom up.The mean value obtained at the central point was the lowest, 4.39 ± 0.01 mGy, corresponding to approximately 50.73% of the mean peripheral values.
For these measurements the standard deviation ranged from 0.23% to 6.64% of the average value.
The irradiation of the central slice of the pediatric phantom was done using the parameters defined in the Table 5.Five values of C k,PMMA,100 were obtained for the five measurement positions.These results demonstrate that, if the same charge (100 mA.s) was used, the A scanner would promote greater dose deposition than the B scanner, both for an adult patient and for a pediatric patient.However, in the routine scans performed with the A scanner, the load value is 150 mA.s and for the B scanner, the load is 250 mA.s.
Considering also the influence of the pitch on the final value of the dose index in CT scans, we can obtain the value of C vol and considering the pitch of 0.984 for the CT scanner A and 0.938 for the B, as presented in Tables 5 and 6.Thus, the values of C vol and CTDI vol shows in Table 7.When comparing the obtained data, it can be concluded that the acquisition performed in the scanner B is responsible for a dose deposition of 21.89% greater than that deposition made in the scanner A, in order to obtain images with the same diagnostic objective of pediatric patients of 8 years.When considering adult patients, scans of the scanner B increase of up to 30.09% of the deposited dose.
Considering the dose variation through the CTDI vol of the pediatric phantom in relation to the adult phantom it is verified that the pediatric phantom receives a dose 59.56% greater than the adult phantom in the scanner A and 49.53% in the B.
The development of the pediatric chest phantom in oblong format allowed the measurement of dose rates in CT and verify the variations presented and compare with the adult chest phantom.
Chest scans with routine protocols have demonstrated that the dose in an eight years old patient when using the same scanning protocol is about 50% greater than in the adult patient.
CONCLUSIONS
The developed pediatric chest phantom allowed the verification of how the dose distribution can vary with the objet shape and volume.When comparing with the data obtained for the standard adult chest phantom, it was found that doses in smaller volumes, such as pediatric patients, are higher when using the same acquisition protocol.
The scans of the central slice in the adult and pediatric chest phantom performed on the A and B CT scanners allowed us to observe the higher doses deposited in the pediatric phantom and which, depending on the section format, the doses are smaller on the longer axis 3, 9 and central positions, and larger in positions 6 and 12.
The results obtained allow us to say that the protocols defined for adult patients are oversized when used for chest scans of pediatric patients.Therefore, equipment that has automatic dose control tools must be activated when scans are performed in pediatric patients.However, it should be emphasized that in Brazil, a part of the equipment installed does not have automatic current adjustment tools, aiming at dose reduction and that even those who do not always have this tool triggered for pediatric patient scans.Even in more advanced technology equipment, such as multislice, which already have an automatic dose reduction system evaluated by patient mass and height, still require dose reduction adjustments for the pediatric patient.
Figure 2 :
Figure 2: Adult chest phantom placed in the gantry isocenter.
Table 2 :Table 3 :
Protocol parameter for irradiation of the chest phantom on scanners A and B the protocols used in the services routines for all patients, regardless of size or age.Routine protocols of CT scanners A and B
Figure 3 :
Figure 3: Graphs of C k,PMMA,100 values for adult and pediatric phantoms on A and B scanners
Table 1 :
Characteristics of CT scanners.
Table 4 :
Values of C k,PMMA,100 in mGy for adult and pediatric chest phantom for 120 kV and 100 mA.s in CT scanner A.
Table 5 :
Values of C k,PMMA,100 in mGy for adult and pediatric chest phantoms in CT scanner B.
. Values C w , C vol and CTDI vol
From the measured values the air kerma values in the air were obtained in PMMA Cw, shown in the Table6for a voltage of 120 kV and a charge of 100 mA.s.The estimated value in the A scanner report was 9.71 mGy, and in the B scanner it was 7.23 mGy.These values were very close to the values measured with the adult phantom.
Table 6 :
C w values (in mGy) for 120 kV and 100 mA.s
Table 7 :
Values of C vol and CTDI vol in mGy. | 3,904.6 | 2019-01-28T00:00:00.000 | [
"Medicine",
"Physics",
"Engineering"
] |
Zoology of a non-local cross-diffusion model for two species
We study a non-local two species cross-interaction model with cross-diffusion. We propose a positivity preserving finite volume scheme based on the numerical method introduced in Ref. [15] and explore this new model numerically in terms of its long-time behaviours. Using the so gained insights, we compute analytical stationary states and travelling pulse solutions for a particular model in the case of attractive-attractive/attractive-repulsive cross-interactions. We show that, as the strength of the cross-diffusivity decreases, there is a transition from adjacent solutions to completely segregated densities, and we compute the threshold analytically for attractive-repulsive cross-interactions. Other bifurcating stationary states with various coexistence components of the support are analysed in the attractive-attractive case. We find a strong agreement between the numerically and the analytically computed steady states in these particular cases, whose main qualitative features are also present for more general potentials.
Introduction.
Multi-agent systems in nature oftentimes exhibit emergent behaviour, i.e. the formation of patterns in the absence of a leader or external stimuli such as light or food sources. The most prominent examples of these phenomena are probably fish schools, flocking birds, and herding sheep, reaching across scales from tiny bacteria to huge mammals. While self-interaction models for one particular species have been extensively studied, cf. Refs. [26,23,20,37,46] and references therein, there has been a growing interest in understanding and modelling interspecific interactions, i.e. the interaction among different types of species. One way to derive macroscopic models from microscopic dynamics consists in taking suitable scaling limits as the number of individuals goes to infinity. Minimal models for collective behaviour include attraction and/or repulsion between individuals as the main source of interaction, see [46,19,20,35] and the references therein. Attraction and repulsion are normally introduced through effective pairwise potentials whose strength and scaling properties determine the limiting continuum equations, see [39,9,8,16]. Usually localised strong repulsion gives rise to non-linear diffusion like those in porous medium type models [39], while longrange attraction remains non-local in the final macroscopic equation, see [16] and the references therein. In this paper we propose a finite-volume scheme to study two-species systems of the form ∂ t ρ = ∇ · ρ∇ W 11 ⋆ ρ + W 12 ⋆ η + ǫ(ρ + η) , (1a) with given initial data ρ(x, 0) = ρ 0 (x), and η(x, 0) = η 0 (x). (1c) Here, ρ, η are two unknown mass densities, W 11 , W 22 are self-interaction potentials (or intraspecific interaction potentials), W 12 , W 21 are cross-interaction potentials (or interspecific interaction), and ǫ > 0 is the coefficient of the cross-diffusivity. The non-linear diffusion term of porous medium type can be considered as a mechanism to include volume exclusion in cell chemotaxis [32,40,12], since it corresponds to very concentrated repulsion between all individuals. This model can also be easily understood as a natural extension of the well-known aggregation equation (cf. [37,46,3,18] ) to two species including a cross-diffusion term. Common interaction potentials for the one species case include power laws W (x) = |x| p /p, as for instance in the case of granular media models, cf. [2,47]. Another choice is a combination of power laws of the form W (x) = |x| a /a − |x| b /b, for −N < b < a where N is the space dimension. These potentials, featuring short-range repulsion and long-range attraction, are typically chosen in the context of swarming models, cf. [36,1,28,29,4,21,17]. Other typical choices include characteristic functions of sets (like spheres) or Morse potentials W (x) = −c a exp(−|x|/l a ) + c r exp(−|x|/l r ), or their regularised versions W p (x) = −c a exp(−|x| p /l a ) + c r exp(−|x| p /l r ), where c a , c r and l a , l r denote the interaction strength and radius of the attractive (resp. repulsive) part and p ≥ 2, cf. [26,22,21]. These potentials display a decaying interaction strength, e.g. accounting for biological limitations of visual, acoustic or olfactory sense. The asymptotic behaviour of solutions to one single equation where the repulsion is modelled by non-linear diffusion and the attraction by non-local forces has also received lots of attention in terms of qualitative properties, stationary states and metastability, see [11,15,27,13,14] and the references therein. Systems without cross-diffusion, ǫ = 0, were proposed in [24] as the formal mean-field limit of the following ODE systeṁ For symmetrisable systems, i.e. systems such that there exists some positive constant α > 0 with W 12 = αW 21 , they show the system can be assigned an interaction energy functional. As a result, the system admits a gradient flow structure and variational schemes can be applied to ensure existence of solutions, cf. [24,33]. However, in many contexts such a condition is too exclusive in the sense that lots of applications exhibit a lack of symmetry in the interactions between different species. In order to treat the system for general, and possibly different, cross-interactions W 12 , W 21 , they modify the well-known variational scheme to prove convergence even in the absence of gradient flow structure. These systems without cross-diffusion appear in modelling cell adhesion in mathematical biology with applications in zebrafish patterning and tumour growth models, see [30,25,41,48] for instance. In this paper we extend their cross-interaction model by a cross-diffusion term which is used to take into account the population pressure, i.e. the tendency of individuals to avoid areas of high population density. As cross-diffusion we choose the form introduced by Gurtin and Pipkin in their seminal paper [31]. Although their work is antedated by results of mathematicians and biologists interested in density segregation effects of biological evolution equations, cf. [44,43] and references therein, the particularity about their population pressure model is the occurrence of strict segregation of densities under certain circumstances, cf. [31,6,7]. This cross-diffusion term has been the basis to incorporate volume exclusions in models for e.g. tumour growth [5] or cell adhesion [38]. Hence, our model is of particular interest from a modelling point of view taking into account non-local interactions between the same species and different species as well as the urge of both species to avoid clustering. We discover a rich asymptotic behaviour including phenomena such as segregation of densities, regions of coexistence, travelling pulses -all of which are observed in biological contexts, cf. [42,45]. Existence of segregated stationary states under certain assumptions on the interaction potentials for small cross-diffusivity has been very recently obtained in [10]. Here we show that it is in fact possible to find explicit stationary states and travelling pulses for certain singular not necessarily decaying interaction potentials showing coexistence and segregation of densities. The rest of this paper is organised as follows: in Section 2 we discuss the basic properties of the system (1) in one dimension, in Section 3 we propose our numerical scheme which is used in Section 4 to explore the model and its long-time behaviour numerically. These insights are used to make reasonable assumptions on the support of the asymptotic solutions in order to derive analytic expressions for their shape and give a first classification of the zoology of the different stationary states. Finally we discuss in Section 5 how generic these phenomena are for different potentials and we draw the final conclusions of this work in Section 6.
2.
A non-local cross-diffusion model for two species. Throughout this paper we consider system (1) in one spatial dimension. Then the model reads for some initial data ρ(x, 0) = ρ 0 (x), and η(x, 0) = η 0 (x), and radially symmetric potentials W ij , for i, j = 1, 2. We can obtain some apriori estimates on solutions by using the following energy We note that for W ij ∈ W 2,∞ (R), along any solution (ρ, η) of system (2), there holds In the case of W ii = C ii x 2 /2 and W ij = ±C ij |x| for i = j with non-negative constants C ij , the estimate is also true, since and similarly for the terms in (2b), as long as ρ, η ∈ L ∞ (0, T ; L ∞ (R)). Thus the terms implying that ρ + η ∈ L 2 (0, T ; H 1 (R)). We deduce that the sum of both species remains continuous for almost all positive times -a property we will make use of later. Now, let us introduce our notion of steady states.
Proof. Clearly, the characterisation is sufficient, since the velocity field vanishes in each connected component of their supports if there exist constants c 1 , c 2 such that Eqs. (3) are satisfied. Conversely, if there holds we note that ρ, η, ∂ x (ρ + η) ∈ L 2 (R) by the definition of steady state, and therefore the right-hand sides are distributional derivatives of L 1 functions. By a well-known result (cf. e.g. [34], Lemma 1.2.1.), we deduce that there exist constants K 1 , K 2 ∈ R such that K 1 = ρ∂ x (W 11 ⋆ ρ + W 12 ⋆ η + ǫ(ρ + η)), Due to the integrabilty properties of the right-hand sides above, we infer that K 1 = K 2 = 0, and thus in the interior of any connected component of the supports of ρ and η, we obtain that there exist constants c 1 , c 2 ∈ R such that using the same argument as above.
Note that the assumption on the interiors of the supports of the species is purely technical and due to the regularity assumptions on our definition of stationary states. This avoids pathological cases such as functions supported on a fat Cantor set.
3. Numerical scheme. In order to solve system (2), we introduce a finite volume scheme based on Ref. [15]. The problem is posed on the domain Ω : and uniform size ∆x := x i+1/2 − x i−1/2 . Finally, the time interval [0, T ] is discretised by t n = n∆t, for n = 0, . . . , ⌈T /∆t⌉. We define the discretised initial data via We integrate system (2) over the test cell [t n , t n+1 ] × C i to obtain whereF n i+1/2 ,Ḡ n i+1/2 denote the flux on the boundary of cell C i , i.e.
Then the finite volume scheme for the cell averages ρ n i and η n i reads where we approximate the fluxes on the boundary, Eqs.(4), by the numerical fluxes using (·) + := max(·, 0) and (·) − := min(·, 0) to denote the positive part and the negative part, respectively. The velocity is discretised by centred differences: Here we have set where W l−k ij = W ij (x l − x k ), for i, j = 1, 2. This scheme has proven very robust for one species, and under a (more restrictive) CFL condition we can also prove the following result.
Proposition 3.1 (Non-negativity preservation). Consider system (2) with initial data ρ 0 , η 0 ≥ 0. Then for all n ∈ N the cell averages obtained by the finite volume method (5) satisfy ρ n i , η n i ≥ 0, granted that the following CFL condition is satisfied .
Proof. Let us assume that ρ n i , η n i ≥ 0, and we need to show that then ρ n+1 We can rearrange the terms so that Clearly, all terms in the second line are non-negative. The first line is non-negative if the CFL condition is satisfied. Application of the same procedure to η n+1 i yields the statement.
4. Numerical study. In this section we study system (2) numerically with emphasis on its long time behaviour. Throughout this chapter we use the self-interaction potentials and the cross-interaction potentials for the interspecific attractive-attractive and attractive-repulsive case, respectively. This choice of potentials allows us to compute steady states of system (2) explicitly. We find a wide range of different behaviours and properties, including segregation phenomena, for different cross-diffusivities and cross-interactions. Notice that the system is translationally invariant and therefore, if for symmetry considerations we can show that the centres of mass of both species in a stationary state are fixed and equal to some particular value, we can suppose that value to be zero without loss of generality. From numerical simulations we observe that steady states are compactly supported which motivates this ansatz when computing the profiles analytically. This is also due to the non-linear diffusion of porous medium type in the volume exclusion term. This chapter is subdivided into two sections addressing the mutually attractive case and the attractive-repulsive case, respectively. 4.1. Attractive-attractive case. Let us begin with the case of attractive interaction between both species, i.e. W 12 = W 21 = |x|. Upon exploring the system numerically, we find a vast variety of stationary patterns, including both symmetric and non-symmetric profiles whose occurrence and stability depends on the crossdiffusivity. In fact, the coefficient ǫ of the cross-diffusivity plays a crucial role in the bifurcations of these profiles, and will be discussed in the next section. Then, we study the system as the cross-diffusivity tends to zero and the stability of the steady states -a matter that seems closely intertwined with the bifurcations.
Steady states and behavioural bifurcation.
We begin by introducing the two types of symmetric steady states observed in the attractive-attractive case. Motivated by numerical simulations, we assume that the stationary distributions are compactly supported, i.e., is then only inhabited by the first species, but not η. Upon rearranging Eq. (3), we obtain The two non-local terms W 11 ⋆ ρ and W 12 ⋆ η can be computed individually. First the self-interaction terms becomes where are the mass and the first two moments of ρ, respectively. Then the cross-interaction term becomes where m 2 , M 2 denote the mass and the centre of mass of the second species. Due to symmetry and translational invariance of the solution, both M 1 and M 2 can be taken as zero without loss of generality. Upon substitution of the non-local terms in (7) and (8), Eq. (6) is simplified into , respectively. Using ρ(±c) = 0 at the boundary (where ρ + η vanishes identically), we get Finally, let us consider the interval [−b, b] where both species coexist. Again, ρ satisfies where the cross-interaction term W 12 ⋆ η can be further reduced, according to Notice that all terms on the right side are twice differentiable. Therefore from (10), ρ + η is twice differentiable in (−b, b), and upon differentiating Eq. (10) twice we obtain and similarly from the second equation in (3) The system of equations (11) and (12) can be solved by first introducing the decoupled system for u := ρ + η and v := ρ − η, giving by Thus, the solutions ρ and η are obtained as In fact, due to symmetry there holdsû 1 = 0, and Eqs. (13,14) can be simplified to Hence the symmetric steady states are determined uniquely by three parameters,û 2 , b and c, which are governed by algebraic equations. Since η is only supported on [−b, b], the condition for the total mass of η becomes From Eqs. (9,15), the condition for the total mass of ρ becomes Whenû 2 is eliminated, Eq. (16) provides a relation between b and c, i.e., Finally, consider the continuity of the sum of the densities ρ+η at Therefore b and c are in the zero locus of Eqs. (17,18) that are numerically solved, cf. Figure 1(a). Then the shape of the steady state is given by two parabola profiles on the parts only inhabited by the first species and cosine profiles where both species coexist: Figure 1(b) shows an excellent agreement between numerical and analytical steady states. Let us remark that Eq. (17) implies b = c in the case of m 1 = m 2 . As a consequence both species completely overlap and the profile is just that of a cosine, cf. Figure 2. Numerical simulations show that the Batman profiles are the only symmetric stationary distribution in a certain range of cross-diffusivities, namely (0, ǫ (1) ]. For ǫ ∈ (ǫ (1) , ǫ (2) ], a new family of profiles (called the second kind ) emerges coexisting with the Batman profiles in this range, cf. Figure 3. Finally, for ǫ > ǫ (2) only profiles of the second kind prevail. Since the steady states are a state of balance between diffusion and attractive interactions, the second kind of profiles can be seen as states in which the attractive force is not strong enough to ensure the formation of a single group for η as observed in the Batman profiles. Similarly to the Batman profiles, we may determine parameters and their governing equations for profiles of second kind. In the symmetric case, using (3) the profiles are given by , and p is the fraction of mass in the corners of η, cf. Figure 3, (areas filled in red). Similarly, It is apparent that there are five unknowns b, c, d for the support, B for the amplitude in regions of coexistence, and p for the mass fraction. Correspondingly, we find four conditions in order to determine all parameters but p: for the mass of ρ and the continuity of the sum σ = ρ + η at x = c and x = b. Since p parameterises a family of solutions and describes both branches (as envelope) of the bifurcation diagram, cf. Figure 4, we are interested in finding the conditions leading to p min (ǫ), p max (ǫ) in the diagram, Figure 4. In order to determine the bifurcation diagram we run simulations with two different types of initial data -on the one hand we start the system with supp(η) ⊂ supp(ρ), on the other hand we initialise the system such that η is supported around ρ, cf. first row of Figure 5. The second row shows the stationary distribution asymptotically achieved with the respective initial data. We note that the mass fraction of η in the corners is different for both simulations albeit having used the same cross-diffusivity. The mass fraction in the left graph corresponds to p = p min and the mass fraction in the right graph to p = p max , respectively. Now we want to give conditions determining the envelopes p min (ǫ), p max (ǫ) of Figure 4. Let us impose non-negativity of η at x = b, i.e. η(b) ≥ 0. This is a reasonable assumption which is also reflected in the numerical simulations, cf. Figure 6(a). The figure shows steady states corresponding to the left initial data in Figure 5 as ǫ increases. While we observe a discontinuity of η at x = b for small ǫ, there is a critical value where η(b) = 0, for all ǫ > ǫ (1) . For the upper envelope we impose that the velocity field u 2 is non-negative at x = c since otherwise any small perturbation will render the stationary state unstable, i.e. mass would get transported into the interior, cf. Figure 6(b). These two conditions describe both envelopes in Figure 4. In all four graphs the masses are m 1 = 0.1, m 2 = 0.6, and the cross-diffusivity is ǫ = 1.7. The first row depicts two different initial data -one (left) where η is included in ρ, and one (right) where η surrounds ρ. In the second row we present the corresponding steady states. Albeit having a similar make-up, they differ in their respective mass fraction of the corner, p. The left graph gives the minimal mass fraction p min while the right graph gives the maximal, pmax, respectively, cf. Vanishing diffusion regime. In this section we study the case of Batman profiles as ǫ → 0. Recall the two equations for b and c, When ǫ is small, both b and c are O( √ ǫ), suggesting b = ǫ 1/2 b 0 + ǫ 1/2 b 1 + ǫb 2 + · · · , and c = ǫ 1/2 c 0 + ǫ 1/2 c 1 + ǫc 2 + · · · .
Upon substitution of the asymptotic expansions into Eq. (19) and (20), the leading order coefficients b 0 and c 0 satisfy Notice that both densities in the Batman profiles will converge to a Dirac Delta at zero with the respective masses while keeping their shape with this described asymptotic scaling for their supports. Asymmetric profiles. So far we only discussed symmetric steady states. However, there is an equally rich variety of non-symmetric stationary states, cf. Figure 7 and Figure 8. In Figure 7 we display the cases where the support only consists of metric profiles for 0 < ǫ < ǫ (1) independent of the masses m 1 and m 2 . Only for larger cross-diffusivities, ǫ > ǫ (1) , asymmetric profiles can be observed. Moreover, there is a whole family of asymmetric profiles as can be seen in Figure 8. This is similar to the case of symmetric stationary states, parameterised by the mass fraction p.
Stability of steady states and symmetrising effect. Let us now discuss the numerical stability of the symmetric steady states. Here the bifurcation point ǫ (1) plays an important role, for the system exhibits a symmetrising effect whenever the crossdiffusivity lies below the critical one, in the sense that there is only one symmetric steady state attracting any initial data.
We fixed ǫ ∈ (0, ǫ (1) ) and chose ρ 0 = 2m 1 ½ [−0.5,0] and η 0 = 2m 2 ½ [0,0.5] for all combinations of masses of the form (m 1 , m 2 ) = 0.1 · (i, j) for i, j = 1 . . . 10. In all cases we observe that there is only one attractor, namely the Batman profile of the form given in Figure 1(b) and Figure 2(b) in the case m 1 = m 2 , respectively. For ǫ > ǫ (1) the system is not symmetrising anymore and small perturbations lead to different stationary states. This can be seen if p is varied in [p min , p max ], for it leads to different states. A similar argument holds for the asymmetric states, by shifting mass from one corner into the other, cf. Figure 8.
4.2.
Attractive-repulsive case. In this section we present the attractive -repulsive case, i.e. W 12 = |x| = −W 21 . Then the steady states have segregated densities, as asserted by the following proposition. Proof. Suppose the interior of a connected componente of supp(ρ) ∩ supp(η) is not empty. We know that both species satisfies Eqs. (3) in that connected component: Similar arguments as above imply that the interaction terms are twice differentiable in this interval, thus we differentiate twice and get 0 = m 1 + 2η + ǫ(ρ + η) ′′ and 0 = m 2 − 2ρ + ǫ(ρ + η) ′′ .
Steady states.
This section is dedicated to studying the steady states of the system with attractive-repulsive cross-interactions. Due to numerical simulations and the previous proposition we make the following assumption on the support where a < b ≤ −c < c ≤ d < e are some real numbers. Using Eqs. (3) we proceed similar as above, cf. Eqs. (7,8), to obtain for shape of the second species on the left part of the support and for the right part, respectively. Similar as above, we can see that the interaction terms are twice differentiable, therefore differentiating Eq. (3) in the support of ρ twice yields 0 = m 1 + ǫ(ρ) ′′ , and thus and analogously Concerning the first species, the parameters β, γ are determined by the continuity condition Eq. (22) and we obtain We can see that there are six unknowns, namely a, b, c, d, e, and M 2 with a total of five conditions: by imposing half of the mass of η to each side of ρ.
Case of strict segregation. Let us start by discussing the case
Then the condition on the mass yields We can solve η L (b) = 0 for a, Since half of the mass is located to the left of the first species, we get where we used Eq. (23a). Similarly, we solve η R (d) = 0 for e to obtain Using this expression we compute So we have determined c, b, d depending only on the masses and the second order moments of the second species, M 2 . We can substitute the values into Eqs. (23a, 23c) to determine a and e.
Critical ǫ and maximal M 2 . We are interested in a condition determining as to when segregation of species occurs. In fact there is a critical value of the crossdiffusivity, ǫ c , such that there only exist adjacent steady states for ǫ > ǫ c . For 0 < ǫ < ǫ c strictly segregated steady states occur if |M 2 | < M 2,max , where M 2 = 0 corresponds to the symmetric case. Figure 9 displays this behaviour. Let us derive an expression for ǫ c and M 2,max . For a fixed ǫ we may compute M 2,max . We begin with the case c = −b. We can solve for the critical M 2 , i.e.
Similarly, we can solve equation c = d for M 2 , which gives (c) ǫ = 1/2. If ǫ = ǫ c both species touch at the points {−c, c} or are partially adjacent. If ǫ < ǫ c but we choose M 2 outside of the aforementioned range we observe steady states consisting of (partially) adjacent bumps. Figure 10 displays the steady states in the symmetric case, i.e. M 2 = 0, for attractiverepulsive cross-interactions. We observe a transition of behaviour for different values of ǫ, ranging from strictly segregated states to completely adjacent states. The numerical results agree perfectly with the results obtained analytically.
Vanishing diffusion regime. As we have seen in Figure 9, there is an ǫ c such that the steady states parameterised by M 2 ∈ [−M 2,max , M 2,max ] are segregated. In this section we consider the case of vanishing cross-diffusion. We can assume that ǫ < ǫ c and This is indeed a measure solution of system. To see this let us consideṙ Since we are looking for a steady state we observė We assume without loss of generality that Fixing X = 0 we get Y 2 = Y 1 + 2m 1 /m 2 and Y 1 ∈ [−2 m1 m2 , 0]. This is exactly the solution of the system as ǫ → 0, cf. Eq. (26).
Stability of steady states. Here we want to discuss the stability of the stationary states of the attractive-repulsive system. In general, the stationary states are not stable as small perturbations may lead to a completely different stationary state. It becomes clear in Figure 9, that perturbing η by shifting it to either side leads to a completely different stationary state. Although this is an arbitrarily small perturbation in any L p -norm, the translated profile is another stationary state. This is why these profiles are not stable. The same argument holds for symmetric stationary states. However, they are stable under symmetric perturbations since any symmetric initial data is attracted by the symmetric profile. Characterising fully the basin of attraction for each stationary state seems difficult. For perturbations shifting mass from η L to η R (or vice versa) there is no stationary state but the profile is then attracted by a travelling pulse solution.
Travelling pulses.
In addition to the convergence to steady states we observe travelling pulse solutions in the case of attractive-repulsive cross-interactions. There are two types of travelling pulses -those consisting of two bumps and those consisting of three. In our numerical study we do not observe more than three bumps, even in the case of exponentially decaying potentials. There are however metastable states where more bumps exist but after a sufficiently long time the collapse into two or three.
Two pulses. In order to compute these profiles, we assume [−a, a] denotes the initial support of u = η(0) and therefore [−a − x 0 , a − x 0 ] the initial support of ρ(0). We transform the system into co-moving coordinates, z = x − vt, and obtain the following conditions for the pulse profiles similarly to Eqs. (3). A computation similar to Eqs. (7,8), leads to the explicit form of the pulse on [−a, a] for some constantc 1 . Since u(z) is a parabola with roots ±a, u is symmetric. As a consequence we obtain M = v − m. By definition of M = zu(z)dz = 0, whence v = m. Hence the shape is given by Then the following consideration determines the boundary of the support, a, If there were travelling pulse solutions of this form they would satisfy the same equations as above. Then, The continuity of the sum suggests that u 1 (0) = u 2 (0) implies m = v. But then We solve this expression for a > 0 and find a = 3 √ 12ǫ. A comparison of the support of the adjacent solutions and the support of segregated solutions, cf. Eq. (28), shows that the adjacent solutions in fact only touch. Figure 11 shows the formation of two travelling pulses. We start with two indicator functions as initial data and let the system evolve. At about time t ≈ 2 we observe a fully established pulse profile. We let the system evolve further and compare the We transform to co-moving coordinates, z = x−vt, and obtain the following conditions for the profile whence we obtain Here Similarly, the profiles of the second species are given by and Again, we use the fact that the sum of both densities has to be continuous, i.e.
as well as Eqs. (30) hold. We consider the case of strictly segregated solutions first, i.e. b < −c, and c < d. Since then ρ(±c) = 0, we may deduce from Eq. (29) that v = m R − m L for the speed of propagation and for the shape of the first species (c is determined by the mass condition, Eq. (31)). Furthermore we obtain in terms of b. Similarly, we can get an expression for e in terms of d, i.e.
Using the expression for a, we obtain Note that Eqs. (32) completely determine the support and the profiles of the pulses. Figure 12 shows the formation of a triple pulse solution. We choose characteristic functions as initial data (dotted). The mass on the left is m L = 1/3 and, respectively, m R = 2/3 on the right. After some time the pulse profile is established. We compare the system (blue and red) at time t = 9 and time t = 24 with the analytical expression derived above (black). The figure displays a great agreement between our numerical result and the analytical. Once the profile is fully established it moves to the right at a constant speed. The numerical velocity is given by ∆x/∆t = 5/15 = 1/3. This is in perfect agreement with the analytically obtained results, i.e. v = m R − m L = 2/3 − 1/3 = 1/3. At this stage, let us draw our attention to two special cases. Remark 3 (Maximal M 2 ). Let us get back to the general case. We study the interval of M 2 . Assuming ǫ fixed, b = −c yields On the other hand, c = d gives where v = m R − m L , as above. It is worthwhile noting that in the case m L = m R both M 2,max and M 2,min coincide with Eqs. (24,25) for the stationary state.
Parallel to the consideration for (partially) adjacent steady states of the attractiverepulsive system we also find the existence of adjacent travelling pulse solutions.
5.
Generality. This section is dedicated to the study of more general or realistic potentials to understand whether the behaviours observed above are specific to our interaction potentials. Different cross-interaction and self-interaction potentials will be investigated. Even though analytic expressions for the steady states and travelling pulses seem no longer avaiablable, the behaviours are indeed generic and, in fact, even richer than the above particular model.
Different cross-interactions.
Let us begin by considering different crossinteraction potentials. We regard two types of potentials -power-laws and Morse-like potentials decaying at infinity, i.e. where p ∈ {1/2, 1, 3/2}. This choice of potentials is motivated as they are similar to the Newtonian cross-interaction. In both cases, we observe a very similar behaviour both in the mutually attractive case and the attractive-repulsive case, respectively. Figure 13 displays the Batman profile for different cross-interaction potentials. In all simulations the same initial data, mass, and cross-diffusivity were used. Each steady state features the salient characteristics observed in the case W cr = |x|, i.e. a region of coexistence surrounded by regions inhabited by only one species. From the steady states we can also infer another information, namely, second type profiles exist and the point of bifurcation depends on the potential, for only Figure 13(d) exhibits a profile of second type. Similarly, we observe a symmetrising effect for small cross-diffusivities and asymmetric profiles.
Different self-interactions.
Here, we keep the cross-interaction potentials fixed as W 12 = |x| = ±W 21 and consider different self-interaction potentials of the form W (x) = |x| p /p, for p ∈ {3/2, 2, 4}. In each case we observe a very similar behaviour. We obtain the same variety including both Batman profiles and the profiles of second type. Again we observe that the system is symmetrising, however for a different ǫ (1) . In the attractive-repulsive case as well we observe the characteristic profiles and the formation of pulses.
6. Conclusions. In this paper we introduced a system of two interacting species with cross-diffusion. We used a positivity-preserving finite-volume scheme in order to study the system numerically. For a specific choice of potentials, the steady states can be constructed with parameters governed by algebraic equations. These numerically simulated and the analytically constructed stationary states and travelling pulses were found to agree with each other. Using the same scheme the model was explored for related potentials and the behaviours observed for the specific potentials turned out to be generic, when the cross-interaction potentials or the self-interaction potentials were exchanged. While this paper gives a first insight as to what qualitative properties can be expected from models taking the general form (1), there is still a lot of analytical work to be done. First and foremost, it is still an open problem to show existence of solutions to the systems. The formal gradient flow structure is lost when the crossinteraction potentials W 12 and W 21 are not proportional to each other, and the main problem is to find the right estimates for individual species since we only control the gradient of the sum of the densities. | 8,244.6 | 2017-05-08T00:00:00.000 | [
"Physics"
] |
DEVELOPMENT OF TEACHING MATERIALS FOR MAKING SIMPLE ENERGY-PRODUCING DEVICES IN RENEWABLE ENERGY TOPIC
: The change in curriculum to a Merdeka Curriculum causes changes in the learning system in Indonesia because this requires teachers and students to be more innovative and creative. To balance this requires teaching materials that can meet these needs, especially renewable energy materials; this material is new, so there are still few teaching materials available. The available renewable energy teaching materials are not carried out in practicum, so teachers still use references to the previous curriculum teaching materials, which are no longer significant. This type of research is educational development research or Educational Design Research (EDR). The stages of development research consist of 3 main stages: preliminary research, prototyping stage, and assessment phase. The development model used in this research is the Plomp development model developed by Tjreed Plomp. The research instruments used were interview sheets and questionnaires in the form of validity sheets which were analyzed with Aiken's V scale and practicality sheets. The validity test results were obtained by Aiken's V scale of 0.93 with high validity, which means that the developed teaching materials are valid. The practicality test results for the small group were 89% with very high practicality. Based on the teacher response questionnaire with very high practicality and obtained 93% based on the student response questionnaire with very high practicality, the teaching materials developed are practical. Based on the study's results, the teaching materials of the Independent Curriculum on renewable energy Phase E are valid and practical.
INTRODUCTION
Indonesia's education system has undergone a significant change in the implementation process due to the impact of Covid-19, which causes aspects of life to change and requires rapid adjustment [1]. COVID-19 has ended, so the government has made several adaptations in the education sector, namely with the release of the Merdeka Curriculum. Merdeka Curriculum continues the development of the previous curriculum, which is holistic, competency-based, and designed according to the context of the needs of students [2]. Merdeka Curriculum demands creativity from teachers and students. In another sense, Merdeka's "Freedom" of learning is freedom of thought determined by The Teacher because the teacher is at the center of this new education system [3].
In this case, innovative and creative students and teachers must adapt quickly. Therefore, this is a concern, especially for the government of the Republic of Indonesia, to provide adequate infrastructure in the face of this global development. One of them is equipping learning resources such as teaching materials. The presence of teaching materials is very important to prepare students for the era of Revolution 4.0 and Civilization 5.0 [4]. This evolution is shown by the use of synchronized technology to create chances that advance education. Therefore, four competencies were added to the education curriculum: critical thinking ability, creativity and innovation, communication skills, and the ability to collaborate [5]. Students with a good interest in reading have high intelligence and 4C skills to win global competition in the 21st century. In fact, students' interest in reading is still low [6]. The commonly used source books are books with relatively long pages. Most of these books use few pictures and colors, so they have an unattractive appearance; these things cause the low reading interest of students [7].
In line with that, the problem that exists in some teaching materials is that there are still many that display illustrations or colorless images that make it difficult for students, so it is necessary to innovate teaching materials that are easy for readers to understand that display illustrations that attract students to learn more about a subject matter [8], especially in teaching materials on renewable energy material. This renewable energy material is a new material that has just appeared in this Merdeka Curriculum. In the teaching materials that researchers find renewable energy material that is already available, practicum activities have not been carried out because, learning with practicum, students get direct experience and can encourage scientific attitudes in students [9], besides that an attitude of curiosity, critical, open and cooperation will appear, This theory is supported in research [10], chemistry lessons will be effective if practicum activities support the explanation of the theory.
In the teaching materials that will be made, researchers discuss how to utilize renewable energy sources and make simple biogas-producing tools from using cow dung waste. The material made is in line with the Pancasila Student profile in part of creative, critical thinking, independence, and cooperation because it is expected that students are responsible for the process and results of their learning, students can carry out joint activities willingly, students can reason critically, and finally, students can produce meaningful, helpful, and impactful. From the problems described above, one of the solutions that can be overcome is that researchers develop teaching materials to support an independent learning curriculum equipped with structured book systematics, more ordered and detailed material content, and more varied and colorful images.
RESEARCH METHODS
This type of research is educational development research (EDR). EDR is the systematic analysis, design, and evaluation of educational interventions with the dual purpose of producing research-based solutions to complex problems in educational practice and increasing knowledge about the characteristics of interventions and the process of designing and developing them [11][12].
The development model used in this study is the Plomp development model developed by Tjreed Plomp. In Plomp's development, the stages of development research consist of 3 main stages: preliminary research, prototyping stage, and assessment phase [12][13]. In this study, we developed teaching materials based on the Merdeka Curriculum on renewable energy material in the E phase. The description of activities at each stage of development can be broken down into the following stages.
Preliminary Research
In this stage, several activities are carried out: needs analysis, context analysis, literature study, and conceptual framework development. It needs analysis, and context analysis is required to develop the learning system. As well as other activities, namely conducting literature studies and developing conceptual frameworks. [12,14]. The framework will briefly explain the problems in the school and provide solutions to them. [15].
Prototyping Stage
At this stage, the previous stage's results, namely preliminary research, will be used as the basis for conducting formative evaluations in prototyping. In each prototype, formative evaluation is carried out to improve and refine the development design made to enhance and refine the development design made. This prototyping stage will be divided into four prototypes consisting of prototype I, prototype II, prototype III, and prototype IV. In the prototyping stage, there are four formative evaluation stages: self-evaluation, expert review, One-to-one evaluation, and small-group testing. Still, this research is limited to small-group testing.
Prototyping I
At this stage is designing teaching materials, such as design, compatibility with the independent curriculum, determining learning objectives, compiling material content, and making activity activities in teaching materials.
Prototyping II
After designing teaching materials in the prototype, I conducted a self-evaluation using a questionnaire on the teaching materials created, such as the completeness of essential components in teaching materials, word alignment, and other minor errors. [12,16]. 3. Prototyping III After making revisions during the selfevaluation, the next is to conduct an expert review; this review requires two chemistry lecturers and three chemistry teachers to assess teaching materials. According to [17], the expert review is carried out through the provision of an evaluation questionnaire which aims to determine the level of validity using Aiken's V scale. In addition to the expert review, in this prototype, a one-to-one evaluation was carried out by interviewing three phase E students; the purpose is to find out the students' responses to the teaching materials being developed.
Preliminar y Design
Prototyp e 1
Self Evaluati
Prototyp e II
One-to-One Evaluation
Prototype III
Small Group
Prototype IV
Development of Conceptual Framework
Need and Context Analysis 4. Prototyping IV at this stage, a small group trial is carried out by gathering nine students who have varying abilities, then dividing students into several groups and carrying out the learning process using these teaching materials; after that, students are asked to fill out a questionnaire and provide suggestions and criticism of the teaching materials that have been made.
Assessment Phase
The assessment phase is carried out by means of a field test. The field test aims to conclude whether the product can be used in practice in the field. However, this stage of the research was not carried out because the research was limited to the prototyping stage ( Figure 1).
RESULTS AND DISCUSSION
Based on the research procedures that have been carried out, chemistry teaching materials are produced by making simple energy-producing devices within the scope of Renewable Energy material to support the Merdeka Curriculum. This research uses the Plomp development model, which consists of 3 stages. The following are the results obtained during the research process.
Preliminary Research
This preliminary research stage is carried out to identify and analyze the requirements needed in teaching material development research; at this stage, a needs analysis, curriculum analysis, student analysis, and concept analysis are carried out. The following are the results obtained from each stage of the initial investigation.
Need Analysis
At the needs analysis stage, interviews were conducted with three chemistry teachers from 3 different schools that have implemented the Merdeka Curriculum; why was it carried out in 3 other schools so that the resulting interview results were more varied, and why was it carried out only in schools that have implemented the Merdeka Curriculum because this research will develop chemistry teaching materials to support the Merdeka Curriculum. Interviews were conducted to discover the general problems that occur during the chemistry learning process, especially on renewable energy material, and how the Merdeka Curriculum is implemented in the school.
The problems with curriculum changes cause teachers to continue using old teaching materials because the available teaching materials still need to be coherent in their presentation. Therefore, a readable Merdeka Curriculum teaching material is required that can be understood by the teacher to maximize the teaching and learning process, especially in teaching materials for renewable energy materials.
Context Analysis
At this stage, you are identifying, detailing, and systematically compiling the scope of learning outcomes, materials, and strategies selected to develop teaching materials.
a. Literature Review
At this stage, researchers will conduct a literature study of several scientific journals related to the problems found and try to find solutions to the difficulties encountered in the field. The results obtained based on the literature study are 1. Teaching materials as a source of resources in achieving independent learning in class and the availability of quality and affordable teaching material facilities supported by high reading interest is a prerequisite for 21st-century life skills [18]. 2. The components of teaching materials used follow the reference teaching materials provided by the Ministry of Education and Culture. 3. It is known that the Plomp model developed by Tjeerd Plomp is one of the appropriate development models for this research.
b. Development of Conceptual Framework
At this stage, connecting problems or problem identification derived from needs analysis and context analysis with literature studies as a reference in developing teaching materials. Conceptual analysis is carried out by determining the main concepts that students will learn and systematically designed according to the following sequence: Prototype I is a prototype resulting from the design and realization of the Preliminary Research stage. Prototype I supports the Merdeka Curriculum on renewable energy materials with complete, systematic, or coherent components and content. As an example of one of the results of prototype I, namely, there is a cover and several pages on teaching materials which can be seen in Figure 3.
Prototype II
The prototype results will then be formative evaluated by conducting a self-evaluation of the prototype I. At this stage of self-evaluation, researchers make corrections and review the completeness of the teaching material components to support Merdeka Curriculum learning with instruments in the form of questionnaires and then complete the incomplete components. Based on the results of the self-evaluation that has been carried out by filling out a self-evaluation questionnaire, the components of teaching materials supporting the Merdeka Curriculum on renewable energy material that have been developed are complete, so there is no need to revise prototype I.
Prototype III
Prototype III is a prototype resulting from revisions made to prototype II. After prototype III is formed, at this stage, formative evaluation is carried out in the form of expert review and one-to-one evaluation.
a. Expert Review
The expert assessment aims to get a scientifically valid prototype. The expert review involves two Chemistry lecturers from FMIPA UNP and three Chemistry teachers from Public High School 14 Padang. In this case, the experts acted as validators who assessed prototype II through an evaluation questionnaire given in the form of a content validity questionnaire. The assessment from these experts aims to determine the level of validity related to the content, presentation, discussion, and graphics. After the data is processed, the resulting content validity analysis data can be seen in the figure. The overall average is 0.93, which is included in the valid category. However, even though prototype II has shown very high validity, the validator gave some suggestions, which must be corrected. This test was conducted on 3 phase E students in Public High School 14 Padang who had studied renewable energy materials. This stage aims to determine how students respond to the teaching materials to be developed. Based on the results of interviews conducted at this stage, it was concluded that teaching materials that support the Merdeka Curriculum on renewable energy materials in terms of the appearance of teaching materials are interesting, presentation of the material is easy to understand, interest in learning and have no difficulty in understanding the teaching materials.
Prototype IV
Practicality results were obtained in small group evaluation to reveal practicality. This small group trial was conducted on 2 Public High School 14 Padang chemistry teachers who taught in Phase E and on 9 Phase E3 students at Public High School 14 Padang with different levels of student ability, namely high, medium-low, which were made into three small groups to determine the level of practicality of the product developed. This small group stage begins with learning about renewable energy materials; after learning, students are asked to carry out teaching materials, such as end-of-chapter exams, let's practice, and other activities in teaching materials. After carrying out the activities, students are asked to fill out a practicality questionnaire which will then be used to determine the level of practicality. After processing, a practicality level of 91% was obtained with a very practical category. The results of the practicality data analysis can be seen in Figure 5.
At the prototype IV stage, the practicality questionnaire is given to students, and two chemistry teachers fill out a practicality questionnaire sheet which helps know the level of practicality. After processing, the practicality value obtained was 93%, 590 with a very practical category. The results of the practicality data analysis can be seen in Figure 6. Based on the practicality of teaching materials that support the independent Merdeka Curriculum on renewable energy material, it is included in the very practical category in terms of ease of use, appearance, learning efficiency, and benefits of the teaching materials. The results of the practicality data analysis on prototype IV that has been designed have good quality and are certainly valid and practical for use in the learning process. One of the activities in the teaching materials, which can be seen in Figure 7, based on the answers that students have made, it is known that the steps of making biogas are very clear from the hydrolysis stage, then to the acetogenesis stage, then to the last methanogenic stage and then biogas (methane) is produced. The pictures in the activity are beneficial in understanding the process of making biogas. The pictures are exciting and easy to read so students can answer the questions correctly. Combining interesting depictions can help students track ideas in the natural world. Without it, students will face misguided assessments, and with the help of depictions, learning is more significant [19].
Safe renewable energy learning development is ideally based on a practicum that illustrates the implementation of renewable energy in daily life [20]. From this reference, researchers load practicum sheets in teaching materials, which makes this teaching material unique, because the practicum available in this teaching material utilizes cow dung to produce biogas. From this practicum, students can illustrate the implementation of renewable energy in daily life.
CONCLUSION
Based on the results of research and development of chemistry teaching materials to support the Merdeka Curriculum on renewable energy materials, it can be concluded that chemistry teaching materials on renewable energy materials can be developed with the Plomp development model consisting of preliminary research, prototyping phase, and research phase (assessment phase). Chemistry teaching materials on renewable energy Phase E materials produced have very high validity at 0.93, and practicality in teachers is very practical at 95% and practicality in students at 91%. | 3,964.8 | 2023-07-31T00:00:00.000 | [
"Environmental Science",
"Education",
"Engineering"
] |
1HNMR-based metabolomic profile of rats with experimental acute pancreatitis
Background Acute pancreatitis (AP) is a common inflammatory disease of the pancreas accompanied by serious metabolic disturbances. Nevertheless, the specific metabolic process of this disease is still unclear. Characterization of the metabolome may help identify biomarkers for AP. To identify potential biomarkers, this study therefore investigated the 1H-nuclear magnetic resonance (NMR)-based metabolomic profile of AP. Methods Fourteen male adult Sprague–Dawley rats were randomized into two groups: the AP group, in which AP was induced by retrograde ductal infusion of 3.5% sodium taurocholate; and the sham operation group (SO), in which rats were infused with 0.9% saline. Blood samples were obtained 12 hours later and a 600 MHz superconducting NMR spectrometer was used to detect plasma metabolites. Principal components analysis (PCA) and partial least squares-discriminant analysis after orthogonal signal correction (OSC-PLS-DA) were used to analyze both longitudinal Eddy-delay (LED) and Carr–Purcell–Meiboom–Gill (CPMG) spectra. Results Differences in plasma metabolites between the two groups were detected by PCA and PLS-DA of 1HNMR spectra. Compared with the SO group, plasma levels of lactate (δ 1.3, 1.34, 4.1), valine (δ 0.98, 1.02), succinic acid (δ 2.38), 3-hydroxybutyric acid (3-HB, δ 1.18), high density lipoprotein (HDL, δ 0.8), and unsaturated fatty acid (UFA, δ 2.78, 5.3) were elevated in the AP group, while levels of glycerol (δ 3.58, 3.66), choline (δ 3.22), trimethylamine oxide (TMAO, δ 3.26), glucose (δ 3–4), glycine (δ 3.54), very low density lipoprotein (VLDL, δ 1.34) and phosphatidylcholine (Ptd, δ 2.78) were decreased. Conclusions AP has a characteristic metabolic profile. Lactate, valine, succinic acid, 3-HB, HDL, UFA, glycerol, choline, TMAO, glucose, glycine, VLDL, and Ptd may be potential biomarkers of early stage AP.
Background
Acute pancreatitis (AP) is a common inflammatory disease of the pancreas caused by premature activation of pancreatic enzymes. Although AP is self-limiting in 80% of patients, it can be life-threatening in the 20% who develop systemic complications, such as multiple organ failure [1]. In addition to a high mortality rate, ranging from 3-15% [2], the rate of hospitalization for AP continues to rise annually [3]. In the United States, the overall hospitalization rate has doubled over the past 20 years [4], and in the Netherlands there was a 75% increase from 1992 to 2004 [5]. A recent study suggested a 3.1% annual increase in the incidence of AP [6] in England, and a meta-analysis from 18 European countries showed that the incidence of biliary pancreatitis has increased linearly and that the mortality rate increases with age [7]. Similar findings were reported in a study investigating the epidemiology of AP in the North Adriatic region of Croatia [8]. A population-based study from Taiwan reported that the proportion of severe cases has increased in recent years, although the overall incidence of AP remained constant [9]. Moreover, throughout the world, AP poses a heavy financial burden on the health care system. Due to unclear pathogenesis, the main treatments of AP are still supportive and symptomatic therapies, although early diagnosis and intervention may mitigate illness and reduce complications and length of hospitalization [10][11][12][13]. Metabolic disturbances, such as hyperglycemia and hyperlipidemia, are always present in the early stages of AP. However, the specific metabolic processes associated with this disease remain unclear.
Metabolomics is a modern approach to the study of biological samples, and can provide detailed information on the metabolic changes taking place in an organism in various pathophysiologic states. 1 H NMR spectroscopybased approaches are used for high-throughput research on biological samples [14][15][16]. Moreover, being noninvasive and providing an impartial profile of all metabolites, 1 H NMR-based metabolomics is widely applied in many areas related to biology and medicine, such as the exploitation of new drugs, disease diagnosis, toxicology, pharmaceutical effects, microorganism metabolomics, and identification of biomarkers [17][18][19][20][21]. Detection of characteristic metabolite changes in AP may increase our understanding of the pathophysiology of this disease, allow early diagnosis, and identify potential therapeutic targets. To identify potential biomarkers of AP, we analyzed the metabolic differences between rats with AP and healthy rats.
Ethics statement
This prospective, randomized controlled trial was performed at the ethnopharmacology laboratory of West China Hospital. The study protocol was approved by the Ethics Committee for Animal Experiments of Sichuan University. All rats were handled according to University Guidelines and the Animal Care Committee Guidelines of West China Hospital. All operations were performed under chloral hydrate anesthesia, and all efforts were made to minimize suffering.
Equipment
An INOVA 600 MHz NMR spectrometer equipped with a triple-resonance probe and a z-axis pulsed field gradient was obtained from Varian Unity (Varian, Inc. USA), a microcentrifuge from Eppendorf MiniSpin Plus, Germany, and a two-channel micro-injection pump from Kd Scientific Company, USA.
Animal model of acute pancreatitis
Healthy male adult Sprague-Dawley rats (224 ± 21 g, 200-250 g b/w), were maintained in air-conditioned animal quarters at 22 ± 2°C with a relative humidity of 65% ± 10%. They were acclimated for 1 week before the experiment with special feed and tap water. The animal experiments were carried out in the Laboratory of Ethnopharmacology at West China hospital, Sichuan University.
Fourteen 2-month-old (55-62 days old) rats obtained from the experimental animal center of Sichuan University were numbered and randomized into two groups of seven rats each, an AP group and a sham operation (SO) group. Animals were fasted for 12 h, and given free access to tap water prior to experiments. All animals were anesthetized by intraperitoneal injection of 3 ml/kg 10% chloral hydrate. The hepatic duct was closed with a small bulldog clamp, and the biliopancreatic duct was cannulated through the offside of the front opening of the duodenum papilla. Rats in the AP group underwent retrograde pancreaticobiliary duct injection with 1 ml/kg 3.5% sodium taurocholate using an infusion pump, whereas rats in the SO group were similarly injected with 1 ml/kg 0.9% saline [22]. Twelve hours later, heparinized blood samples were obtained from the angular vein and centrifuged for 15 minutes at 3000 rpm. Plasma samples were collected and stored at −80°C until use. After the experiment, the rats were sacrificed and cremated.
Sample preparation and NMR data acquisition
Plasma samples (150 μl) were mixed with 100 μl 1 mg/ ml TSP in deuterium oxide D 2 O and 350 μl D2O, and centrifuged at 14000 rpm for 10 min. A 550 μl aliquot of supernatant was transferred into 5 mm NMR tubes, and NMR spectra were recorded at 26°C using an INOVA 600 MHz NMR spectrometer equipped with a tripleresonance probe and a z-axis pulsed field gradient. Information about micromolecular metabolites was acquired using a CPMG pulse sequence [−RD-90°-(r-180°-r) n -ACQ] during a relaxation delay of 2 s. Sixty-four free induction decays (FID) were collected into 64 k data points with a spectral width of 8000 Hz and acquisition time of 4 s. Information about macromolecular metabolites was collected by LED pulse sequence (−RD-90°-G1-180°-G1-90°-T-90°-G1-180°-G1-90°-ACQ) during a relaxation delay of 2 s. Sixty-four FID were collected into 64 k data points with a spectral width of 8000 Hz, an acquisition time of 4 s and a diffusion time of 100 min. FID was zero-filled and multiplied by an exponential line-broadening function of 1 Hz (for CPMG) and 3 Hz (for LED) prior to Fourier transformation.
NMR data processing and analysis
After Fourier transformation, the data were phased and subjected to baseline correction. For CPMG data, spectra in the region of δ 0.4-4.4 were subdivided into integrated regions of 0.04 PPM width. LED data were subdivided into integrated regions of 0.04 PPM width corresponding to the region of δ 0-6.0, and the spectra in the δ 4.6-5.0 range were excluded from data reduction. Each data point was normalized to the sum of its row to compensate for any variation in total sample volumes. The obtained data were exported to Excel and subjected to multivariate analyses as variables for the multivariate pattern recognition analysis using Soft Independent Modeling of Class Analogy (SIMCA-P) software package (v10.04, Umetrics, Umeå, Sweden). Principal components analysis (PCA) was performed after data were pretreated by mean centering and Pareto scaling. For samples with obvious internal individual differences, partial least squares (PLS) and discriminant analysis (DA) were conducted after data processing based on orthogonal signal correction (OSC). These two approaches were performed to differentiate between sample groups. Score plots were used to visualize the separation of the groups, while the loading plots were used to determine which spectral variables significantly contributed to the separation of the samples on the score plots.
1H-NMR spectra (CPMG) and pattern recognition analysis of plasma samples
A comparison of the 1H-NMR spectra of plasma samples taken from rats in the AP and SO groups showed obvious differences in the levels of small molecule metabolites ( Figure 1). To identify these differences in metabolic profiles, the 1H-NMR spectra were segmented and subjected to PCA. The scores plot showed a cluster distribution of the two groups without distinct separation, with the point AP10 located outside the confidence interval (Figure 2a). The clusters became more obviously distributed after excluding the AP10 point (Figure 2b). With the loading plot (Figure 2d), a sequence of metabolic alterations was detected in plasma samples from rats with AP: (1) increased levels of lactate, valine, succinic acid, and 3hydroxybutyric acid (3-HB); and (2) decreased levels of glycerol, choline, trimethylamine oxide (TMAO), glucose, and glycine (Table 1). These altered metabolites may be potential biomarkers of AP.
1H-NMR spectra (LED) and pattern recognition analysis of plasma samples Similar to the analysis of small molecule metabolites, the levels of macromolecule lipid metabolites differed markedly between the AP and SO groups, as shown by the 1H-NMR (LED) spectra of their plasma samples (Figure 3). To illustrate the differences in metabolic profiles required OSC-PLS (ctr) analysis (Figure 4a,b) was conducted because PCA analysis was not able to detect differences between these two groups (Figure 4c,d). The score plot showed distinct separation between the two groups ( Figure 4a Table 2). Therefore, HDL, UFA, VLDL, and Ptd may be potential biomarkers of AP.
Discussion
By analyzing the plasma metabolites of rats with experimental AP using the 1H-NMR-based metabolomic approach, we obtained a series of finger-prints containing information on plasma metabolites. Except for one point, the separation between the two groups was distinct, as shown in the score plot of PCA models of the CPMG data for small molecules. Similarly, we observed a separation of metabolites between the two groups in the score plot of PLS-DA models for macromolecules, although the two groups were mixed by PCA.
The plasma 1H-NMR spectra of CPMG data for small molecules showed a difference between the two groups. The score plot with PCA of 1H-NMR (CPMG) spectra of plasma samples showed that most of the metabolites in the AP group could be separated from those in the SO group, indicating a significant difference in metabolomics between AP and control rats. The score plot with PCA of 1H-NMR (LED) spectra from the two groups showed a cross distribution. The cluster distribution of the PLS-DA could distinguish between the two groups, thus illustrating their metabolomic differences.
This study also showed differences in plasma metabolite levels between the two groups. Rats with AP had higher levels of lactate, valine, succinic acid, 3hydroxybutyrate (3-HB), HDL, and UFA, and lower levels of glycerol, choline, TMAO, glucose, glycine, VLDL, and phosphatidylcholine, than the control group. Because of acute systemic inflammation response syndrome, AP always triggers a hypercatabolic state, resulting in increased energy requirements and protein catabolism [23]. Our results indicate that multiple metabolic pathways were mobilized, resulting in changes in metabolite concentrations. Lactate is mainly generated by anaerobic glycolysis and is not associated with the primary energy supply pathway under normal conditions. During an intense workout or under conditions of hypoxia, an insufficient oxygen supply can reduce Krebs cycle reactions, produce less ATP, and enhance glycolysis, resulting in decreased removal ability of the liver and kidneys and ultimately to the accumulation of lactate in plasma [24,25]. The increased levels of lactate and succinic acid in the AP group were likely because of anaerobic glycolysis, which was enhanced by the increased energy consumption and oxygen deficit during early stages of AP [26]. Since lactate concentration is influenced by oxygen supply and fluid resuscitation, this elevation was not detected in urine samples from patients with pancreatitis [27]. As an aerobic process, gluconeogenesis was inhibited by an inadequate oxygen supply, which may be partly responsible for the decrease in glucose level. Further, insulin released from injured acinar cells also contributed to decreased glucose levels. TMAO, the product of dietary choline and L-carnitine [28] , although mainly regarded as a biomarker of renal function [29], may participate in energy production as an external electron acceptor in an hypoxic environment [30]. Moreover, decreased TMAO has been reported to accompany a chemiosmotic mechanism of energy conversion [31]. The decreased TMAO we observed may indicate renal damage caused by AP as well as energy conversion under conditions of relative oxygen deficit. Similar changes in TMAO have been observed in serum samples of patients with pancreatitis [32]. In contrast, 3-HB, a ketone body synthesized in the liver and used as an energy source by the brain under conditions of hypoglycemia or enhanced demand for gluconeogenesis [33], was not increased in serum samples of patients with pancreatitis [32]. Inflammatory responses in AP progressively damage pancreatic acinar cells and impair mitochondrial respiratory capacity, limiting ATP production [34]. In addition, increased energy consumption mobilizes FA to the periphery as an energy supply, reducing FA and increasing 3-HB. This results in increased HDL level at the periphery, where it is required to carry cholesterol and triacylglycerol. Serum VLDL transports triacylglycerol into tissue for energy metabolism, and phosphatidylcholine moves into tissue to preserve cell function, leading to elevated serum HDL levels and decreased LDL, VLDL, and phosphatidylcholine levels. UFA, which is important in maintaining the relative liquidity of cell membranes and normal cell function, is released into circulation under stress, damaging the stability of cell membranes [35]. Moreover, glutaminate production is increased to protect against tissue injury, and alanine accumulates to inhibit the proteolysis of skeletal muscle proteins, resulting in increased serum levels of glutaminate and alanine.
One of the limitations of this study was that we only investigated changes in plasma concentrations of metabolic factors. Further studies investigating urine and pancreatic tissue samples are needed to confirm our findings. Moreover, insufficient plasma was available for assay of all factors, and this study was based on the 1HNMR approach, which in itself is limited by the incomplete data obtained. The combined use of LC-MS or GC-MS is needed to validate our results.
Conclusion
We found that the characteristic metabolomic profile differed in AP and SO rats. Lactate, valine, succinic acid, 3-HB, HDL, UFA, glycerol, choline, TMAO, glucose, glycine, VLDL, and Ptd may be regarded as potential biomarkers of early stage AP. These findings may provide deeper insight into the pathophysiology and metabolic state of AP and may facilitate early intervention in patients with this disease. The 1HNMR-based metabolomic approach was capable of distinguishing between plasma samples of AP rats and SO controls, providing a new and non-invasive methodology for the study of AP.
Competing interests
The authors declare that they have no competing interests. | 3,539.2 | 2014-06-30T00:00:00.000 | [
"Biology"
] |
A Highly Sensitive Two-Dimensional Inclinometer Based on Two Etched Chirped-Fiber-Grating Arrays †
We present a novel two-dimensional fiber-optic inclinometer with high sensitivity by crisscrossing two etched chirped fiber Bragg gratings (CFBG) arrays. Each array is composed of two symmetrically-arranged CFBGs. By etching away most of the claddings of the CFBGs to expose the evanescent wave, the reflection spectra are highly sensitive to the surrounding index change. When we immerse only part of the CFBG in liquid, the effective index difference induces a superposition peak in the refection spectrum. By interrogating the peak wavelengths of the CFBGs, we can deduce the tilt angle and direction simultaneously. The inclinometer has a resolution of 0.003° in tilt angle measurement and 0.00187 rad in tilt direction measurement. Due to the unique sensing mechanism, the sensor is temperature insensitive. This sensor can be useful in long term continuous monitoring of inclination or in real-time feedback control of tilt angles, especially in harsh environments with violent temperature variation.
Introduction
Due to the increased requirements on the accuracy of contemporary civil engineering and mechanical control, high-precision two-dimensional inclinometers are a necessity in modern industry. Precise measurement of the tilt angle and direction is very important in many fields, such as in level determination for buildings or instrumentation, mechanical alignment, aircraft control, satellite antenna positioning, motion control of robots, etc. There are many conventional methods for tilt angle and direction measurements using electrical, ultrasonic, mechanical, and optical techniques. Among these methods, optical fiber grating based sensors have been found ideal in many applications due to their intrinsic advantages of small size, high sensitivity, long-term stability multiplexing capability, and immunity to electromagnetic interference (EMI), which make them suitable in field-deployed monitoring [1,2]. In recent years, several fiber Bragg grating (FBG)-based inclinometer or tilt sensors with different configurations for one or two-dimension (1-D or 2-D) measurements have been reported [3][4][5][6][7][8][9][10][11][12][13][14][15]. For example, Dong et al. have proposed a design based on three FBGs. Each FBG is fixed on the top surface of a steel flake to form an inverted pendulum. The accuracy of the measured tilt angle is ±0.13 • with a resolution of 0.02 • [3]. Ni et al. reported a tilt sensor with an improved sensitivity of 0.009 • based on connecting four FBGs to a mass to form an inverted tetrahedron. As the sensor tilt, the tensions on the four FBGs change and sensitive measurement can be achieved [4]. In [5,6], Bao et al. used a similar operating principle as in [4], but with different FBG numbers and structures. A tilt angle detection range of ±40 • and a sensitivity of 0.096 nm/degree were demonstrated. Although the tile angle detection range was improved, the sensitivity was compromised. All of these designs relied on the swing of the mass when tilt the sensors. As the mass is hung directly from the fiber, any unknown resonance leads to a random vibration of the pendulum system. In addition, this kind of design inevitably renders a large sensor size.
Optical fiber based sensors are not only immune from EMI, but also not susceptible to humidity or corrosive damage as in electronic sensors. The typical resolution of conventional electronic inclinometer is on the order of 0.01 • . It was desirable to have higher sensitivity in a wide detection range. In our recently studies, we proposed a novel detection mechanism based on etched chirped fiber Bragg grating (CFBG). It is known that it is possible to greatly improve the sensing sensitivity of a FBG by removing most of the cladding layer to expose the evanescent wave to the surrounding medium [16]. There have been demonstrated inclinometers based on etched fiber grating [17], but the resolution is not improved compared to conventional methods. We recently demonstrated a novel etched-CFBG based sensing mechanism with superior sensitivity. By putting part of the etched chirped grating in liquid, the effective refractive index of this part is varied, which results in a shift in its reflection spectrum, while the reflection spectrum from the other part in air remains unchanged. With proper arrangement, the reflected spectra from the two parts would overlap to form a superposition peak in the measured spectrum. When the air-liquid boundary moves along the grating, the superposition peak shifts accordingly. This is a truly novel way of fiber Bragg grating based sensing and is first demonstrated by our group. We have demonstrated using this method as a liquid level indicator with a sub-10 µm resolution [18]. Based on the high accuracy in liquid-level measurement, we further extend its application to a two-dimensional (2D) inclinometer by installing two etched CFBG in the inner wall of a cylindrical container separated from each other by 90 • in the azimuth direction [19]. By examining the peak wavelengths and relative peak positions, we can deduce the tilt angle and direction of tilting. The detection range of the tilt angle is 0-35 • and the directional angle is 0-360 • , respectively. The sensitivity for the tilt angle is 0.303 nm/degree, which corresponds to a resolution of 0.033 • when acquired by an optical spectrum analyzer with a resolution of 0.01 nm.
Here we propose a disk-shaped 2-D inclinometer with a totally different configuration, which not only greatly reduces the sensor footprint but also greatly improves the dynamic range and sensitivity. Particularly, the sensor design is readily compatible with typical inclinometer or level meter, so it can be applied intuitively. The present inclinometer has a resolution of 0.003 • for tilt angle measurement, which is about one order improvement compared to the previous design. The sensor configuration is detailed in the next section. Briefly, the container is partially filled with liquid and air as is in a typical level meter. The sensor contains four etched CFBGs fixed on the curved top cover of the plate-shaped container. When the air bubble moves freely in the container, the superposition peaks of the four CFBGs move accordingly. By examining the peak wavelengths and relative positions, we can deduce the tilt angle and direction simultaneously in real-time. In addition, this sensor is highly flexible in its detection range and sensitivity, which can be modified by adjusting the geometry of the container and the arrangement of the CFBGs.
For many applications, it is desirable to have temperature-insensitive sensors. There are many FBG based temperature-insensitive tilt sensors or inclinometers [7][8][9][10][11]14]. However, these sensors are either large in size or lack high sensitivity. We have demonstrated that because the sensing mechanism is based on measuring the peak shift of the overlapped spectra, the thermal or strain effect on the FBG is compensated. The superposition peak shift has a very low temperature dependence of 0.008 nm/ • C [18,19]. For the present sensor, because the tilt angle is determined by subtracting the wavelengths of the two peaks on the same array, the temperature effect is further eliminated. Therefore, this sensor provides temperature-insensitive measurement on inclination, which is highly desirable in many applications, especially for long-term monitoring of environments with violent temperature surges.
In addition, this inclinometer has a real-time sensing capability, which is critical for security monitoring systems, such as construction structure surveillance or geological environment monitoring for emergency alerts. A small-sized design not only makes the sensor suitable for embedded multiplexing monitoring but also robust for field-deployable measurements in harsh environments. The sensor design is completely compatible with conventional sensors and is readily applicable to ongoing applications.
Principle and Sensor Configuration
A CFBG is a type of fiber Bragg grating, which was made by axially varying either the grating period (Λ) or the core effective refractive index (n eff ). In this study, the CFBGs were fabricated by exposing a 248 nm laser beam from a KrF excimer laser through a chirped phase mask on standard single mode fibers. The chirped phase mask used in this paper has a linear increment in the grating period with a chirped rate of 9.08 nm/cm. The Bragg reflection wavelength at the axial location z along the fiber core of the CFBG can be expressed as [20,21]: where Λ 0 is the initial grating period, which corresponds to the smallest reflection wavelength of the CFBG, n eff denotes the effective index, and C = dλ/dz is the chirp rate. A CFBG can be regarded as a grating structure made up of a series of short Bragg gratings with increasing period. The CFBG used for this study was fabricated on a standard SMF-28 (Fujikura Corp., Tokyo, Japan) with a core diameter of 9.2 µm. The cladding layer of CFBG was etched off from the original 125 µm to 12 µm in diameter by a 20% HF solution. Figure 1 shows the sensor configuration in which the shorter grating period part was immersed in the liquid for level measurements. For increasing the mechanical strength of the sensing head, the CFBG was glued on a Teflon holder. After etching, the CFBG was not moved out of the holder and the whole apparatus was immersed in water for the following measurements [18]. In addition, this inclinometer has a real-time sensing capability, which is critical for security monitoring systems, such as construction structure surveillance or geological environment monitoring for emergency alerts. A small-sized design not only makes the sensor suitable for embedded multiplexing monitoring but also robust for field-deployable measurements in harsh environments. The sensor design is completely compatible with conventional sensors and is readily applicable to ongoing applications.
Principle and Sensor Configuration
A CFBG is a type of fiber Bragg grating, which was made by axially varying either the grating period (Λ) or the core effective refractive index (neff). In this study, the CFBGs were fabricated by exposing a 248 nm laser beam from a KrF excimer laser through a chirped phase mask on standard single mode fibers. The chirped phase mask used in this paper has a linear increment in the grating period with a chirped rate of 9.08 nm/cm. The Bragg reflection wavelength at the axial location z along the fiber core of the CFBG can be expressed as [20,21]: where Λ0 is the initial grating period, which corresponds to the smallest reflection wavelength of the CFBG, neff denotes the effective index, and C = dλ/dz is the chirp rate. A CFBG can be regarded as a grating structure made up of a series of short Bragg gratings with increasing period. The CFBG used for this study was fabricated on a standard SMF-28 (Fujikura Corp., Tokyo, Japan) with a core diameter of 9.2 μm. The cladding layer of CFBG was etched off from the original 125 μm to 12 μm in diameter by a 20% HF solution. Figure 1 shows the sensor configuration in which the shorter grating period part was immersed in the liquid for level measurements. For increasing the mechanical strength of the sensing head, the CFBG was glued on a Teflon holder. After etching, the CFBG was not moved out of the holder and the whole apparatus was immersed in water for the following measurements [18]. In this study, we etched the chirped fiber gratings to expose the evanescent field to the surrounding medium to improve the sensing sensitivity. In the etching process, an optical spectrum analyzer (OSA) was used to monitor the fiber diameter. When the grating reflection wavelength was shifted to the shorter side, it indicated that the cladding layer had been etched thin enough and the diameter of the fiber was about 12 μm. Meanwhile, the effective index was strongly affected by the In this study, we etched the chirped fiber gratings to expose the evanescent field to the surrounding medium to improve the sensing sensitivity. In the etching process, an optical spectrum analyzer (OSA) was used to monitor the fiber diameter. When the grating reflection wavelength was shifted to the shorter side, it indicated that the cladding layer had been etched thin enough and the diameter of the fiber was about 12 µm. Meanwhile, the effective index was strongly affected by the surrounding medium. The effective index change induced shift of the grating wavelength λ CFBG can be expressed as: where ∆n is the effective index variation due to the surrounding medium. When the shorter period part of the etched CFBG is immersed in the liquid, the increased effective index causes the reflection spectrum of this part to redshift. Therefore, a portion of the spectrum of the immersed grating overlaps with the spectrum of the longer period CFBG. The overlapped spectra result in a superposition-spectrum peak, as illustrated in Figure 1c. This superposition-spectrum peak wavelength λ p is a function of liquid level z and can be expressed as [18]: where n eff is the grating effective index, Λ 0 is the grating initial period, C is the chirp rate, z is the position of liquid level, and ∆nΛ 0 is the variation of reflection wavelength.
In order to use this method to detect the liquid level variation, one can simply take a derivative of Equation (3) as: where ∆λ p is the wavelength shift of the overlapped peak and ∆z is the variation of liquid level. In this study, two etched CFBGs arrays are cross-wisely installed in a plate-shaped container as the sensing elements of the inclinometer as shown in Figure 2a. Each fiber has two inscribed CFBGs. The length of each chirped fiber grating is 7 mm. The separation between two chirped fiber gratings is 6 mm with the longer period part facing the center of the sensor. Diethyl-ether (ethoxyethane, or simply ether) and an air bubble are filled in the container. The inner diameter of the plate is 20 mm and the diameter of the bubble is 10 mm. Therefore, the air-liquid boundaries of the bubble are located at the middle of the CFBGs as shown in Figure 2. The structure is similar to a typical level meter. To avoid saturation of the superposition of the peaks, the reflectivity of the CFBGs is designed as 40%. The tilt angle and direction can thus be monitored through the peak wavelength shifts of the four CFBGs. Figure 2b,c illustrate the relative change of the superposition peaks at different situations. When the sensor is not tilted, the four peaks are located at their center positions as shown in Figure 2b. When the sensor is tilted to 0 • , due to the movement of the air bubble, as illustrated in Figure 2a, for CFBGa, the liquid-air boundary shifts to the longer period grating side, which results in a red shift for the peak of CFBGa. Similarly, for CFBGb, the liquid-air boundary shifts to the shorter part and results in blue shift of the peak. For CFBGc and CFBGd, due to the movement of the air bubble, the liquid-air boundaries both move to the longer period part and cause the peaks to redshift, but not as much as CFBGa.
2b. When the sensor is tilted to 0°, due to the movement of the air bubble, as illustrated in Figure 2a, for CFBGa, the liquid-air boundary shifts to the longer period grating side, which results in a red shift for the peak of CFBGa. Similarly, for CFBGb, the liquid-air boundary shifts to the shorter part and results in blue shift of the peak. For CFBGc and CFBGd, due to the movement of the air bubble, the liquid-air boundaries both move to the longer period part and cause the peaks to redshift, but not as much as CFBGa.
Experimental Results and Discussions
The setup that we used to evaluate the proposed two-dimensional fiber-optic inclinometer is illustrated in Figure 3. The tilt angle is controlled by slanting the electrical platform. The tilting direction (directional angle) was controlled by rotating the azimuthal angle of the sensor head. The range of tilt angle was controlled between 0 • and 2.5 • , and the range of directional angle was from 0 to 360 • . Two etched CFBG arrays were connected to the optical spectrum analyzer (OSA, Q8384, Advantest Corp., Tokyo, Japan) and a wide-band amplified-spontaneous-emission (ASE, FL7002, Thorlabs Corp., Newton, NJ, USA) light source through a 3-dB coupler for real-time spectrum analysis. The acquired spectra by the OSA were sent to a computer for further analysis.
Experimental Results and Discussions
The setup that we used to evaluate the proposed two-dimensional fiber-optic inclinometer is illustrated in Figure 3. The tilt angle is controlled by slanting the electrical platform. The tilting direction (directional angle) was controlled by rotating the azimuthal angle of the sensor head. The range of tilt angle was controlled between 0° and 2.5°, and the range of directional angle was from 0 to 360°. Two etched CFBG arrays were connected to the optical spectrum analyzer (OSA, Q8384, Advantest Corp., Tokyo, Japan) and a wide-band amplified-spontaneous-emission (ASE, FL7002, Thorlabs Corp., Newton, NJ, USA) light source through a 3-dB coupler for real-time spectrum analysis. The acquired spectra by the OSA were sent to a computer for further analysis. When the tilt angle or directional angle was changed, the lengths of the CFBGs immersed in the ether were also changed. Thus, the tilt angle and the tilt direction could be obtained by measuring the peak wavelength shifts of the four CFBGs. Figure 4 shows reflection spectra of the CFBGa and CFBGb array at 0, 1, and 2° tilt angles at the directional angle of 0°. The spectra are shifted in the yaxis to clearly show the variation in the relative positions of the superposition peaks. The bandwidth of CFBGa is from 1529.54 to 1537.10 nm, and the bandwidth of CFBGb is from 1539.12 to 1547.53 nm. As seen in the figure, when the tilt angle increases, the superposition peak wavelength of CFBGa shifts toward a longer wavelength, while the peak of CFBGb shifts toward a shorter wavelength. The peak wavelength is determined as the local maximum data point in the spectrum. Therefore, the tilt angle can be obtained by measuring the relative wavelength shifts of the two peaks. Since the two peaks both shift when tilted, the larger dynamic range greatly improves the sensor resolution when compared to using a single peak for measurement as in our previous version [19]. The sensitivity for tilt angle measurement at the directional angle of 0° is 3.3 nm/°, which corresponds to a resolution of 0.003° when measured with an OSA with a resolution of 0.01 nm, which is about one order of magnitude improvement compared to the previous version. Due to the unique sensing mechanism, the superposition peak shift already has a very low temperature dependence of 0.008 nm/°C due to the compensated thermal and strain effects on the FBG as can be seen from Equation (3) [19,20]. Here, When the tilt angle or directional angle was changed, the lengths of the CFBGs immersed in the ether were also changed. Thus, the tilt angle and the tilt direction could be obtained by measuring the peak wavelength shifts of the four CFBGs. Figure 4 shows reflection spectra of the CFBGa and CFBGb array at 0, 1, and 2 • tilt angles at the directional angle of 0 • . The spectra are shifted in the y-axis to clearly show the variation in the relative positions of the superposition peaks. The bandwidth of CFBGa is from 1529.54 to 1537.10 nm, and the bandwidth of CFBGb is from 1539.12 to 1547.53 nm. As seen in the figure, when the tilt angle increases, the superposition peak wavelength of CFBGa shifts toward a longer wavelength, while the peak of CFBGb shifts toward a shorter wavelength. The peak wavelength is determined as the local maximum data point in the spectrum. Therefore, the tilt angle can be obtained by measuring the relative wavelength shifts of the two peaks. Since the two peaks both shift when tilted, the larger dynamic range greatly improves the sensor resolution when compared to using a single peak for measurement as in our previous version [19]. The sensitivity for tilt angle measurement at the directional angle of 0 • is 3.3 nm/ • , which corresponds to a resolution of 0.003 • when measured with an OSA with a resolution of 0.01 nm, which is about one order of magnitude improvement compared to the previous version. Due to the unique sensing mechanism, the superposition peak shift already has a very low temperature dependence of 0.008 nm/ • C due to the compensated thermal and strain effects on the FBG as can be seen from Equation (3) [19,20]. Here, because the tilt angle is obtained by subtracting the wavelengths of the two peaks, the temperature has the same effect on both CFBGs, after subtracting, the temperature effect is eliminated. Therefore, the sensing mechanism for the proposed inclinometer is temperature insensitive, which is highly desirable in many applications, especially in environments where the temperature changes violently. Figure 5 shows the relation between the peak wavelengths of CFBGa and the tilt angles when the sensor is tilted at different directional angles, respectively. By examining Figures 4 and 5, it is obvious that the tilt angle and direction can be simultaneously obtained by the permutations of the red-shifted and blue-shifted peaks of the two CFBGs arrays. In Figure 5, it is clear that when the tilt direction is at 0°, we have a positive maximum wavelength shift, while the negative maximum wavelength shift occurs at a tilt direction of 180°. This is expected as in the two directions the displacements of the air bubble are the largest, because the CFBGa-CFBGb array is installed on the 0°-180° axis of the disk-shaped sensor, as shown in Figure 2. Therefore, the relationship curves of CFBGb are similar to those of CFBGa, except the order of the directional angles are reversed. Similarly, the relationship curves of CFBGc are almost identical to those of Figure 5 except for a directional angle difference of 90° because the CFBGc is installed orthogonally to CFBGa. Thus, the maximum wavelength shifts are located at 90° and 270° directional angles, respectively, for CFBGc, and CFBGd has a relation symmetric to CFBGc. The knowledge about the relations between the peak wavelengths and tilt angles and directions allows us to compute the tilt angle and direction simultaneously in realtime. The sensor, therefore, enables real-time feedback control of the tilt angle and direction, which can be useful in precision robotic control. Figure 5 shows the relation between the peak wavelengths of CFBGa and the tilt angles when the sensor is tilted at different directional angles, respectively. By examining Figures 4 and 5, it is obvious that the tilt angle and direction can be simultaneously obtained by the permutations of the red-shifted and blue-shifted peaks of the two CFBGs arrays. In Figure 5, it is clear that when the tilt direction is at 0 • , we have a positive maximum wavelength shift, while the negative maximum wavelength shift occurs at a tilt direction of 180 • . This is expected as in the two directions the displacements of the air bubble are the largest, because the CFBGa-CFBGb array is installed on the 0 • -180 • axis of the disk-shaped sensor, as shown in Figure 2. Therefore, the relationship curves of CFBGb are similar to those of CFBGa, except the order of the directional angles are reversed. Similarly, the relationship curves of CFBGc are almost identical to those of Figure 5 except for a directional angle difference of 90 • because the CFBGc is installed orthogonally to CFBGa. Thus, the maximum wavelength shifts are located at 90 • and 270 • directional angles, respectively, for CFBGc, and CFBGd has a relation symmetric to CFBGc. The knowledge about the relations between the peak wavelengths and tilt angles and directions allows us to compute the tilt angle and direction simultaneously in real-time. The sensor, therefore, enables real-time feedback control of the tilt angle and direction, which can be useful in precision robotic control.
angle difference of 90° because the CFBGc is installed orthogonally to CFBGa. Thus, the maximum wavelength shifts are located at 90° and 270° directional angles, respectively, for CFBGc, and CFBGd has a relation symmetric to CFBGc. The knowledge about the relations between the peak wavelengths and tilt angles and directions allows us to compute the tilt angle and direction simultaneously in realtime. The sensor, therefore, enables real-time feedback control of the tilt angle and direction, which can be useful in precision robotic control. In order to understand how the superposition peaks of the four CFBGs shift as the sensor tilts, we plot the relations between the peak wavelengths and the tilt angles, as shown in Figure 6. The tilt direction is 0 • for this plot. The points for CFBGa and CFBGb are labeled in black and the points for CFBGc and CFBGd are red. The two CFBG arrays are inscribed at distinct wavelength ranges for easier reading. In order to put the data points from the two CFBG arrays on the same plot to illustrate the shifts of the peaks as the sensor tilt, we overlapped the distinct wavelength ranges in Figure 6. The black labels are referred to the ordinate on the left, while the red ones are referred to the right ordinate. As seen in the figure, as the tilt angle increases, only the peak wavelength of CFBGa increases accordingly, while the other three CFBGs decrease with different tendencies. CFBGa and CFBGb have the same amount of wavelength shifts, but with different signs. CFBGc and CFBGd do not have a linear relationship between the peak wavelength change and the tilt angle. This is because the peak wavelength variation is due to the air-liquid boundary movement along the grating. The change of the peak wavelength for CFBGc and CFBGd is due to the shape of the circular circumference of the air bubble as shown in Figure 2. The two CFBG arrays are crisscrossed, placed in the container with each CFBG separated by 90 • . The reason for similar wavelength shifts, but toward opposite sides for CFBGa and CFBGb, is because they are connected in series and the chirping is symmetric with a longer period connected to each other. When the sensor is tilted to 0 • , the air bubble moves toward the direction of 180 • and the amount of the liquid level change on CFBGa and CFBGb are the same. As the air bubble moves, the CFBGa immerses more into the liquid, which causes the superposition peak to shift toward the longer side. In contrast, as the bubble moved toward CFBGb, less grating is immersed in the liquid, resulting in the opposite peak shift. On the other hand, the relation between the superposition peak wavelength shift and the tilt angle is a parabolic line for CFBGc and CFBGd. This is due to the circular circumference of the air bubble as it moves along the gratings. The distinct tendencies among the gratings make it straightforward for us to determine the tilt direction.
CFBGb are the same. As the air bubble moves, the CFBGa immerses more into the liquid, which causes the superposition peak to shift toward the longer side. In contrast, as the bubble moved toward CFBGb, less grating is immersed in the liquid, resulting in the opposite peak shift. On the other hand, the relation between the superposition peak wavelength shift and the tilt angle is a parabolic line for CFBGc and CFBGd. This is due to the circular circumference of the air bubble as it moves along the gratings. The distinct tendencies among the gratings make it straightforward for us to determine the tilt direction. Figure 6. The relation between the peak wavelengths of four CFBGs and the tilt angle at the direction angle of 0°. The black points belong to the ordinate on the left and the red points belong to the ordinate on the right. The arrows help to identify the ordinate the data points belong to.
From the above discussion, it is obvious that the relation between the peak wavelengths of the four CFBGs and the tilt and directional angles is a 1-to-1 correspondence. With the measured peak wavelengths, we can deduce the tilt angle and directional angle immediately. Since what we would like to obtain are the two angles (parameters), we only need two parameters to compute the 1-to-1 mapping operation. We can use wavelength differences, From the above discussion, it is obvious that the relation between the peak wavelengths of the four CFBGs and the tilt and directional angles is a 1-to-1 correspondence. With the measured peak wavelengths, we can deduce the tilt angle and directional angle immediately. Since what we would like to obtain are the two angles (parameters), we only need two parameters to compute the 1-to-1 mapping operation. We can use wavelength differences, |λ a − λ b | and |λ c − λ d | as the two parameters. If we properly design the wavelength ranges of the four FBGs to make |λ a − λ b | and |λ c − λ d | distinct from each other at a certain directional angle, say 0 degrees, due to the different tendencies of the peak shifts, we have non-overlapped data points when using |λ a − λ b | and |λ c − λ d | to represent the tilt and directional angles. Using the 1-to-1 mapping operation, we can obtain the tilt and directional angles simultaneously in real-time. For example, in the present case, |λ a − λ b | = 14.2 nm and |λ c − λ d | = 8.1 nm at a 0 • tilt angle (initial point, see Figure 6). When tilted to a 0 • directional angle at a 2.5 • tilt angle, |λ a − λ b | = 5.5 nm and |λ c − λ d | = 8.1 nm, while when tilted to a 180 • directional angle, |λ a − λ b | = 22.3 nm and |λ c − λ d | = 8.1 nm. From the above data, we can also deduce the resolution of directional angle measurement. At a tilt angle of 2.5 • , |λ a − λ b | changed from 5.5 nm to 22.3 nm when the directional angle changed from 0 • to 180 • , and we have a directional angle measurement resolution of 0.00187 rad when using an OSA with a resolution of 0.01 nm. However, the accuracy of the directional angle measurement is inevitably dependent on the tilt angle because the larger the tilt angle, the greater the peak wavelength shifts.
Conclusions
In this paper, a temperature-independent highly-sensitive two-dimensional inclinometer based on two crisscross-etched chirped fiber Bragg grating arrays is experimentally demonstrated with a best tilt angle sensing resolution of 0.003 • . Due to the unique sensing mechanism, the sensor is temperature insensitive. This sensor is ideal for real-time monitoring of very small tilting in harsh environments. For proof-of-concept, the current data were presented using ether as the liquid medium. Other materials can be used to improve the sensitivity and the robustness. Depending on the applications, it is possible to further improve the dynamic range and sensitivity by optimizing the design parameters of the sensor. For example, increasing the distance between the gratings to increase the dynamic range, or redesign the curvature or shape of the container to increase the interaction length of the grating to increase the sensitivity. This sensor is compact in size and readily compatible with typical inclinometers. We envision this sensor to be useful as a cost-effective field-deployable inclinometer for demanding applications where precision is critical. | 7,324.8 | 2017-12-01T00:00:00.000 | [
"Engineering",
"Physics"
] |
On functional representations of the conformal algebra
Starting with conformally covariant correlation functions, a sequence of functional representations of the conformal algebra is constructed. A key step is the introduction of representations which involve an auxiliary functional. It is observed that these functionals are not arbitrary but rather must satisfy a pair of consistency equations corresponding to dilatation and special conformal invariance. In a particular representation, the former corresponds to the canonical form of the exact renormalization group equation specialized to a fixed point whereas the latter is new. This provides a concrete understanding of how conformal invariance is realized as a property of the Wilsonian effective action and the relationship to action-free formulations of conformal field theory. Subsequently, it is argued that the conformal Ward Identities serve to define a particular representation of the energy-momentum tensor. Consistency of this construction implies Polchinski’s conditions for improving the energy-momentum tensor of a conformal field theory such that it is traceless. In the Wilsonian approach, the exactly marginal, redundant field which generates lines of physically equivalent fixed points is identified as the trace of the energy-momentum tensor.
Conformal field theories
The essential information content of any quantum field theory (QFT) is encoded in its correlation functions. As such, the various different approaches to the former ultimately amount to different strategies for computing the latter. In an ideal situation, it could be imagined that the correlation functions are determined entirely by some symmetry, allowing one to concentrate solely on the representation theory of the appropriate algebra, having dispensed with standard notions such as an action and corresponding path integral.
In general, such a strategy is not available. However, a partial realization occurs for QFTs exhibiting conformal symmetry -the conformal field theories (CFTs). If we suppose that the correlation functions involve a set of local objects, {O(x)}, then a special set of 'conformal primary fields', O i (x), can be identified for which the correlation functions exhibit covariance under global conformal transformations. Focussing on the conformal primaries, the various two-and three-point correlation functions are determined by the con-formal symmetry in terms of the a priori unknown CFT data: the scaling dimensions, i , spins and three-point coefficients, C i jk . At the four-point level and beyond, the direct constraints of conformal symmetry are weaker, still.
Further progress can be achieved by applying the operator product expansion (OPE). Within correlation functions, consider taking a limit such that the positions of two of the fields approach each other. According to the OPE, in this limit the pair of fields can be replaced by a linear sum over fields; schematically, this can be written (1.1) A particularly powerful effect of conformal symmetry is that the complete content of the OPE can be rephrased in terms of just the conformal primary fields. If the OPE converges for finite separations, then n-point correlation functions can be determined in terms of n − 1 point correlation functions. In this manner, the content of conformal field theories can, in principle, be boiled down to the CFT data introduced above. However, to determine the various combinations of CFT data which correspond to actual CFTs (possibly subject to constraints, such as unitarity) requires further input. One approach is to exploit associativity of the OPE to attempt to constrain the CFT data (this technique is known as the conformal bootstrap). In general, the task is extremely challenging since one can expect an infinite number of conformal primaries, the scaling dimensions of which must be selfconsistently determined. Nevertheless, substantially inspired by work of Dolan and Osborn [1][2][3], remarkable recent progress has been made in this area [4][5][6][7][8][9][10].
In two dimensions, additional structure is present. Whilst the global conformal group is always finite dimensional, in d = 2 there exists an infinite dimensional local conformal algebra, the Virasoro algebra. Fields can now be classified according to their transformations under local (rather than just global) conformal transformations and, as such, arrange themselves into multiplets comprising a Virasoro primary and its descendants. In the seminal paper [11] it was shown that there are a set of special theories, the 'minimal models' for which there are only a finite number of Virasoro primaries possessing known scaling dimensions. This simplification is sufficient for the bootstrap procedure to determine the CFT data and for all correlation functions to be expressible as solutions to linear partial differential equations.
However, even in this situation, there are some natural questions to pose, at least coming from the perspective of the path integral approach to QFT: is it possible to encode the dynamics of these theories in an action and, if so, is there a concrete recipe for doing so? Is this procedure possible for all such theories or only some of them? Are the resulting actions guaranteed to be local and, if so, why? In this paper, it will be attempted to provide answers to some of these questions and hopefully to offer a fresh perspective on others.
These questions are equally valid (and perhaps less academic) in situations where the conformal bootstrap is insufficient to provide a complete understanding of the theories to which it is applied. We will take the point of view that, in this situation, one approach is to try to introduce an action formulation of the theory in question. Notice that this has been deliberately phrased so as to reverse the logical order compared to the path integral approach. Typically, within the path integral paradigm, the first thing that one does is write down a (bare) action. The conformality or otherwise of the resulting theory must then be determined. In our approach, however, we envisage starting with correlation functions which are conformally covariant by assumption and then introducing the action as an auxiliary construction.
At heart, the underlying philosophy of this paper is to take an intrinsically quantum field-theoretic starting point i.e. the symmetry properties of the correlation functions of the theory at hand. The idea then is to show that, perhaps given certain restrictions, this implies that (should one so desire) a local action can be constructed, from which the correlation functions can, in principle, be computed. If one is to take QFT as fundamental, this seems more philosophically satisfactory than taking a classical action as the starting point. Moreover, it clarifies the relationship between two largely disassociated textbook approaches to QFT.
The exact renormalization group
As will be exposed in this paper, the formalism which binds together the classic CFT approach to field theory with its path integral counterpart is Wilson's exact renormalization group (ERG) [12]. Starting from conformally covariant correlation functions, the strategy is to encode the information thus contained in various functional representations. 1 Each representation will yield different expressions both for the conformal generators and for the conformal primaries and their descendants. The most direct representation follows from introducing sources and embedding the correlation functions in the Schwinger functional, W (the subtleties of doing this in the presence of infrared (IR) and ultraviolet (UV) divergences are discussed later). Associated with the Schwinger functional is a representation of the conformal algebra; for CFTs, each of the generators annihilates W.
For simplicity, we will largely consider theories for which all conformal primary fields are scalar (relaxing this, at least in the absence of gauge symmetry, is straightforward). More importantly, we assume that there is at least one conformal primary field for which the Schwinger functional -written in terms of the conjugate source, J -exists. To proceed, we shift this source by the derivative of a new, auxiliary field: (1.2) resulting in another representation of the conformal algebra.
Note that ϕ will essentially end up playing the role of the fundamental field (for brevity, we implicitly consider theories which involve just a single fundamental field). The form of the shift (1.2) may seem a little odd. Ultimately, it can be traced back to Morris' observation that the Wilsonian effective action naturally generates the correlation functions with an extra factor of momentum squared on each leg [13].
Next, we introduce a deformation of the Schwinger functional obtained by adding an apparently arbitrary functional of ϕ and J , which, amongst other things, means that the deformed functional may depend separately on the field and the source. The motivation for this follows from previous studies of the ERG: this deformed functional is recognized as something which can be generated from a Wilsonian effective action, S. To put it another way, we know the answer that we are looking for! Recall that, in the Schwinger functional representation, a CFT is such that the generators annihilate W. This is translated into the statement that the generators in the new representation annihilate exp −S. However, whereas the generators in the Schwinger functional representation are linear in functional derivatives, in the new representation the generators associated with dilatations and special conformal transformations are quadratic. The upshot of this is that two of the linear conditions implied by the annihilation of exp −S can be replaced two by non-linear conditions on S. The first of these is identified with the fixed-point version of an ERG equation and the second -constituting one of the central results of this paper -is recognized as a new analogue of the special conformal consistency condition discovered long ago by Schäfer [14]. Associated with these conditions is a representation of the conformal algebra in which the generators depend explicitly on the Wilsonian effective action.
The non-linearity of the ERG equation seems to be crucial (as emphasised by Wegner [15]). In the linear Schwinger functional representation, the scaling dimensions of the fields must be determined in a self-consistent fashion using the bootstrap equations. In the Wilsonian approach, a different strategy is used. One field, 2 with a priori unknown scaling dimension, δ, is separated from the rest and used to formulate an ERG equation (as anticipated above, we identify this field as the fundamental field). As such, it appears that an 2 In much of the ERG literature, 'operator' is used in place of field; however, following CFT conventions, we shall generally use the latter. ERG equation contains two unknowns: the Wilsonian effective action and δ. The correct interpretation is that an ERG equation is a non-linear eigenvalue equation [16]; however, this hinges on one further ingredient: we demand that the solutions to the ERG equation are quasi-local. 3 It is the combination of non-linearity and quasi-locality which allows, in principle, for the spectrum of δ to be extracted from the ERG equation. Indeed, by demanding quasi-locality, the spectrum of possible values of δ can be shown to be discrete [17]. Let us emphasise that the spectrum of δ does not correspond to the spectrum of fields within a given CFT; rather, each value of δ obtained by solving the ERG equation corresponds to a different CFT.
Presuming that some solution to the ERG equation has been obtained, the second step would be to compute the spectrum of fields. With both S and δ now known, the dilatation generator has a concrete form. It now provides a linear eigenvalue equation for the fields and their scaling dimensions. In general, the spectrum is rendered discrete by the condition of quasi-locality: this is illustrated for the Gaussian fixed point in [15,17]. Within the derivative expansion approximation scheme, see [16] for an excellent description of how discreteness of the spectrum arises for non-trivial fixed points.
From the perspective of different representations of the conformal algebra, it is locality, together with non-linearity, which singles out the ERG representation as special. Remember that the reason for considering elaborate representations of the conformal algebra is more than just academic: part of the motivation is to provide tools for understanding conformal field theories for which the conformal bootstrap seems intractable. In the ERG approach, scale-invariant theories can be picked out from an equation by applying a constraint which is easy to implement on the solutions: that of quasilocality. The price one pays for this is the introduction of a considerable amount of unphysical scaffolding, notably the UV regularization. One can imagine other representations of the conformal algebra which entail similar complication but without the redeeming feature of a simple condition which can be imposed on solutions of the scale/special conformal consistency conditions. An interesting question to ask is whether the set of conformal field theories (perhaps subject to constraints of physicality) is in one-to-one correspondence with the set of equivalence classes of quasi-local actions. It is tempting and perhaps not too radical to speculate that, at the very least for the sorts of theories which form the focus of this paper -non-gauge theories, on a flat, static background, for which the energy-momentum tensor exists and is non-zero -the answer is yes. While there are some suggestive numerical results [18], it is desirable to have a proof, one way or the other. The thrust of this paper gives some clues as to how this can be achieved (as discussed further in the conclusion) but at a rigorous level the question remains unanswered, for now.
The energy-momentum tensor
It is worth emphasising that the approach advocated above is precisely the opposite of the standard path integral approach: our starting point is the correlation functions; then we introduce sources; next we introduce a field and arrive at an action! Everything within this picture, with the exception of the correlation functions, themselves, is an auxiliary construction. As such, this sits rather uncomfortably with standard expositions of the role of the energy-momentum tensor in QFT: for these tend to start with the classical action.
This tension is reconciled as follows. One of the key results of this paper is that, for conformal field theories, the usual Ward identities associated with the energy-momentum tensor should, in fact, be recognized as defining the energymomentum tensor in a particular representation of the conformal algebra. 4 To see how this comes about, consider the Ward identity associated with translation invariance. Taking T αβ to denote a quasi-local representation of the energy-momentum tensor, we have [19] loc is a quasi-local representation of the conformal primary field conjugate to J . Multiplying by one source for each instance of the quasi-primary field and integrating over the corresponding coordinates yields where, in accord with the notation of [20] (which we largely follow throughout this paper) Next, we sum over n and observe that the result can be cast in the form where we have chosen to define T (Sch) αβ such that it is only contains connected contributions (multiplying by e W[J ] restores the disconnected pieces). A crucial point is that (modulo some subtleties to be dealt with later) we interpret T (Sch) αβ as a representation of the energy-momentum tensor; the 'Sch' serves to reminds us that this representation involves the Schwinger functional. When working in an arbitrary representation, we will utilize the symbol T αβ .
Evidence will be assembled for this in Sect. 4 as follows. As we will see in Sect. 4.1, the Schwinger functional representation makes it particularly transparent that the two main ingredients on the right-hand side of (1.5), J and δW/δ J are (again, modulo some subtleties to be discussed later) representations of a pair of conformal primary fields with scaling dimensions, d − δ and δ: The subscript J adorning the conformal primary fields is a reminder that we are considering a particular representation. Let us emphasise again that this particular representation of O (δ) is non-local and that we will see later how to obtain a reassuringly local representation, via the ERG.
J can be combined in various ways to express translation, rotation and dilatation invariance. For example, translational invariance of the Schwinger functional can be stated as which suggests the existence of a tensor field such that . (As will be discussed more fully later, this is not quite the full story: existence of a quasi-local representation of the theory is required.) Rotational invariance implies symmetry of F αβ . Furthermore, it will be shown, under certain conditions, that F αβ can be 'improved' in such a way that its trace corresponds to the Ward identity associated with dilatation invariance. Assuming this improvement to be done, conformal invariance is confirmed in Sect. 4.3.
This analysis of the improvement procedure will be seen to have close parallels to that of Polchinski's classic paper [21]. Indeed, as in the latter, a sufficient condition for this improvement is essentially that primary vector fields of scaling dimension d − 1 are absent from the spectrum. In the same paper, Polchinski completed an argument due to Zamolodchikov [22] showing that, in two dimensions, the energymomentum tensor of a scale-invariant theory can be rendered traceless if the theory is unitary and the spectrum of fields is discrete. The veracity of this for d > 2 has been much debated [23].
As additional confirmation of the consistency of our approach it will be shown in Sect. 4.2.2 that T αβ has the same properties under conformal transformations as a tensor, conformal primary field of scaling dimension, d. (We use the term field with care since the associated representation is non-local, but henceforth will be less assiduous.) Let us emphasise that we are not claiming T αβ is a representation of the energy-momentum tensor in the sense of having the correct transformation properties under the appropriate representation of the conformal group; only for the full T αβ does this hold.
While this section began with the standard representation of the energy-momentum tensor -i.e. a quasi-local objectfrom the perspective of this paper we view as more primitive the non-local representation furnished by the Schwinger functional, T αβ . For theories supporting a quasi-local representation, T αβ can be recovered via the ERG, as will become apparent in Sect. 4.4. With this achieved, another of the central results of this paper will become apparent: in the ERG representation, the trace of the energy-momentum tensor is nothing but the exactly marginal, redundant field possessed by every critical fixed point. (Redundant fields correspond to quasi-local field redefinitions.) It is the existence of this field which causes quasi-local fixed-point theories to divide up into equivalence classes: every fixed-point theory exists as a one-parameter family of physically equivalent theories [15][16][17]24,25]. This is the origin of the quantization of the spectrum of δ.
The construction of the energy-momentum tensor will be illustrated in Sect. 4.5 using the example of the Gaussian fixed point; Sect. 4.6 demonstrates how the construction breaks down for a simple, non-unitary theory.
Elementary properties of the conformal group
In this section, we recall some basic features of the conformal group; henceforth, unless stated otherwise, we work in Euclidean space. The generators {P μ , M μν , D, K μ }, respectively, generate translations, rotations, dilatations (scale transformations) and special conformal transformations; the non-zero commutators are (2.1) Though it will not exploited in this paper, it is worth noting that the commutation relations can be recast in a manner which makes explicit the isomorphism between the conformal group and SO(d + 1, 1) (see, for example, [19] where {∂ μ , L μν , D ( ) , K ( ) μ } are taken such that they satisfy a version of the commutation relations above in which the signs are flipped. This is crucial if (2.2) is to be consistent with the commutation relations. For example, it follows from (2.2) that from which we deduce that D ( ) , K ( ) μ = +K ( ) μ , as compared with D, K μ = −K μ in (2.1). With this in mind, we take The general modification of (2.2) appropriate to non-scalar fields can be found in [19]. For our purposes, we explicitly give the version appropriate to tensor fields: (2.5b) These relationships will play an important role when we deal with the energy-momentum tensor in Sect. 4. Let us emphasise that, at this stage, the representation of the {P μ , M μν , D, K μ } and the O(x) are yet to be fixed; a key theme of this paper will be the exploration of certain representations thereof, some of which are non-standard.
Correlation functions
In the context of QFT, the chief consequence of conformal symmetry is that various correlation functions are annihilated by {∂ μ , L μν , D ( ) , K ( ) μ }. Specifically, correlation functions involving only the conformal primaries are annihilated by all members of the set, whereas those involving descendant fields (the derivatives of the conformal primaries) are annihilated only by those corresponding to translations, rotations and dilatations. Thus we have, for all n, whereas the remaining conditions read 6 now for all a 1 , . . . , a n n j=1 The ultimate aim is to find solutions to (2.6) and (2.7) that correspond to acceptable QFTs.
A key step for what follows is to introduce a set of sources, J i (x), conjugate to the conformal primary fields O i (x) (any Euclidean indices are suppressed). There is no need to introduce sources for the descendants since the associated correlation functions can be generated from the analogue involving just primaries by acting with appropriate derivatives. Restricting to conformal primary fields, we tentatively rewrite (2.6) and (2.7) as In general, considerable care must be taken defining the expectation value of exponentials, due to both IR and UV singularities. However, this paper will only directly utilize expectation values involving J (which, we recall, can loosely be thought of as coupling to the lowest dimension conformal primary field); indeed, for brevity we will henceforth deal only with this single source, the scaling dimension of which is d − δ (it is a simple matter to insert the remaining sources, should one so desire). At certain stages, we will simply assume that the Schwinger functional involving solely J , W[J ], is well defined. To be precise, when we talk of existence of the Schwinger functional, it is meant that the correlation functions of the field conjugate to J can be directly subsumed into W[J ] and so the naïve identities (2.8a)-(2.8d) hold. Note that existence of W[J ] is considered a separate property from W[J ] being non-zero.
By definition, we take J i · O i to have zero scaling dimension; this implies that J i (x) has scaling dimension d − i . This leads us to the first of several functional representations of the conformal generators that will be presented in this paper.
Representation 1 Schwinger Functional Representation
It is easy to check that these generators satisfy the conformal algebra by utilizing (2.4a), (2.4b) and (2.4c), together with the following relationships which follow from integrating by parts: Note that the fact that {∂ μ , L μν , D ( ) , K ( ) μ } satisfy a version of the conformal commutation relations in which the order of the commutators is flipped is crucial.
Now that we have a concrete functional representation of the conformal algebra, it is appropriate to mention a subtlety pertaining to volume terms. To illustrate this issue, consider the effect of the dilatation operator on an integrated field. Recalling (2.2) and (2.4b), it is apparent that we expect (2.12) In deriving this, we have implicitly assumed that O depends on a field which dies of sufficiently rapidly at infinity. However, for the identity operator this is not the case. To match the two sides of (2.12) in this situation -and bearing in mind that = 0 -suggests that the dilatation generator should be supplemented by a term with V being the volume of the space on which the field theory lives. For this paper, however, we will generally ignore volume terms; as such, we henceforth understand equality in functional equations to hold only up to volume terms. This issue will be addressed more fully in [26].
From sources to the fundamental field
Up until this point, our functional representation has utilized sources. The transition to fields proceeds in several steps, along the way giving new representations of the conformal algebra. The first such step is provided by the shift (1.2). Clearly, at this stage, the dependence on J and ϕ will not be independent. However, the link will be severed in a subsequent representation. To prepare for this severing, our aim in this section is, given the shift (1.2), to construct a representation in which the generators involve functional derivatives with respect to ϕ (rather than ∂ 2 ϕ).
As mentioned earlier, we anticipate that ϕ will play the role of the fundamental field. Before proceeding, it is worth pointing out that there is a subtlety over precisely what is meant by the latter. Strictly speaking, both the Wilsonian effective action and the field to which J couples are built out of ϕ. Within the ERG representation (and assuming sufficiently good IR behaviour), ϕ coincides with a conformal primary field only up to non-universal terms, which vanish in the limit that the regularization is removed. While this subtlety will be largely glossed over since it seems to have no great significance, the issue of theories for which bad IR behaviour prevents ϕ from corresponding to a conformal primary in any sense will be returned to later.
With the aim of producing a representation of the generators involving functional derivatives with respect to ϕ, we exploit the commutators where δ 0 (which we recognize as the canonical dimension of the fundamental field) is given by (2.14) Next, define G 0 to be Green's function for −∂ 2 : (2.15) Employing notation such that, for fields ϕ(x), ψ(x) and kernel K (x, y) where we recall from the introduction that δ is the scaling dimension of the fundamental field. Performing similar manipulations for the special conformal generator we arrive at where we have introduced the anomalous dimension, η, defined via Representation 2 Para-Schwinger functional representation: where P μ , M μν , . . . correspond to the expressions for the various generators in the present representation. It is straightforward to confirm from (2.4a), (2.4b) and (2.4c), together with translational and rotational invariance of G 0 , that these generators satisfy the requisite commutation relations. In this representation, a conformal field theory is such that each of these generators annihilates W[J + ∂ 2 ϕ].
Before introducing the next representation, it is worth mentioning that the functional W[J + ∂ 2 ϕ] may have different (quasi)-locality properties with respect to J and ϕ. For non-trivial fixed points this will not be the case, as can be seen at the two-point level. In momentum space, the two-point correlation function goes like 1/ p 2(1−η/2) . For non-trivial fixed points, η/2 is some non-integer number. While multiplying by a factor of p 2 removes the divergence as p 2 → 0, it does not remove the non-locality. For trivial fixed points, however, non-locality may be ameliorated. This can be convenient and is exploited in Sect. 4.5.
From the fundamental field to the ERG
The aim now is to go from this representation to one in which the dynamics of the theory is encoded in some auxiliary object. To begin, we introduce an auxiliary functional, U, which, save for insisting translational and rotational invariance, we leave arbitrary for now. We define (2.21) Notice that W U [ϕ, J ] may depend independently on J and ϕ. The arbitrariness in U is a manifestation of the freedom inherent in constructing ERGs, which has been recognized since the birth of the subject [15,24]. As particularly emphasised in [27], this can be understood from deriving the ERG equation via a quasi-local field redefinition under the path integral, which will be elaborated upon at the end of this section. In Sect. 3 we will focus on a particular choice of U, which turns out to reproduce what is essentially Polchinski's ERG equation.
The idea now is to encode the dynamics in an object, S[ϕ, J ], and introduce an operator, Y (about which more will be said, below), such that Thus, given S we can, in principle, recover the correlation functions. In this sense, S encodes the dynamics of the theory. It should be pointed out that any vacuum contributions to the Wilsonian effective action are unconstrained within our approach. The conditions on W U implied by conformal invariance are blind to vacuum terms. Consequently, we are free to add any vacuum term we like to U, which amounts, via (2.22), to an arbitrary vacuum contribution to the Wilsonian effective action. Before moving on let us not that, in general, the Wilsonian approach deals not just with scale (or conformally) invariant theories but with theories exhibiting scale dependence. Scaleindependent actions are typically denoted by S and solve the fixed-point version of an ERG equation. However, since this paper will only ever deal with fixed-point quantities, the will henceforth be dropped.
There is an implicit assumption that it is possible to find a non-trivial Y such that (2.22) exists. Given this, a representation can be constructed as follows. Given a generator, g, and a representation of this generator, denoted by G , define where the arrow indicates that the generator acts on everything to their right, with it being understood that further terms may follow the e Y (without the arrow, we would take the generator just to act on the explicitly written terms to its right). By construction, if generators G and G satisfy some commutation relation, then the same is true of G U and G U . Immediately, this allows us to construct a representation as follows.
Let us now explore some possibilities for Y. Translation invariance of the correlation functions and of U implies that with a similar expression implied by rotational invariance. Next consider substituting for W U using (2.22) and commuting e Y to the left-hand side. Now demand manifest translation invariance of S, by which we mean 7 This, together with the similar constraint coming from demanding manifest rotational invariance, implies The most obvious solution to these constraints is Y = bϕ · δ/δϕ, for some constant b. However, in this case S[ϕ] is related to W U by rescaling each leg of every vertex of the latter by a factor of e −b , which gives us nothing new. Instead, we solve the constraints by introducing a kernel, G (x − y) 2 , and taking Typically, G has, roughly speaking, the form of a regularized propagator (care must be taken with this identification, as discussed in [17]). Given a momentum-space UV cutoff function, K ( p 2 ), and using the same symbol for position-space objects and their Fourier transforms, we write the Fourier transform of G as Of course, we have been guided to (2.28) and (2.29) by our pre-existing knowledge of both the form of the ERG equation and the (related) role of the propagator in the standard path integral approach to QFT. Let us stress that we have not derived these equations and the uniqueness or otherwise of this particular solution is an important question to answer, but beyond the scope of this paper. Given our prior knowledge of what to look for, we anticipate that (2.28) and (2.29) will lead to a useful representation of the conformal algebra (as discussed in the introduction, by 'useful' we mean that the constraint which picks out physically acceptable theories is easy to implement; for the ERG this constraint is quasilocality). Before moving on, let us mention that (2.29) suffers from IR problems in d = 2. 8 Strictly speaking, this suggests that in d = 2 we should work in finite volume, at least at intermediate stages.
Observe that it is possible to simplify the expressions for P μ and M μν . Since U is taken to be invariant under translations and rotations, we can write Given (2.27), it is tempting to try to simplify these expressions further, but a little care must be taken. If these generators act on something which is transitionally and rotationally invariant, then P μ and M μν are transparent to e Y , which can be trivially commuted to the left, whereupon it is annihilated by e −Y , leaving behind just P μ . But suppose, for example, 8 Indeed the true propagator at the Gaussian fixed point in d = 2 has logarithmic behaviour, emphasising that the interpretation of G as a regularized propagator must be taken with a pinch of salt.
that P μ acts on something not translationally invariant, such as Using (2.28), it is easy to check that The origin of this remainder relates to the discussion under (2.12); indeed, for many purposes of interest it is consistent to take P U μ = P μ . Finally, we construct a representation in which the generators of dilatations and special conformal transformations contain the action. Recalling (2.23), let us define By construction it is apparent that, if G U and G U satisfy some commutation relation, then so too do G S and G S , leading to the next representation.
Representation 4 ERG representation
We will now study some of the properties of the last two representations. As remarked above, in the auxiliary functional representation, a conformal field theory is such that e −S is annihilated by each of the generators. For translations and rotations, this implies that S, itself, is thus annihilated. However, the same is not true for dilatations and special conformal transformations. In the ERG representation, the associated constraints are most naturally expressed as These translate into non-linear constraints on S, as we will see in an explicit example in the next section. Indeed, Given certain restrictions (pertaining to quasilocality) to be discussed in Sect. 3, (2.33a) will be recognized as nothing but an ERG equation (in the presence of sources) specialized to a fixed point. Equation (2.33b) is an additional constraint on the action enforcing conformal invariance, along the lines of [14]. If we choose to restrict U to depend only on ϕ, then the only source dependence in (2.33a) occurs through the action and the O i can be picked out of the latter in a simple manner. Anticipating this, let us reinstate all sources and write Substituting into (2.33a) and (2.33b), it is apparent that where D S [ϕ] and K Sμ [ϕ] correspond to the pieces of D S and K Sμ which remain when the source is set to zero. This pair of equations confirms our expectation that the sources are conjugate to the fields, as expected. Note that the constraint of quasi-locality is necessary for the promotion of these equations to eigenvalue equations for the scaling dimensions, i , as mentioned in Sect. 1.2. Let us conclude this section by discussing in a little more detail how the freedom inherent in U is related to the freedom inherent in the ERG. For (2.33a) to correspond to a bona-fide ERG equation, D U must on the one hand be quasi-local and, on the other, must be such that (up to vacuum terms), (2.33a) can be cast in the form [27] and (which itself depends on the action) is quasi-local. It will be apparent from the next section that the constraint of quasi-locality rules out the apparently simplest choice U = 0.
Polchinski's equation from the conformal algebra
Our treatment so far has been very general; in this section we will provide a concrete realization of our ideas by showing how to derive what is essentially Polchinski's equation [28].
Mimicking the previous section, we will take the Auxiliary Functional Representation as our starting point, deriving the generators in this representation. The constraint equation (2.33a) will then be seen to produce the desired ERG equation, with (2.33b) producing its special conformal partner. Finally, we will give the expressions for the associated conformal generators corresponding to the ERG representation.
To this end, we take U to be bi-linear in the field and, for brevity, work with a single source: where h will be specified momentarily. Recalling (2.20c), (2.23) and (2.24c), it is apparent that
2)
where D h stands for D U , given the special choice (3.1). To process this, let us begin by noting that where we understand (as in [20]) Choosing h such that the expression for D h becomes Next, define G according to which, in momentum space, translates to G( p 2 ) = 2 d K ( p 2 )/dp 2 . This implies from which we observe that where, following the discussion under (2.12), a volume term has been discarded. Substituting back into (3.5) yields the final expression for the dilatation generator in this representation: The constraint Eq. (2.33a) now yields the 'canonical' ERG equation, specialized to a fixed point: (3.10) An equation like (3.10) was first written down (without sources, but allowing for scale dependence) in [29]. It can be thought of as a modification of Polchinski's equation in which the anomalous dimension of the fundamental field is explicitly taken into account; see [17,20] for detailed analyses. A principal requirement for a valid ERG equation is that the kernels G and G −1 -related via (3.7) -are quasi-local. Typically, G is chosen according to (2.29), with the cutoff function conventionally normalized so that K (0) = 1 (further details can be found in [17,20]). Volume terms, discarded in this paper, are carefully treated in [20].
Deriving the analogous equation arising from special conformal transformations will be facilitated by the following. (3.11) Then it follows that Proof The result follows from the form of D ( ) and K ( ) μ given in (2.4b) and (2.4c).
Applying this result to (3.4), it is apparent that where Recalling (2.20d), (2.23) and (2.24d), it is apparent that (3.14) Commuting e 1 2 ϕ·h·ϕ to the left, the generated of the form ϕ · ∂ μ G 0 · h · ϕ vanishes due to the asymmetry of ∂ μ G 0 · h under interchange of its arguments. In a little more detail we have, for some H , where in the second step we have swapped the dummy variables x and y. Consequently, we arrive at the following analogue of (3.5): (3.17) As before, the strategy is now to commute e −Y to the right.
To facilitate this, we note the following. First, recalling (3.7) and Proposition 1 it is apparent that Processing the next term in (3.17) gives where we have used the result This can be seen by reinstating arguments. Equivalently, note that the shorthand for (3.11 Finally, the last term in (3.17) gives, on account of translational invariance of G 0 : where, in accord with the discussion under (2.30), equality strictly holds only up to a possible vacuum term. We thus deduce that (3.22) where, noticing that the η from the second term's δ − η has been pulled into the final term, We now recast f μ in a simpler, manifestly quasi-local form.
Recalling that G = G 0 · K and G −1 = −K −1 ∂ 2 it follows that where the last line follows from exploiting G 0 · K = K · G 0 , together with ∂ μ K ·G 0 = −K ·G 0 ← − ∂ μ . Thus, we can simplify However, where, to go from the first line to the second, we have exploited translational invariance of K , with the final step following from (3.6). From this, we deduce that Therefore, the constraint on the Wilsonian effective action implied by invariance under special conformal transformations, (2.33b), reads This equation is to the canonical ERG Eq. (3.10) what Schäfer's equation [14] is to Wilson's ERG equation [12]. The generators in the ERG representation are constructed from (3.9) and (3.22) using the recipe in (2.32c) and (2.32d). The resulting expressions can be simplified by utilising the constraint Eqs. (3.10) and (3.28).
Representation 5 Canonical ERG representation
where G and G μ are defined in terms of G via (3.6) and (3.11), the volume terms have been neglected and S satisfies (3.10) and (3.28).
Though the analysis up to this point has been phrased in terms of conformal primary fields, we are at liberty to consider non-conformal theories: this can be done simply by taking the fields to which J i couple as not being conformal primaries.
Proposal
Given the scalar, conformal primary field, O (δ) , we can furnish a representation of both this and a partner of scaling dimension d − δ in terms of the appropriate sources: where we recall that the subscript J denotes the Schwinger functional representation. It is immediately apparent that the pair of fields (4.1a) and (4.1b) satisfy (2.2). However, satisfaction of (2.2) is a necessary but not sufficient condition for a field to belong to the spectrum of conformal primaries of a given theory. Indeed, we can construct any number of solutions to (2.2), but only various combinations of solutions will correspond to the field contents of actual, realisable theories. With this in mind, there are two assumptions at play in the statement that O (δ) and O (d−δ) are conformal primaries. First, it is assumed that W[J ] exists and is non-zero; we will encounter theories for which one or other of these conditions is violated in subsequent sections. More subtly, it is assumed that O (d−δ) is amongst the spectrum of fields. As will be seen in Sect. 4.4, if the ERG representation is quasi-local then O (d−δ) is present in the spectrum as a redundant field.
Note that there are interesting theories for which the assumption that O (d−δ) is in the spectrum of fields does not hold, in particular the mean field theories. This class of theories (recently featuring in e.g. [7,8,30,31]) are such that the n-point functions are sums of products of two-point functions and cannot be represented in terms of a quasi-local action. The latter restriction amounts to defining mean field theories so as to exclude the Gaussian theory, plus its quasi-local but non-unitary cousins [17] (see also Sect. 4.6); this is done for terminological convenience. Thus, for mean field theories, (4.1b) amounts to minor notational abuse since, strictly, O should be reserved for conformal primaries. Accepting this, we henceforth interpret O (d−δ) J as an object we are at liberty to construct, that in most -though not all -cases of interest is indeed a conformal primary. A surprising feature of mean field theories is that the energy-momentum tensor is not amongst the spectrum of conformal primary fields. 9 Sticking with the Schwinger functional representation, we construct a scalar field of scaling dimension d: where the factor of −δ is inserted so that, at least for theories satisfying the assumptions given above, we can identify O with the trace of the energy-momentum tensor. The × symbol is just to emphasise that no integral is performed. For theories for which the Schwinger functional exists and is non-zero, but O (d−δ) is not in the spectrum of the fields, we are again at liberty to construct O (d) J , so long as we accept minor notional abuse and, more pertinently, that the energy-momentum tensor will not be amongst the spectrum of conformal primary fields. Recalling the discussion around (1.5), note that (4.2) is nothing but a statement of the Ward Identity corresponding to dilatation invariance of the Schwinger functional.
The above can be translated into a representation of our choice, though there is some subtlety in so doing. Leaving the choice of representation unspecified, let us tentatively write (4.5) For the ERG representation, as will be seen explicitly in Sect.
4.4, the solution is to extend O
, with the latter such that (4.6) With this in mind, we rewrite (4.3) as with the understanding that, for 'first order' representations, Certain properties which are true of O (d) and its component fields are particularly transparent in the Schwinger functional representation. First of all, observe that, as discussed in the introduction, translation invariance implies Integrating by parts it follows that, for some F αβ , Actually, in principle there could be an additional term which cannot be written as a total derivative but rather vanishes, when integrated, due to the integrand being odd. An example would be However, such terms are excluded if we insist that the theory in question possesses a quasi-local representation as we will do, henceforth. Recall that, in a quasi-local representation, all functions of the field have an expansion in positive powers of derivatives (it is blithely assumed that this expansion converges). For example, the derivative expansion of the action reads where V (ϕ) is the local potential which, like Z (ϕ), depends on x only via the field (the ellipsis represent higher derivative terms). With this in mind, let us consider (4.8) in a quasi-lcoal representation. Quasi-locality implies that any terms which vanish when integrated must take the form of total derivatives establishing that, for theories which permit a quasi-local formulation, (4.9) is correct as it stands. Note that by focussing on theories supporting a quasi-local representation excludes mean field theories, in particular, from the remainder of the discussion. We recognize that the form of (4.9) is that of the Ward Identity associated with conservation of the energymomentum tensor; inspired by this and (4.2) we propose that, for theories in which the energy-momentum tensor exists, the Ward Identities can be interpreted as defining a nonlocal representation of the energy-momentum tensor. Denoting the energy-momentum tensor in an arbitrary representation -which may or may not be quasi-local -by T αβ , we tentatively define this object via 10 :
Justification
In this section, we justify, for d > 1, the proposal encapsulated in (4.10a), (4.10b) and (4.10c), which comprises three steps. First it is shown that an object which satisfies these equations is implied by translation, rotation and dilatation invariance so long as Polchinski's conditions [21] for the improvement of the energy-momentum tensor are satisfied. Secondly, it is shown how both the traceful and longitudinal components of T αβ transform in a manner consistent with T αβ being a conformal primary field of dimension d. Finally, the extent to which (4.10a), (4.10b) and (4.10c) serve to uniquely define T αβ is discussed.
Existence
The most basic requirement for the existence of a non-null T αβ , as defined via (4.10a), (4.10b) and (4.10c), is that the fieldsÔ (d−δ) and O (δ) exist and are non-zero. There is some degree of subtlety here since it is conceivable that O (δ) does not exist in the Schwinger functional representation but does exist in a quasi-local representation. An example would be the Gaussian theory in d = 2. The IR behaviour of this theory is sufficiently bad that the lowest dimension conformal primary is not ϕ but rather ∂ μ ϕ. One method for dealing with this theory would be to perform the analysis of this section in terms of vector fields. An alternative, however, is to implicitly work within a quasi-local representation; note that though O (δ) exists, we are accepting a degree of notational abuse since it is not a conformal primary in the standard sense.
(Later, where more care must be taken, the symbol φ used, instead). With this in mind, for the duration of this section we assume that at least one representation ofÔ (d−δ) and O (δ) exists, and at least one of these representations is quasi-local. Given this, we now move on to determining the conditions under which (4.10a), (4.10b) and (4.10c) are implied by a combination of translation, rotation and dilatation invariance. In Sect. 4.1, we have already seen that, for some F αβ , translation invariance plus the existence of a quasi-local representation implies (4.9). Similarly, from rotational invariance it follows that Substituting in (4.9) we have implying that, for some f λαβ , antisymmetric in its last two indices, We might wonder whether, as in the case of translation invariance, an additional term can appear on the right-hand side that cannot be expressed as a total derivative. This would be of the form Y αβ − Y βα , where d d x Y αβ is symmetric. Again, quasi-locality guarantees that such contributions can in fact be absorbed into the total derivative term, ∂ λ f λαβ . Inspired by the standard derivation of the Belinfante tensor we observe that, for some F λαβ antisymmetric in its first two indices, (4.9) is left invariant by the shift (4.14) Under this transformation, (4.13) becomes (4.15) and so we choose F λαβ such that Note that the choice of F λαβ is not unique: we can add to it further terms, antisymmetric in the first pair of indices and symmetric in the second, which leave both (4.9) and (4. 16) invariant.
Let us summarize what has been accomplished so far. On the one hand we have demonstrated the existence of a tensor field, F αβ , which satisfies On the other hand, we have shown the existence of a scalar field, T αα , satisfying (4.10a). Next we must show that these two objects are, in fact, related. To do this, we start by multiplying (4.17a) by x β and integrating over all space, giving The first term on the right-hand side vanishes as a consequence of dilatation invariance and so we conclude that, for some f λ , But, as noted above, (4.17a) and (4.17b) are left invariant by the shift (4.20) where (4.21) In d = 1 it is impossible to construct a non-zero Z λβα . For d > 1, it would appear that we can eliminate the unwanted term via the shift (4.20), while leaving (4.17a) and (4.17b) invariant. However, there is a subtlety. Let us observe that, apparently, for d > 1 a solution to the constraints on Z λαβ always exists: The transverse structure guarantees that the result of contracting with either ∂ α or ∂ β vanishes, as required. However, the theories under examination are required to support a quasilocal representation. Since ∂ α ∂ β G 0 is non-local, the above solution is not always valid. If f λ is a descendant field of the form ∂ λ O or ∂ 2 O λ then there is no problem since the nonlocality is ameliorated. Interestingly, there is an additional possibility: it could be that f λ can be written as ∂ λ φ, where here and below we understand φ as being neither a primary nor descendant field. This may seem exotic but recall that, for the Gaussian fixed point in d = 2, the fundamental field is just such a scalar; indeed, in this case the lowest dimension primary field is ∂ λ φ. Excluding this exotic case, it is clear that the solution (4.22) is no good if f λ is a primary field. Moreover, it fails for the case that f λ = ∂ σ f σ λ for some f σ λ that does not reduce to δ σ λ . In d = 2, this is the end of the story, but this is not so for higher dimensionality. Let us suppose that, for some f σ λ (4.23) If f σ λ contains the Kronecker-δ then we write f σ λ = δ σ λ f . The quasi-local solutions are Observe that these conditions correspond to the recipe found by Polchinski [21] for improving the energy-momentum tensor of a conformal field theory such that it is traceless. With these points in mind, consider the sufficient conditions for translation, rotation and dilatation invariance to imply (4.10a), (4.10b) and (4.10c). In d > 2, absence of a primary vector field of scaling dimension d − 1 is sufficient. In d = 2 this condition must be supplemented by at the absence of vector fields that can be written as ∂ σ f σ λ , where f σ λ does not reduce to the Kronecker-δ. In some sense, this is academic since it cannot be realised for unitary theories. Moreover, as we shall see in Sect. 4.3, this additional condition is relevant only for theories with sufficiently bad IR behaviour.
To conclude this section, let us mention an alternative way to recover Polchinksi's conclusion as to the conditions under which improvement of the energy-momentum tensor is possible. A version of the analysis below forms a key part of [32], in which an argument is given as to why scale invariance is automatically enhanced to conformal invariance for the Ising model in three dimensions.
Using the 'auxiliary functional representation' of the conformal algebra, (2.24a)-(2.24d), consider (2.33a) and (2.33b), supposing that conformal invariance is yet be established but scale invariance holds: Invariance of E Sμ under translations and rotation follows by acting on (4.25a) with P μ and M μν and exploiting invariance of S under translations, rotations and dilatations. Thus, as claimed in [32], (4.26) implies that E Sμ [ϕ, J ] must be expressible as a combination of integrated fields of dimension d − 1. Therefore, scale invariance implies conformal invariance if either there are no primary vector fields of scaling dimension d − 1 or any such fields can be expressed as ∂ μ φ.
Conformal covariance
In this section we will show that (4.10a), (4.10b) and (4.10c) are consistent with T αβ being a candidate for a conformal primary field of dimension d. By 'candidate field' we mean an object that has the desired properties under conformal transformations but may or may not turn out to be amongst the spectrum of conformal primaries for a given theory. Let us start by noting that, by construction, T αα is a candidate for a conformal primary field (cf. (4.2)). The rest of this section will be devoted to showing that the longitudinal parts of T αβ also transform correctly. As a warm up, first let us confirm translational covariance of T αα . Operating on (4.10a) with the generator of translations, P μ : where we have exploited (2.2). Therefore, as expected, T αα is translationally invariant. We can now play a similar game with (4.10b) to show that ∂ α T αβ is translationally invariant.
In the same vein, it is straightforward, by considering the action of the dilatation generator, to show that both T αα and the longitudinal components of T αβ have scaling dimension, d.
Covariance of T αα under rotations and special conformal transformations follows exactly the same pattern. Dealing with (4.10b) is only ever so slightly more involved. To start with, let us consider rotations: Comparing (4.28) and (4.29), we conclude that the longitudinal pieces of T αβ transform under rotations like a conformal primary tensor field. Finally, we deal with special conformal transformations: Now, given a symmetric conformal primary tensor field, αβ , the result of which we can compute using (2.5b). Exploiting symmetry under α ↔ β it is straightforward to show that Comparing (4.30) and (4.31) it is apparent that the longitudinal pieces of T αβ transforms under conformal transformations like a conformal primary tensor field of dimension d.
Uniqueness
A two-index tensor has d 2 a priori independent components. The condition of symmetry under interchange of indices imposes d(d − 1)/2 constraints; conservation imposes a further d, whereas (4.10a) yields one additional constraint. This reduces the number of independent components to Immediately it is apparent that (4.10a), (4.10b) and (4.10c) uniquely define the energy-momentum tensor in d = 2.
For d > 2, we must accept that, in general, T αβ is not uniquely defined. Notice that the equations (4.10a), (4.10b) and (4.10c) are invariant under where The results of the previous sub-section show that the traceful and longitudinal components of T αβ transform as expected for a conformal primary of dimension d. Let us now focus on conformal field theories for which the energy-momentum tensor exists. We assume that Z αβ is chosen such that any remaining components of T αβ also transform homogeneously. However, this still leaves a residual freedom to add to Z αβ a contribution,Z αβ , which also transforms like a conformal primary of dimension d. This requirement, together with (4.33), implies that [33] Z αβ = ∂ ρ ∂ σ C αρβσ , (4.34) where C αρσβ is a conformal primary field of dimension d −2 with the same symmetries as the Weyl tensor: For d = 3, these constraints do not have a non-trivial solution and so extend the uniqueness of the energy-momentum, for a conformal field theory, to this dimensionality. Beyond this, uniqueness or otherwise depends on whether or not the theory in question supports C αρβσ as a conformal primary field of dimensions d − 2 [33]. Though we will not rely on the following restriction in this paper, it is expected that the energy-momentum tensor is unique for unitary theories. 11 In d = 4, C αρβσ transforms under the (2, 0) ⊕ (0, 2) representation. However, Mack rigorously established that, for a representation of type ( j, 0), unitarity demands that the scaling dimension > 1+ j [34]. This implies that the scaling dimension of ∂ ρ ∂ σ C αρβσ is greater than five and so this field cannot contribute to the energy-momentum tensor which, in the considered dimensionality, is of scaling dimension four. A similar result is expected to hold in higher dimensions.
Conformal invariance
We have previously established the conditions under which (4.10a), (4.10b) and (4.10c) hold. Given these equations, it is a simple matter to demonstrate conformal invariance (indeed, we have essentially shown that the energy-momentum tensor can be improved to a traceless, symmetric form). Recall that the condition for conformal invariance reads δ J = 0 (4.36) 11 I would like to thank Osborn for informing me of this and for providing the argument as to why.
which, in an arbitrary representation, becomes (4.37) With this in mind, consider a theory for which full conformal invariance is yet to be established. Utilizing (4.10a), (4.10b and (4.10c), we see that where, to go from the second to the third line, we have integrated by parts, and to go to the last line, we have exploited symmetry of T μα under interchange of indices. Therefore, conformal invariance has been demonstrated. It is interesting to consider theories for which the energymomentum tensor cannot be improved to be traceless. According to (4.19), there is a residual term of the form ∂ λ f λ , which spoils conformal invariance. Repeating the analysis of (4.38), it is apparent that The intriguing thing about this condition is that, in d = 2, the sufficient conditions for the improvement of the energymomentum tensor include the absence of a vector field which can be written as ∂ σ f σ λ , where f σ λ does not reduce to the Kronecker-δ. However, suppose that f μ can be written in this fashion; according to (4.39), conformal invariance is present since the right-hand side vanishes! This apparent paradox is resolved by noting that, in the quasi-local representation appropriate to the discussion of the improvement energymomentum tensor,
Quasi-local representation
The defining equations for the energy-momentum tensors, (4.10a), (4.10b) and (4.10c) are independent of any particular representation. As already apparent, a prominent role is played by the Schwinger functional representation; the other representation of particular interest is furnished by the ERG, which provides a quasi-local framework. For the sake of definiteness, in this section we will explore the energymomentum tensor using the canonical ERG equation, discussed in Sect. 3. Recall that δ can be written in terms of the anomalous dimension of the fundamental via (2.19).
In this context, we have where, in momentum space, for η < 2 with K the momentum-space cutoff introduced in (2.29). The expressions for and O (δ) first appeared in [35] and played a prominent role in much of the analysis of [17]. The pair of fields (4.40a) and (4.40a) appears in both [17,20]. Note that the h appearing in (3.1) is (given appropriate boundary conditions) related to according to [17] For our purposes, though, we seek a slight modification to O (d−δ) loc , as discussed around (4.3). To motivate this, consider (4.7). The novelty of the current representation is that the dilatation generator (3.29c) has a term containing not one but two functional derivatives. Consequently, Therefore, we seek an extension of O (4.43) In this way we can construct which by construction satisfies The solution is to takê There are various ways to obtain this equation. On the one hand, a brute force calculation can be performed, along the lines of appendix C of [17]. However, there is a more elegant approach. Notice that we may writê (4.47) Recalling (2.31) and (3.5), it is apparent that Splitting δ − η = δ 0 − η/2 and noting that it follows that confirming (4.43).
As we know from (4.10a), the fields discussed above can be combined to form the trace of the energy-momentum tensor. Integrating over space, we recognize the resulting object as nothing other than the exactly marginal, redundant field which exists at every critical fixed point. Recall that the definition of a redundant field is that it can be cast as a quasi-local field redefinition. This is essentially manifest in the case of the trace of the energy-momentum tensor -which in the ERG representation we denote by T αα -since Recalling (2.37) we have, for infinitesimal : (4.52) On account of the total functional derivative on the right-hand side, it follows that the partition function is invariant under an infinitesimal shift of the action in the direction of the (integrated) trace of the energy-momentum tensor; in standard parlance, this field is redundant. It has been appreciated for a long time that every critical fixed-point solution of the ERG equation in fact exists as a line of physically equivalent fixed points [15][16][17]24,25].
The exactly marginal, redundant field generates infinitesimal motion along this line: if the line is parametrized by b, then (4.53) For the canonical ERG equation, a generic expression for the entire line of fixed points can be found in [17] (see also [36,37]). Within the ERG formalism, it has been shown that, for any (quasi-local) fixed point for which the exactly marginal, redundant field exists, the value of η is isolated [17] (the converse was proven in [15]). From the perspective of this paper, this property can now be understood as arising for quasi-local theories for which the (trace of the) energymomentum tensor exists and is non-zero.
The Gaussian fixed point
An instructive illustration of many of the concepts discussed above is provided by the Gaussian fixed point, which describes a free theory for which the fundamental field has scaling dimension δ = δ 0 = (d − 2)/2. Before providing the canonical ERG representation of this theory, we will derive the expression for the energy-momentum tensor in the para-Schwinger functional representation. We do this since, for the special case of the Gaussian fixed point, this representation is, in fact, strictly local and, as such, equivalent to an unregularized action approach. Consequently, this should provide a familiar setting prior to our exposition of the less conventional ERG approach. Note that the difference between O (d−δ 0 ) andÔ (d−δ 0 ) amounts only to a vacuum term, which we ignore (the same is true in Sect. 4.6).
Para-Schwinger functional representation
In this representation, (and employing canonical normalization) we have O (d−δ 0 ) = −∂ 2 ϕ and O (δ 0 ) = ϕ, from which we observe that (4.54) Upon comparison with (4.10b), and using a tilde to denote the para-Schwinger functional representation, it is apparent that where Z λαβ (ϕ) satisfies the conditions (4.21) but is thus far undetermined; the factor of δ 0 /(d − 1) has been inserted for convenience. Taking the trace and comparing with (4.10a): This is solved by taking yielding the standard Gaussian energy-momentum tensor, Before moving on, it is instructive to consider the expression for the energy-momentum tensor in the Schwinger functional representation. Recalling (1.2) and (2.15), this can be obtained from (4.58) simply by making the substitution (4.59) It is thus apparent that, in the Schwinger functional representation, precisely as we expect for the Ward identities involving the connected correlator of the Gaussian theory.
ERG representation
In the ERG formalism, the Gaussian theory exhibits a line of physically equivalent fixed points, as expected, which terminates in a non-critical fixed point for which both the Schwinger functional vanishes and the energy-momentum tensor vanish. The Gaussian solution of the canonical ERG equation is (in momentum space): where, in accord with convention, K (0) = 1 and p ≡ (2π) −d d d p . It is thus apparent that the Gaussian fixed point exists as a line for −∞ < b < 1. At b = 1, the action is still a fixed point in the sense of solving the ERG equation. However, Taylor expanding K ( p 2 ) = 1 + O p 2 , it is clear that the action does not describe a theory with long-range order: this theory is non-critical. As emphasised by Wegner, such theories support only redundant fields and, as we will see below, both the energy-momentum tensor and the correlation functions vanish. Note that, for b > 1, the coefficient of ϕ( p) p 2 ϕ(− p) turns negative, which manifests itself as a loss of positivity of the two-point correlation function, as will also be seen below. Defining the Gaussian solution can be rewritten: Substituting into (4.40a) and (4.46), it can readily be confirmed that The full energy-momentum tensor can be obtained from (4.58) by making the substitution Furthermore, as shown explicitly in [17], the Schwinger functional for the Gaussian theory is given by Thus it is apparent that, at the point the theory turns non-critical, both the correlation functions and the energymomentum tensor vanish. For b > 1, positivity of the twopoint function is violated.
A non-unitary example
Having observed the successful construction of the energymomentum tensor in the simplest local, unitary theory, in this section we will provide a simple non-unitary example where the construction breaks down -at least in d = 2.
(For a pedagogical exposition of various aspects of unitarity, see [38].) Specifically, we will consider a free theory for which η = −2.
In momentum space, it is a simple matter to show that [17] where b parametrizes the line of equivalent fixed points and is given by (4.41). Note that the two-point function for the full action, cf. (2.37), starts at O p 4 . It follows that Taking b = −1 (to attain canonical normalization) let us define giving O (d−δ) = −∂ 4 and O (δ) = . The attempted construction of the energy-momentum tensor precedes in a similar vein to before. Observe that (4.70) Therefore, (4.10b) implies Taking the trace yields However, from (4.10a), we know that the trace of the energymomentum tensor is to be equated with −δO (d−δ) × O (δ) , which in this case amounts to setting This simplifies to Comparing with (4.24b) we see that, in d = 2, the presence of the first term prevents the construction of a quasi-local (4.75) In d > 2, improvement of the energy-momentum tensor along the lines of (4.24b) is thus possible. For d = 2 the energy-momentum tensor cannot be improved. Recalling the discussion around (4.39), the η = −2 free theory thus provides an example where, in the quasi-local representation, the action is apparently conformally invariant but, nevertheless, the full quantum theory is not. It is easy to see that W [J ] does not exist, since the propagator ∼ 1/ p 4 . To conclude, note that for d > 2 the energy-momentum tensor can be improved by taking 12 : (4.77) By virtue of the symmetries it is apparent that, as required, Finally, it can be checked that, upon taking the trace, we recover (4.74).
Conclusions
The essence of the philosophy advocated in this paper is a conservative one. At its heart is the desire to view, as far as possible, QFT as fundamental. (Whether or not this ultimately turns out to be the case is beside the point; the goal is partly to see how far one can go by pursuing this agenda.) Taking this seriously, we are driven to look for theories which make sense down to arbitrarily short distances (i.e. theories exhibiting non-perturbative renormalizability). Wilsonian renormalization teaches us that a sufficient condition for this is scale-invariant behaviour in the deep UV, suggesting that we investigate either fully scale-invariant theories or relevant/marginally relevant deformations, thereof.
Our exclusive focus has been on theories exhibiting invariance under the full conformal group. In this context, there are two largely disjoint approaches: one based on exploring the constraints implied by conformal invariance on the correlation functions and the other a path integral approach built upon a quasi-local action. True to our philosophy, the former is viewed as more primitive due to its inherently quantum 12 I am very grateful to Hidenori Sonoda for supplying me with this solution.
field-theoretic nature whereas, through the action, the latter manifests its classical heritage. Ideally, then, what we would like is to be able to start with an approach based on the correlation functions and to show how an action-based description emerges.
This paper largely shows how to achieve this. Starting from the statements of conformal covariance of the correlation functions, the first step is to wrap these up into functionals of sources (accepting a degree of formality in this step). Associated with this is a functional representation of the conformal algebra. This forms the basis for constructing more elaborate representations, involving auxiliary functionals. These auxiliary functionals satisfy consistency conditions, and our development culminated with a representation in which the condition corresponding to dilatation invariance is nothing but the fixed-point version of the canonical ERG equation of [29]. The explicit form of the partner encoding special conformal invariance is a new result of this paper.
Nevertheless, it must be acknowledged that we were guided towards this representation because we knew what we were looking for. This, in of itself, is not an issue. More pressing is that, coming from the path integral perspective, it is expected that all physically acceptable solutions to ERG equations correspond to quasi-local actions [12,17]. The step that is missing in this paper is to show that ERG representations of CFTs necessarily have a Wilsonian effective action that is, indeed, quasi-local. Or, to put it another way, of all the possible representations of the conformal algebra, what makes the ERG representation so special? Suggestively, as alluded to in Sect. 4.4, if the ERG representation of a CFT is quasi-local, then the energy-momentum tensor is amongst the spectrum of conformal primaries. Indeed, the ERG and the energy-momentum tensor share an intimate relationship revealed in this paper: lines of physically equivalent fixed points are generated by the trace of the energy-momentum tensor.
Therefore, referring to the questions posed in the introduction, the state of affairs is as follows. A concrete recipe has been provided for encoding conformal dynamics in an object recognizable as the Wilsonian effective action. This assumes (2.22) which, given the choice (2.28), amounts to an assumption of the existence of a path integral. As noted, in d = 2 it may be necessary to work in finite volume. Plausibly, the rather formal process presented will work for theories possessing an energy-momentum tensor, in which case we expect the Wilsonian representation to furnish a quasi-local formulation of the theory in question. It is clearly desirable, however, to place all of this on a more rigorous footing.
Beyond this matter, it is worth posing the question as to whether there may exist theories supporting representations of the conformal algebra for which the constraint which picks out physically acceptable theories is entirely different from quasi-locality, but equally powerful. Besides exploring this theme further, several avenues of future research suggest themselves. Transcribing our approach to supersymmetric theories should be largely a matter of working with the appropriate potential superfields, as in [39], and being mindful that the conformal algebra is enhanced to be superconformal. A controlled environment in which to further explore the CFT/ERG link is in d = 2, where it may be profitable to investigate functional representations of the entire Virasoro algebra. As indicated earlier, a rigorous treatment in d = 2 may entail a careful finite-volume treatment. Gauge theories present special problems [17,40] and it is my belief that appropriately extending the ideas of this paper will require new ideas.
Furthermore, it is desirable to extend the scope of the analysis to include scale-dependent theories. It is anticipated that the renormalizability (or otherwise) of such theories is tied up with the renormalization of composite operators. Since, for irrelevant/marginally irrelevant perturbations, renormalizability is lost this suggests that, in order to properly define the fixed-point Schwinger functional involving the corresponding sources, some form of point splitting should be performed on the composite operators, to improve their UV behaviour. It may be that this engenders a natural way to uncover the operator product expansion within the ERG formalism, raising the hope of making concrete links between the ideas of this paper and recent developments in the application of the conformal bootstrap.
Finally, it is worth considering the question as to whether theories exist in which there are multiple, distinct quasi-local representations. This leads naturally to the subject of dualities and it is hoped that the ideas of this paper and the fresh perspective it gives on the nature and origins of Wilsonian renormalization will offer new insights in this area. friend, Francis Dolan, who died, tragically, in 2011. It is gratifying that I have been able to honour him with work which substantially overlaps with his research interests and also that some of the inspiration came from a long dialogue with his mentor and collaborator, Hugh Osborn. In addition, I am indebted to Hugh for numerous perceptive comments on various drafts of the manuscript and for bringing to my attention gaps in my knowledge and holes in my logic. I would like to thank Yu Nakayama and Hidenori Sonoda for insightful correspondence following the appearance of the first and third versions on the arXiv, respectively. I am firmly of the conviction that the psychological brutality of the post-doctoral system played a strong underlying role in Francis' death. I would like to take this opportunity, should anyone be listening, to urge those within academia in roles of leadership to do far more to protect members of the community suffering from mental health problems, particularly during the most vulnerable stages of their careers.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecomm ons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Funded by SCOAP 3 . | 17,497.2 | 2017-07-01T00:00:00.000 | [
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Temporal Characterization of Microglia/Macrophage Phenotypes in a Mouse Model of Neonatal Hypoxic-Ischemic Brain Injury
Immune cells display a high degree of phenotypic plasticity, which may facilitate their participation in both the progression and resolution of injury-induced inflammation. The purpose of this study was to investigate the temporal expression of genes associated with classical and alternative polarization phenotypes described for macrophages and to identify related cell populations in the brain following neonatal hypoxia-ischemia (HI). HI was induced in 9-day old mice and brain tissue was collected up to 7 days post-insult to investigate expression of genes associated with macrophage activation. Using cell-markers, CD86 (classic activation) and CD206 (alternative activation), we assessed temporal changes of CD11b+ cell populations in the brain and studied the protein expression of the immunomodulatory factor galectin-3 in these cells. HI induced a rapid regulation (6 h) of genes associated with both classical and alternative polarization phenotypes in the injured hemisphere. FACS analysis showed a marked increase in the number of CD11b+CD86+ cells at 24 h after HI (+3667%), which was coupled with a relative suppression of CD11b+CD206+ cells and cells that did not express neither CD86 nor CD206. The CD11b+CD206+ population was mixed with some cells also expressing CD86. Confocal microscopy confirmed that a subset of cells expressed both CD86 and CD206, particularly in injured gray and white matter. Protein concentration of galectin-3 was markedly increased mainly in the cell population lacking CD86 or CD206 in the injured hemisphere. These cells were predominantly resident microglia as very few galectin-3 positive cells co-localized with infiltrating myeloid cells in Lys-EGFP-ki mice after HI. In summary, HI was characterized by an early mixed gene response, but with a large expansion of mainly the CD86 positive population during the first day. However, the injured hemisphere also contained a subset of cells expressing both CD86 and CD206 and a large population that expressed neither activation marker CD86 nor CD206. Interestingly, these cells expressed the highest levels of galectin-3 and were found to be predominantly resident microglia. Galectin-3 is a protein involved in chemotaxis and macrophage polarization suggesting a novel role in cell infiltration and immunomodulation for this cell population after neonatal injury.
Immune cells display a high degree of phenotypic plasticity, which may facilitate their participation in both the progression and resolution of injury-induced inflammation. The purpose of this study was to investigate the temporal expression of genes associated with classical and alternative polarization phenotypes described for macrophages and to identify related cell populations in the brain following neonatal hypoxia-ischemia (HI). HI was induced in 9-day old mice and brain tissue was collected up to 7 days post-insult to investigate expression of genes associated with macrophage activation. Using cell-markers, CD86 (classic activation) and CD206 (alternative activation), we assessed temporal changes of CD11b + cell populations in the brain and studied the protein expression of the immunomodulatory factor galectin-3 in these cells. HI induced a rapid regulation (6 h) of genes associated with both classical and alternative polarization phenotypes in the injured hemisphere. FACS analysis showed a marked increase in the number of CD11b + CD86 + cells at 24 h after HI (+3667%), which was coupled with a relative suppression of CD11b + CD206 + cells and cells that did not express neither CD86 nor CD206. The CD11b + CD206 + population was mixed with some cells also expressing CD86. Confocal microscopy confirmed that a subset of cells expressed both CD86 and CD206, particularly in injured gray and white matter. Protein concentration of galectin-3 was markedly increased mainly in the cell population lacking CD86 or CD206 in the injured hemisphere. These cells were predominantly resident microglia as very few galectin-3 positive cells co-localized with infiltrating myeloid cells in Lys-EGFP-ki mice after HI. In summary, HI was characterized by an early mixed gene response, but with a large expansion of mainly the CD86 positive population during the first day. However, the injured hemisphere also contained a subset of cells expressing both CD86 and CD206 and a large population that expressed neither activation marker CD86 nor CD206.
Interestingly, these cells expressed the highest levels of galectin-3 and were found to INTRODUCTION Hypoxic-ischemic (HI) brain injury is an important contributor to neonatal mortality as well as permanent neurological impairments in surviving infants. HI triggers an imbalance of CNS homeostasis and initiates peripheral and central inflammatory responses, which can be detected within 2-3 h of insult in rodent models (Hedtjärn et al., 2004;Bonestroo et al., 2013). Persistence of inflammation in the injured human infant brain is poorly defined, but hypothesized to continue for weeks to years contributing significantly to neurological outcome (Hagberg et al., 2015). Indeed, altering or reducing inflammation in the context of perinatal brain injury may have beneficial effects such as reducing lesion size (Hedtjärn et al., 2002;Kigerl et al., 2009;Bolouri et al., 2014).
Microglia are the primary immune competent and phagocytic cells of the brain (Kreutzberg, 1996). Despite ontogenetic dissimilarities (Ginhoux et al., 2010), microglia are broadly viewed as CNS counterparts to peripheral monocytes and macrophages. Experimental evidence from adult models show that brain injury rapidly activates microglia and lead to increased phagocytic activity and altered production of cytokines and reactive oxygen metabolites (Hanisch, 2002), features that are also well documented in neonatal HI (Hedtjärn et al., 2004). In the adult brain there is also a considerable contribution of infiltrating peripheral immune cells to the brain after strokelike injury (Iadecola and Anrather, 2011). In contrast, little infiltration of peripheral cells is seen acutely after neonatal stroke (Denker et al., 2007), however, it remains unclear to what extent peripheral immune cells contribute to the inflammatory response after neonatal hypoxia-ischemia .
Early studies identified cytokines capable of inducing proinflammatory (classical) or anti-inflammatory (alternative) activities in macrophage cultures. Classically activated macrophages are commonly associated with the expression of surface antigen cluster of differentiation (CD) 86 and the expression of inducible nitric oxide synthase (iNOS) and pro-inflammatory cytokines including interleukin (IL) 1 and tumor necrosis factor alpha (TNF-α). Alternatively activated cells instead express CD206 and arginase 1 and have an enhanced production of anti-inflammatory cytokines (e.g., IL-4 and IL-10) and factors facilitating resolution of inflammation, immunomodulation, angiogenesis, and wound healing (Mantovani et al., 2004). Similarly, polarized pro-and anti-inflammatory phenotypes were demonstrated in cultured microglia in response to specific cytokine stimuli (Chhor et al., 2012). However, microglia phenotype expression patterns are age and region dependent (Scheffel et al., 2012;Grabert et al., 2016) and recent studies suggest a considerable overlap and complex pattern of activation states (Murray et al., 2014), which may be particularly apparent in vivo.
Galectin-3, a β-galactoside-binding lectin, is important for the regulation of alternative activation in macrophages (MacKinnon et al., 2008) and its expression is induced in microglia by antiinflammatory cytokines (IL-4/IL-10) and repressed in response to pro-inflammatory stimulation (LPS) in vitro (Chhor et al., 2013). Microglia express galectin-3 after ischemic injury in adult and neonatal brain (Walther et al., 2000;Doverhag et al., 2010) and in the adult brain galectin-3 is associated with protective IGF-1-expressing microglia after stroke (Lalancette-Hébert et al., 2007). However, galectin-3 is also a strong chemoattractant for monocytic cells (Sano et al., 2000), induces production of proinflammatory cytokines and we have previously demonstrated that galectin-3 contributes to neonatal HI injury (Doverhag et al., 2010). Galectin-3 is thus of specific interest in the polarization and modulation of microglia phenotypes following HI injury.
In this study we induced HI in postnatal day (P) 9 mouse pups, an age equivalent to the near term human infant with respect to brain developmental stage (Craig et al., 2003). We investigated the temporal expression of genes previously associated in vitro with classical and alternative polarization phenotypes and used well-defined macrophage cell-surface CD antigens to identify specific phenotypes within the CD11b + population (general microglia/macrophage marker) in the brain following neonatal HI. Finally, to explore the role of the immunomodulatory factor galectin-3 in polarization of CD11b + cells after HI, we characterized the expression of galectin-3 in different post-HI cell populations in the brain.
Animals
Pregnant C57BL/6 mice were sourced from Charles River Laboratories International (Sulzfeld, Germany). Lys-enhanced green fluorescent protein (EGFP)-ki mice were obtained from Dr. Tomas Graf, Autonomous University of Barcelona. Animals were housed at the Laboratory for Experimental Biomedicine at University of Gothenburg under specific pathogen free conditions on a 12 h light/dark cycle with ad libitum access to standard laboratory chow (B&K, Solna, Sweden) and water.
Hypoxic-Ischemic Brain Injury Model
Hypoxic-ischemic (HI) brain injury was induced in P9 mice (of both sexes) based on methods developed by Rice et al. (1981), with some modifications for mice (Doverhag et al., 2010). In brief, mice were anesthetized with isoflurane in a 1:1 oxygen and nitrous oxide mix and the left common carotid artery was permanently ligated with a 6-0 prolene suture. Mice were returned to their home cage for 1 h of recovery and then transferred to a temperature regulated incubator for a 50 min period of hypoxia (36 • C, 10% O 2 ). The HI insult result in injury in the ipsilateral (ipsi) hemisphere, typically in the cortex, hippocampus and striatum, while there is no morphological injury in the contralateral (contra) hemisphere as previously reported by our group (Svedin et al., 2007). Sham-operated animals were not exposed to artery ligation and hypoxia.
Reverse Transcription and qRT-PCR
Mice were deeply anesthetized and transcardially perfused with ice-cold 0.9% saline. Brains were rapidly removed, hemispheres separated, and snap-frozen on dry ice before being stored at −80 • C. Total RNA was isolated using an RNeasy Lipid Tissue Mini Kit (Qiagen, Sollentunna, SE) in accordance with the manufacturer's instructions. RNA concentration was measured using a NanoDrop 1000 spectrophotometer (NanoDrop, Wilmington, USA) and RNA quality was determined by Experion Chip RNA analysis (BioRad, Solna, SE) (RQI value 8-10 for all samples). Reverse transcription was performed in duplicate using a QuantiTect Reverse Transcription Kit (Qiagen). qRT-PCR was performed on a Roche LightCycler480 (Roche, Bromma, SE) using a QuantiFast SYBR Green PCR kit (Qiagen) with the following cycling protocol: 10 s denaturation at 95 • C followed by 30 s annealing/extension at 60 • C for 40 cycles. All primers were purchased from Qiagen (Table 1) and amplification specificity was confirmed by melting curve analysis. Relative quantitation was performed in accordance with the standard curve method and expression values were normalized to the reference gene glyceraldehyde 3-phosphate dehydrogenase (GAPDH).
Immunohistochemistry
Animals were deeply anesthetized and transcardially perfused with ice-cold 0.9% saline followed by buffered 6% formaldehyde (Histofix; Histolab, Gothenburg, Sweden). Brains were rapidly removed, post-fixed for 24 h at 4 • C, cryoprotected in 30% sucrose, and sectioned at 25 µm on a Leica CM3050 S cryostat (Leica, Sweden). Non-specific antibody binding sites were blocked through a 30 min room temperature incubation in TBS containing 3% donkey serum and 0.1% Triton X-100 (hereafter referred to as blocking buffer). Sections were then incubated overnight at 4 • C with the following primary antibodies diluted in blocking buffer: rabbit anti-ionized calcium binding adapter molecule 1 (Iba1) (1:1000, cat. Images were captured on a Zeiss Laser Scanning 700 inverted confocal microscope equipped with Zen Black control software (Zeiss, Oberkochen, DE) and processed using Velocity (Perkin-Elmer). Figures were compiled using Adobe CS6 (Adobe, Kist, SE).
Fluorescence-Activated Cell Sorting (FACS)
Sham-operated and HI animals were deeply anesthetized and sacrificed via decapitation at 24 h, 72 h, and 7 days after surgery. Brains were rapidly removed, hemispheres separated, and transferred to ice-cold Hibernate-A (Invitrogen). In order to generate sufficient material for downstream analysis, corresponding hemispheres from two animals were pooled.
Galectin-3 Protein Analysis
Cell pellets were lysed using a Bio-Plex Cell Lysis Kit (BioRad) in accordance with manufacturer's instructions. Briefly, lysing solution was added and cells resuspended by repeated pipetting before agitation on a microplate shaker (150 rpm, 4 • C, 15 min). Samples were then centrifuged (4000 g, 10 min) and supernatants collected and stored at −20 • C. Protein concentration was measured using a Pierce BCA Protein Assay Kit (Thermo Scientific) as outlined in the manufacturer's instructions. Galectin-3 protein was measured using a Galectin-3 enzymelinked immunosorbent assay (ELISA) Kit (cat. no 12727, BG Medicine). Data is presented as total amount target protein per ml (pg/ml) or as normalized to protein concentration and presented as pg target protein per µg total loaded protein. Sample values falling below the lower limit of detection were substituted with the manufacturer stated lower detection limit divided by the square root of 2.
Statistical Analyses
All data are presented as group mean ± SEM. Data from males and females were combined in each group as breakdown by sex revealed no sex-specific expression of any of the markers analyzed. qRT-PCR and FACS data were assessed by two-way analysis of variance (ANOVA) followed by Tukey's multiple comparisons test. Galectin-3 protein concentrations over time were assessed by Kruskal-Wallis followed by Dunn's multiple comparison test for each cell population vs. sham. Differences were considered significant at * p ≤ 0.05; * * p ≤ 0.01; * * * p ≤ 0.001. Analyses were performed using Prism (Graphpad, v.6.05)
Neonatal HI Induces Rapid Expression of Genes Associated with Classical and Alternative Activation
Using total cortical homogenates we performed a qRT-PCR assessment of temporal expression profiles of genes associated with classical activation (CD86, IL-6, IL-1β, Cox2, iNOS) and alternative activation (CD206, IL-10, Fizz1, Arg1) in macrophages, as well as the immunomodulatory factor galectin-3 (Gal3) following HI (Figure 1). For all genes examined there was a significant interaction between expression in the ipsior contralateral hemisphere and with time, except for CD206 and iNos (Supplementary Table 1). Post-hoc analysis revealed acute regulation in the ipsilateral hemisphere compared with the contralateral hemisphere of genes associated with classical activation: CD86 (4.0-fold; p < 0.001), IL-6 (8.6-fold; p < 0.001), IL-1β (46.3-fold; p < 0.001); as well as genes associated with alternative activation: IL-10 (6.0-fold; p < 0.001), Fizz1 (2.1-fold; p < 0.001), Arg1 (4.3-fold; p < 0.001) at 6 h after HI, with no significant regulation at later time points. Enhanced expression of the immunomodulatory gene Gal3 could be detected at 6 h (7.0-fold; p < 0.001) and 24 h (2.4-fold; p < 0.05) after HI. The genes Cox2, iNos, and CD206 displayed no significant differences between contralateral and ipsilateral hemispheres at any of the time points investigated.
Different CD11b + Cell Subpopulations Are Present in the Injured Hemisphere after Hypoxia-Ischemia
Having observed acutely elevated expression of inflammationassociated genes in the ipsilateral hemisphere, we next asked how the composition of microglia/macrophages in the brain may be regulated in response to HI. We employed FACS analysis to assess the total number of CD11b + cells and to characterize cell phenotypes within this population at different time points after HI. Cells were characterized by a stepwise gating strategy based on methods described by Bedi et al. (2013). This facilitated FIGURE 1 | Expression of pro-and anti-inflammatory genes following neonatal hypoxia-ischemia. Expression of genes associated with classic activation (CD86, IL-6, IL-1β, Cox2, iNOS; A-E), alternative activation (CD206, IL-10, Fizz1, Arg1; F-I), and immunomodulatory (Gal3; J) was measured by qRT-PCR at 6, 24, 72 h, and 7 days in the contralateral (C) and ipsilateral (I) hemisphere after HI. Values are presented as mean ± SEM. Analysis by two-way ANOVA followed by Tukey's multiple comparisons test between ipsilateral and contralateral hemispheres; n ≥ 10 per group; *p ≤ 0.05, ***p ≤ 0.001.
There was an interaction between hemisphere and time after HI that determined the ratio of different cell subtypes (Supplementary Table 3). In the ipsilateral hemisphere, the CD11b + CD86 + CD206 − population, in relative terms, was the dominant cell type at 24 h after HI constituting 56% of the total number of CD11b + cells, compared to 7% in the contralateral hemisphere (ipsi 56.4 ± 2.4% vs. contra 7.2 ± 1.1%, p < 0.0001, Figure 2I). At 72 h post-injury, 35% of the CD11b + cells in the ipsilateral hemisphere were CD86 + CD206 − , compared to 5% in the contralateral hemispheres (ipsi 35.1 ± 1.2% vs. contra 4.8 ± 0.3%, p < 0.0001). At 7 days post-HI, the percentage of this cell population in the ipsilateral hemisphere was reduced compared to levels at 24 h post-injury, yet remained 2.5-times higher compared to the contralateral hemisphere (ipsi 24.4 ± 0.9% vs. contra 10.0 ± 0.9%, p < 0.0001).
The proportion of CD11b + CD86 +/− CD206 + cells never exceeded 8% of the total CD11b + population, in either the contra-or ipsilateral hemisphere, at any time point examined. Despite an early increase in absolute numbers (Figure 2G), the percentage of CD11b + CD86 +/− CD206 + cells was reduced in the ipsilateral compared to the contralateral hemisphere, at 24 h (ipsi 3.2 ± 0.2% vs. contra 5.7 ± 0.7%, p < 0.01, Figure 2J). By 3 days post-injury the CD11b + CD86 +/− CD206 + population in the ipsilateral hemisphere had approximately assumed the same relative size as in the contralateral hemisphere ( Figure 2J).
Identification of Microglia/Macrophage Phenotypes by Immunohistochemistry
The presence of different cell phenotypes was confirmed by confocal analysis on immuno-stained histological sections. Cells, expressing Iba-1 (microglia/macrophage marker), but neither CD86 nor CD206, were readily observed in injured areas ( Figure 3A) as well as in the contralateral hemisphere (data not shown). Iba-1 positive cells with strong expression of CD86 were also found in the ipsilateral hemisphere ( Figure 3A). In white matter areas, such as the corpus callosum (Figure 3B), Iba-1/CD206-positive cells were noted adjacent to Iba-1 positive cells clearly expressing both CD206 and CD86. Interestingly, Iba-1 positive cells expressing CD206 only, were mainly found in the meninges (Figure 3C) or the contralateral hemisphere (data not shown).
Galectin-3 Is Primarily Expressed in CD11b + Cells That Lack CD86 and CD206 after Hypoxia-Ischemia
To evaluate immunomodulatory properties of the different cell populations we investigated the protein expression of galectin-3 in lysates of FACS-sorted cell populations. Considering the marked changes in cell numbers of the different populations after HI, we analyzed both changes in protein expression in the total cell populations (pg/mL; reflecting the overall contribution of each cell population, Figure 4A) as well as corrected for protein content (pg/µg protein, Figure 4B) to represent the protein expressed per cell. Galectin-3 expression was upregulated in several cell populations ( Figure 4B) with significant changes observed at 24 h (942.1%; p < 0.001) and at 72 h (790.9%; p < 0.001) in the CD11b + CD86 − CD206 − cell population. In CD11b + CD86 + CD206 − cells, increased galectin-3 expression was detected at 7 days (371.4%; p = 0.0413) and in CD11b + CD86 +/− CD206 + cells at 72 h (623.3%; p = 0.0015). When investigating the protein expression in the total cell populations (pg/mL), CD11b + CD86 − CD206 − cells were the main source of increased galectin-3 protein in the injured hemisphere at all three time points (Figure 4A).
Immunohistochemical Identification of Galectin-3 in Microglia with Low CD86 and CD206 Expression
To validate galectin-3 levels measured by ELISA relative to phenotypic markers in vivo, we conducted confocal microscopic examination on histological sections stained for galectin-3, CD86 and CD206 (Figure 5). Tile scanned photomicrographs of whole brain sections 24 h after HI revealed robust galectin-3 immunoreactivity in typically injured brain regions in FIGURE 4 | Galectin-3 protein expression in different CD11b + cell populations following neonatal hypoxia-ischemia. Hypoxia-ischemia (HI) was induced in P9 mice and animals were sacrificed at 1, 3, and 7 days post HI. Brain hemispheres were processed into single cell suspension, stained with antibodies against CD11b, CD86, and CD206 and sorted by FACS. Galectin-3 protein expression was determined in lysates of sorted cell populations by ELISA. Sham operated animals (white bars), ipsilateral hemisphere in CD11b + CD86 − CD206 − cells (light gray bars), ipsilateral hemisphere in CD11b + CD86 + CD206 − cells (dark gray bars), ipsilateral hemisphere in CD11b + CD86 + / − CD206 + cells (almost black bars). Protein concentrations expressed as target protein concentration per ml (A) and as concentration of target protein per cell (B). Statistical comparisons were made using Kruskal-Wallis followed by Dunn's multiple comparison test for each cell population vs. sham. *p < 0.05, **p < 0.01, ***p < 0.001. n = 6-7 animals/group. the ipsilateral hemisphere, including cortical regions and the striatum, with staining absent from the contralateral hemisphere ( Figure 5A). In line with our ELISA results displaying increased galectin-3 expression particularly in CD11b + CD86 − CD206 − cells at 24 h after HI, confocal examination of individual cells in the ipsilateral cortex showed that strongly galectin-3 positive cells expressed low levels of CD86 and CD206 immunoreactivity ( Figure 5B). These galectin-3 immunoreactive cells displayed amoeboid or hypertrophic but not highly ramified morphologies. In contrast, classically and alternatively polarized cells that were more strongly immunoreactive for CD86 and CD206, generally displayed a low level of galectin-3 staining ( Figure 5B).
By using Lys-EGFP-ki mice, that express EGFP in peripheral myeloid cells but not in microglia (Faust et al., 2000), we were able to determine that the cells expressing galectin-3 were mainly resident microglia (Figure 6).
DISCUSSION
In this study we investigated the applicability of using classical and alternative activation characterization of cerebral microglia/macrophages to the context of neonatal HI brain injury. We demonstrate that neonatal HI caused a rapid and transient increase in the mRNA levels of genes related to both pro-and anti-inflammatory phenotypes within the first 24 h after the initial insult. Using classical macrophage CD antigens as markers for classical and alternative activation, we identified three major CD11b + cell populations in the brain by FACS analysis; cells expressing predominantly CD86 or CD206, and a cell population that lacked CD86 and CD206 expression. A dramatic expansion of the CD86 positive cells in the ipsilateral hemisphere was observed at 24 h after HI. In contrast, although increasing in real numbers, the relative proportions of CD206 + cells or cells lacking both CD86 and CD206 expression were reduced after injury. Using immunohistochemistry, we were able to identify Iba-1 positive cells with predominantly CD86 or CD206 staining, but the CD206 positive cells frequently coexpressed CD86 in injured areas while cells expressing CD206 only were mainly found in meninges or uninjured areas. Interestingly, protein expression of the immunomodulatory protein galectin-3 was markedly increased in cells that lacked CD86 and CD206 and this novel finding suggest that the population of these "non-polarized" cells may be important for immune responses in the injured neonatal brain.
It is well understood that macrophages and microglia can adopt distinct pro-and anti-inflammatory phenotypes in response to specific polarizing stimuli in vitro (Stein et al., 1992;Gordon, 2003;Chhor et al., 2013). However, the degree to which such distinct inflammatory phenotypes exist in the complex inflammatory environment of the injured CNS is less clear. Studies investigating expression of genes associated with different activation stages in the mouse middle cerebral artery occlusion (MCAO) stroke model have suggested rapid, yet transient, induction of genes associated with alternative activation followed by a later, yet sustained, induction of genes associated with classical activation (Hu et al., 2012). This data is in contrast to our observation of rapid and transient induction of genes associated with both classical (CD86, IL-6, and IL-1β), as well as alternative (IL-10, Fizz1, Arg1, and IL-10) activation followed by return to baseline expression at 24 h post HI. However, our results are in line with previous investigations in neonatal rodent HI models, which reported peak induction of IL-1β and TNF-α at 12 h after HI (Bona et al., 1999) or upregulation of IL-1β and IL-10 at 3 h (Bonestroo et al., 2013), suggesting that the inflammatory response to injury differ in the neonatal brain compared to the adult.
Although useful in supplying information about the general inflammatory response in the brain, examination of whole hemispheric gene expression fails to address the phenotypic composition of the microglia/macrophage pool. In order to address these issues we employed FACS to characterize and isolate CD11b + cells based on their differential expression of CD86 and CD206, both well characterized markers of different activation phenotypes in vitro (Stein et al., 1992;Chhor et al., 2013). This approach allowed identification of three major CD11b + cell populations: the CD86 − CD206 − and the CD86 + CD206 − populations were largely homogenous, while the cells positive for CD206 were more heterogeneous. Based on previously well-established gating strategies (Bedi et al., 2013), these cells were defined by their expression of CD206 but included cells also expressing CD86 antigens. Such findings are not without precedent in the adult brain: flow cytometry studies have displayed co-expression of CD206 and the pro-inflammatory marker major histocompatibility complex class II (MHCII) in the intact CNS (Li et al., 2014), and CD206 + /FcγRII/III + cells have been detected in a mouse model of traumatic brain injury (Bedi et al., 2013). In addition, immunohistological interrogation of HLA-DR + foamy macrophages in active human multiple sclerosis lesions indicated that 70% display co-immunoreactivity for CD206 and the pro-inflammatory marker CD40 (Vogel et al., 2013). Further, our previous in vitro work with microglia using these markers supports the complexity of our in vivo observations. We observed that even using pro-typical inducers of classic and alternative activation (LPS & IL-4), the expression of CD86 and CD206 could not be used to discriminate between these two polarization states at all time points (from 4 to 72 h postexposure) (Chhor et al., 2013). Interestingly, using inducerswitching experiments, we also demonstrated that expression of these two markers is significantly altered by previous activation suggesting that over time in vivo microglia might be primed by the complex milieu of cytokines and chemokine in the local micro-environment modulating the expression patterns observed. In our model, immunohistochemistry revealed that the cell populations expressing CD206 only or CD206 as well as CD86 were distinctly different regarding location. We identified a small population of "pure" CD206 + cells, which was frequently observed in the meninges. These cells have previously been identified and described as "non-parenchymal macrophages" (Galea et al., 2005). Further, we found single CD206-expressing cells in the contralateral hemisphere, as well as in sham-operated animals, consistent with the hypothesis that some microglia possess an alternative activation-like phenotype in the intact CNS (Ponomarev et al., 2007). The presence of a "mixed" population expressing both CD206 and CD86, particularly in the cerebral white matter, as well as a large population of seemingly nonpolarized cells (lacking both CD86 and CD206 expression) also illustrates the complexity of the cellular response in the brain in vivo. Taken together, our data suggest that the traditional classic vs. alternative activation classification scheme oversimplifies the concept of distinct inflammatory cell phenotypes in the brain in vivo, which is also being recognized by the macrophage research field (Murray et al., 2014;Nahrendorf and Swirski, 2016).
Within the first 24 h after HI all three cell populations increased in the injured hemisphere with the largest expansion seen for cells expressing CD86. This population dominated in the HI hemisphere, and although both the total number and the proportion of these cells steadily decreased with time after injury the total number of cells was still elevated at 7 days in the ipsilateral compared to contralateral hemisphere. Concomitant with this, cell populations expressing CD206 or lacking both CD86 and CD206 constituted a relatively smaller proportion of cells for several days after HI, despite their increase in absolute numbers. Studies of adult spinal cord injury (Kigerl et al., 2009) and MCAO (Hu et al., 2012) have suggested a gradual increase in both classically and alternatively activated microglia in the first days after insult, with the presence of classically activated microglia continuing to increase up to 28 days, whilst the alternative activation response appeared transient with numbers peaking at 5-7 days and decreasing gradually thereafter. Thus, our findings suggest differences in neonatal and adult CNS immune responses to injury.
A novel finding in this study is that the cell population lacking CD86 and CD206 expression was the major contributor of galectin-3 protein expression after HI. In support, immunohistochemical analysis showed that cells with the highest galectin-3 staining intensity expressed little CD86 or CD206 activation markers, yet exhibited the amoeboid appearance associated with activated phenotypes. These results further emphasize the inadequacy of using CD86 and CD206 as markers of microglia/macrophage activation. Galectin-3 is an immunomodulatory factor that is involved in activation and polarization of inflammatory cells, probably by inducing pro-inflammatory cytokines (Jeng et al., 1994) and the release of oxygen free radicals (Karlsson et al., 1998). Galectin-3 expression in microglia is increased in response to the pro-typical alternative activation inducer IL-4 in vitro (Chhor et al., 2013) and it has been suggested that galectin-3 is essential for polarization through a feed-back loop initiated by IL-4 (MacKinnon et al., 2008). Our results demonstrate galectin-3 to be strongly upregulated in response to injury. It is presently unknown to what extent peripheral monocytes/macrophages may contribute to cellular immune responses after neonatal HI . Our data suggest that there is some degree of infiltration of myeloid cells as indicated by the presence of EGFP positive cells in the brain after HI. However, few of the EGFP positive cells expressed galectin-3, suggesting that galectin-3 is mainly expressed by microglia. Potentially, these cells may be important in attracting and priming cells to additional stimuli and thus modulating the inflammatory response, which appears to be critical for development of brain injury according to previous work (Doverhag et al., 2010).
CONCLUSIONS
We have shown a dynamic expression pattern of pro-and antiinflammatory mRNA in the brain after neonatal HI. CD11b + cells that express the CD86 surface antigen, which has been associated with classical activation of macrophages, dominated in the injured brain during the first days after HI. Cells expressing antigen associated with alternative activation (CD206) demonstrated a similar expansion over time, but with a smaller magnitude of the increase resulting in a relative suppression of this cell type. The CD206 expressing cells were heterogeneous and there were cells expressing CD206 as well as CD86, thus illustrating the complexity of the cellular immune response in the brain after injury. A novel finding is that a large population of CD11b + cells in the brain after neonatal HI is "nonpolarized" with regard to classical activation markers CD86 and CD206, but express high amounts of the immunomodulatory factor galectin-3. We speculate that this population may be important for attracting cells to injured areas and could be involved in modulation of the post-injury inflammatory response.
ETHICS STATEMENT
All animal experiments were conducted in accordance with regulations and general guidelines of the Swedish Board of Agriculture (Sweden) and were approved by the regional Gothenburg Animal Ethics Board (No. 374/09 and 139/13). | 7,126 | 2016-12-15T00:00:00.000 | [
"Biology",
"Medicine"
] |
Spectral Shaping Based via Integrated Coupled Sagnac Loop Reflectors in a Self-Coupled Nanowire
We propose and theoretically investigate integrated photonic filters based on coupled Sagnac loop reflectors (SLRs) formed by a self-coupled wire waveguide. By tailoring coherent mode interference in the device, three different filter functions are achieved, including Fano-like resonances, wavelength interleaving, and varied resonance mode splitting. For each function, the impact of device structural parameters is analyzed to facilitate optimized performance. Our results theoretically verify the proposed device as a compact multi-functional integrated photonic filter for flexible spectral shaping.
I. INTRODUCTION
ITH a compact footprint, flexible topology, and high scalability, integrated photonic resonators (IPRs) have enabled diverse functional optical devices such as filters, modulators, sensors, switches, and logic gates [1,2]. As compared with IPRs based on subwavelength gratings [3] and photonic crystal structures [4] that have submicron cavity lengths, IPRs formed by directional-coupled wire waveguides with longer cavity lengths (typically > 10 μm) have smaller free spectral ranges (FSRs) that match with the spectral grids of the state-of-the-art wavelength division multiplexing (WDM) optical communication systems, thus rendering them more widely applicable to these systems. Moreover, the directional-coupled wire waveguides with longer coupling regions and simpler designs also yield a higher tolerance to fabrication imperfections.
Generally, there are two types of basic building blocks for IPRs formed by directional-coupled wire waveguides. The first is a ring resonator, and the second is a Sagnac loop reflector (SLR). In contrast to ring resonators that involve only unidirectional light propagation, the SLRs allow bidirectional light propagation as well as mutual coupling between the light propagating in opposite directions, thus yielding a more versatile coherent mode interference and spectral response. In addition, a standing-wave (SW) resonator formed by cascaded SLRs has a cavity length almost half that of a travelling-wave (TW) resonator based on a ring resonator with the same FSR, which allows for a more compact device footprint.
Here, we advance this field by introducing the novel approach of using coupled SLRs formed by a self-coupled wire waveguide. This allows us to achieve versatile spectral responses with a simpler design and a higher fabrication tolerance. We tailor the coherent mode interference to achieve three different filter functions, including Fano-like resonances, wavelength interleaving, and varied resonance mode splitting. The requirements for practical applications are considered in our design. Excellent performance parameters are achieved for each filter function, analysis of the impact of the structural parameters and fabrication tolerance is also provided. Fig. 1 illustrates a schematic configuration of the proposed structure, consisting of three SLRs formed by a single selfcoupled wire waveguide. The device structural parameters are defined in Table I. To simplify the discussion, we assume that LSLR1 = LSLR2 = LSLR3 = LSLR and L1 = L2 = L. The resonator is equivalent to three cascaded SLRs (which is an infiniteimpulse-response (IIR) filter) when t2 = 1 and a SLR with an interferometric coupler [9] (which is a finite-impulse-response (FIR) filter) when t1 = t3 = 1. When ti (i = 1-3) ≠ 1, this device is a hybrid filter consisting of both IIR and FIR filter elements, which allows for versatile coherent mode interference and ultimately a diverse range of spectral responses.
II. DEVICE STRUCTURE
We use the scattering matrix method [5,7] to calculate the spectral response of the device. In our calculation, we assume Table I. a waveguide group index of ng = 4.3350 for transverse electric (TE) mode and a propagation loss of α = 55 m -1 (i.e., 2.4 dB/cm) based on our previously fabricated silicon-on-insulator (SOI) devices [5,6]. The device is designed based on, but not restricted to, the SOI platform.
III. FANO-LIKE RESONANCES
Fano resonances that feature an asymmetric spectral lineshape are fundamental physical phenomena that have underpinned many applications such as optical switching, data storage, sensing, and topological optics [10][11][12]. In this section, the spectral response of the device in Fig. 1 is tailored to realize optical analogues of Fano resonances with high slope rates (SRs) and low insertion loss (IL). The power transmission and reflection spectra with input from Port 1 is depicted in Fig. 2(a-i). The device structural parameters are LSLR = L = 100 µm, t1 = t3 = 0.82, t2 = 0.92, and t4 = 1. Clearly, the output from Port 2 shows periodical Fano-like resonances with an asymmetric resonant lineshape in each period. The high uniformity of the filter shape across multiple periods, or channels, is highly desirable for WDM systems. A zoom-in view of Fig. 2(a-i) is shown in Fig. 2(a-ii), together with another curve showing the corresponding result for another device with the same structural parameters except for a different t2 = 1. As can be seen, when t2 = 1, there is no Fano resonance, distinguishing between the device in Fig. 1 and the three cascaded SLRs in Ref. [5]. The Fano resonances in Fig. 2(a-ii) show a high extinction ratio (ER) of 30.2 dB and a high SR (defined as the ratio of the ER to the wavelength difference between the resonance peak and notch) of 747.64 dB/nm. Table II compares the performance of the Fano-like resonances generated by the coupled SLRs in our previous work [7,8] and the device in Fig. 1. As compared with previous devices, the device reported here has a much lower insertion loss of 1.1 dB, along with a slightly improved SR. We note that a low IL of 1.1 dB is outstanding among the reported Fano-resonance devices on the SOI platform [13,14], a ai = exp(-αLi / 2), asi = exp(-αLSLRi / 2), α is the power propagation loss factor. b φi = 2πngLi / λ, φsi = 2πngLSLRi / λ, ng is the group index and λ is the wavelength. c tsi 2 + κsi 2 = 1 and tbi 2 + κbi 2 = 1 for lossless coupling are assumed for all the directional couplers. which renders the device here more attractive for practical applications in optical communication systems.
In Figs. 2(b)-(e), we investigate the impact of the device structural parameters including ti (i = 1-4) and length variations of the feedback loop (∆LFL, LFL = 2L + LSLR), respectively. In each figure, we changed only one structural parameter, keeping the others the same as those in Fig. 2(a-i). Figs. 2(b-i) and (b-ii) compares the power transmission spectra and corresponding IL and SR for various t1 or t3, respectively. The SR decreases with ti (i = 1, 3), while the IL first decreases with ti (i = 1, 3) and then remains almost unchanged. The spectral response and corresponding IL and SR for different t2 are shown in Figs. 2(c-i) and (c-ii), respectively. The SR decreases with t2, while the IL shows an opposite trend, reflecting that both of the two parameters can be improved by enhancing the coupling strength between SLR1 and SLR2. As shown in Fig. 2(d), both IL and SR remain almost unchanged with varied t4. In Figs. 2(e-i) and (e-ii), we compare the corresponding results for various ΔLFL. As ΔLFL increases, the filter shape remains unchanged while the resonance redshifts, indicating that the resonance wavelengths can be tuned by introducing thermo-optic micro-heaters [14] or carrierinjection electrodes [15] along the feedback loop to tune the phase shift.
IV. WAVELENGTH DE-INTERLEAVING
Optical interleavers and de-interleavers are core elements for signal multiplexing and demultiplexing in WDM optical communication systems [16,17]. In this section, we engineer the spectral response of the device in Fig. 1 to achieve wavelength de-interleaving function. Fig. 3(a) shows the power transmission and reflection spectra with input from Port 1. The device structural parameters are LSLR = L= 100 µm, t1 = 0.992, t2 = t3 = 0.95, and t4 = 1. The input signal is separated into two spectrally interleaved signals, with one group transmitting to Port 2 and the other reflecting back at Port 1. The IL, ER, and 3-dB bandwidth for the passband at Port 2 are 0.36 dB, 12.7 dB, and 83.65 GHz, respectively. The IL, ER, and 3-dB bandwidth for the passband at Port 1 are 0.33 dB, 12 dB, and 91.9 GHz, respectively.
We also investigate the impact of varied ti (i = 1-4), ΔLFL, and ∆LSLRi (i = 1, 2) in Figs. 3(b)-(h), respectively. For simplification, we only show the spectral response at Port 2. In Fig. 3(b), as t1 increases, the ER of the passband decreases while the top flatness improves, reflecting the trade-off between them. In Figs. 3(c)-(e), the bandwidth of the passband increases with t2, t3, t4, respectively, while the ER shows an opposite trend. In Figs. 3(f)-(h), as ΔLFL or ∆LSLRi (i = 1, 2) increases, the filter shape remains unchanged while the resonance redshifts, indicating the feasibility of achieving tunable de-interleavers with this approach. Since the resonant cavity of the device is formed by a single self-coupled wire waveguide, random length fabrication errors in each part will not induce any asymmetry in the filter shape. This yields a higher fabrication tolerance as compared with the coupled SLRs in Refs. [7,8], which is particularly attractive for optical interleavers that require a flat-top symmetric filter shape. Note that the de-interleaving function is designed for the telecom C band. According to our previous fabricated devices [17], the slight variation in ti (i = 1-4) arising from the dispersion of silicon would not significantly deteriorate the periodical response across this wavelength range.
V. VARIED RESONANCE MODE SPLITTING
Resonance mode splitting in IPRs induced by coherent mode interference can yield a range of highly useful spectral responses, including electromagnetically induced transparency (EIT), electromagnetically induced absorption (EIA), and Autler-Towns splitting, which have been used for applications such as optical buffering, signal multicasting, analog signal computing, and sensing [9,18,19]. In this section, we tailor the spectral response of the device in Fig. 1 to achieve varied resonance mode splitting with diverse spectral response.
Figs. 4(a) and (b) shows the power transmission and reflection spectra for various t4, respectively. The input is from Port 1 and the structural parameters are LSLR = L= 100 µm, t1 = t3 = 0.825, and t2 = 0.99. As can be seen, by increasing the coupling strength of the directional coupler in SLR3 (i.e., reducing t4), the single resonance is gradually split into two resonances with an increased spectral range between them. This is a typical phenomenon for resonance mode splitting similar to those in Ref. [9]. The energy coupling between the light propagating in opposite directions can be changed by varying the reflectivity of SLR3, thus resulting in different mode splitting degrees. Figs. 4(c) and (d) show the power transmission spectrum and group delay response of a Butterworth filter and a Bessel filter formed by resonance mode splitting, respectively. The structural parameters are the same as those in Fig. 4(a) except for a different t4. As shown in Fig. 4(e), the Butterworth filter shape gradually transits to a Chebyshev Type I filter shape by further decreasing t1 or t3. In Fig. 4(f), we compare the spectral response for various t2. It can be seen that more significant resonance mode splitting can be obtained by enhancing the coupling strength between SLR1 and SLR2 (i.e., reducing the t2). In particular, when t2 = 1 (which corresponds to three cascaded SLRs), the resonance is still not split, this indicates that the device reported here shows a significantly enhanced resonance mode splitting as compared with the three cascaded SLRs in Ref. [5]. Finally, this work could have applications to nonlinear devices [20][21][22][23][24][25][26][27][28][29][30] as well as to microwave photonic chips and integrated quantum optics [64-] where advanced optical filter shapes are extremely useful.
VI. CONCLUSIONS
We theoretically investigate integrated photonic filters based on coupled SLRs formed by a self-coupled wire waveguide. Three different filter functions have been realized, including Fano-like resonances, wavelength interleaving, and varied resonance mode splitting. The compact footprint, versatile spectral responses, and high fabrication tolerance make this approach highly promising for flexible spectral shaping in a diverse range of applications.
Competing interests: The authors declare no competing interests. | 2,791.6 | 2021-04-19T00:00:00.000 | [
"Physics",
"Engineering"
] |
A framework to predict the load-settlement behavior of shallow foundations in a range of soils from silty clays to sands using CPT records
Using a set of cone penetration test (CPT) records, the current paper develops a general framework based on regression analyses to model the load-settlement (q-s) behavior of shallow foundations resting on a variety of soils ranging from silty clays to sands. A three-parameter hyperbolic function is employed to rigorously examine the obtained q-s curves and to determine the model parameters. Also, the results of some CPT soundings, including the corrected cone tip resistance (qt) and the skin friction (Rf), are adopted to predict the results of plate load tests (PLT). The findings corroborate the high accuracy of the proposed model, the reasonable performance of the hyperbolic function and the use of the Volterra series to predict the q-s curves. Moreover, the obtained curves from the newly developed model are compared to those from other methods in the literature which cross-confirms the efficacy of the current model. A sensitivity analysis is also conducted, and the exclusive effects of all the contributing parameters are assessed among which Rf is shown to be the most influential. Ultimately, simple solutions are adopted to determine various key geotechnical parameters, like the ultimate bearing capacity (qult), the allowable bearing capacity (qa) and the modulus of subgrade reaction (ks).
Introduction
Load-settlement (q-s) behavior of soils is commonly investigated by the plate load test (PLT) through which the ultimate bearing capacity (q ult ) and allowable bearing capacity (q a ) of shallow foundations are determined. As a result of PLT, the settlement (s) value is measured against the specified applied pressure (q), which consequently provides the basic geotechnical properties required for the design of shallow foundations. Based on the PLT results, different criteria have been suggested to compute q ult from the q-s curves. In the study performed by Kulhawy (2004), the loading corresponding to the settlement/width ratio of 0.1 ( s B ¼ 0:1) was proposed to be q ult , for all soil types except the sensitive clays, where the loading associated with s B ¼ 0:04 introduces q ult . The mentioned criterion is well-known and distinguished in European standard (Amar et al. 1998).
One of the consequential benefits from q-s curves is the determination of the modulus of subgrade reaction (k s ), which is simply acquired from dividing the applied pressure by the corresponding settlement (k s ¼ q s ). k s can be suggested based on the allowable settlement associated with different types of foundations, including shallow footings and mat foundations, and according to various standards in different countries. It can also be suggested as the slope of the initial tangent line to the load-settlement curve at zero settlement; yet, this definition is not widely used in geotechnical engineering practice. Generally, the calculation of k s ¼ q s yields more conservative designs in the former method, where it is dependent on the settlement level and is effectively estimated for each specific allowable settlement value. In many previously proposed correlations, like the one presented by Bowles (1996), k s is calculated for the settlement of 1 inch which is simplified as the following relation: where FS is the safety factor, and q a is the allowable bearing capacity. It is worth noting that k s depends on some parameters like the shape and width of foundation as well as the spatial variability of the stiffness/strength parameters of the soil underneath (Mohseni et al. 2018). Vesic (1975) showed different values of k s for foundations having the same sizes and applied pressures. Also, Farouk and Farouk (2014) indicated that the rigidity of the soil-footing system should not be neglected for the determination of k s . In terms of linear elastic models, soil plasticity is ignored, which is the reason why the distribution of k s is anomalous at the edges of the foundation. To allow for such an anomaly, nonlinear models should be employed. Terzaghi (1955) proposed Eq. (2) in order to evaluate the modulus of subgrade reaction of full-sized footings resting on sandy subgrades.
where k sp is the modulus of subgrade reaction from PLT, k sf is the corresponding value for the actual foundation, B p is the plate diameter, and B f is the foundation width. Given the very fact that PLTs are costly and time-consuming, researchers have been recently more inclined to invoke empirical relationships to yield k s , the majority of which are endorsed by in situ tests (Naeini et al. 2018). A variety of field tests, among which the SPT and cone penetration test (CPT) are the most recent common ones, have garnered the attention of researchers to provide experimental correlations for PLT parameters. So far, less attention has been paid to the correlation between the results of PLT and CPT.
CPT is one of the most useful common in situ tests, which can lend itself to the prediction of non-linear soil constitutive parameters, time-dependent stress-strain characteristics and profiling the soil elasto-plastic behavior (Holtz et al. 2011). On the other hands, given the very fact that repeatability is easily achieved in CPT soundings, and also that the accurate stratification and soil layering interpretations are viable with CPT, even in small thicknesses, it is therefore preferred among other common in situ tests (Eslami et al. 2017(Eslami et al. , 2019. Of late, the link between the PLT parameters and those of CPTs has been investigated in two different categories, the first of which is to directly obtain the bearing capacity based on CPT results and the second one is to predict the q-s curves through which q ult can be estimated. In this article, the second category is adopted. The proposed methods and relationships for the determination of the ultimate bearing capacity from CPT results are enlisted in Table 1 in chronological order (Saftner and Dagger 2018).
Deploying CPT results, many researchers have tried to correlate q to the dimensionless parameter, s B , which consequently has resulted in the following general formula (Fellenius and Altaee 1994;Decourt 1999;Briaud 2007).
where q is the footing bearing pressure, s/B is the footing settlement normalized against the footing width B, and a f and b f are the model parameters. Based on Mayne et al. (2012), the value of b f was suggested to be 0.5, and the value of a f for sands was reported to be dependent on the particle size distribution, relative density, geological condition and the percentage of fine grains. Regarding the ultimate bearing capacity criterion for sandy soils, when s B ¼ 0:1, q ult equates to 0.316a f . Based on the theoretical studies conducted by Briaud (2007) and Mayne et al. (2012), Eq. (4) was proposed using 32 q-s data sets on 13 different soil types (note that q c is the cone tip resistance).
Stuedlein and Holtz (2010) assigned 1.77 MPa for a f of the soil known as delta soil, yet it should be noted that the number of the studied data was quite limited. Mayne and Woeller (2014) used q net instead of q c in Eq. (4) and rewrote it as Eq. (5).
where q net is the net cone resistance, q capacity is the foundation bearing capacity of the ground, and h s is the empirical fitting term which was considered to be 0.58, 1.12, 1.47 and 2.7, for sands, silts, crushed (fissured) soils and clays, respectively. It is worth noting that the value of q capacity is approximately close to the maximum value of q in the load-displacement profile (q max ). Mayne (2014) incorporated the soil material index, I c , as an indicative of the type of soil behavior, into the other empirical relationships and proposed a correlation which could predict the q-s trend [Eq. (6)].
Most researchers, who have previously studied the relationship between q-s profiles and CPT results, have confirmed that q is an a priori function of s B À Á 0:5 based on the correlations they have presented whose differences lay solely on the magnification factor. However, the mentioned relationships are open to question as q grows excessively in higher settlements. Their proposed correlations were therefore more acceptable for the values of s B up to 0:1, beyond which they would render unrealistic q values. In this study, an attempt has been made to reconcile this by establishing a novel and more appealing model, which could intrinsically capture the limiting nature of the bearing pressure.
Generally, it should be noted that the q-s curves in this study were obtained from reliable sources including 46 PLTs and their corresponding CPT logs. In the following sections, first, the collected database and the input and A framework to predict the load-settlement behavior of shallow foundations in a range of soils from… 3547 *B is considered as the width and the diameter of the square and circular footings, respectively output variables are explained, and then, the results of the modeling are provided in terms of equations and predicted versus measured trends of q-s. Also, the validation of the proposed hyperbolic function, and the comparison with previous models are discussed and the variations of q ult , q a and k s with CPT parameters are thoroughly elaborated. Finally, sensitivity analysis of the input variables is presented.
Method of analysis
Naturally, in q-s curves, values of the imposed pressure tend to be bounded to two extremes. In the suggested models, two different boundary conditions are expected for the lower extreme (s ! 0) and the higher extreme (s ! þ1), where q tends to 0 and q max , respectively. There are some limitations associated with the previous models, including failure to incorporate the asymptotic behavior at limit settlements (s ! þ1); hence, suggesting the need for simpler models with far superior applicability. It should be noted that the proposed function q ¼ f s ð Þ to fit a PLT load-displacement profile should meet the following conditions: f 0 ð Þ ¼ 0; f 0 0 ð Þ should be the global maximum, and f 0 1 ð Þ % 0 should be satisfied. Therefore, it is deemed that if a function meets the aforementioned criteria and is capable of precise prediction of the q-s curve, it can accurately serve to estimate the q max , q ult , q a and k s parameters, as schematically illustrated in Fig. 1.
Many functions have been proposed to predict the loadsettlement behavior of geo-materials among which the hyperbolic function has been admittedly used effectively in analyzing geotechnical properties, such as predicting the settlement, assessing the compressibility behavior and describing the relationship between the void ratio and effective stress (Al-Shamrani 2005;Sridharan 2006;Zhang et al. 2014;Ahmed and Siddiqua 2016;Soltani et al. 2017). Upon reviewing the literature, to the best of the authors' knowledge, very limited efforts have been devoted to the prediction of the q-s behavior of shallow footings on the basis of CPT records using the hyperbolic function. The hyperbolic function considered in the present paper is given in Eq. (7), which has three constant coefficients.
where a; bandc are the model parameters, which can be obtained from PLT results using regression analysis. Schematic illustration of the proposed hyperbolic model is depicted in Fig. 1 along with the index parameters. As shown in Fig. 1, q max is defined as the horizontal asymptotic of the bearing pressure function, q ult is the value of bearing capacity corresponding to s B ¼ 0:1, q a is the allowable bearing capacity equivalent to the allowable settlement (s a ) and k s is the slope of the line starting at the origin and ending at the arbitrary point with the settlement of s i and the bearing pressure of q i .
CPT strength measurement is based on the soil failure with respect to the cone penetration, which is driven consistently and at a slow pace. Such properties presumably make CPT one of the most viable options among the in situ tests to determine the above-mentioned hyperbolic model parameters. Herein, by adopting some CPT records, a; bandc can be estimated as the main contribution of the current paper that can be suggested from the load-displacement profiles of PLT. In other words, these parameters are linked to q max , q ult , q a and k s (Eqs. (8a) to (8d)).
where a, b and c can be presented as functions of the cone tip and shaft resistances, q c and f s . Therefore, with the CPT records at hand, model parameters a, b and c can be predicted accordingly. By and large, a general model can be established to estimate the q-s profile on the basis of a database containing CPT and PLT results.
It is important to note that the foundation width (B) is also considered in the modeling. To this end, s B has been used to consider the effect of the plate dimension. This makes the settlement dimensionless consistent with previous studies like Mayne and Dasenbrock (2018). Ergo, Eq. (7) is rewritten as follows: Although a, b and c are primarily functions of q c and f s , they are assumed to be functions of q t and R f herein to take the influence of pore water pressure into account. Hence, q t (corrected cone resistance) is defined as: where u 2 is the pore water pressure, and a is the net area ratio of cone tip. Hence, in terms of the dimensional analysis for the hyperbolic model parameters, shown in Eq. (9), the unit of a is kPa, and b and c are both dimensionless. It is worth noting that the effect of embedment depth, D f is reflected in q t in such a way that the more the depth of the foundation, the more effectively it will impact q t . In general, the current study seeks to validate the hyperbolic model and derive a relationship between the model and CPT parameters.
Review of the database
The experimental data employed for the validation of Eq. (9) were gathered from credible sources, including 46 CPT logs and 46 q-s results from PLTs. Furthermore, other parameters like the footing width (B) and embedment depth (D f ) of the PLTs were documented. For CPT data, the depth of 2B has been regarded as the effective zone of load influence, according to the majority of the common methods for the estimation of the settlement beneath the foundation under symmetric loading (Valikhah and Eslami 2019). The parameters acquired from CPT and used in the analyses are the tip resistance q t (q c corrected for pore pressure) and skin friction (R f ¼ f s q c ). The mentioned CPT parameters were introduced in an arithmetic average sense through a depth of 2B so as to reflect the mean soil shear strength (Eslami and Mohammadi 2016). Based on the soil and loading conditions and according to Schmertmann (1978), the effective depth under the foundation is equal to approximately 2B. Table 2 lists the experimental data related to a series of tests performed on a wide range of soil types, from silty clays to sands. The parameter q ult is reported corresponding to s=B ffi 0:1. On the other hands, for any of the q-s curves in different cases, several data points with respect to various settlements were considered as the values for the input parameter, and the amount of pressure was considered as the output. Bar charts of the data are depicted in Fig. 2, where the vertical axis is the relative frequency. As shown in Fig. 2, the data covers a wide range of CPT values, which belong to silty clays and sands.
The main scope of this paper is the examination of the relationships between CPT and load-settlement parameters. It is worth noting that several geotechnical parameters could be estimated from CPT data, as highlighted in a number of previous studies (Eslami et al. 2019).
Hyperbolic model for load-displacement profiles
Based on the presented database, 46 PLTs were selected from the literature whose results were then fitted by the well-established hyperbolic model. The selected data set was compiled from all over the globe and was not restricted to a specific location so as to introduce sufficient diversity. The fitting parameters, including a; bandc, were computed based on the least squares error optimization scheme. Table 3 enlists the parameters for all the 46 cases. Furthermore, absolute fraction of variance (R 2 ), root mean square error (RMSE) and mean absolute deviation (MAD) are defined in Eqs. (11), (12) and (13), respectively, and were exploited herein to assess the fitting accuracy of the relevant correlations.
where q mi and q ci are the measured and calculated pressures, respectively. Lower values of RMSE and MAD (close to zero) and higher values of R 2 (close to one) are indicators of superior model performance. Table 3 corroborates the accuracy of Eq. (9) in replicating the load-displacement trends acquired from PLTs, substantiated in forms of high R 2 and low RMSE and MAD values. To be more specific, the R 2 values have remained higher than 99% and the RMSE and MAD values are lower than 34 and 17 kPa, respectively; hence, bearing witness to the efficacy of Eq. (9). It should be noted that k s0 is the maximum modulus of subgrade reaction, values of q a and k s are corresponding to S B ¼ 0:05, and q max is the asymptotic load. Maximum soil strength means that the soil has reached the failure state or is on the verge of failure. CPT has also the same mechanism with its resistance parameters (R f and q t ) being equivalent to the soil failure state. Based on the experimental and numerical studies, a logarithmic spiral failure mode has been considered for the CPT results of homogenous soils as shown in Fig. 3. According to Eslami and Mohammadi (2016), the failure mechanism of CPT tests is approximately similar to that of shallow foundations. Therefore, it can be observed that the pressure corresponding to the ultimate bearing capacity state or the
Prediction of model parameters from CPT data
With regard to (14) with the objective of reaching a general correlation for the hyperbolic model parameter(s).
To date, various approaches have been adopted to derive a general correlation for a. The aim in this study is to find a viable formulation, which correlates the model parameters in hyperbolic load-displacement model to the CPT data available in the proximity of the PLT location. To this end, the Volterra series is employed, the implication of which is on the basis of GMDH-type neural network (MolaAbasi et al. 2013;MolaAbasi and Shooshpasha 2017). Instead, the core concept of this regression scheme is to invoke genetic algorithm in combination with the multi-layer perceptron numeral networks to find an optimized configuration of hidden layers and neurons to form the polynomial correlation. Herein, the Volterra series is rewritten for the two input variables, including q t and R f , and a single output, a, as Eq. (15): where the parameters a i are constant variables which are obtained from the regression analysis.
To fairly evaluate the efficacy of the proposed model and to compare it with the previous relationships, data were randomly categorized in two groups of training and
Fig. 5 Graphical representation of the accuracy of empirical correlations
A framework to predict the load-settlement behavior of shallow foundations in a range of soils from… 3553 Fig. 6 Comparison of the accuracy of the current study in estimation of the ultimate bearing capacity of shallow footings with other relationships proposed in the literature validation, 70% of which were used for training and the rest were kept for validation. Therefore, 14 out of the total 46 data sets, obtained from the q-s curves, were randomly selected for validation data, and the rest were utilized for the sake of training. In order to equate the ranges of training and validation in the modeling, their statistical parameters, including minimum, maximum and average, were monitored to remain comparable (MolaAbasi et al. 2015; MolaAbasi and Eslami 2018), as enlisted in Table 4. It is evident that the statistical characteristics are in a similar level and are quite close to each other. Aforementioned regression analysis converts Eq. (9) to Eqs. (16a) and (16b). It should be noted that these correlations are based only on the training data and the validation data have not been introduced to the regression process.
a MPa ð Þ¼292:65 À 1026:95R f À 0:008q t þ 964: where q t is the corrected q c and R f is the skin friction. With regard to the proposed roughly simple equation, predicted and measured values can be compared. Cases related to the predicted and measured q-s curves are presented in Fig. 4, which clearly proves that Eq. (16) is a powerful modelling tool, according to the statistical parameters provided in Table 5. Fig. 7 Results of the sensitivity analysis of the input parameters A framework to predict the load-settlement behavior of shallow foundations in a range of soils from… 3555
Comparison with previous models
Given the very fact that the validation data were not incorporated in the model training process, they are used hereinafter for the purpose of comparison with previous methods to elaborate on the aptitude of different models to imitate the load-displacement trends.
To compare the current method with the previous ones, two specific model sets were considered. In the first set, relationships, which predicted q-s curves, including those proposed by Mayne and Dasenbrock (2018), Mayne and Woeller (2014) and Stuedlein and Holtz (2010), were considered and in the second set, correlations proposed by Briaud (2007), Lehane et al. (2013), as well as Robertson and Cabal (2014) are employed, considering S B ¼ 0:1 to constitute q ult . In the former set, scaled cumulative frequency (SCF) is presented against the relative error defined in Eq. (17) for comparison purpose. Figure 5 shows the results of the first set where the relationships suggested by Mayne and Woeller (2014) and Stuedlein and Holtz (2010) is observed to render lower estimations for q ult (E r is in the negative range). However, the prediction model proposed by Mayne and Dasenbrock (2018), which is based on the soil type, I c , seems to yield estimations at both sides of conservatism. As it is plainly visible, the proposed formula in the current study is fairly accurate as it yields SCFs close to the vertical axis (E r ¼ 0%); hence, implying to provide veritable predictions.
However, it is to be noted that the provided comparisons are only valid in the deterministic (nominal) realms, and it does not bear witness to the absolute superiority of the model proposed in the current study over others. In other words, the reliability of different models and methods should be looked as if they are probabilistic in nature. To do so, different model parameters involved in the loaddisplacement profile predictions are considered probabilistically, and by assuming different load factors, it would be possible to yield information about the reliability index of different models. However, this issue is beyond the scope of this paper, and in this study, the model parameters have been assumed in average sense and only the resistance side of the performance function has been covered.
In the latter set, however, the calculated vs. measured ultimate bearing capacity values have been employed to indicate the accuracy of the proposed relationships. Likewise, statistical parameters, such as R 2 , RMSE, and MAD, have been superimposed on the curves to make a quantitative comparison, as depicted in Fig. 6. It is evident that the method presented in the current study poses more aptitude to estimate q ult in comparison to the other approaches.
Sensitivity analysis
In order to examine the effect of every single input variable on the output parameter, sensitivity analyses were performed by changing each of the input parameters at a constant pace, while the rest were unwavering (Liong et al. 2000). The considered rate of changes ranges from -10% to 10%. As a result of the changes in every input variable, RMSE in the estimation of output (q) was determined and presented in Fig. 7. In other words, the sensitivity analysis with respect to the changes of the parameter under study is drawn, while other parameters were adopted in the average sense; that is, changes of RMSE with respect to the input variables. As it is plainly demonstrated, the changes in parameters B and s barely affect q, whereas the variations of R f and q t , particularly R f , have substantial influences on the output parameters. Variations of the left sides of Fig. 7 in terms of R f and q t are almost similar, whereas changes in the right-hand side of R f curve are more pronounced. Such a result corroborates that R f is the most influential parameter on RMSE.
Another observation from Fig. 7 is that any perturbation in the measured soil parameters q t and R f , which can be considered as epistemic uncertainty and could be presumably due to measurement error, will have a reflection on the accuracy of the load/pressure estimations for shallow foundations. In other words, one could easily deduce that the soil parameters measurements, substantiated in form of in situ tests logging, have paramount impacts on the accuracy of the relevant predictions as appears from Fig. 7. This would imply that the type of in situ test equipment and its measurement accuracy play a crucially important part in the appropriate estimation of other parameters, let's say the ultimate bearing capacity of shallow footings, for example.
Application of the proposed model for future cases
The efficiency of the current approach for the new data set related to sands and silty sands and the calculation of the corresponding settlement are presented schematically in Fig. 8. First, a CPT log is considered, and then, parameters q t and R f are drawn against the depth (Fig. 8a). With regard to the defined D f and B, CPT data series are derived from D f to D f ? 2B and their average values are taken into account (Fig. 8b). The arithmetic mean values of the parameters q t and q c obtained from CPT data are considered in the current study. Using this arithmetic mean, resistance peaks are filtered using the method presented by Eslami and Fellenius (1997). Finally, by introducing the mean values of q t and R f , acquired from the CPT log, a presented in Eq. (16b) is computed. Thereafter, the values of the applied pressures corresponding to various settlement levels could be obtained from Eq. (16a), and the graph presented in Fig. 8c could be drawn accordingly. To this end, six values for the settlement (s 1 to s 6 ) are considered schematically, and the respective values of the applied pressure (q 1 to q 6 ) are acquired so as to draw a complete load-settlement profile.
Discussion
The main purpose of the current study was to find a robust relationship for the load-settlement behavior of soils based on CPT results. Such end was obtained in accordance with the gathered in situ test results. The proposed formula is Eq. (16), which correlates q to s, B and other properties obtained from CPT data components, such as R f and q t . The results show the superiority of the proposed relationship over previous ones.
Ultimate bearing capacity (q ult )
Based on different criteria for q ult obtained from PLTs, loading up to 0.1B settlement is valid particularly for coarse-grained soils and sands. Hence, applying this criterion and putting it into Eq. (16), Eq. (18) can be proposed for the evaluation of the ultimate bearing capacity based on CPT results. q ult ¼ 5:32 292:65 À 1026:95R f À 0:008q t À þ964:37R 2 f þ 8:45 Â 10 À7 q 2 t þ 0: where q t is the corrected q c in kPa and R f is the skin friction in percent. A 3D illustration of the variation of q ult with respect to q t and R f is given in Fig. 9. As depicted, the increase in either CPT parameters leads to an increase in the ultimate bearing capacity. However, the rate of increase in the q ult value with the increase of q t is more than that of R f . Moreover, for higher values of tip resistance, R f is observed to be more influential. This phenomenon shows that the cohesive property will be enhanced in soils due to the increase of R f , which consequently gives rise to the augmentation in the ultimate bearing capacity. Based on the results of a PLT, the settlement corresponding to the failure of the plate can be obtained. In order to link the settlement values of a PLT to a true scale foundation, Eq. (19) can be adopted from Terzaghi et al. (1996), which relates the settlement of the foundation (s f ) to the settlement of the plate (s p ).
where B f and B p are the width (diameter) of the foundation and plate, respectively. Accordingly, the ultimate bearing capacity of the foundation (q ult,f ) and plate (q ult , p ) can be related as follows: Based on the above-mentioned discussion, the factor of safety can be reached as follows: 1. Calculating the allowable settlement of the plate (s p,all ) based on the values of B f , B p and s f,all , using the relations provided in foundation manuals for the relevant soil type. 2. Based on the value of q t from the CPT data (i.e., the average q t values corresponding to the depths of D f to D f ? 2B) and the value of s p , all , the value of q a for the plate can be obtained.
Load-settlement curve (q-s)
One of the applications of Eq. (16) is to delineate the q-s profile, while representing the load-displacement behavior of the footing, as depicted in a three-dimensional fashion in Fig. 10 for B = 1 m. From the graphs, it is observed that qs surfaces grow with R f , implying higher q values in similar settlement levels. On the other hands, for the predetermined settlements of 50 and 100 mm, q a can be drawn in the q-q t plane, as also shown in Fig. 10. As it can be seen, the values of q a corresponding to 100 mm settlement are detectably higher than those corresponding to 50 mm settlement with both increasing with R f value.
Modulus of subgrade reaction (k s )
Another application of Eq. (16) is to predict the modulus of subgrade reaction (k s ). As stated before (Fig. 1), k s can be predicted from the q-s curve acquired from PLT data and can be computed for foundations employing Eq. (9). Figure 11 shows the three-dimensional representation of k s as a function of q t and s for the case of B = 1 m. It should be noted that the considered value of R f for this graph is the average of all data; i.e., R f = 0.6. As it is clear from the figure, settlement is inversely related to the modulus of subgrade reaction, whereas q t , as an indicative of soil strength properties, has an augmenting influence on k s . Generally, settlement is more of consequence than q t .
Conclusions
In the current paper, a general framework was developed to predict and model the load-settlement response of shallow foundations based on CPT results. To this end, 46 q-s curves were carefully assessed, and a sensitivity analysis was also conducted. Moreover, the proposed model was compared to previous relationships readily available from the literature. Prominent results obtained in the course of this study include: -The proposed hyperbolic function was proven to have a high accuracy to predict the load-settlement behavior of shallow foundations. -Constant parameters of the current hyperbolic model, including c and b, stem from the general form of the q-s curves and the variable coefficient, a, are dependent on the soil strength properties obtained from CPT results. a was related to the corrected cone tip resistance (q t ) and skin friction (R f ) via regression analysis and the Volterra series. -Dimensionless parameter s B was used, and simple equations with high accuracy were proposed to estimate the allowable and ultimate bearing capacities of shallow foundations.
-To have a more accurate investigation, data were categorized into two groups of training and validation, and the model parameters were estimated. Validation data were employed to make a comparison between the proposed model and previous ones, the results of which showed considerably high accuracy of the developed model (R 2 [ 99%). -Sensitivity analysis was performed to assess the individual impacts of the input variables, the results of which demonstrated the higher sensitivity of the model output to R f . -All the results of q max , q ult , q a and k s were given in the forms of example 3D graphs to be readily used by potential readers.
Funding No funding was received for conducting this study.
Declarations
Conflict of interest The authors declare no conflict of interest.
Ethical approval This article does not contain any studies with human participants performed by any of the authors.
Informed consent Participants of the study were the authors, and informed consent is not valid.
Fig. 11
Variation of the modulus of subgrade reaction against q t with respect to different settlement levels (R f = 0.6) | 7,887.6 | 2021-07-12T00:00:00.000 | [
"Geology"
] |
The effect of cosmic vacuum on the properties of scalar field
. The thesis explains the effect of cosmic vacuum of gravitational field on properties of scalar field equation. In the space-time plane, the scalar field equation has periodic solution φ (x,y,z,t) = Acos(kx ± ωt) . Consideration the cosmic vacuum of gravitational field (using De Sitter metric in its synchronization time) the equation of scalar field will have accurate solution in form of Beseel function. By using the asymptotic representation, the periodic solution (t → ±∞ ) will vanish. The scalar field equation when t→+∞ will decrease regularly, and when 𝑡 → −∞ it will increasing fluctuate.
INTRODUCTION
The study of cosmic vacuum is one from import lines studying in modern cosmology. Cosmological observations shows presence cosmic vacuum in universe [2]. Vacuum create antigravitation field, which call for acceleration cosmological expansion. The detection of cosmic vacuum made substantial evolution on the modern's nature of universe.
THE DISCOVERY OF COSMIC VACUUM
In cosmological science occur developments that many specialists consider it revolution, thanks only three points in cosmology: a. In the universe dominates vacuum of energy density exceeds all the "usual" forms of cosmic matter together.
b. Antigravity governs the dynamics of the cosmological expansion.
c. Cosmological expansion is accelerating, and the space in four-dimensional space-time is static, because the time a static [2].
Discovery made by astronomer's observers, who have been studying distant supernovae.
Observers have data on only a few supernovae, but already it was enough to notice the cosmological effect of decrease in the apparent brightness with the distance [9]. More precisely, it is better to look not at a distance, but a redshift "as is usually done in the case of distant sources". It was found that the decrease in the average brightness is faster than that expected for the cosmological theory, which has recently been considered the standard [4].
The theory of the expanding universe was created by Friedman in 1922-1924 [1]. With the opening of the cosmological expansion all doubts in the introduction of the cosmological constant disappeared.
The geometry of Friedman's four-dimensional space describes the metric element Friedman's theory assumes that the distribution of matter is homogeneous in the universe. In his theory Friedman predicts the cosmological expansion in homogeneous and isotropic space must occur according linear law [6]: "in any moment the velocity distant source, which exist at distance R proportion to this distance".
Vacuum appear in cosmology with Einstein's cosmological constant. In the first role cosmological constant became how to explain anti-gravity. Einstein predicts in that way possible equilibrium gravity material's universe, and i.e. the universe itself stationary [12].
THE SCALAR FIELD
Scalar field explains particles with spin s=0 .Effective (pseudo)scalar field explains natural spinless mesons. Complex (pseudo)scalar field explains charge spinless mesons [11]. The difference between scalar and pseudo scalar conclude with transforming law for reflection even number of axial coordinate and appear just in form possibly interaction law with other fields [7].
THE EFFECT OF COSMIC VACUUM ON SOLUTION OF SCALAR FIELD EQUATION:
Scalar field equation in general form [6]: In the first we looking for solution this equation in the space-time plane with metric By using this metric, Eq. 6 written in form: Solution of Eq. 8: ( , , , ) = 1 ( − ) + 2 ( + ) , 1 2 − .
International Letters of Chemistry, Physics and Astronomy Vol. 61 59
This solution is periodic function. Now, we are looking for solution of Eq. 6 using De Sitter metric.
Now we study the asymptotic representation of solution Eq. 18 considering that expansion of university corresponds → ∞ и → 0 .
ILCPA Volume 61
Comeback to Eq. 16 we find: This function non-periodic, it is decrease regularly with time.
For → ∞ we find the following expression: Considering Eq. 21 we find: Therefore This function increase and fluctuate with time.
We can write it in another form "real part": Eq. 39 increase and fluctuate with time.
CONCLUSIONS:
In the space-time plane, the scalar field equation has periodic solution. In gravitational field for expansion of university for t→+∞ the solution of scalar field equation will decrease regularly or decreasing fluctuate according to sign of the difference | 984.2 | 2015-11-01T00:00:00.000 | [
"Physics"
] |
In Vitro Anthelmintic Activity of Crude Extracts of Artemisia herba-alba and Punica granatum against Haemonchus contortus
Gastrointestinal nematodes (GINs) are the major limiting factor for the successfulness of livestock production throughout the world. Emergence of resistance strains as well as scarcity and high cost of the currently available drugs has led to the evaluation of other alternative helminth control options, mainly from plants. The current study is aimed at investigating the in vitro anthelmintic efficacy of crude methanolic extracts of two traditionally important medicinal plants, Artemisia herba-alba and Punica granatum, against Haemonchus contortus using adult motility assay (AMA) and egg hatch inhibition assay (EHIA). Four graded concentrations of the extracts were tested for both the AMA (10, 5, 2.5, and 1.25 mg/mg) and EHIA (0.1, 0.25, 0.5, and 1 mg/mL) in replicates. Albendazole and phosphate-buffered saline (AMA) or distilled water (EHIA) were used as the positive and negative controls, respectively. The crude extracts of A. herba-alba and P. granatum exhibited a potential anthelmintic activity at all dose levels in a concentration- and time-dependent fashion. The highest concentration (10 mg/mL) of all the extracts caused a significantly (p < 0.05) superior nematocidal activity compared to the negative control. Moreover, significant and concentration-dependent egg hatching inhibition effect was observed from both plant extracts. Maximal (98.67%) egg hatching inhibition effect was exhibited by the flower extract of A. herba-alba at 1 mg/mL concentration. The relative egg hatch inhibition efficacy indicated that both plants caused a significantly (p < 0.05) greater egg hatch inhibition within 48 hr of exposure. The current study validated the traditional use of both plants as a natural anthelmintic against H. contortus justifying a need to undertake detail pharmacological and toxicological investigation on both plants.
Introduction
Gastrointestinal nematodes (GINs) remain a major threat to the health and welfare of small ruminants throughout the world [1]. GINs represent a major economic hurdle in ruminant systems through mortality, weight loss, and reduced milk and meat production [2,3]. In Ethiopia, a total loss of US $81.8 million is reported annually due to helminth parasites [4].
Haemonchus contortus is an important abomasal helminth of small ruminants responsible for disease and major production losses worldwide [5]. Moreover, it is one of the major livestock parasites in tropical and temperate farming areas [6]. Compared to other nematodes, H. contortus is a highly pathogenic parasite of small ruminants and is capable of causing acute disease and high mortality in all classes of stock [7]. Heavy burdens of this blood-feeding parasite can cause severe anemia and rapid death in affected livestock [5]. It was reported to be one of the top ten constraints of sheep and goat production in East Africa [7].
GIN control has an important role to play in improving livestock production from a limited natural resource base and to improve animal health and welfare [8]. Synthetic anthelmintic agents are commonly employed to control GINs [9]. However, inappropriate and exclusive application of these drugs has contributed to the development of extensively drug-resistant parasites. This, in turn, increased risks of residues in the meat and milk of these animals and the environment [5,10]. Additionally, these synthetic agents are likely unaffordable and expensive. Consequently, demand for alternative control measures has constantly increased during the last years [1]. Hence, medicinal plants practiced in folk medicine can serve as a source of affordable and effective anthelmintic agents [11]. In the current study, we have attempted to correlate traditionally claimed anthelmintic activity of two plants in the context of experimental evidences.
The plant Artemisia herba-alba (Chukun in Amharic), which belongs to the Asteraceae family, is used as an anthelmintic agent as well as for other common applications in folk medicine [12,13]. From the Lythraceae family, Punica granatum (Roman) is used against GI nematodes [14]. P. granatum has been used in natural and holistic medicine to expel tapeworms and treat various ailments [15,16]. The aim of the present study was thus to evaluate the in vitro anthelmintic effect of extracts from these plants against H. contortus.
Collection of Plant Samples.
Based on a preliminary interview conducted among livestock raisers of Midaga-Tola district, two plants (A. herba-alba and P. granatum) were selected. These plants were commonly used as anthelmintic agents in Ethiopian folkloric medicine. Therefore, fresh flower and aerial parts (stem and leaves) of A. herba-alba and peel and root parts of P. granatum were collected from their natural habitat around Midaga-Tola district, East Hararghe zone, 582 km away from Addis Ababa. Herbal identification of the collected plants was then made by a taxonomist at the herbarium of Plant Science Department, Haramaya University, where a voucher specimen (AH001/17 for A. herba-alba and AH002/17 P. granatum) were deposited for future references.
Plant Extract Preparation.
The collected plant materials were cleaned, shade dried, mechanically ground, and coarsely powdered using a laboratory mortar and pestle. Then, the powdered specimens were subjected to a cold maceration extraction technique using the methanol solvent system for 72 hr. For each sample, a total of 250 g of the coarsely powdered plant materials was separately soaked in the extraction solvent (1 : 10). The extraction process was facilitated using a mechanical shaker at 120 rpm. The same volume of solvent was used to remacerate the residue for another 72 hr, twice. Finally, the filtrates were recombined and concentrated on rotavapor (Buchi, Switzerland) at 40°C under reduced pressure. Moreover, the concentrated filtrate was freeze-dried in a lyophilizer to earn a dried extract.
The dried extract was weighed and provided a percent yield of 14.3% (w/w) and 12.5% (w/w) for the flower and aerial parts of A. herba-alba, respectively. Extract from the peel and root of P. granatum, on the other hand, yielded 13% (w/w) and 9.4% (w/w), respectively. The resulting extracts were transferred into well-labeled vials and kept in a refrigerator until required for use.
Phytochemical
Screening. All extracts were screened for the presence and absence of different phytochemicals. Standard screening tests using conventional protocol, procedure, and reagents were conducted to identify the constituents as described in Trease and Evans [17] and Sofowora [18].
Biological Assay
2.4.1. Collection of Parasites. Adult parasites of H. Contortus were collected from the abomasum of a sheep obtained from Haramaya municipal abattoir. The abomasum was collected immediately after slaughtering and transported to Veterinary Parasitology laboratory of Haramaya University. In the laboratory, abomasum was washed by running water and worms were then isolated by incising the greater curvature of the abomasa and the parasites were kept in phosphate buffer saline (PBS) until the in vitro evaluation was started. The female worms were then ground using a mortar and pestle to liberate the eggs.
Adult Motility Assay (AMA).
A total of about 368 adult H. contortus parasites were used to assess the anthelmintic effect of extracts against mature H. contortus worms on adult motility assay (AMA), according to the technique described by Sharma et al. [19]. Each plant extract was tested on different concentrations (10, 5, 2.5, and 1.25 mg/mL) prepared in PBS.
The assay was conducted in six groups. Group I and Group II received crude methanol extract from the aerial and flower parts of A. herba-alba, respectively. Group III was treated with crude methanol extract of P. granatum peel part while Group IV received the methanol extract of P. granatum root part. Group V and VI received 0.25 mg/mL of albendazole (positive control) and PBS (negative control), respectively.
Inhibition of motility was taken as an indication of worm mortality/paralysis. To assess the motility inhibition effect of the extracts, the observations were taken at regular time intervals until the 7 th hour after treatment. Worms not showing any motility were taken out and placed in lukewarm PBS for 10 minutes and, in case of revival in motility, the observed worms were counted as alive; otherwise, they were counted as dead.
Egg Hatch Inhibition Assay (EHIA).
The ability of the extracts to inhibit egg hatching was conducted according to the procedure described by Coles et al. [20]. Eggs were washed thrice with distilled water and adjusted to a concentration of 100-200 eggs/mL using the McMaster technique [21]. The suspension was centrifuged for 5 minutes at 1500 rpm and the supernatant was discarded. Approximately, 100 eggs in 200 μL of distilled water were pipetted into each well of a 48-well microtiter plate.
Data
Analysis. Data were organized, edited, and analyzed using SPSS Version 20. Results generated from both assays were analyzed with one-way ANOVA followed by Tukey's HSD multiple comparison. p value of less than 0.05 was considered statistically significant.
Results
3.1. Phytochemical Screening. The preliminary phytochemical screening of the plant materials revealed the presence of alkaloids, saponins, flavonoids, tannins, glycosides, and phe-nols in all of the tested extracts (Table 1). Moreover, the strong presence of alkaloids, tannins, flavonoids, glycosides, and phenols were detected from the root crude extract of P. granatum.
Adult Motility
Test. The present study indicated that all concentrations of methanolic flower and aerial part extracts of A. herba-alba as well as the highest concentration of methanolic peel extract of P. granatum produced a relatively comparable anthelmintic activity with the conventional anthelmintic agent, albendazole (Figure 1). The anthelmintic activity of plant extracts increased with time. Accordingly, after 7 hr exposure of adult H. contortus to the highest concentration (10 mg/mL) of extracts, both plants produced a significant (p < 0:05) mortality of adult H. contortus. Albendazole, on the other hand, killed all parasites within 5 hr at a concentration of 0.25 mg/mL ( Table 2).
Egg Hatching Inhibition
Assay. Both A. herba-alba (flower and aerial extract) and P. granatum (peel and root extract) induced a significant egg hatching inhibition effect in a concentration-dependent manner. Flower and aerial part methanolic extract of A. herba-alba exhibited a 98.67% and 88.3% inhibition, respectively, at 1 mg/mL concentration. Values are mean ± SEM. All superscripts indicate significance at p < 0:05, a compared to untreated (PBS), b compared to albendazole, and c compared to the lowest concentration of methanolic extract of A. herba-alba flower, and d compared to the lowest concentration of methanolic extracts of A. herba-alba aerial part, e compared to the lowest concentration of methanolic extract of P. granatum peel part, and f compared to the lowest concentration of methanolic extract of P. granatum root.
Discussion
The emergence of resistant strains, the presence of anthelmintic drug residues in animal products, and synthetic drugs' toxicity have led to a rebirth of interest in the use of natural products [22]. Plant materials tested for their in vitro anthelmintic activity in the present study have been identified by local livestock raisers. In vitro techniques such as the AMA and EHIA are preferred to in vivo methods due to their low cost, simplicity, and rapid turnover [23]. Moreover, for in vitro studies, H. contortus is proved to be a good test worm because of its longer survival in PBS. This abomasal helminth has recently been used for in vitro studies by other workers [23,24].
In the current in vitro study, 10 mg/mL concentration of methanol peel extract of P. granatum produced a statistically significant anthelmintic activity that is comparable with the conventional anthelmintic agent, albendazole. This finding is additionally in line with the clinical study that confirmed the efficacy of the plant against nematodes in calves [25] and superior to an in vitro study that reported a moderate level of anthelmintic activity from the rind of P. granatum [26]. Moreover, similar to a study done by Prakash et al. [27] on the alcoholic extract of P. granatum, our study showed a significant anthelmintic activity of the plant as revealed by a concentration-dependent inhibition of transformation of eggs to the larva of H. contortus.
Some previous works similarly indicated that P. granatum has a marked effect on cestode and nematodes [28] as well as protozoan infections [29]. Moreover, our study substantiated a previous report on the traditional application of P. granatum plant, in which various parts of the plant can be used as a traditional anthelmintic agent [30,31].
The plant, A. herba-alba, is mainly used as an anthelmintic agent in traditional practice [10]. Concordant with this, in EHIA of the present study, flower part methanol extract of A. herba-alba induced a significant egg hatching inhibition of 98.67%, at 1 mg/mL concentration. This is in line with a study done by Boonmasawai et al. [11] in which shoot parts are used as an anthelmintic in H. contortus infestation of sheep as the result of its santonin. The result exhibited by the plant in AMA, moreover, is in agreement with a previously reported activity of a plant in the same genus, A. absinthium, which significantly affected motility and viability of H. contortus, in vitro [32]. Furthermore, the genus is a rich source of sesquiterpene lactones and flavonoids that might have anthelmintic activity with low risk of mammalian toxicity [33].
The exhibited anthelmintic effect of the two plants might be attributed to the existing secondary metabolites. Joshi et al. [34] assimilated that tannins may exert anthelmintic activity by reducing hatching, blocking its development to the infective larval stage and decrease in adults' motility. Besides, tannins have been shown to interfere with coupled oxidative phosphorylation and block ATP synthesis in H. Journal of Parasitology Research contortus [35]. Wang et al. [36] has confirmed the anthelmintic efficacy of plant-based alkaloids. The environmental stimuli on the host lead to the release of enzymes by larvae, which degrade the egg membrane [37]. The action of alkaloids in these two plants might be linked to the inhibition of these enzymes' activity.
Once a plant has proven its efficiency in vitro, further in vivo testing will be necessary to confirm the obtained results and evaluate risks, side effects, and future applicability [38]. Therefore, in vivo anthelmintic evaluation of these plants is imperative prior to their clinical use.
Conclusion
The in vitro anthelmintic activity of tested plants is characterized by a decrease in hatching and reduced motility of the larvae and adult stage of H. contortus. Accordingly, they have the potential to contribute in controlling gastrointestinal parasites of ruminants. Therefore, fractionation of the crude extracts and isolation of compounds to further evaluate the anthelmintic efficacy of these plants involving other parasite developmental stages are warranted.
Data Availability
Upon reasonable request, the supporting dataset are available from the corresponding author. Moreover, the dried specimen of tested plants and their voucher numbers are deposited in the herbarium of Haramaya University.
Ethical Approval
This research work was approved by the research and ethics committee of Haramaya University, Ethiopia. | 3,364.2 | 2020-01-27T00:00:00.000 | [
"Agricultural And Food Sciences",
"Biology"
] |
Future challenges in electrochemistry: linking membrane-based solar energy conversion mechanisms to water harvesting
As a short personal perspective, this feature article is written to capture a vision for electrochemistry as a subject fundamentally linked to energy conversion mechanisms. As such, electrochemistry will make considerable future impact, both academically and practically, in traditional and in emerging topics linked to energy and linked to new mechanisms for energy conversion (optical, chemical, mechanical, thermal, etc.). The field of electrochemical science is broad and diverse, and it offers fundamental and interdisciplinary challenges at many levels (which is linked also to educational challenges, e.g. at university level where electrochemistry often appears inaccessible to students and at professional development level where there is considerable demand for training courses [1]). Electrochemistry contributes to the development of technologies such as battery systems, (bio-)fuel cells, organic and inorganic materials electrosynthesis, electroanalysis, and solar-/ photo-electrochemical systems including artificial photosynthesis. Many of these technologies are associated with complex multiphase electrochemical systems (which are challenging to unravel and understand at fundamental level). Both current state-of-the-art in situ imaging or spectroscopy tools and current state-of-the-art computational tools are still not sufficiently advanced for fully resolving or explaining/ predicting many important phenomena, but a lot of progress is being made [2–4]. As a key contribution to analytical measurement tools, electrochemistry has now been able to reach the single entity and/or the single molecule domain [5]. Devices have been developed to detect single redox-active molecules or enzymes based on rapid feedback signal amplification between two very closely spaced electrodes in nanogaps or based on modulated ion transport in nanochannels [6]. The understanding and exploitation of electrochemical mechanisms in nanospaces or at nanoelectrodes remains an interesting and important challenge with opportunities. In electroanalytical sensing, new types of devices with multiple amplification strategies (based on nanostructures or based on molecular mechanisms) have been developed to probe extremely low concentrations in biological/health applications, e.g. for diagnostic microRNA in blood [7]. This field also presents formidable future challenges with many more crucial analytical targets in medicine and environmental analysis to be detected reliably and at low cost. Mechanisms at electrode surfaces and in composite catalyst materials require nanoscale study and understanding to unravel the complexity in important electrocatalytic reactions, such as oxygen evolution or carbon dioxide reduction. Recent progress towards single nanoparticle electrocatalysis, for example, with MOF-derived oxygen evolution catalysts has been very revealing [8] in terms of true quantifiable catalyst particle behaviour. However, for practical applications, the microscopic catalyst performance is only one part of the factors affecting the overall system performance. There are many more criteria for technologies to become viable or competitive. Often challenges cannot be addressed solely by dissection. Electrochemical processes occur not only at electrodes but also at membranes [9]. Potential-driven membrane processes are well-known in biology, where many transport phenomena as well as photosynthetic machinery are membrane-localized [10]. The key reason for processes being naturally associated with membranes is the interfacial energy conversion from electrochemical potentials to chemical and vice versa. Only at a membrane can electrochemical potential (notionally the sum of a chemical potentials and a term related to the interfacial Galvani potentials) gradients persist and be converted based on intriguingly complex mechanisms such as that reported for ATPases [11]. Therefore, artificial membrane * Frank Marken<EMAIL_ADDRESS>
Electrochemical science challenges
As a short personal perspective, this feature article is written to capture a vision for electrochemistry as a subject fundamentally linked to energy conversion mechanisms. As such, electrochemistry will make considerable future impact, both academically and practically, in traditional and in emerging topics linked to energy and linked to new mechanisms for energy conversion (optical, chemical, mechanical, thermal, etc.). The field of electrochemical science is broad and diverse, and it offers fundamental and interdisciplinary challenges at many levels (which is linked also to educational challenges, e.g. at university level where electrochemistry often appears inaccessible to students and at professional development level where there is considerable demand for training courses [1]). Electrochemistry contributes to the development of technologies such as battery systems, (bio-)fuel cells, organic and inorganic materials electrosynthesis, electroanalysis, and solar-/ photo-electrochemical systems including artificial photosynthesis. Many of these technologies are associated with complex multiphase electrochemical systems (which are challenging to unravel and understand at fundamental level). Both current state-of-the-art in situ imaging or spectroscopy tools and current state-of-the-art computational tools are still not sufficiently advanced for fully resolving or explaining/ predicting many important phenomena, but a lot of progress is being made [2][3][4].
As a key contribution to analytical measurement tools, electrochemistry has now been able to reach the single entity and/or the single molecule domain [5]. Devices have been developed to detect single redox-active molecules or enzymes based on rapid feedback signal amplification between two very closely spaced electrodes in nanogaps or based on modulated ion transport in nanochannels [6]. The understanding and exploitation of electrochemical mechanisms in nanospaces or at nanoelectrodes remains an interesting and important challenge with opportunities. In electroanalytical sensing, new types of devices with multiple amplification strategies (based on nanostructures or based on molecular mechanisms) have been developed to probe extremely low concentrations in biological/health applications, e.g. for diagnostic microRNA in blood [7]. This field also presents formidable future challenges with many more crucial analytical targets in medicine and environmental analysis to be detected reliably and at low cost.
Mechanisms at electrode surfaces and in composite catalyst materials require nanoscale study and understanding to unravel the complexity in important electrocatalytic reactions, such as oxygen evolution or carbon dioxide reduction. Recent progress towards single nanoparticle electrocatalysis, for example, with MOF-derived oxygen evolution catalysts has been very revealing [8] in terms of true quantifiable catalyst particle behaviour. However, for practical applications, the microscopic catalyst performance is only one part of the factors affecting the overall system performance. There are many more criteria for technologies to become viable or competitive. Often challenges cannot be addressed solely by dissection.
Electrochemical processes occur not only at electrodes but also at membranes [9]. Potential-driven membrane processes are well-known in biology, where many transport phenomena as well as photosynthetic machinery are membrane-localized [10]. The key reason for processes being naturally associated with membranes is the interfacial energy conversion from electrochemical potentials to chemical and vice versa. Only at a membrane can electrochemical potential (notionally the sum of a chemical potentials and a term related to the interfacial Galvani potentials) gradients persist and be converted based on intriguingly complex mechanisms such as that reported for ATPases [11]. Therefore, artificial membrane systems could offer a wealth of future opportunity and challenges for electrochemical systems. Lewis, Freund, and coworkers reviewed recent progress in artificial energy conversion membrane mechanisms for solar energy harvesting and for electrolytic water splitting [12]. Figure 1 shows a classic four-electrode electrochemical measurement cell configuration for applying a bias voltage across a membrane. The working and sense electrodes on the right and the counter and reference electrode on the left provide control over potential or current and allow membrane processes to be studied. Here, the membrane is based on a microhole, e.g. a 20-μm diameter hole laser drilled into a polymer support (as introduced by Girault and coworkers [13]). The resulting experimental system offers microelectrode-like mass transport and steady-state electrochemical responses accessible at conventional time scales [14].
The measurement with an empty microhole and with symmetric electrolyte solution on both sides would result in Ohmic behaviour associated with the specific conductivity of the electrolyte [15]. When applying an ionomer such as Nafion [16] asymmetrically onto one side (see Fig. 1b), a new effect occurs: due to redistribution of electrolyte in the microhole region, semiconductor-diode-like "closed" and "open" states are observed at negative or positive bias, respectively. When creating a "junction" of Nafion with other porous materials, the effects can be enhanced and the mechanism modified [17]. When employing semipermeable ionomers such as Nafion, there are many nanochannels within this material to allow ion transport and ionic current rectification as defined by the material properties. Similar and more individually tuneable effects (with substantially lower currents) are observed also for single nanochannels with asymmetry in charge or shape [18,19]. In contrast to conventional microelectrode processes, where electron transfer and redox chemical transformations occur, here at the asymmetrically modified microhole, primarily ion transport (either for cations or for anions) occurs unidirectionally. This can be exploited, for example, by combining two diodes in the AC-driven desalination of seawater [20]. In contrast to DC-driven electrolytic processes, the AC-driven mechanism can avoid external driver electrode side product formation and is therefore inherently less energy intensive. Could this or similar types of rectifier processes lead to new membrane mechanisms for solar energy conversion processes?
Membrane-based solar energy conversion mechanisms
In view of a global human population approaching 8 billion, it is important to ask what the future role of electrochemical science and technology could be to help ensuring supply of energy and food and water (all three are closely interconnected). The supply of water has to be seen as a truly global challenge. In his book on urbanization, Geoffrey West [21] highlighted the need for ever more rapid innovation and a need for technologies to become more sustainable and based on solar power as an obvious abundant energy source: "…the scale of solar energy is so vast that in one year it is about twice as much as will ever be obtained from all the Earth's nonrenewable resources of coal, oil, natural gas, and uranium combined". This should obviously happen in a fair way to provide benefits to everybody and not just a few. Could membrane (photo-)electrochemistry help provide power, food, and water in a sustainable manner?
As an interdisciplinary science, electrochemistry can benefit from a closer look at biological processes for guidance. Membrane processes in biology are ubiquitous and the key to many crucial processes: transmembrane ion transport, water transport, "hoovering" out of undesirable molecular species from within the cell [11], photoelectrochemical energy conversion, and electrical signalling/communication. Electrochemistry has been instrumental in unravelling the principles of bioenergetics [10,22] and in analysing the function of many membrane components. Could this knowledge be the starting point for new types of membrane processes based on artificial materials and based on artificial mechanisms to mimic and advance some of the critical processes we need to water, power, and feed the population? Nature offers beautifully intricate and effective solutions to problems like water transport, for example, in the case of watertransporting channels such as aquaporins [23].
Let us envisage new types of membrane mechanisms may be with two non-equivalent ionic diodes working against each other: one diode "pumps" cations and water from one reservoir into another reservoir; the second diode "pumps" cations back but with a different amount of water cotransport. Combining the two diodes to operate simultaneously (in opposite direction) leads to zero net ion transport coupled to water pumping across membranes. This effect could avoid externally applied pressure as required in traditional water purification processes, and it could be powered by solar electricity. Similarly, membrane pump mechanisms could be developed for other types of neutral or charged molecules. In more complex energy conversion scenarios, transport of molecules across the membrane could be coupled to bipolar redox chemical conversions within the membrane, similar to those in bipolar electrochemistry in freely moving objects [24].
Externally applied solar electricity from photovoltaic panels will be commercially highly competitive as compared with more complex integrated technologies, as is the case for solar water splitting to hydrogen. However, it might also be possible to configure or design membrane mechanisms with a low-cost directly integrated solar electricity generation [12]. This will require light absorption, charge separation, interfacial redox reactions at opposite sides of the membrane, and associated unidirectional ion/molecular transport to balance the overall processes. Designing new materials and composite structures as well as new mechanisms to give effective artificial membranes with internal charge separation is a future challenge, but not impossible. The key here appears to be finding new integrated mechanisms, for example, by exploiting ionic diode phenomena. Nanoengineering of new materials will be required for this type of membrane development. Low-cost and sustainable materials will be desirable. In the (not too distant) future, solar-powered membranes could perform tasks like atmospheric water harvesting, irrigation for food production, carbon dioxide reduction and formation of solar fuels, or the treatment of polluted environments. | 2,858.8 | 2020-06-13T00:00:00.000 | [
"Chemistry"
] |
Macroeconomic factors, liquidity issues and research and development investments: empirical evidence from the EU pharmaceutical industry
In recent decades, the business landscape is influenced by corruption, a pervasive phenomenon, faced by all countries, irrespective of their stage of development. The pharmaceutical industry is recognized as a “fertile ground” for corrupt practices. The paper aims to investigate the impact of corruption, economic freedom, and gross domestic product (GDP) growth on research and development (R&D) investment using a dataset of European Union (EU) pharmaceutical companies from 2011 to 2019. It also investigates the moderating effect of liquidity issues on the relationship between corruption and R&D investment. The study employs a quantitative approach using fixed effects models. Results show that corruption has a negative influence on pharmaceutical firms’ decision to undertake R&D activities, while economic freedom and GDP growth have a positive and significant impact on R&D investment. The findings are especially important given the deleterious effects of corruption and may be useful for both managers and policy-makers.
Introduction
Innovation is crucial for the pharmaceutical industry. At the heart of innovative activities lie research and development (R&D) investments. An unfavourable institutional environment may lead to inappropriate behaviour regarding R&D investment decisions, particularly in the case of pharmaceutical companies which have a high level of control over the R&D activity. In recent decades, R&D behaviour and its determinants have represented a concern of economists. The institutional theory is considered more adequate for explaining the significant trends of R&D expenditures than other firm-level theories (Alam et al., 2019). Institutions are considered a "heart determinant" of investment in general (Hashi & Stojcic, The article is structured as follows. A theoretical discussion regarding the link between R&D investment, corruption, economic freedom and GDP growth rate is presented in the next section. The research methodology is described in Section 3, Section 4 presents the results and robustness checks, while the last section concludes the study.
An institutional theory perspective on R&D investment
According to institutional theory, a country's investments are facilitated by its institutional frameworks as they provide incentives and support and create a stable business environment, decreasing risks and uncertainty. Waarden (2001) stated that institutional quality generates effects on R&D investment. Wang et al. (2015) consider that institutions can have a significant influence on firms' innovative activities. This influence can be realized through regulations, laws, and policies. Laeven (2003) stated that stronger institutional frameworks can improve knowledge accumulation in a country, prompting innovation in general. North (1990) associated institutional quality with economic and political governance, as well as societal interactions. He stated that low-quality institutional settings hinder society to collect productivity gains from innovation, technologies or the specialized division of labour and hence they fail to achieve economic growth. In this regard, their development trajectories can be modified by promoting principles aimed at combating corruption, developing human capital and promoting freedom (economic, political or religious) (Lee & Kim, 2009).
According to Wu et al. (2016), "Better institutional environment may stimulate R&D activity by providing enhanced collaborative capacity to the firms". Bringing several arguments, Alam et al. (2019), emphasize the importance of institutional factors for innovative activities. R&D investments are risky, bear fruit in the long run and can be affected by agency problems. Choi et al. (2014) document that high-quality institutional factors contribute to the reduction of agency problems, thereby leading to increased R&D investments. The high quality of institutional factors facilitates access to resources, is likely to attract foreign investments (Bénassy-Quéré et al., 2007), increases the transparency of information (Hillier et al., 2011), and facilitates the access of firms to external finance (La Porta et al., 1997).
Corruption and R&D expenditures in the pharma industry
The quality of the institutional environment can be affected by corruption. Widely known as a major deterrent to economic growth (Chen et al., 2022), corruption can have a corrosive impact on health outcomes (Dincer & Teoman, 2019). The pharmaceutical industry is prone to corruption for a number of reasons. The commercialization of medicines is lucrative, thereby creating a favourable context for embezzlement and misuse of power (Zirojević, 2020). Patients are often in a vulnerable position as their health comes first. Therefore, consumer price sensitivity tends to be lower as compared to other industries. Generally speaking, patients are less likely to discontinue treatment than are consumers to give up other types of products. Although the elasticity of medicines is influenced by the availability of substitutes and their prices, previous literature (Landsman et al., 2005;Yeung et al., 2016) shows that the demand for pharmaceutical products is relatively inelastic, especially for highvalue drugs. The high degree of asymmetry of information in the pharmaceutical industry and the large number of actors (medical suppliers, pharmaceutical companies, health care providers, payers and policy-makers) hinder the detection of conflicts of interest and smooth the path for different forms of corruption such as collusion, favouritism/nepotism, extortion, and fraud (Hussmann, 2010).
Although there are universally accepted forms of corruption (pharmaceutical drug counterfeiting, misuse of funds, sham contracts with doctors, bribery, illegal promotion), one has to bear in mind that there is a fine line between gifts, socially accepted favours and informal payments or bribes (Deliversky, 2016;Martinez et al., 2017;Stepurko et al., 2017).
Within this context, the pharmaceutical industry represents a good setting to scrutinize the impact of corruption on R&D decisions. The development of a drug portfolio is not possible without R&D activities. The pharmaceutical industry spends on R&D to find the cure to different diseases or to develop generic drugs and to stay competitive in a highly dynamic market (Nandy, 2022). It is widely acknowledged as the industry with the highest R&D intensity in the manufacturing sector (Mahajan, 2020). As far as these activities are concerned, Sismondo (2021) draws attention to the "ghost-management" of medical research. In other words, the medical literature is often biased because drug trials are funded, designed, and written up by pharmaceutical companies. As Egharevba and Atkinson (2016) emphasise, clinical trials are the mainstay in process of authorizing medicines. Apparently, the industrysponsored trials are conducted by independent researchers, but previous literature (Martinez et al., 2017;Sismondo, 2021) suggests that it is very likely that pharmaceutical companies silently control them. In this context, it comes as no surprise that the treatment schemes prescribed by physicians are often viewed with scepticism (Marmat et al., 2020). Unethical practices of the industry adversely influence the trust of consumers (Stepurko et al., 2017).
Hypotheses development
The pharmaceutical sector is vulnerable to corruption. Investments in innovative activities are discouraged by the low level of institutional trust caused by corruption (Anokhin & Schulze, 2009). International business literature recognizes that corruption shapes and affects the firms' behaviour (Rodriguez et al., 2005) and foreign direct investment (Hannafey, 2003). According to Daude and Stein (2007), a high level of corruption causes managers and investors to engage in acts of bribery to obtain licenses and permits, which translates into increases in the cost of the investment. Through these increased costs, corruption depresses the development of new products, services, and technology. Furthermore, a high level of corruption is associated with more uncertainty and less profitable investments, thereby making investors less motivated by such costly investments like R&D. Corruption also hinders entrepreneurship, productivity, and investment in R&D (Anokhin & Schulze, 2009). Moreover, a high level of corruption generates an increase in information asymmetries and the cost of doing business.
As this phenomenon remains a major problem that makes the actors of the pharmaceutical sector be distracted from promoting the well-being of the population, health, and innovation in the healthcare sector (Lexchin, 2019), the following hypothesis is formulated: H1: Corruption negatively influences R&D investment.
Economic freedom refers to all the rights of individuals, including labour and property rights. Nordin (2014) defines economic freedom from three points of view based on individuals, government, and the economy. Individuals have the right to choose where to live and work, their own properties and can control their productivity. The concept of freedom on government view refers to the transparency, visibility and openness of the decision-making process and the removal of discrimination. As for the economic view, every individual or firm has an equal chance of success because free and open competition permits an appropriate allocation of resources for consumption and production, and the power of economic decision-making is widespread. Countries with a high level of economic freedom accept diversity and promote creativity which encourages innovation.
Widely considered one of the main factors that generate economic prosperity, economic freedom influences the effectiveness and efficiency of resource use. There is a set of studies that shows that nations with a high level of economic freedom have evolved economically (Dawson, 1998;Easton & Walker, 1997;Hanson, 2000;Weede & Kamph, 2002). In a report conducted by McQuillan and Murphy (2009), it is stated that higher economic freedom encourages, especially in developing countries, both income growth and production growth. Depken and Sonara (2005) infer that the growth of trade flows is strongly correlated with a high level of economic freedom. Using Latin America as a research setting, Calvo and Robles (2003) show that a high level of economic freedom from the host country is conducive to increased foreign direct investment inflows. At the same time, researchers (Calvo & Robles, 2003;Pourshahabi et al., 2011) note that economic growth from the host country promotes FDI and economic freedom fosters economic growth (Nordin, 2014). Berggren (2003) shows that economic freedom has a complex character, as some components (in particular, the use of property rights, business freedom) of the economic freedom index cause economic growth, while other components (monetary freedom, government integrity, investment freedom, financial freedom, and trade freedom) come as a result of economic growth.
Turning to the pharmaceutical industry, whose products are designed to protect the health of individuals, economic freedom presupposes that patients' access to safe and effective treatments should take precedence over profit (Kreiner, 1995). Moreover, the profit obtained from the development of new drugs gives pharmaceutical companies the economic freedom to choose what drugs to develop (Hole et al., 2000). Economic freedom is also correlated with patent protection in the pharmaceutical industry (Qian, 2007) which stimulates innovation (Haley & Haley, 2011). Therefore, the following hypothesis is proposed: H2: Economic Freedom has a positive effect on R&D investment.
R&D investment and income growth mutually interact (Wang, 2010). On the one hand, Coe & Helpman (1995) stated that a high level of productivity is created by R&D outcome and spillover mechanism, and this leads to higher revenue growth. A high level of GDP growth rate makes firms consider that there are possibilities for greater use of existing production capacity, increased sales and rising profits. This is confirmed by the acceleration principle which shows that the GDP growth rate rates influence the variation in R&D investment (Schmookler, 1966). The effort involved in the R&D activity materializes in a diversified portfolio and superior quality products, which generates high returns. This increases productivity, value added, and further ensures income growth (Nordin, 2014).
On the other hand, Markusen (1986) confirmed that R&D-intensive products are more sought after by high-income consumers. Researchers have found a direct relationship between GDP growth rate and R&D investment. Cheung (2014) demonstrated that the higher its per capita real GDP, the more innovative a state is. Alam et al. (2019) observed that in developed markets GDP growth rate is correlated with the firms' R&D expenditure. The global pharmaceutical industry is changing landscape and moving towards mergers and acquisitions, contract manufacturing and R&D activities. In this case, the impact of GDP growth rate is paramount (Vaidya et al., 2018). Tran (2021) assumed that a high GDP growth rate indirectly favours R&D projects by providing companies with lower costs of external financing. A high level of GDP growth rate is expected to increase interest in innovation and technological progress in the pharmaceutical industry. Thus, following Wang (2010) who remarked that R&D investment can be stimulated by GDP growth rate, the following hypothesis is proposed: H3: Gross domestic product (GDP) growth has a positive effect on R&D investment.
The level of investments is affected by the firms' financial status (Alam et. al., 2019). External financing, and in particular debt, is considered inadequate for financing R&D investments (Hall, 1992). Obtaining funding for R&D activities can be hampered by a series of barriers, like uncertainty, risk and the absence of collateral that characterizes R&D projects (Hall & Lerner, 2010). R&D expenditures of multinational and domestic corporates are positively influenced by cash flows (Bae & Noh, 2011). According to Rafferty and Fund (2005), R&D projects are stimulated by cash flow increases. Results show that R&D projects are sustained by the success of new medicines that generate large cash flows. Firms' internal funds are considered the most important sources of R&D investment funding (Czarnitzki & Hottenrott, 2011). At the same time, companies are reluctant to use external funds to finance R&D projects in order to avoid revealing sensitive information regarding their R&D projects (Bhattacharya & Ritter, 1983). Thus, besides government funding, internal financial resources represent the safest source of financing. Himmelberg and Petersen (1994) estimate that R&D decisions depend on the constant trend of increasing cash flow. If there are no prospects for increasing cash flow, managers are reluctant to R&D investments (Brown et al. 2012;Krammer, 2015;Sasaki, 2016). However, the permanent character of the increase in the cash flow determines the firms' managers to be more willing to carry out R&D activities. According to Hubbard (1998), the firms' decisions to invest are affected by capital market imperfections. These arise as a result of the asymmetric information and agency problems between investors and management (Myers & Majluf, 1984). The firms can obtain certain public contracts in exchange for paying bribes (Liu et al., 2017). An agency problem may easily occur when corporate cash is used by managers for paying bribes, without shareholders' knowledge (Tran, 2019). Consequently, the firms' cash flow sensitivity increases. At the same time, firms may be more tempted to engage in corruption if they face certain liquidity issues. In light of these findings, it is expected that the relationship between corruption and R&D investment is influenced by liquidity issues: H4: Liquidity issues moderate the relationship between corruption and R&D investment. Figure 1 exhibits the conceptual framework of the research.
Sample and variables
The paper scrutinises the influence of corruption (captured through a composite indicator retrieved from the World Bank database), index of economic freedom (IEF), and gross domestic product (GDP) growth on R&D investment of pharmaceutical manufacturing firms listed in the European Union 1 . Furthermore, it is empirically assessed the moderating effect of liquidity issues on the corruption-R&D investment nexus. Firm-level variables are retrieved from ORBIS. Only those companies that reported R&D expenditures for at least 3 consecutive years were considered. Several observations were deleted due to a lack of data for the variables of interest. Following the use of the two filters, the final sample consists of 118 companies. The analysis is conducted on unbalanced panel data with 749 firm-year observations and spans 9 years (2011-2019).
The study uses R&D expenditures as a dependent variable. Consonant with earlier research (Chen et al., 2016;Lee & Hwang, 2003), R&D investment is quantified using the natural logarithm of R&D expenditures. The log transformation facilitates discussions and enables findings comparability.
The main independent variable is corruption. Corruption in all forms is more likely to occur in an environment characterised by uncertainty, divergent interests, and information gaps between pharmaceutical companies (insiders) and customers (outsiders) as emphasised by Global Corruption Report 2006 (Transparency International, 2006). Wang (2010) also assumed corruption as an explanatory variable of R&D investment. Secondary data concerning corruption are retrieved from the World Bank database. Therefore, corruption is quantified using a composite indicator, constructed using a plethora of individual variables that reflect the misuse of power (irregular payments, frequency of bribery, corruption in different sectors, etc). This aggregate indicator is computed using the unobserved components model (UCM) and it is based on a multitude of different data sources (such as survey institutions, think tanks, organizations and private companies) (Alam et al., 2019).
As explanatory variables, the models also include the index of economic freedom and GDP growth rate. The index of economic freedom (IEF) shows the extent to which the factors of production can move freely in a given economy. Data on the index of economic freedom comes from the World Heritage Foundation (WHF) database. According to WHF, the aggregate index is computed as the simple average of the following sub-indicators: "Property rights, Freedom from corruption, Fiscal Freedom, Government Spending, Business Freedom, Labor Freedom, Monetary Freedom, Trade Freedom, Investment Freedom, and Financial Freedom". A country's economic health is proxied by GDP growth rate, a country-level variable extracted from the World Bank database.
An indicator named liquidity issues was constructed, a dummy variable that takes value 1 if the company encounters liquidity issues and 0 otherwise. It is considered that a company faces liquidity issues if the liquidity ratio is less than 1 (Abusalah & Ng, 2012). Data regarding liquidity ratio, also known as quick ratio, is retrieved from the ORBIS database.
In addition, the models include control variables, three firm-specific factors, commonly known as good predictors of corporate innovative activity, namely: return on assets, the number of employees, which serves as a proxy for firm size, and leverage. Scott (1995) and Oliver (1997) inferred that R&D behaviour may be determined by both external and internal factors. The paper considers the abovementioned factors to minimize the omitted variable bias. Table 1 summarizes the main information about the variables included in the models.
Empirical models
Panel data analysis is based on two fixed effects models, consistent with the results of the Hausman test. The study adds cross-section fixed effects, a widely employed approach by studies that investigate the drivers of investment decisions (Sun et al., 2019). R&D expenditures are seen as a function of several macroeconomic factors and internal factors: LnR&D = β0 + β1Corruption + β2IEF + β3GDPG+ β4ROA + β5LEV + β6LnEMPL (1) LnR&D = β0 + β1Corruption + β2IEF + β3GDPG+ β4Corruption x LqI + β5ROA + β6LEV +β7LnEMPL (2) Equation (1) represents the basic model and allows the exploration of the influence of corruption, IEF, and GDP growth rate on the R&D activity of pharmaceutical companies, while equation (2) allows scrutinising the moderating role of liquidity issues on the impact of corruption on R&D investment. Data analysis is performed using EViews.
Descriptive statistics and correlation
The main indicators of descriptive statistics are presented in Table 2. The average value of R&D expenditures is 116,968 € and the standard deviation is 587.180 €. It can be inferred that pharmaceutical companies invest considerable amounts in R&D projects. Official statistics regarding the R&D landscape point out that the pharmaceutical industry is one of the top investors in R&D, right after ICT producers, owning together almost 43.5% of R&D investment in 2019 (European Commission, 2020). The average value of the corruption index is equal to 1.5417 and the standard deviation is 0.6749. The range is between -0.2673 (for Bulgaria) and 2.4049 (for Denmark). This indicates that Bulgaria suffers from a lack of control of corruption, while Denmark enjoys a strong control of corruption. As far as economic freedom is concerned, the mean value of IEF is 70.4727 which suggests that, overall, UE countries are mostly economically free. The minimum value (53.2) corresponds to Greece which indicates a mostly unfree economy, and the maximum value (80.90) corresponds to Ireland which implies that its economy is one of the freest in 2020. On average, 22,94% of the sampled companies encounter liquidity issues. The average GDP growth rate is 1.7622% and the standard deviation is relatively high (3.1278), which suggests that the countries in the sample have GDP growth rate rates that are not clustered around the mean. It is observed that the companies in the sample have, on average, negative ROA (-14.8748), which is not necessarily a sign of low efficiency of assets. Typically, firms that invest heavily in assets are associated with lower ROA due to the time-lagged impact on profit. The sampled companies are large, with an average number of employees of 3650.8. Debtto-assets ratio (leverage) mean value (0.4571) shows that, overall, the companies are not in a risky position.
To ensure there are no suspicions of multicollinearity, the matrix of correlation and the variance inflation factors (VIF) are computed and displayed in Table 1. The values of correlation coefficients are low and all the VIF values are below the reference value of 10, introduced by Kennedy (2008) and Hair et al. (2010), respectively 5, proposed by Studenmund (2016). Additionally, the condition number was examined and the results (less than 100) (Montgomery et al., 2001) confirm that the issue of multicollinearity does not arise in this study. Notes: *significant to 10%; **significant to 5%; and ***significant to 1%. Source: Authors' representation
Regression results
As previously mentioned, this paper scrutinises the impact of some of the potential institutional determinants on research and development (R&D) investment of pharmaceutical manufacturing companies listed in the European Union. As it can be seen from Table 1, corruption adversely affects the R&D behaviour of European pharmaceutical companies. This result is congruent with the prediction and supports the institutional-based view and the "sanding-the-wheels" hypothesis. More specifically, an increase in corruption is associated with around 0.7321% fall in companies' R&D expenditure, other factors being fixed. It is evident that R&D activity is sensitive to malfeasance, bribery, irregular payments, and embezzlement. These practices have a detrimental effect on resource allocation and undermine the company's growth (Bukari & Anaman, 2021). The literature also postulates that corruption exacerbates the costs (Ivanovic-Djukic et al., 2019;Nguyen et al., 2016). Therefore, the high cost of obtaining licenses or loans acts as a deterrent to a firm's decision to undertake R&D activities (Sena et al., 2018). The paper corroborates the findings by Alam et al. (2019) who analysed 663 firms from emerging markets and concluded that corruption harms R&D activity, as it leads to higher investment costs and hinders foreign investments. Using a longitudinal dataset of 48 U.S. states and two measures of corruption, Dincer (2019) also demonstrates that corruption decelerates innovation. The inverse relationship between corruption and innovation is also empirically evidenced by other analyses (Lee et al., 2020;Mahagaonkar, 2008).
Concerning the second hypothesis, table 3 clearly shows that the index of economic freedom has a positive impact on R&D investment, consonant with conventional wisdom. Economic freedom is widely recognized as a catalyst for economic development (Rapsikevicius et al., 2021). The report of McQuillan & Murphy (2009) lists many benefits of greater economic freedom, inter alia, increased investments, and more innovation. The view that economic freedom enhances innovation is also shared by other scholars. Using panel data of 5809 companies, spanning 22 years, Zhu & Zhu (2017) provide evidence that economic freedom is a key driver of corporate innovation. Similarly, Erkan (2015) finds a positive association between innovation and IEF and emphasizes the importance of economic freedom in devising policy recommendations. Asandului et al. (2016) find a positive correlation between IEF and GDP per capita and between IEF and social progress index. The hypothesised direct relationship between GDP growth rate and R&D investment is supported by the empirical analysis. A rise in GDP growth rate leads to increased R&D investments. The result is hardly surprising and merely confirms that firms have the confidence to invest more when economic growth is strong. Galindo & Méndez (2014) demonstrate that the direction of causality runs both ways as economic growth positively influences innovation and vice-versa. Hypothesis 3 is thus supported. Table 3 also conveys the results of the regression analysis examining the moderating effect of liquidity issues on the corruption -R&D investment relationship. The findings highlight that liquidity issues moderate the influence of corruption on R&D activity (β=-0.1079). In other words, the adverse effect of corruption on the R&D activity of the manufacturing pharmaceutical industry is more pronounced when firms deal with liquidity issues. One possible explanation found in the literature is that debt is not suitable for financing R&D activities (Ughetto, 2008;Xu & Yano, 2017), and internal equity should be employed instead. It is concluded that corruption and economic freedom play a relevant role in explaining the R&D behaviour of pharmaceutical companies.
Robustness checks
Several additional tests are performed to check the robustness of the results. To reinforce the results, the sample is further divided into subsamples based on the median of the variables GDP growth rate and government effectiveness. Sub-sample analysis running the abovementioned specifications is performed (equation 1 and equation 2). The use of alternative sub-samples in running supplementary analyses to ensure the generalizability of the findings is a recommended practice (Hair et al., 2010). The country-level variable 'government effectiveness' was retrieved from the World Bank database and refers to the competency and the capacity of the government. Third robustness test considers an additional variable (i.e. ECenforcing contracts) that measures the time and cost for resolving a commercial dispute through a local first-instance court, and the quality of judicial processes index. The results presented in Tables 4-6 lend strong support to the baseline findings and the hypotheses. There are no noteworthy changes in the values or statistical significance of the coefficients. The results are quite robust.
As a final exercise, we performed an analysis to eliminate endogeneity concerns. The independent variables, suspected to be endogenous, were tested. First, independent variables were regressed. The resulting residuals and Wald Test were used to ensure that there are no problems of endogeneity.
Conclusions
To bring the paper to a close, the main points are summarised here: corruption, economic freedom and GDP growth rate play a meaningful role in explaining the R&D behaviour of European pharmaceutical companies and the adverse effect of corruption on the R&D activity is more evident when firms encounter liquidity issues.
Corruption in the pharmaceutical sector is a fervent topic. Raising awareness about this issue by studying the nexus between corruption and R&D behaviour of pharmaceutical manufacturing companies is a paramount step in developing effective policies to address this issue and stimulate a collective effort of mitigating the effects of this nefarious phenomenon. Understanding corruption and its consequences are not solely of academic importance but are also relevant in designing anti-corruption policies. The results yield important implications for managers and policy-makers and may be of interest to both civil society and scholars concerned with the issue of corruption in the pharmaceutical industry and the determinants of R&D activity. By providing anecdotal evidence on the impact of corruption and economic freedom on R&D, the study can contribute additional pieces to the knowledge of factors susceptible to influence R&D expenditures. Most importantly, the paper emphasizes the moderating role of liquidity issues corruption -R&D investment relationship. It is recommended that pharmaceutical firms take notice of the corruption phenomenon in all its forms owing to its deleterious effect on R&D activity and take several measures such as adopting new technologies throughout the pharmaceutical value chain to raise transparency and establishing a management oriented towards promoting anti-corruption principles. It is paramount that all actors from the health sector understand that patients are more important than profits. The problem of corruption exacerbates when firms face liquidity issues. Therefore, managers may take into account to access a flexible line of credit or negotiate favourable credit terms with their suppliers, as needed. Governments are expected to create a climate conducive to R&D investment through fiscal facilities and discourage corrupt practices through unequivocally enforced regulations and severe sanctions.
The research has some limitations due to the lack of firm-level evidence regarding corruption, a relatively small-time span of analysis, and the inclusion of all EU countries, disregarding the development level. Notwithstanding that the results are related to the EU context, they could have international relevance as well. The shortcomings of this paper offer opportunities for future research. Therefore, it would be useful to include firm-level data regarding corruption, extend the period of analysis, conduct the same study on different industries and develop the analysis by investigating different subsamples such as euro area and non-euro area states. | 6,526.8 | 2023-01-01T00:00:00.000 | [
"Business",
"Economics"
] |
Wellbore Stability of a Deep-Water Shallow Hydrate Reservoir Based on Strain Softening Characteristics
Engineering College of Southwest Petroleum University, Sichuan, Nanchong 637000, China Nanchong Key Laboratory of Robot Engineering and Intelligent Manufacturing, 63700, China CNOOC Unconventional Oil and Gas Branch, China United Coalbed Methane Corp., Ltd., Beijing 100011, China State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, No. 8 Xindu Avenue, Xindu District, Chengdu, Sichuan 610500, China
Introduction
Natural gas hydrate (NGH) is a clathrate crystalline compound formed by water molecules enveloping methane molecules in the form of hydrogen bonds. It exists widely in deep-water shallow strata and permafrost zones [1]. One cubic meter of NGH can release 164 cubic meters of methane gas and 0.87 cubic meters of water [2]. According to Kvenvolden's statistics, the proven carbon reserves of NGH in the world are more than twice the carbon reserves of conventional fossil fuel energy sources (coal, oil, and natural gas) [3]. Therefore, NGH is currently one of the most promising energy types. With the advancement of deep-water oil and gas resource development, how to efficiently, economically, and safely exploit deep-water shallow hydrates has attracted increasing attention.
Borehole instability is one of the main problems faced in the drilling and production of gas hydrate formations. Key factors affecting borehole stability are the petrophysical and mechanical properties of the hydrate formation and the stability of the hydrate in the formation. The stability of NGH is a core factor. Since the stability of hydrate depends on certain temperature and pressure conditions and the exploitation of hydrate will inevitably disturb or even destroy the original temperature, pressure, and stress state of the sedimentary layer, study of the borehole stability of the hydrate layer is a key to effective exploitation. Due to the influence of gas hydrate characteristics and geological environment, this kind of drilling will face more complex problems than general oil and gas drilling. Before drilling, the formation is in pressure balance state. But after drilling, the original support force is lost, and then, the cementing strength becomes weak, which will also lead to the instability of borehole wall. In particular, under the influence of temperature and pressure, the decomposition of the supporting solid hydrate will cause the borehole to collapse. The increasing of water content will further threaten stability of the hydrate.
There has been a series of studies investigating the borehole stability of the hydrate layer. Thermal and poroelastic effects are preferably considered to estimate wellbore stability [4]. Birchwood et al. proposed an elastic-plastic wellbore stability prediction model based on the Mohr-Coulomb criterion, which took into account the effect of temperature on the thermodynamic state of the hydrate layer [5]. By studying the influence of the mud circulation rate and sedimentary salinity on the decomposition of hydrate, they found that the mud circulation rate was the most critical factor in keeping the hydrate stable. Freij-Ayoub et al. established a numerical model of hydrate borehole stability coupled with thermodynamic effects. The simulation results showed that when the drilling fluid temperature was 5°C higher than the reservoir, the yield zone around the borehole expanded by 32% [6]. Rutqvist and Moridis used numerical simulations to study the influence of deep heat flow intrusion, gas production, and the weight of mining equipment on the mechanical state of the hydrate layer [7]. Their results showed that heat flow intrusion and increasing gas production weakened the mechanical stability of the hydrate layer. Mining equipment above the seabed can increase reservoir pressure and help maintain the mechanical stability of the reservoir. Gao and Gray analyzed the wellbore stability through a coupled geomechanics and reservoir simulator [8]. Khabibullin et al. proposed a one-dimensional semianalytical model to describe the transfer of heat and fluid and coupled it into a numerical model for temperature field prediction around the well [9]. They found that the amount of hydrate decomposition depended on the initial reservoir characteristics and the bottom hole temperature and pressure conditions [9]. Kou et al. established a mathematical model of wellbore stability in hydrate formations considering factors such as heat conduction and hydrate decomposition [10,11]. The simulation results revealed the influence of drilling fluid temperature on the decomposition of hydrate and indicated that the thermal decomposition of hydrate led to deterioration of the mechanical environment of the reservoir. Rutqvist et al. established a numerical model of coupled multiphase flow to study the effect of decompression mining methods on the mechanical states of two different sedimentary layers [12]. They found that the gas production rate and bottom hole pressure drop determined the pressure state of the entire reservoir and also changed the mechanical state of the near-well zone. Chong et al. studied the impact of horizontal well mining on hydrate production with experimental equipment and found that horizontal well mining could increase gas production while reducing water production [13]. Yu et al. studied the process of hydrate decomposition and gas intrusion into reservoirs through experiments and numerical simulations [14]. The experimental results showed that drilling fluid temperature, hydrate saturation, and reservoir pressure were the main factors leading to hydrate decomposition and gas invasion. The numerical simulation results showed that the use of low-temperature drilling fluid and low circulating rate was beneficial for controlling gas intrusion into the reservoir. Sun et al. conducted a numerical simulation analysis of borehole stability based on the characteristics of the hydrate layer in the Shenhu area of the South China Sea [15]. The results showed that the thermal effect of drilling and the high salinity of the drilling fluid caused the release of free gas in the reservoir, which led to an increase of the pore pressure in the near-wellbore zone. Controlling the salinity of the drilling fluid could effectively control the generation of free gas and prevent borehole wall instability.
Although there have been some experimental and numerical simulation studies on the borehole stability of the hydrate layer, the influence of temperature and flow on the decomposition of reservoir hydrate is still not well understood. There have been few pure mechanical studies on the stress and strain state of the hydrate formation around the well, and it is impossible to intuitively understand the influence of the wellbore on the original stress state of the hydrate formation. Considering the effect of stress on rock strength is better to understand the stability of the borehole [16]. Connected to collapse and fracture gradients is the stress around the wellbore [17]. The drilling process disrupted the stress balance of the formation rock and caused the redistribution of stress around the borehole. The stability of the formation will be expressed through stress. When the stress is unbalanced, the formation will be destroyed. Determining the hydrate formation stress is the prerequisite for studying the stability of the borehole wall. The research results are always uncertain because of the complex working conditions and the dynamic changes of underground stress, which makes it difficult to solve the problem of borehole stability. This paper therefore uses discrete element method to establish a numerical model of deep-water shallow hydrate reservoir borehole with actual stratigraphic environment based on strain softening characteristics to capture the stress and strain states of the borehole, which are used to describe the stability. For verifying the reliability of the numerical model, a comparison of borehole stability in the discrete element numerical model and an elastoplastic analytical model was conducted. It also simulates the influence of factors such as reservoir depth and hydrate saturation on wellbore stability in order to provide more theoretical support for the drilling and production of deep-water shallow hydrates.
Borehole Stability Model for Deep-Water
Shallow Hydrate Reservoirs 2.1. Analytical Model of Borehole Stability Based on Strain Softening Characteristics. Timoshenko and Goodier deduced elastic mechanics expressions of radial and circumferential stress of a cylindrical vessel with uniformly distributed internal and external forces [18]. Yu further considered the special case when the outer boundary of the cylinder tended to infinity, and the stress expression at this time was the elastic 2 Geofluids solution of the horizontal isotropic formation stress distribution [19]. Therefore, equations (1) and (2) give the elastic zone stress solution of the borehole wall stability model in the cylindrical coordinate system, and equation (3) gives the radial displacement expression: where σ h is the horizontal stress, σ p is the radial stress at the elastoplastic boundary, r p is the radial coordinate of the elastoplastic boundary, r is the radial coordinate of a point, E is the elastic modulus, v is Poisson's ratio, σ r is the radial stress, σ θ is the circumferential stress, and u r is the radial displacement.
Chen and Abousleiman took the strain softening model as the constitutive model of the formation and gave a plastic model of horizontal isotropic formation stress distribution [20]. Based on the Drucker-Prager criterion, a strain softening constitutive model in the form of internal friction angle was given as: where β i is the initial internal friction angle, ε is the strain, and A and B are the parameters related to the constitutive model. Based on the research of Chen and Abousleiman, the plastic zone stress differential expressions of the hydrate formation borehole stability model are: According to previous research of Chen and Abousleiman [21,22], the boundary conditions of the elastoplastic interface are: where ξ is the ratio of radial displacement to coordinates, b ij (i = 1, 2, 3; j = 1, 2, 3) and Δ are the transition parameters, ε v is the volumetric strain, and p 0 is the initial average effective stress. Thus, equations (1) and (2) are the stress expressions in the elastic zone of the formation around the well, equations (5)-(7) are the stress differential expressions in the plastic zone, and the boundary conditions of equations (8)- (11) are added together to form the wellbore stability model of hydrate formation.
Numerical
Model of Borehole Stability Based on the Discrete Element Method. This paper uses the discrete element numerical simulation method to simulate the stability of a horizontal borehole during the mining process. The discrete element method was first proposed by Cundall and Strack to study the mechanical behavior of rocks and soils [23]. In discrete element simulation, the model body is composed of particles. After setting microscopic parameters (such as stiffness and bonding strength) for particles and contact points and applying external forces, the movement and collision between particles can produce different mechanical responses of the model body. When the mechanical response conforms to the real mechanical behavior of the material, the microscopic parameters are applicable to the material. Figure 1 shows the discrete element model of the borehole stability. The yellow particles are sand, and the blue particles are hydrates existing in the pores of the sediment. The model is a cuboid space surrounded by six invisible walls with a length and width of 3 m and a depth of 1 m. The "particle expansion method" is adopted to successively generate sand particles and hydrate particles [24] to ensure that all particles can be stably generated within the specified area 3 Geofluids and conform to the pore characteristics of real sediments. Subsequently, the servo mechanism is adopted to control the movement of the wall [25] so that the model reaches the consolidation state in three directions with the horizontal maximum and minimum ground stress and vertical ground stress.
To simulate the influence of the borehole on the hydrate formation, a through-hole model is selected, and all particles in the range are deleted. By establishing a cylindrical wall that fits the inner wall of the borehole, the servo mechanism is used to apply mud pressure on the inner wall of the borehole. When the inner wall pressure of the wellbore reaches a stable state, the borehole deformation and the stress state around the wellbore reflect the model's prediction of the real situation. Since the discrete element model simulates the effective stress state, the ground stress and mud pressure of the model are the differences between the actual stress and the pore pressure.
To simulate the composition of sediments, the established model takes sand particles with a porosity of 0.5 and a radius of 4 cm as the sediment skeleton, hydrate particles with a radius of 1.5 cm are generated between the pores of the sediment skeleton, and the hydrate saturation in sediments can be changed by setting the number of hydrate particles. The microscopic parameters of model particles and contact are based on the discrete element numerical simulation study of hydrate sediments [26,27]. Due to the large discrete element model of borehole stability, to ensure the calculation speed of the model, the sand particles and hydrate particles are also amplified. However, this amplification process is directly related to the setting of the particle microscopic parameters, so the particle size changes will not cause changes in the mechanical response of the model.
Verification of Numerical and Analytical Models.
For deep-water shallow hydrate reservoir, the in situ stresses are decided by the overburden stress. So two horizontal stresses can be set as equal. The model in Figure 1 can be modified as Figure 2. Since the analytical model is based on the assumption of horizontal isotropic stress, to compare and verify the calculation results of the numerical model and the analytical model, it is necessary to establish a cylindrical discrete element model of the hydrate reservoir ( Figure 2) and apply the same horizontal and vertical ground stress as the analytical model so that the discrete element model and the analytical model have the same ground stress conditions. The model dimension adapted is large enough to eliminate the boundary effect. During calibration, the horizontal ground stress was 3 MPa, the vertical stress was 5 MPa, and the shaft wall support stress was 1 MPa.
In addition to ensuring that the calibrated models have the same ground stress conditions, it should also be ensured that the constitutive characteristics and mechanical responses of the hydrate formation are the same. The constitutive model in the form of internal friction angle described by equation (4) determines the constitutive characteristics and mechanical response of the reservoir in the analytical model. To fit the strain ε corresponding to the peak value tanβ, the expression of strain ε in equation (4) is transformed to obtain equation (12). By changing β i , A, B, C, and D in formula (12), a combination of parameters with the same mechanical response as the discrete element model can be fitted. Figure 3 shows the relationship between tanβ and strain ε. Table 1 lists the parameter combinations of equation (12) 4 Geofluids is used to study the influence of different saturations, the corresponding parameter combinations in Table 1 are also used.
where β i is the initial internal friction angle, ε is the strain, and A, B, C, and D are the parameters related to the constitutive model. Figure 4 compares the calculation results of the analytical model and the discrete element model, where a is the deformed borehole radius in the analytical model and r is the distance between a point and the borehole center. It can be seen from the figure that the stress distribution states around the well according to the analytical model and the discrete element model are very similar. Since the analytical model is based on the continuity assumption of elastoplastic mechanics, the calculation results of the analytical model are more continuous, while the discrete element model is composed of discrete element granular elements, so the measured stress values are more volatile, but the trend of the two changes is consistent.
Parametric Analysis of Wellbore Stability
In 2007, China's NGH drilling project successfully drilled a physical sample of NGH in the Shenhu area in the northern South China Sea. The hydrate layer was 18-34 m thick, with a saturation of 20%-43%, and the methane content in the released gas was higher than 99% [28]. Several trial mining works led by the Guangzhou Marine Geological Survey in the Shenhu waters have proved that there are abundant hydrate resources in the Shenhu seabed [29,30], and the Shenhu waters of the South China Sea have gradually become an important area for hydrate exploration and mining research in China.
With the advancement of hydrate exploration and research, hydrate reservoir mining methods and concepts are constantly being updated. A deep-sea shallow hydrate reservoir has the characteristics of large reserves and poor cementation and is a weakly consolidated or unconsolidated nondiagenetic hydrate reservoir. The exploitation of this type of hydrate reservoir can be accompanied by environmental pollution and geological disasters such as massive releases of methane gas and submarine landslides [31]. The Marine Hydrate Development and Research Team proposed for the first time a new method of "solid fluidization mining of submarine non-diagenesis hydrate deposits." This had core advantages such as low pollution, low secondary disasters, and no damage to the lower porous reservoir hydrate [32]. The present paper assumes that the solid fluidization method is used to mine the deep-sea shallow hydrate, and it is necessary to study two types of wells in the hydrate formation drilling: drilling vertical wells and producing horizontal mining wells (see Figure 5) [33]. This paper takes a shallow hydrate reservoir in Shenhu sea area as the research object and adopts an analytical model and discrete element method to study drilling a vertical well and a mining horizontal well, respectively.
Chongyuan et al. studied the in situ stress state of a seabed formation in the northern South China Sea and found that the ratio of the maximum horizontal principal stress to the vertical stress in the northern South China Sea was about 0.76, and the ratio of the maximum to minimum horizontal principal stress ranged from 1.07 to 1.18 [34]. Sun
Geofluids
and gave the pore pressure and mud pressure of the SH2 well at different depths [35]. Since the analytical model and discrete element model used in this article are drainage models, the actual stress conditions used are effective stresses. Combined with the abovementioned studies, Table 2 lists the ground stress, mud pressure, pore pressure, threedimensional effective ground stress and borehole support stress (effective mud pressure), and other parameter values.
Since the borehole stability analytical model is based on the assumption of horizontal isotropic stress, when using this analytical model to study the wellbore stability of a vertical well, the horizontal stress is the maximum horizontal stress in the table. It can be seen from the table that the gap between the maximum level and the minimum ground stress is relatively small, so the use of this approximation method will not cause too much deviation in the analytical model calculation results, and the results still reflect the stress state of the hydrate formation around the well. Figure 6 shows the relationship between borehole support stress and a 0 /a at different depths, where a 0 and a are the initial borehole radius and the deformed borehole radius in the analytical model. The larger the a 0 /a ratio, the smaller the deformed borehole radius. In Figure 6, the 200 meters below sea floor (mbsf), 400 mbsf, and 600 mbsf borehole support stresses all decrease with increase of a 0 /a, and all have experienced a process of deceleration of decline. When a 0 /a is small, the strain near the borehole is small, and the stratum deforms elastically only. The formations of 200 mbsf, 400 mbsf, and 600 mbsf appear to have a plastic deformation at a 0 /a = 1:0037, 1.0217, and 1.037, respectively. At this time, the speed of the borehole support stress curve decreases significantly. Figures 7-9 show the relationship between radial stress, circumferential stress, and vertical stress around the well and r/a at different depths, respectively. In the analytical model, r represents the distance between a point and the borehole center; the larger the r/a ratio, the further away 6 Geofluids the point is from the borehole. Figures 7-9 show that the greater the depth, the greater the three-dimensional stress. The radial stress increases with increase of r/a, and the circumferential stress and the vertical stress decrease with increase of r/a, but this trend has nothing to do with the depth. In the figures, the back of the elastoplastic interface is the elastic deformation zone, the area between the elastoplastic interface and the strain softening-hardening interface is the strain hardening zone, and the strain softening zone is before the strain softening-hardening interface. As the depth increases, the r/a ratios of the elastoplastic interface and the strain softening interface around the well gradually decrease. Table 3 lists the positions of the elastic-plastic interface and the strain softening-hardening interface corresponding to different depths. Figure 10 shows the relationship between borehole support stress and a 0 /a under different hydrate saturations. When a 0 /a is small, only elastic deformation occurs in the formation around the well. When a 0 /a is greater than 1.0037, a plastic deformation zone appears around the well, and the stress curve of the borehole support turns and starts to slow down. Figure 10 shows that the hydrate saturation has little effect on the stress of the borehole support. Figure 11 shows the distribution of radial stress, circumferential stress, and vertical stress around the well under different hydrate saturations. Figure 11 shows that the saturation change has a small effect on the threedimensional stress state. Table 4 lists the positions of the elastic-plastic interface and the strain softening-hardening interface corresponding to different saturations. It can be seen from the table that the r/a ratio of the elastic-plastic interface under the three saturations remains unchanged, but the r/a ratio of the strain softening-hardening interface changes slightly, which increases with increasing saturation. Figures 12-14 show the relationships between borehole radial strain, borehole diameter reduction, and time at different initial borehole diameters at depths of 200 mbsf, 400 mbsf, and 600 mbsf. As the number 7 Geofluids of time increases, the radial strain of the borehole and the shrinkage of the borehole diameter gradually tend to remain unchanged, indicating that the stress state around the borehole reaches equilibrium after deformation and the borehole shape no longer changes. Figure 15 shows the effect of depth on the maximum radial strain and hole diameter reduction. The maximum radial strain in the figure is the value of borehole radial strain tending to be constant in Figures 12-14. It can be seen that as the initial borehole diameter increases, the absolute reduction in borehole diameter also increases, but the radial strain of the borehole first increases and then decreases. The initial borehole diameter is in the range from 0.8 to 1.2 m, and the radial strain is large, indicating that the relative deformation of the borehole is small at this time. Therefore, the initial borehole diameter is in the range from 0.6 to 1.2 m, which can be used as a relatively optimal diameter for production boreholes.
Conclusion
This paper has used a discrete element method to establish a borehole stability model of a deep-water shallow hydrate reservoir. The discrete element numerical model has been compared with an elastic-plastic analytical model of borehole stability based on strain softening to verify the reliability of the numerical model. The analytical model and the discrete element model were used to study drilling vertical wells and production horizontal wells, respectively, and the influence of factors such as depth and saturation on the stress state and borehole strain around the well were analyzed. The results show that the near-wellbore zone can be divided into a plastic strain softening zone, Vertical stress Circumferential stress Radial stress Figure 11: Relationships between radial, circumferential, and vertical stresses and r/a at different hydrate saturations. 8 Geofluids a plastic strain hardening zone, and an elastic zone according to the different mechanical characteristics. Reservoir depth and hydrate saturation can change the stress state near the well. The greater the depth and the lower the hydrate saturation, the greater the borehole shrinkage. The diameter of the optimal horizontal well in the goaf is in the range from 0.6 to 1.2 m, the actual hydrate reservoir may have strong heterogeneity, and the optimal production hole diameter may be slightly smaller than this range. The calculated results should be verified by experiment. However, the experiment has not been carried out owing to difficultly constructing the borehole of hydrate in laboratory. The next step is to carry out a field experiment for the stability study of hydrate borehole.
Data Availability
The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study. | 5,721.8 | 2020-12-09T00:00:00.000 | [
"Engineering",
"Environmental Science"
] |
Experimental Study of Stress and Deformation of Reclaimed Asphalt Concrete at Different Temperatures
Asphalt concrete has been used as a material for dam core walls because of its impermeability, durability and reliability. Firstly, asphalt is a temperature-sensitive material, and many of its characteristics are related to temperature. Secondly, because of the increasing construction height of the dam, the pressure on the asphalt concrete core wall is also great. Finally, for the purpose of resource utilization, it is necessary to verify whether the reclaimed asphalt concrete can be used in dam construction. Therefore, it is necessary to study the stress and deformation characteristics of recycled asphalt concrete under different temperatures and confining pressures. In this study, three groups of triaxial tests of reclaimed asphalt concrete were carried out for the first time in a new temperature-controlled room. Duncan Zhang’s E-v model was used to fit the test results. The results show that the stress–strain curves of reclaimed asphalt concrete show softening characteristics at low temperatures and low confining pressure. It evolves to a hardening type with the increase in temperature and confining pressure. The bulk curve is first contracts but is followed by dilatancy. The dilatancy characteristics become more obvious at low temperatures and low confining pressure. With the increase in temperature and confining pressure, the dilatancy characteristics will weaken. Duncan Zhang’s E-v model has a good fitting effect on the stress–strain relationship but a poor fitting effect on the volumetric curve. The research of this paper can better combine the utilization of waste resources with engineering and achieve the aim of resource-saving and waste utilization under the premise of ensuring the safety of the engineering
Introduction
Asphalt concrete is a very good engineering material. Because of its impervious deformation and coordination characteristics, it is not only used in industry, agriculture and other fields but also widely used in roads, airports and water conservancy projects. Especially with the rapid development of water conservancy constructions in recent years, asphalt concrete is widely used in the seepage control of dams, and a series of asphalt concrete core wall dams are constructed [1][2][3][4][5]. Many scholars [6][7][8][9][10][11] have conducted a lot of research on its strength and deformation characteristics. Asphalt concrete is a typical temperature-sensitive material, and its mechanical properties are greatly affected by temperature. Wei Yun [12] studied the asphalt concrete's mechanical properties with the variation of temperature using the triaxial test. Based on Duncan Zhang's model, the variation rule of the model parameters with temperature is studied. The fitting degree of the model under different temperatures is analyzed with the statistics. Wang Jingwen [13] studied the mechanical properties of asphalt concrete at 0~20 • C with the triaxial compression test and triaxial creep test, finding different effects on the material properties of the temperature. Wang Liang [14] established a three-dimensional aggregate model according to the aggregate gradation in asphalt concrete specimens and used this model to conduct a discrete element study on uniaxial compression tests under different strain rates. Chen Yu [15] conducted two kinds of asphalt concrete tests, respectively, at different temperatures by indoor high pressure and a temperature control triaxial instrument to study the influence of temperature on its mechanical properties.
In addition, in order to achieve the purpose of recycling waste resources, many scholars have conducted a lot of research on the performance of recycled asphalt concrete. Liu Song an [16] studied recycled asphalt concrete's design method of mix ratio, road performance and durability modified with composite fiber and natural polymer asphalt. Zhou Zhi gang [17] proposed an optimal design method for recycled asphalt that comprehensively considers the requirements of technical performance and economic benefit index of reclaimed asphalt through the study of plant heat mix and SBS-modified asphalt pavement engineering. Hu Ya chun [18] proposed a research idea of improving the strength of coldreclaimed asphalt concrete by using a water-based environment-friendly asphalt pavement regenerating agent. Wang Hai feng [19] studied the adaptability between cement-fly ash and recycled aggregate systems based on the recovery of asphalt pavement materials. Bian Hai ning [20] studied and discussed the mixed design of recycled asphalt concrete for old pavement. Using the recycling technology of discarded pavement materials to achieve the goal of saving production costs and reducing energy consumption, Li Cai hui [21] conducted a splitting test and compression test on a cold-reclaimed asphalt mixture with different used material contents to determine the reasonable mixing amount of light oil regenerated agents under different used material contents. Then, a water stability test, high-temperature stability test and low-temperature anti-cracking performance test were conducted on a cold-reclaimed asphalt mixture with a reasonably regenerated agent to study the mixing amount of used material and the cold-reclaimed asphalt with light oil regenerated agent's relationship to the road performance of mixtures. Sumeda Paranavithana [22] found that recycled concrete aggregates (RCA), which are produced by crushing demolished concrete elements, differ from fresh aggregates due to the cement paste attached to the surface of the original natural aggregates after the process of recycling. This highly porous cement paste and other contaminations contribute to the lower particle density and higher porosity variation in the quality of the RCA and higher water absorption. It was also found that all the volumetric properties (except the percentage of air voids), resilient modulus and creep values of asphalt specimens containing RCA as coarse aggregates were relatively lower compared with the values found for similar specimens made with only fresh aggregates. Xun hao Ding [23] investigated the performance of recycled asphalt concrete with stable crumb rubber asphalt (SCRA) binder. Both the normal recycled asphalt mixtures and the SCRA recycled asphalt mixtures were prepared with 0, 30 and 50% content of the reclaimed asphalt pavement (RAP). Laboratory tests were carried out to compare the performance of different mixtures, and the comprehensive recycling effect of the SCRA and rejuvenator were evaluated further. The SCRA is much better than virgin asphalt (VA) in recycling aged asphalt mixtures with large RAP content, which could reach 50%. The rejuvenator has a positive effect on lowtemperature performance, moisture stability and fatigue resistance. By combining the use of the SCRA and rejuvenator, the low-temperature performance of the SCRA recycled asphalt mixtures could be further improved while the other performance retains a high level. Jie Ji [24] studied the recycled asphalt concrete (RAC) fatigue properties test plan, and the influence of RAs on it was analyzed, finding that it ignores the applicability of different test methods and the impacts of regional temperature and climate conditions. Future research directions and recommendations for a test plan regarding the fatigue properties of RAC are proposed. Research should focus on the effect of RA properties on fatigue properties. It should be carried out with reasonable test methods, service life characterization models, and climate-identical test conditions to clarify the durability index. The evaluation system of fatigue properties of RAC should be established, and solid theoretical supports for the application of construction and demolition wastes (CDWs) should be provided, thereby accelerating the application of recycled asphalt pavement containing CDWs.
Chen, J.S [25] used three reclaimed asphalt concrete (RAC) stockpiles sampled, and the aged binders recovered from RAC binders were mixed with recycling agents at ten levels to produce bitumen blends. The blends using virgin bitumen as the softening agent exhibited a significantly different rheological behavior from the ones using the rejuvenating agent. The addition of a recycling agent could shift up or down the master curve of the blend, depending on the engineering properties of the recycling agent. A normalized viscosity ratio (NVR) model was used to characterize the rheological properties of aged bitumen mixed with softening and rejuvenating agents. An interaction parameter was introduced into the model to consider the physico-chemical reaction between aged bitumen and the recycling agent. This mixing rule was compared to the method specified in the blending chart by the Asphalt Institute (AI). The blending chart was shown to be applicable to determine the amount of the softening agent required to meet the target viscosity. The NVR model appeared to be a better tool for the rejuvenating agent to predict the viscosity of a recovered bitumen blend than the AI chart.
M. R studied [26] a total of four different mixtures prepared by partially replacing natural aggregates with recycled asphalt concrete (RAC) in different proportions. The results showed that adding RAP to the mixture reduced the mechanical strength of the roller-compacted concrete (RCC) mixture. The best mechanical strength was obtained at 50% RAC replacement. To increase the mechanical strength of RCC made with 50% RAP, Micro Silica (MS) with partial replacement of cement at 3, 6, 9 and 12% was used. Increasing the MS content from 3 to 12% caused the mechanical strength of all mixtures to increase. The results [27][28][29] showed that RCC with 50% RAC and 9% MS had about 20% more compressive strength. Moreover, the increase in tensile splitting and flexural strength was 6 and 2%, respectively. The statistical analysis indicates that there was a strong relationship (R2 > 0.98) between flexural strength values estimated from the regression model and the measured laboratory values (this relationship was about 0.84 for compressive strength and tensile splitting strength). The estimation of tensile splitting strength and flexural strength with respect to compressive strength showed that there was a strong (R2 > 0.98) and good relationship (R2 > 0.75) between them, respectively.
However, there are a few pieces of research on regenerating old asphalt pavement concrete that were applied to the dam core wall. Reusing waste has always been the goal of our human society to seek sustainable development; based on this purpose, studying the performance of recycled asphalt concrete is very necessary. In order to study the influence of temperature and confine pressure on the characteristics of recycled asphalt concrete further, three groups of triaxial tests under different temperatures and confining pressure were carried out in this paper, and then the test results were fit with Duncan Zhang's E-v hyperbolic model.
Test Facility
The triaxial test of recycled asphalt concrete was carried out on SY-250 (Jiang Su Yong Chang, Jiangsu, China) as shown in Figure 1. The sample size of this test is Φ101 mm × 200 mm. Strain control was adopted in the test. The test speed was at rate of 0.5 mm/min, and the test was stopped when the axial strain reached 25%. Stress and strain during the test are reflected by dial gauge and ring readings. Considering the pressure on the asphalt concrete core wall, four confining pressures were set at 0.2, 0.5, 0.8 and 1.1 MPa, respectively. During the test, the confining pressure is provided by a high-pressure gas cylinder, which is connected to the electric air compressor. This ensures reliable and stable pressure during the test. The volume variation in the test is measured by measuring weight of confining pressure control chamber. When the volume of the sample expands, the water in the triaxial pressure chamber is discharged to the confining pressure control chamber, and the weight of the confining pressure control chamber increases. On the contrary, when the volume of the sample shrinks, the water in the confining pressure control chamber is sucked into the triaxial pressure chamber. The confining pressure control chamber weight is reduced. The volume change is converted by mass transformation of the confining pressure control chamber. The biggest difference between this temperature control triaxial instrument and the previous one is that the triaxial instrument is placed in a room enclosed by thermal insulation materials. The kind of room can play a role in isolating the external environment temperature. It also has the effect of heat insulation to meet the temperature required by the test. The required temperature is adjusted by air conditioning before the 8 h of the test. Therefore, the ambient temperature can be maintained within the allowable error range of the test time. It can better study the influence of temperature change on the results of the triaxial test.
Test Sample Preparation
The asphaltic concrete in this test was taken from the old pavement. The a crete was heated, and then the regeneration agent was added and then was The compaction hammer with a weight of 4536 g, and the height of asphaltic concrete is 457 mm. First, the asphalt material was heated to 130 °C, and the was heated to 150 °C; then, the asphalt was added and mixed in the mixing po and the regeneration agent was added and mixed again for 2 min. The discha ature was 140 ± 5 °C. The sample is compacted into 3 layers, 110 times for each the test samples cooled for 24 h together with the mold. The samples were plac for seven days. Before the test, the samples were placed in a thermostatic which was adjusted to the temperature of the test. After curing for 24 h, the on was carried out. In the whole test process, the temperature change of the enc did not exceed ±0.5 °C. The test equipment and scheme are shown in Figure 1, respectively.
Test Sample Preparation
The asphaltic concrete in this test was taken from the old pavement. The asphalt concrete was heated, and then the regeneration agent was added and then was compacted. The compaction hammer with a weight of 4536 g, and the height of asphaltic compaction concrete is 457 mm. First, the asphalt material was heated to 130 • C, and the mixing pot was heated to 150 • C; then, the asphalt was added and mixed in the mixing pot for 1 min, and the regeneration agent was added and mixed again for 2 min. The discharge temperature was 140 ± 5 • C. The sample is compacted into 3 layers, 110 times for each layer. Then, the test samples cooled for 24 h together with the mold. The samples were placed in room for seven days. Before the test, the samples were placed in a thermostatic water bath, which was adjusted to the temperature of the test. After curing for 24 h, the triaxial test on was carried out. In the whole test process, the temperature change of the enclosed space did not exceed ±0.5 • C. The test equipment and scheme are shown in Figure 1 and Table 1, respectively.
Stress-strain Relation Curve
The stress-strain curves of the three groups of samples obtained by the large strain triaxial tests are shown in Figure 2. As we can see from Figure 2, the stress-strain curves of recycled asphalt concrete at different temperatures have two types: hardening and softening. At the low temperature of 4 • C, the curves basically show a softening type. The lower the confining pressure is, the more the softening effect is obvious. The stress drops quickly after softening. When the confining pressure is 0.2 MPa, the softening stress decreases to half of the peak stress at the final strain, which is obviously different from that of other brittle materials. It is clear that the asphalt played a role in the damage. However, with the increase of confining pressure, the curve gradually has a trend of softening to hardening. At the temperature of 12 • C, when the confining pressure is 0.2 MPa, the curve shows an obvious softening type. When the confining pressure increases to 0.5, 0.8 and 1.1 MPa, the softening effect becomes not obvious, and it turns into a hardening type when it reaches 1.1 MPa. At the temperature of 25 • C, in addition to the curve of 0.2 MPa, the curves are all hardening types basically. The stress keeps increasing with the increase of strain. When the strain reaches 10%, the stress basically remains unchanged. In summary, it can be seen that the stress-strain curves of reclaimed asphalt concrete are closely related to temperature and confining pressure. Under the condition of low temperature and low confining pressure, it presents a softening type. With the increase in temperature and confining pressure, the softening type gradually evolves into the hardening type.
Stress-strain Relation Curve
The stress-strain curves of the three groups of samples obtained by the large stra triaxial tests are shown in Figure 2. As we can see from Figure 2, the stress-strain curv of recycled asphalt concrete at different temperatures have two types: hardening and s tening. At the low temperature of 4 °C, the curves basically show a softening type. T lower the confining pressure is, the more the softening effect is obvious. The stress dro quickly after softening. When the confining pressure is 0.2 MPa, the softening stress d creases to half of the peak stress at the final strain, which is obviously different from th of other brittle materials. It is clear that the asphalt played a role in the damage. Howev with the increase of confining pressure, the curve gradually has a trend of softening hardening. At the temperature of 12 °C, when the confining pressure is 0.2 MPa, the cur shows an obvious softening type. When the confining pressure increases to 0.5, 0.8 a 1.1 MPa, the softening effect becomes not obvious, and it turns into a hardening type wh it reaches 1.1 MPa. At the temperature of 25 °C, in addition to the curve of 0.2 MPa, t curves are all hardening types basically. The stress keeps increasing with the increase strain. When the strain reaches 10%, the stress basically remains unchanged. In summa it can be seen that the stress-strain curves of reclaimed asphalt concrete are closely relat to temperature and confining pressure. Under the condition of low temperature and lo confining pressure, it presents a softening type. With the increase in temperature and co fining pressure, the softening type gradually evolves into the hardening type.
Volume Change Relation Curve
The volume variation curves of the three groups of samples obtained by the la strain triaxial test are shown in Figure 3. As we can see from Figure 3, under differ temperatures and confining pressures, the volumetric variation curves of reclaimed phalt concrete basically start with shear contraction but are followed by dilatancy shows a state of shear contraction before the axial strain a reaches 3% and then chan to dilatancy.
Volume Change Relation Curve
The volume variation curves of the three groups of samples obtained by the large strain triaxial test are shown in Figure 3. As we can see from Figure 3, under different temperatures and confining pressures, the volumetric variation curves of reclaimed asphalt concrete basically start with shear contraction but are followed by dilatancy. It shows a state of shear contraction before the axial strain ε a reaches 3% and then changes to dilatancy.
Volume Change Relation Curve
The volume variation curves of the three groups of samples obtained by the large strain triaxial test are shown in Figure 3. As we can see from Figure 3, under different temperatures and confining pressures, the volumetric variation curves of reclaimed asphalt concrete basically start with shear contraction but are followed by dilatancy. It shows a state of shear contraction before the axial strain a reaches 3% and then changes to dilatancy. At the low temperature of 4 °C and confining pressure of 0.2 MPa, the dilatancy rate can reach 12% with the increase of strain. Combined with the stress-strain curve, it can be seen that the dilatancy occurs before the peak stress, which indicates that the internal particles need to roll over another part of the particles and produce relative dislocation, which requires greater bite force and is manifested as higher stress. With the increase of strain, one part of the particle bypasses another part of the particle, the structure becomes loose, the stress is reduced, and therefore, the performance is softened. As a whole, the lower the temperature, the smaller the confining pressure and the more severe the dilatancy; with the increase in temperature and confining pressure, the dilatancy effect will be weaker and weaker. It shows that the deformation of recycled asphalt concrete is also At the low temperature of 4 • C and confining pressure of 0.2 MPa, the dilatancy rate can reach 12% with the increase of strain. Combined with the stress-strain curve, it can be seen that the dilatancy occurs before the peak stress, which indicates that the internal particles need to roll over another part of the particles and produce relative dislocation, which requires greater bite force and is manifested as higher stress. With the increase of strain, one part of the particle bypasses another part of the particle, the structure becomes loose, the stress is reduced, and therefore, the performance is softened. As a whole, the lower the temperature, the smaller the confining pressure and the more severe the dilatancy; with the increase in temperature and confining pressure, the dilatancy effect will be weaker and weaker. It shows that the deformation of recycled asphalt concrete is also closely related to temperature and confining pressure.
Shear Strength Parameter Curve According to the peak deviatoric stress of recycled asphalt concrete at different temperatures, the molar coulomb circle was drawn, and the shear strength parameters were fitted. As can be seen from Figure 4, the shear strength parameters of reclaimed asphalt concrete at different temperatures are different. With the increase in temperature, the value of c decreases while the value of ϕ increases. The higher of temperature is, the smaller of c is and the larger of ϕ. This indicates that the shear strength of recycled asphalt concrete is temperature dependent, which requires special attention. The temperature increase has a great influence on the internal friction angle, which makes the reclaimed asphalt concrete show different shear characteristics at different temperatures, and it has a great influence on the dam core wall constructed by it.
Introduction of Duncan Zhang's E-v Hyperbolic Model
Duncan Zhang E-ν model E t ; Poisson's ratio ν t ; Stress level failure ratio R f ; stress level S; Initial Poisson's ratio ν i and A are calculated as follows: In the formulas, (σ 1 − σ 3 ) f is the maximum value of the deviatoric stress test; (σ 1 − σ 3 ) u is the extreme asymptotic value of deviatoric stress; p a is the atmospheric pressure; c is cohesive force; ϕ is the angle of internal friction; D, F, G, K, n are the model parameter.
Duncan Zhang's E-v model parameters of the three groups of recycled asphalt concrete materials determined according to the above calculation formula are shown in Table 2.
The Results of Stress-Strain Fit of Duncan Zhang's E-v Model Are Compared with Experimental Results
The stress-strain curves of reclaimed asphalt concrete under different temperatures and confining pressure can be fitted by Duncan Zhang's E-v model parameters. According to Figure 5, at the low temperature of 4 • C and before the peak point of the test curve, the rest of the fitting curve and the test curve have a certain degree of fit. However, after the peak point, the stress value decreases with the development of the strain since Duncan Zhang's model is a hardened curve. With the development of the strain, the stress value increases continuously. At 12 • C, all the test curves showed a hardening type. At 25 • C, in addition to the curve of 0.2 MPa, the test curves were all hardened.
In summary, it can be seen that recycled asphalt concrete has softening characteristics under low confining pressure, and Duncan Zhang's E-v model is a hardening model, so the stress-strain relationship fitting effect of the reclaimed asphalt concrete under low confining pressure is poor, and the softening phenomenon after the peak cannot be fitted. However, it has a certain applicability under high confining pressure. In summary, it can be seen that recycled asphalt concrete has softening characteristics under low confining pressure, and Duncan Zhang's E-v model is a hardening model, so the stress-strain relationship fitting effect of the reclaimed asphalt concrete under low
Comparison of Duncan Zhang's E-v Model with Experimental Results of Volume Variation
The volume curves of reclaimed asphalt concrete under different temperatures and confining pressures can be fitted by Duncan Zhang's E-v model parameters. It can be seen from Figure 6 that test curves at different temperatures are basically shear contraction but followed by dilatation, while the fitted curves are all dilatation. Under the same strain, for test curves, the larger the confining pressure, the larger the dilatancy. However, different from Poisson's ratio of Duncan Zhang's E-v model, the larger the confining pressure, the smaller the test measured Poisson's ratio. The test measured Poisson's ratio increases with the stress level in a positive correlation too.
Comparison of Duncan Zhang's E-v Model with Experimental Results of Volume Variation
The volume curves of reclaimed asphalt concrete under different temperatures and confining pressures can be fitted by Duncan Zhang's E-v model parameters. It can be seen from Figure 6 that test curves at different temperatures are basically shear contraction but followed by dilatation, while the fitted curves are all dilatation. Under the same strain, for test curves, the larger the confining pressure, the larger the dilatancy. However, different from Poisson's ratio of Duncan Zhang's E-v model, the larger the confining pressure, the smaller the test measured Poisson's ratio. The test measured Poisson's ratio increases with the stress level in a positive correlation too. There is a poor fit effect between the fitting curves and test curves at 4 °C. However, there is a large deviation between the fitting curves and the test curves at the other two temperatures. This indicates that Duncan Zhang's E-v model can represent the dilatancy characteristics of materials, but its fitting effect on the experimental results is poor. In addition, when using Duncan Zhang's E-v model to fitting dilatancy, all Poisson's ratios are greater than 0.5. It can be seen that the fitting effect of Duncan Zhang's E-v model on the volume variation of reclaimed asphalt concrete is poor.
Comparison of Poisson's Ratio between Experimental and Duncan Zhang's E-v Model
The measured test ratio is the tangent Poisson's ratio There is a poor fit effect between the fitting curves and test curves at 4 • C. However, there is a large deviation between the fitting curves and the test curves at the other two temperatures. This indicates that Duncan Zhang's E-v model can represent the dilatancy characteristics of materials, but its fitting effect on the experimental results is poor. In addition, when using Duncan Zhang's E-v model to fitting dilatancy, all Poisson's ratios are greater than 0.5. It can be seen that the fitting effect of Duncan Zhang's E-v model on the volume variation of reclaimed asphalt concrete is poor.
Comparison of Poisson's Ratio between Experimental and Duncan Zhang's E-v Model
The measured test ratio is the tangent Poisson's ratio ν = dε r dε a . The test body curve has two points A (ε a1 , ε r1 ), B (ε a2 , ε r2 ). The tangent Poisson's ratio of middle point C (ε a3 , ε r3 ) between A and B is ν c = dε r dε a = ∆ε r ∆ε a = ε r2 −ε r1 ε a2 −ε a1 . On the stress-strain curve, the corresponding stresses at two points A and B are σ m1 , σ m2 , σ m3 = σ m1 +σ m2 2 , because the Level of stress S = σ m σ Max , σ Max is the maximum value of the stress-strain curve. The measured experimental Poisson's ratios under different stress levels are obtained successively and compared with the Poisson's ratios calculated by Duncan Zhang's E-v model.
It can be seen in Figure 7 that at 4 and 12 • C, Poisson's ratio of Duncan Zhang's E-v model increases with the stress level in a positive correlation. When the stress level is same, the confining pressure and Poisson's ratio increases. Both of them are more than 0.5, which indicates that the volume is dilatant. The larger the confining pressure, the larger of dilatancy. However, different from Poisson's ratio of Duncan Zhang's E-v model, the larger the confining pressure, the smaller the test measured Poisson's ratio. The test-measured Poisson's ratio also increases with the stress level in a positive correlation. However, when the stress level is the same, the larger the confining pressure and the smaller the Poisson's ratio. The Poisson's ratio is less than 0.5 at a low-stress level and greater than 0.5 at a high-stress level, which indicates an initial volume shrinkage and then dilatation. In addition, it can be seen that except for the low confining pressure of 0.2 MPa, Poisson's ratio of Duncan Zhang's E-v model is larger than that of the test measured, and the gap between the two decreases with the increase of stress level. This indicates that the Poisson's ratio of Duncan Zhang's E-v model is poor at predicting the test-measured Poisson's ratio when the stress level is low. At the same time, it is fit at high-stress levels.
Since the Poisson's ratio of Duncan Zhang's E-v was greater than 0.5, but the Poisson's ratio of the test is less than 0.5 at a low level and is greater than 0.5 at a high-stress level, there is a large gap between the volume of Ducan Zhang's E-v model and test. So the fitting effect of Ducan Zhang's E-v model to the test volume was poor, which was consistent with the conclusion of Section 4.3.
It can be concluded from Figure 7 that, different from the low-temperature condition, when the temperature is 25 • C, the measured Poisson's ratio is more than 0.5 at the lowstress level. This indicates that recycled asphalt concrete has no shrinkage, only dilatancy at high temperatures. This indicates that the shear shrinkage of recycled asphalt concrete becomes weaker, and the dilatancy becomes stronger at high temperatures. In addition, because Duncan Zhang's E-v model is a hardening type, Poisson's ratio can be calculated until the max stress level. However, for the softening test curves, after reaching the max stress level, the stress level will decrease and also have Poisson's ratio. So, Poisson's ratio after the max stress level cannot be calculated by Duncan Zhang's E-v model.
In summary, the differences between Poisson's ratio of Duncan Zhang's E-v model and the test-measured Poisson's ratio are the reason for its poor fitting effect on the volumetric curve.
1.
The shear strength parameters of recycled asphalt concrete at different temperatures have a great difference. The value of c decreases with the increase of temperature, while the value of ϕ increases. Therefore, the influence of temperature on the shear strength parameters of recycled asphalt concrete is particularly worth paying attention to. In the future constitutive model parameters, temperature as an influencing factor cannot be ignored. It is necessary to establish a temperature-related constitutive model, which will make the calculation of dam deformation and stability more realistic.
2.
The stress-strain relationship of reclaimed asphalt concrete shows softening characteristics at low temperatures and confining pressure. It gradually evolves into a hardening type with the increase in temperature and confining pressure. The bulk transformation of reclaimed asphalt concrete is mainly shear contraction but followed by dilatancy. The dilatancy characteristics become more obvious at low temperatures and low confining pressure. With the increase in temperature and confining pressure, the dilatancy characteristics will weaken. 3.
At low confining pressure, the fitting effect of Duncan Zhang's E-v model on the stress-strain relation of recycled concrete is poor but better at high confining pressure. However, the fitting effect on the volume variation of asphalt concrete is not ideal and generally larger. The test curve consists of two parts: shear contraction and dilatancy, while the fitting curve is only dilatancy.
4.
Under the same stress level, Poisson's ratio of Duncan Zhang's E-v model increases with the increase of confining pressure, while the measured Poisson's ratio decreases.
Poisson's ratio calculated by Duncan Zhang's E-v model is greater than 0.5, while the measured Poisson's ratio is less than 0.5 at a low-stress level, and Poisson's ratio is greater than 0.5 after reaching a certain stress level.
Author Contributions: J.Z. and M.Z. performed data curation, formal analysis, investigation, methodology, validation, and writing of the original manuscript; J.L. and X.H. contributed to data curation, conceptualization, investigation, supervision, and editing of the manuscript. All authors have read and agreed to the published version of the manuscript. | 7,526.4 | 2023-02-01T00:00:00.000 | [
"Engineering",
"Materials Science"
] |
Maximum Interval of Stability and Convergence of Solution of a Forced Mathieu’s Equation
This paper investigates the maximum interval of stability and convergence of solution of a forced Mathieu’s equation, using a combination of Frobenius method and Eigenvalue approach. The results indicated that the equilibrium point was found to be unstable and maximum bounds were found on the derivative of the restoring force showing sharp condition for the existence of periodic solution. Furthermore, the solution to Mathieu’s equation converges which extends and improves some results in literature.
Introduction
Consider a harmonically forced Mathieu's equation defined by ( ) For small ε , this equation describes a simple harmonic oscillator whose frequency is a periodic function of time with the boundary condition as; is the second derivative with respect to time, f is the amplitude of a periodic driving force, w and ε are the Mathieu's parameters and λ is the angular frequency of the periodic driving force.
Mathieu's equation is a special case of a linear second order homogenous equation [1]. In [2], Equation (1) was discussed in connection with problem of vibrations in elliptical membrane and developed the leading terms of the series known as Mathieu's function. Mathieu's function was further investigated by a number of researchers who found a considerable amount of results. [3] [4] [5] [6] wrote that Mathieu's differential equation occurs in two main categories involving elliptical geometrics, such as analysis of vibrating modes, elliptical membrane, the propagation modes of elliptic pipes and the oscillation of water in a lake of elliptic shape. Mathieu's equation arises after separating the wave equation using elliptic coordinates. Secondly, problems involving periodic motion are the trajectory of an electron in a periodic array of atoms [7].
Stability is an important concept in linear and nonlinear analysis. For instance, roughly speaking, a physical system is stable if small changes at sometimes cause only a small change in the behavior of the system in future [8]. Analytically, stability is determined by the interval placed on the total derivative of the system form by the given differential equation. , ,
Preliminaries
, , x t t x for later times.
x is a regular singular point and Then Frobenius method is effective at regular singular point of the form.
and that are analytic at 0 x = , then they will have Maclaurin series expansion with radius of convergence 1 0 r > and 2 0 r > respectively. That is Then the point 0 0 x = is called a regular singular point of (5).
with radius of convergence R, then term by term differential and integration of the power series is permitted and does not change the radius of convergence that is; Theorem 2.6. Let A be an n n * matrix and let the eigenvalue of A be de- Re A λ ≤ and all the eigenvalues of A with real part zero are simple, then zero is a stable fixed point of (10) Re A λ < , then zero is a globally asymptotically stable solution of (10) (iii) If there is an eigenvalue of A with positive real part, then zero is unstable
Stability Analysis of Mathieu Equation
We consider the equation where p is a positive constant. Equation (11) can be written as (12) can be written as The equivalent system is given by (14) can be reduced in matrix form as (15) can further be written as For the eigenvalue of A we compute ip λ = ± (20) Since the eigenvalue is in complex form with real part equals to zero, then the equilibrium point is unstable.
Convergence of Mathieu Equation
We consider the Mathieu equation of the form; n n p a a n k n k Given the value of 0 a , we can evaluate 2 a , 4 a , etc. The odd n a are completely independent and as far as getting a solution is concerned, we can put them all to zero. This independent of the odd and even n a is a consequence of the fact that odd and even solution of the differential equation are possible.
In order to generate these odd/even solution, it is easiest to put 1 0 a = in order not to create extra solution by merely using some of the key solution into that of 0 k = .
Define an additional argument for solving the ODE
Conclusions
From our result, we observed that the solution existed using the Frobenius method and also periodic. The solution converged at the equilibrium point but unfortunately this convergence did not imply asymptotic stability, and the converse is true. The solution was observed to be unbounded for the given parameters w-ε. Since the solution is unbounded, we concluded that the corresponding equilibrium point in w-ε plane is unstable. This can be seen in Figure 3 where In Figure 2, the solution was also periodic using the second solution function values and independent variable values. The starting point of the trajectory was far from the origin hence showing instability of the system.
In Figure 3, phase portrait of Mathieu's equation was obtained by relating X 2 and X 1 . The phase portrait was seen to be far away from the equilibrium point.
This shows that the solution of Mathieu's equation is unstable with the maximum displacement coinciding with the maximum displacement of X 1 in Figure 1. These values represent the maximum interval of stability of the system. | 1,276.8 | 2020-11-10T00:00:00.000 | [
"Mathematics",
"Engineering"
] |
Abode in heaven
In 2 Corinthians 5:1-10, Paul uses different methods to explain his view on life after death. He uses the metaphors of a tent, a building, clothing and being at home with God. It is clear that Paul accepted that the future with God is certain and that he will receive a building from God in heaven even though he may die. There is life with God even before the final resurrection. A life of bliss is assured for those who believe in God. This has implications for missions, namely that the future with God is ascertained.
Paul, although not always in the same way, often refers to life after death. In the first and second letters to Corinthians he explains that the resurrection of Christ makes life with Him possible, even after death. In this regard 1 Corinthians 15 is of importance because the aspect of the resurrection is explained clearly. He explains that it is difficult to understand, but that it is like a grain that falls into the ground and later sprouts into quite a new existence. Death has been conquered and the resurrection of the body is a wonderful reality in the promise of God. Two Corinthians also refers to aspects of life after death. Paul's personal expectations are expanded by his explanation of his view on eternity. Two Corinthians 5:1-10 is a notoriously difficult passage/pericope, but also highly informative regarding the Christian belief of life after death and eschatology.
Background of 2 Corinthians
2.1 2 Corinthians as letter Collins (2013:3-5) explains that the letters to the Corinthians are generally regarded as authentic Pauline letters (see also Harris 2005:1ff). Paul visited Corinth during his second missionary voyage somewhere around AD 50 (Acts 18:1-18). The letters, however, do not offer definite confirmation on the aspects referred to in Acts. It is well known that at least four letters were written. The first letter, then 1 Corinthians, a third letter, also known as the tearful or severe letter, followed by 2 Corinthians. The text of 2 Corinthians is well attested and parts are found on papyri as early as AD 200 (P 46). It is a long letter by ancient standards. It is a highly personal letter: "Paul, in fact reveals so much of himself in this letter that it can aptly be called the most personal of his letters" (Collins 2013:5). Some new issues are the reasons for the letter, such as to spare them another painful visit, to demonstrate his affection for the Corinthians, to put their obedience to his apostolicity to test and to make them aware of him as their spiritual father (Harris 2005:4). It is addressed to all the saints in Achaia, which means that a larger audience than just the Corinthians would read the letter (Omanson & Ellington 1993:11).
Paul dictated his letters to a scribe. He was an orator and evangelist. He used many rhetorical devices in his letter. Paul is in debate with his adversaries and readers and very often departs from prescribed letter-writing aspects, such as explained by Demetrius (Collins 2013:6). An abrupt transition in the way in which the letter is structured is sometimes regarded as unacceptable (Collins 2013:6-7).
The troublesome intruders in 2 Corinthians are regarded as Judaizers, although not the same as those in Galatians (Collins 2013:13). Harris regards them as protognostic in their views of denial of future bodily resurrection and their pride in knowledge or gnosis after he discussed the possibility that they are Jewish Christian Gnostics. They were Judaizers from Palestine who infiltrated the church (Harris 2005:85). They proclaimed their assurance with power and might; Paul with humbleness and brokenness (Matera 2003:24). In 2 Corinthians 5:1-10 Paul is aware of his own fragility, weakness and difficulties, but he does not succumbed to these, because he believes in the future life (Collins 2013:15). His mortality and the future which awaits him are described in many metaphors.
In 2 Corinthians 5:1-10 the implications of life after death are explained. There are many views on this pericope and some (Barrett 1976:150ff, Harris 2005:365ff, Dunn 1998ff.) regard it as a clear and visible statement of the fact that we will receive life after death, namely that our earthly life is like a tent broken down and destroyed, but that we will have life after death in the fullness of a building from God. Others (Pop 1971:138ff.), are of the opinion that it is all about the second coming of Christ and that not so much must be read into the explanation of the tent being pulled down, and the way in which the tent is pulled down, but that we must understand the second coming of Christ as bringing a whole new life with Him to us (see Pop 1971:138 to 141).
2.2
The macro context of 2 Corinthians 5:1-10 Paul's authentic letters deal with essential aspects of the Christian faith, reconciliation with God and salvation. It also deals with aspects of eschatology, death and life after death. Dunn (1998:26) is of the opinion that various engagements with Paul's theology is possible and that dialogue with the Apostle is necessary. Especially relevant is the fact that Paul has in mind the scheme of already and not yet (Dunn 1998:466). Something decisive has already happened but the work of God is not yet completed. The future holds the resurrection of the body as consummation of God's promises (Dunn 1998:488). In Christ the future is possible (Dunn 1998:493). Schnelle (2005:596) explains how Paul expects God trough his life-giving power to continue his relation with a person even after death. The Jesus Christ history continues even after death. God's love overcomes death (2005:597). The resurrection of the body is the culmination of this truth. (2005:596). Wright (2005:137) regards the Messianic renewal in Christ as essential for the understanding of Paul's eschatology: "We can the trace, in Paul's exposition of what God did in Jesus the Messiah, all the key elements of the Jewish eschatology, now reshaped around Jesus" (2005:142-143). According to Wright (2005:143) Wright NT (2008:153) explains that Paul regards the resurrection of the dead as not debatable. The future is secured in the resurrection of the dead. This is also the true aspect of life after death. The longing must therefore be not to go to heaven one day but to be resurrected in the new transformed body. Although he accepts that the dead in Christ are included in his salvation in what he accepts as an intermediate state, he regards the future as God's full and comprehensive renewal of the cosmos in the resurrection (Wright NT 2008:172) Harris (2005:365ff.) explains that 2 Corinthians 5:1-10 is clearly related to 2 Corinthians 4:7-18 because it states that in the midst of affliction, perplexity and persecution, the hope of divine intervention is present; a hope of life after death. Paul is confident in the presence of death (Harris 2005:366). By walking in the realm of faith, Paul experiences the future possibility of new life in Christ (Harris 2005:366). In 2 Corinthians 4:7-18 Paul explains that the life of Christ is present even in the mortal flesh and that that the relation with God is possible even in this life because Jesus makes life with God possible,, but he then explains that it also has implications for the future life (Barrett 1976:143).
3. Themes in 2 Corinthians 5:1-10 3.1 Semiotic implications of the metaphors Paul uses metaphors abundantly such as those concerning the church in 1 Corinthians 12. The semiotic implications of these metaphors must be acknowledged. They affect the referred aspects, explain the suggested issue, and are interrelated. The criteria for identifying the metaphors are where Paul relates a certain issue to an image to explain it better. The metaphors relate to the issues at hand and Paul uses it to enhance the understanding thereof. Van der Watt (2000:6) gives full attention to the definition and nature of metaphors. He explains that some form of comparison is necessary but that two disparate meanings are linked. It is when some kind of identification and comparison is made possible and meaning is transferred: "To a certain extent the interpretation process is brought to a halt and thrown into 'reverse'". The reader is referred back to the semantic competence of the word to look for alternative possibilities of performance (2000:8). Barrett (1976:150ff.) refers to quite a few important aspects. Turning to the text itself it is clear that Paul firstly refers to the fact that the tent in which he lives will be broken down and destroyed, but he explains that even if the tent is broken down and destroyed there will be a building from God, an eternal house in heaven not built by human hands. Barrett (1976:150) is of the opinion that Paul failed to understand the dualism of his adversaries, but that he explains the glory of his eschatology. In fact, Barrett (1976:150) is of the opinion that in both epistles Paul's real concern focuses on the way Christians are to live here and now. On the other hand, he also makes it very clear that the future life is a reality and that there will be a future in the abode in heaven, a house from heaven that will be put on like new clothes. Paul uses different metaphors and images to explain his idea. First of all, the tent and then the abode in heaven, the eternal house in heaven made by God. He also uses the metaphor of clothes to explain that the subjects need to be clothed so that they will not be found naked. Barrett (1976:150) is of the opinion that it should not be regarded as a reference to the proximity of the feast of tabernacles.
One of the main questions is whether Paul uses the metaphors in 2 Corinthians 5:1-10 as evidence of the resurrected body (Wright NT 2008:153) or the heavenly state of believers until the Parousia (Barrett 1976:151ff).
Referring to the metaphors, it is suggested that 2 Corinthians 5:1-10 explains the wonder of immediate life after death with Christ in heaven as an intermediate state until the Parousia.
Tent
The tent is insecure and impermanent. Barrett (1976:151) refers to the fact that it is a common picture of the earthly life (see also Wisdom 9:15). Bultmann (1985:131) refers extensively to the use of tent, or dwelling, or house, for our earthly existence in antiquity, frequently found in Hellenistic literature (see also Isaiah 38:12). The implication is that Paul makes use of a well-known metaphor in which the tent is usually regarded as the temporary abode of the soul. Barrett (1976:151) is also of the opinion that Paul wants to release the soul, or whatever the non-material part of man should be called, from all corporal containment. Thus, the tent is taken down in transformation at the end of the parousia of Christ when the person will be clothed, as stated by Paul, by the building from heaven. In the tent we groan; the tent is a place of affliction, but we long to put on the new building of God-our habitation which comes from heaven (Barrett 1976:152).
Paul refers to the time the tent is pulled down as the moment of death, according to Omanson and Ellington (1993:89). They also state that the present suffering leading to the dismantling of the tent is relevant in this regard. Dunn (1998:489) explains the implications of this metaphor: "But its most obvious function is to express Paul's confidence (4.16) that the present process of wasting away ('outer nature') and renewal ('inner nature) will climax in the transformation into the resurrection body (4.17-5.4), of which the Spirit is already the first instalment and guarantee (5.5)."
Building
Paul explains his hope, especially in 2 Corinthians 5:5,6. He hopes that by putting on this new building from heaven, he will not be discovered to be naked. Harris (2005:375ff.) refers to different possibilities, namely a) present possession of the Pieter Verster spiritual body in 1. heaven, or 2. on earth in embryonic form, or b) future acquisition of the spiritual body, 1. at death, a) in reality, or b) as an ideal possession actualised at the parousia, or 2. at the parousia.
Harris is of the opinion that it only refers to those who will one day experience the parousia (Harris 2005:383). Wolff (1989:103-104) is of the opinion that the building from God is not the individual resurrected body. He refers to many viewpoints, such as that it is the new aeon in heaven, the higher existence, the church, or the eschatological church. He views it as the impersonal life in heaven.
The relation to the Hellenistic view on nakedness is very important, because it is generally not regarded as unbecoming but Barrett (1976:154) refers to the fact that some people see the soul as being naked and undesirable, while Philo (De Virtutibus 76) shares the Greek view of the nakedness of the soul as a desirable thing. Paul's view, however, was that nakedness has to be shunned. Paul does not hold a positive view of the nakedness of the soul. For him, nakedness was something to abhor and avoid (2 Corinthians 5:3). Is the nakedness of the bodily existence sin? Is it the natural body? Is it body without Christ? Is it his understanding of the Corinthianostic position? Barrett (1976:154ff) states that 2 Corinthians5:4 shows that we are burdened in the tent, because we groan. We groan for the fullness of the spirit, so that the spirit can fill us in order to experience the fullness of the spirit, instead of groaning in fear of death. Barrett (1976:156) explains that Paul is not in the ordinary sense afraid of death; he dreads death precisely for the reason he proceeds to give-because he would be much happier to survive until the parousia. He continues to explain this idea that means not to die, but to be transformed immediately (1 Corinthians 15:51) by the substitution of the spiritual for the natural body (1 Corinthians 15:44); to put on the new dwelling over the old in the notion of the heavenly clothing and the heavenly body and Paul's horror of nakedness. Paul wishes for the mortal to be swallowed up by the glory of God-and this can be done through the Spirit. The Spirit gives this fullness of the exchange so that he can experience it on the basis of faith and therefore he is confident that God will give this fullness of life (See Dunn 1998:494) Schnelle (2005:486) writes: "Pauline theology is profoundly stamped with the insight that since Jesus Christ has been raised from the dead, the Spirit of God is again at work." (see 2 Cor 1:22;5:5 Rom 8:23). Wright (2005:145) is of the opinion that Paul's eschatology is reimagined around the Spirit. Collins (2013:105) refers to the fact that Paul uses the metaphor of the building to emphasise that God alone produces the resurrected body. This house is, therefore, not made by hands, but a spiritual home made by God (Omanson & Ellington 1993:90). Pop (1971:138) explains that the metaphor of the tent is not about the end of life in our death, but rather the parousia, and that the tent will be exchanged for the heavenly abode at the parousia. When the parousia takes place, there will be a different new life. One will be clothed from above and will be changed so that the new life can be possible. This will happen at the end of life when the parousia takes place. Paul longs (2 Corinthians 5:6) for the time that he will no longer be in the tent, but in the glory of living in heaven (2 Corinthians 5:8) after Christ has come to take all the troubles of this life away and he can enjoy the fullness of the glory of God. This longing of Paul is also very present in Philippians 1:23. The metaphor of the clothing by the heavenly body, as seen by the Apostle, is not only to cover the earthly body, but to absorb and transfigure it (Hughes 1962:168). Paul longs for the heavenly garment to experience the fullness of being clothed and not being naked. He polemicizes against the Gnostics (Bultmann 1985:138). Barnett (1988:99) understands the clothing as the moment Paul became a Christian and he was clothed in Christ and had the hope of eternal life; God supplies the new life.
At home with God
The fourth metaphor according to Barnett (1988:100) implies living by faith and not sight. Walking in faith is essential for the person awaiting heaven. Life in the spirit is living in the expectation of the realisation of the future.
Main implications
4.1 Paul's theology Dunn (1998:487ff) explains that Paul's theology would be incomplete if it did not state that life is not a repeating cycle of birth and rebirth. The process of salvation would be incomplete if did not include the final vindication of the resurrection of the body. If the believer hoped only for this life on God he/she would be pitiable (1 Cor. 15:19). The obvious element of the hope in God is the resurrection of the body. Dunn (1998:488) writes: "The importance of that hope lay not the least in the fact that so many aspects of Paul's theology come together in it. It is the immediate consequence of cross and resurrection (1 Corinthians 15), is integral to the gospel (15,(12)(13)(14)(15)(16)(17)(18)(19), and confirms that victory over death is central to the gospel (15. [21][22]26,[54][55][56][57]. It resolves forever the tension between flesh and body (15.42-54) It completes God's purpose in creating humanity by renewing the image of God in resurrected humanity (15.45-49) it is the final outworking of the process of inner renewal and outward decay (2 Cor. 4. 16-5.5)." This all was made possible by Christ's resurrection. Christ's resurrected body is the one the new resurrected bodies will conform to. Christ is the firstborn and the prototype. Dunn has full confidence that Paul expects life after death. In 1 Corinthians the emphasis is on the resurrected body. In 2 Corinthians 5:1-10 the emphasis is on the fact that life after death is explained by bringing down the tent and being found endowed by the building in heaven. In both instances Paul explains life after death. Schreiner (2001:37) also emphasises that Paul had magnified God in Christ as his central position. He explains that Paul, as missionary, had a missionary focus. He explained the gospel in terms of his worldwide endeavour. He was a coherent thinker, and although not a dogmatician, his message was to proclaim the gospel of Christ in fullness. His missionary message had implications for the churches to which he conveyed his wonderful essential gospel. Paul's theology has the wonderful implication that life and death are in God's hand and that God creates the future with glory for those in Christ. Green (2002:48) is of the opinion that Paul affirms a profound continuity between life in this world and life everlasting with God. He says that the present humanity is frail, deteriorating and weak, but to share eternal life the bodies must be transformed. He proclaims the promise of transformation of the bodies into glorified bodies to his audience (2002:48). He is, therefore, of the opinion that, for Paul, death is near. However, the transition from the tent-like house to the house from God means that he will not be naked but clothed. The explanation of life after death is regarded in the realization that he may die before the parousia, something Paul earlier did not expect. Danker (1968:553) states that Paul wishes to explain the hope for life after death as a new life with God. Although death is at work in Paul, the life of Jesus became apparent in his mortal body, therefore, consolation is present. The contrast is between the benefit that is the result from death and the sufferer's present situation. Paul experiences the groaning as being in proportion to the desire for the future blessing and that the body will be equipped for the future blessing. The body will be equipped for celestial existence (Danker 1968:554), therefore, it does not place him at a disadvantage (1968:555). Paul wants to explain that if he dies before the parousia, his authority as apostle will not be diminished. He seeks consolation in the fact that, though he may die, the future is ascertained in God (1968:556). Collins (2013:105) also regards Paul's view on his own death as part of his discussion of the theme. He may still believe that he will be alive at the parousia, but also refers to his imminent death and the death of his readers in general. Therefore, he uses the metaphor of the tent. Bultmann (1985:133) asks whether the tent's breaking down refers to Paul's own death or the parousia and he explains that death is clearly not regarded as annihilation, but rather as wonderful new life, because a new garment/building is prepared. Paul expects the parousia soon and regards it as normal that one will see it (Bultmann 1985:138). Matera (2003:118) is of the opinion that Paul shifted his thinking on the resurrection of the body from 1 Corinthians 15 because of the new situation of his own imminent death. Death has been conquered and Paul is of the opinion that he will be clothed by the heavenly body (Hughes 1962:171). Matera (2003:122) sees nakedness as referring to his death, but he will not be found naked because at death he will be clothed from heaven by the new body.
Paul's own death
It is clear that Paul has the unconditional belief that he will experience full life with Christ after death (see Dunn 1998:487ff). He is clearly of the opinion that he will die soon, but that death will not be a disaster as he will receive a building in heaven-full life with God. He will experience total bliss because God gives life even after death. Pop (1971:152 ff.) refers to the intermediate state between death and the resurrection and he asks whether biblical material anticipates a waiting between death and the resurrection of the dead person, or whether the biblical material anticipates immediate resurrection (1971:152 ff). In the Old Testament, Sheol is originally explained as the abode after death, but in later eschatology resurrection of the body is expected. In the New Testament passages, such as the reference to the rich man and Lazarus, the words of exchange between Jesus and the murderer on the cross, and when Luke explains that the resurrection has not yet taken place since the rich man's brothers are still alive on earth, and Jesus' account, refer to the rich man in heaven who has not yet experienced the resurrection (Pop 1971:142 ff.). According to Pop, Paul also refers in 2 Corinthians 5:1-10 to an intermediate state because we know that even though the earthly tent is dismantled, but we have the house of God until the resurrection (Pop 1971:141ff.). He is of the opinion that Paul's perspective is from an eschatology grounded in a Greek dualism, because the soul will flee the problems of the body (1971:147). Hanhart (1969:446) refers to the fact that Culmann envisaged an intermediate state between the coming of Christ and the death of the person, and that the final resurrection will only take place at a later stage. He is, however, critical towards Culmann's views and is of the opinion that this viewof the intermediate state cannot be substantiate. Zorn (1989:97) accepts that many scholars say that there must be some kind of intermediate state between death and the resurrection. The question is whether Paul expects an intermediate state after death because of his views in 2 Corinthians 5 and 1 Corinthians 15. Does he have conflicting views? Zorn (1989:97) is of the opinion that Paul obviously is contrasting the house made with hands eternal in heaven with the present earthly tent-house. He is of the opinion that Paul is seriously considering the possibility that his death may take place before Christ's return. The interpretation is, thus, in favour of individual eschatology. A building not made with hands can only properly be a reference to the corporate solidarity with the church in Christ, but the building of God stresses the heavenly glory and permanence of the individual resurrected body as contrast with the present transition mortal bodies: "The fact that Paul is hoping for resurrection transformation during his lifetime so that it will not be necessary for him to experience the unclothed state of death and of being a naked spirit is confirmed by Paul's use of the verb 'to be clothed upon' (ependusaslhai) both in VSS. 2 and 4 (Zorn 1989:99). If the believer dies before the Lord returns he leaves his earthly tent-house, which is buried and remains in the grave until the parousia and emigrates to be with his Lord in the meantime, for to be absent from the body is to depart out of the body to be present and dwell in the presence of, or to be at home with the Lord" (Zorn 1989:102). In 2 Corinthians 5:1-10 Paul expects that he will immediately experience life with God; in 1 Corinthians 15 he expects resurrection of the body. Cranford (1976:95) refers to the real question of the intermediate state and he refers to the metaphorical nature of Paul's expression. He mentions three obstacles, namely the belief that 1 Corinthians 15 is clearly parallel to 2 Corinthians 5; secondly, that in 2 Corinthians 5 the Apostle speculates on the metaphysical details of the afterlife; and thirdly, the thought of Paul does not lend itself to a systematically neat theological package. He, however, explains that the moment death is derived from the 'in Christ' concept, the metaphors and judgements are seen as stressed. He writes: "Did Paul believe in an intermediate state? This interpretation answers affirmatively. But Paul was not concerned about metaphysical details. For him, death means the deepening of our union with Christ as we possess the heavenly home (vv. 1-2), put on this heavenly life (v. 2-4), and make our home in the true homeland with Christ (v. 8). This existence whatever its nature-body or spirit-is conscious union with Christ. That is the 'gain' of death (Phil. 1:21)." (Cranford 1976:100).
Intermediate state
Osei-Bonsu (1986:81-82) asks whether 2 Corinthians 5 teaches the reception of the resurrected body at the moment of death. He differs from those who see Paul as receiving a spiritual new body at the moment of death by referring to firstly, the destruction of the earthly house or tent, which refers possibly to Paul's pre-parousia death, and secondly, that the building from God at death means the individual resurrected body, not the church as the body of Christ. He understands 2 Corinthians 5:6-9 as an intermediate state where the soul is disembodied from the body and it is an intermediate state between death and the resurrection. Hanhart (1969:445-446) is of the opinion that Paul was a revered agnostic concerning the nature of life to come, but that he, nevertheless, fostered a radiant hope of life eternal with Christ. He is of the opinion that it is very clear that the death in Christ is the death with Christ and that when you die you are with Christ and you receive the fullness of life with Christ. He refers to the fact that Paul's age and experience of being in mortal danger could have influenced his view of death: "Paul's Pauline eschatology appears to have two poles. His hope is expressed both in terms of the parousia, or the resurrection of the dead, and in terms of the entrance into an eternal home upon death in order to live with Christ". Dunn (1998:490) is of the opinion that all we need to note is that Paul envisaged an intermediate state. Beyond death and the parousia the process of salvation is still incomplete, which can only be resolved by the new body of the resurrection.
It must be accepted that Paul, indeed, had the idea of an intermediate state. He accepted that God will rule over his life and death. Even if he dies, he will be with God, although the resurrection has not yet taken place. He will receive a place in heaven, full of glory. This is made clear from his reference to the building and clothes in 2 Corinthians 5 but according to 1 Corinthians 15 the resurrection of the body will take place at the parousia. The way in which the metaphors are structured in 2 Corinthians 5 allows for an expectation of life with Christ immediately after death while waiting for the resurrection of the body. The implications are that the resurrection is still to come. The resurrection will be the final consummation of the glory that the believer had already received at death. He does not fear the intermediate state, but longs for the building in heaven. The future will also mean that he will experience the resurrection. There is, therefore, no uncertainty in his mind. The future is secured in Christ. 4.4 Challenge to the belief in heaven: symbolic future life? Mackay (1991:162-165) explains that that the metaphors may be largely ornamental and that the reference to the tent and the abode in heaven is only superficial, or that it can be interpreted literally: "The essential difference in practice between these two approaches is this: ornamental metaphors just need to be translated into literal speech, in order to make clear the information intended; exploratory metaphors, on the other hand, like all literary works, need to be explored imaginatively, their hints, allusions and implications followed as far as they lead us. In order to practice that exploring we must do the following: (1) guess what the subject is that the particular symbol can most appropriately be taken to be a window onto; (2) discover as much as we can about the reality used as a symbol, that is, what it was that the author was concretely imagining when using it; (3) look at the (mysterious) subject through the window of the (betterknown) symbol, thereby taking in the glimpses, following the trails pointed out, making guesses." According to him, Paul refers to symbols as his earthly tenthouse, as the wilderness tabernacle is destroyed, but the end of all earthly things at the parousia is a building from God, a house not made with hands, the symbol he devotes to glorious heavenly temple. His conclusion is, thus, that Paul's corporate language can be taken as intentional and his symbolism can be taken as revealing, and not simply as ornamental.
4.5 Universalistic eschatology? Collins (2013:112-113) emphasises that Paul refers to well-known Hellenistic views, but that he also wishes to emphasise the full glory of the eschatological life with Christ. His own frailty is changed by die wonder of Christ's renewal. Bultmann (1985:145) is of the opinion that Paul's zeal to serve God is free from anxiety, because it does not fear death, but has a tacit longing for death. On judgement day the person will receive the full benefit of the heavenly house (Omanson & Ellington 1993:95). Although the glory after death is certain, it is not for all. Although Paul accepts the intrinsic value of the universalistic eschatology, he clearly sees the life in heaven as the life for the believer who receives the glory from God. It is for those with God. They will receive the fullness of glory.
Missiological implications
What are the missiological implications of Paul's view that the tent will be taken down and that future life of glory is possible?
First of all it gives the sense of the importance of mission. This life will pass. A future life with God is possible. This must be proclaimed in the present world. This does not mean that the present life is totally unimportant. Paul's reference to the life of the church in the present world explains that fully. But, life with God after the tent has been demolished will be full of glory. Therefore Bosch (1991:414) also writes: "Evangelism offers people salvation as a present gift and with it assurance of eternal bliss. People are, even without realizing it, desperately searching for a meaning to life and history; this impels them to look for a sign of hope amid the widespread fear of global catastrophe and meaninglessness." (it. Bosch).
Secondly the full glory of the resurrection means that the beauty of the gospel must be proclaimed. There can be no doubt that Paul regards the building and clothes of the future as beautiful because God supplies it. The gospel is full of the wonder of God. Mission is about the beautiful message of life with God.
Thirdly the gospel entails new life. Mission has to do with new life. Life is not dreadful for the believer because God makes life with Him possible. In this regard Bevans and Schroeder (2006:345) write: "Full humanity is achieved not only through economic security or political autonomy, but also and most fundamentally through the communion with God in Christ and transformation by the gospel. This is because, as Catholics, Evangelicals and Pentecostals acknowledge, human beings are sinners and so are in need of a restoration of right relation with God as well as with other human beings of all of creation." Fourthly there is hope possible in the new life. Because of God's intervention life can be good awaiting the glory after this life. Skreslet (2012:70-72) explains how salvation has to integrate horizontal and vertical elements. Salvation can therefore include aspects such as deliverance from danger, redemption from judgement and peace between enemies.
Fifthly the image of God can be restored in humans in the resurrection. Life after death has the implication that the full image of God in creation is restored. Schreiner (2001:466) writes: "An investigation of 2 Corinthians 5:1-10 reveals no departure from standard Pauline teaching on the resurrection. Our present body is compared to an earthly house that is slowly becoming dilapidated and will eventually be torn down. Our future body, on the other hand, is heavenly and eternal, for it is from God himself".
Sixthly mission is proclaiming radically that even the suffering of this life has not the last word. God's comprehensive redemption includes new possibilities on political, economic, social and spiritual life (Wright CJH 2008:268-269) but also that suffering will be overcome in the full redemption in Christ.
Finally Harris (2005:402-403) is of the opinion that Paul, in 2 Corinthians 5:1-8, although he did not despise mortal embodiment, eagerly awaited the future life with Christ and the end of the imperfections of earthly life.
Conclusion
Paul realizes that he will not live till the parousia. He believes that he will immediately be with Christ. He will experience full glory. Heaven is for real. Heaven is not a myth. Paul emphasises the fact that Christian eschatology is radically linked to the belief in heaven and that aspect should be proclaimed in the church of Christ. This is essential for mission. The present day emphasis on this life alone does not take into account the glory of Paul's expectation. In mission, it is necessary to proclaim the fullness of the gospel of Christ's expectation of life after death and that the building from God is awaiting the believer. It should be recognised that Paul's explanation is essential for the hope and the comfort of the Christian. In mission, it is possible to spread the comfort of life after death to all. In 2 Corinthians 5:11- | 8,295 | 2016-07-30T00:00:00.000 | [
"Philosophy"
] |
Electron energy can oscillate near a crystal dislocation
Crystal dislocations govern the plastic mechanical properties of materials but also affect the electrical and optical properties. However, a fundamental and quantitative quantum field theory of a dislocation has remained undiscovered for decades. Here we present an exactly-solvable one-dimensional quantum field theory of a dislocation, for both edge and screw dislocations in an isotropic medium, by introducing a new quasiparticle which we have called the ‘dislon’. The electron-dislocation relaxation time can then be studied directly from the electron self-energy calculation, which is reducible to classical results. In addition, we predict that the electron energy will experience an oscillation pattern near a dislocation. Compared with the electron density’s Friedel oscillation, such an oscillation is intrinsically different since it exists even with only single electron is present. With our approach, the effect of dislocations on materials’ non-mechanical properties can be studied at a full quantum field theoretical level.
Introduction
Crystal dislocations are a basic type of one-dimensional topological defects in crystalline materials [1]. Since Volterra's ingenious prototype in 1907 [2], and Taylor, Orowan and Polyani's simultaneous formal introduction in 1934 [3][4][5], a dislocation has been shown to have strong influences on material properties, including the governing role in the plastic mechanical process, and the widespread impact on the thermal, electrical and optical properties [1,6]. Since a dislocation can strongly scatter an electron and thereby changes material electrical properties, such as reduces the electron mobility or increases the electrical resistivity, it is of central importance to obtain a theory describing the electron-dislocation interaction, to understand the role of a dislocation in the electronic properties of materials.
In general, the theoretical approaches of studying electron-dislocation interactions can be divided into the following mainstream categories: (1) Classical scattering theory: dislocation can be modeled by its partial feature (e.g. dislocation modeled as charged line in certain semiconductors) [7][8][9][10]. This allows one to study the electron-dislocation scattering using classical theory, but such modeling has a pure electrostatic origin and does not capture the scattering processes that occur with a genuine dislocation, which contains both strain scattering effects and vibration scattering effects [1,6].
(2) Geometrical approach: dislocated crystal is treated as a manifold in a curved space (e.g. spacetime in general relativity) [11][12][13][14][15]. This approach can describe the single electron motion quite well near a dislocation under the framework of the one-particle Schrödinger equation, yet it also experiences some problems such as the cumbersome mathematics caused by a curved metric, limiting this approach to the first-quantized single particle level without a generalization to many-body cases.
(3) First-principles density functional theoretical calculations: in principle the electronic structure near a dislocation core can be studied. However, due to the long-range nature of a dislocation, it requires one to build a supercell leading to an exceedingly high computational cost. To the best of our knowledge, only ground-state properties such as the atomic configuration near a dislocation core can be studied using this approach [16,17].
(4) The classical affine gauge theory of dislocations [18][19][20]: structurally similar to quantized gauge theory, but is limited only to a classical elasticity field, without being quantized at the time of this study. Since the step of quantization is necessary in order to study the electronic properties properly, the investigation of electronic properties using this approach have not started yet.
However, despite the wide variety of approaches to study electron-dislocation interaction, a unified electron-dislocation interacting theory at a quantum many-body level is still not available. Such a theory is essential to go beyond single-electron picture by taking into account the electron exchange and correlation, and other many-body effects, and is also essential to properly considering the higher-order multiple scattering events. If fact, unlike the case of the electron-point defect interaction where the complete impurity interacting field theory is well established [21], the lack of a field theory of dislocations not only impedes a further understanding of dislocations on material electronic properties at a fundamental many-body level, but also limits the usage of the terms 'impurity' and 'disordered systems' referring to quenched, point defect-related properties under many circumstances [22].
Here, we take a very different approach to study the electronic behavior in a dislocated crystal. Instead of treating a dislocation line as a charged line, or strain field, or a quenched defect, we treat the dislocation itself as a fully quantized object. Based on well-established classical dislocation theory and a canonical quantization procedure, we provide an exact and mathematically manageable quantum field theory of a dislocation line. We find that in an isotropic medium, the exact Hamiltonian for both the edge and screw dislocations can be written as a new type of harmonic-oscillator-like Bosonic excitation along the dislocation line, hence the name 'dislon'. Just as a phonon is a quantized lattice displacement with both kinetic energy and potential energy, a dislon is similar in the sense that it is also a lattice displacement with both kinetic and potential energy, but further satisfies the dislocation's topological constraint = - where b is the Burgers vector, L is a closed contour enclosing the dislocation line (denoted as D in figure 1(a)), and u is the lattice displacement vector, i.e. the atomic position deviation occurs after the crystal is dislocated, and du is the differential displacement along the contour L. Using this approach, the scattering between an electron and the 3D displacement field induced by the dislocation can easily be solved via a many-body approach, with the topological constraint = - respected all along this study.
where L is the loop enclosing the dislocation line D. On the other hand, an equivalent definition is based on an arbitrary surface S (blue) with line D as its boundary. A dislocation can be defined as an overall shift of surface S by a constant amount of the Burgers vector b (blue surface is shifted to the yellow one). V is the coordinate perpendicular to the surface S, and is convenient for defining the strain tensor u . ij (b) A long dislocation line along z-direction vibrating within slip plane (xz) with ( ) Q z the transverse displacement. Such vibration shares similarities with a phonon as it is also a quantized lattice displacement, but is constrained by = - where L is an arbitrary loop circling dislocation. An electron located at position r will be scattered by dislocations. (c) Quantized vibrational excitation dispersion relations along dislocation line ('dislon') for both edge (hot-colors) and screw (cool-colors) dislocations at various Poisson ratios ν. The classical shear wave is shown as a linear-dispersive black-dotted line. The classical shear wave is shown as a linear-dispersive blackdotted line, and the arrows indicate a decreasing trend of Poisson ratio for edge (red arrow) and screw (blue arrow) dislons, respectively.
The classical foundation prior to dislocation quantization
To begin with, we provide a self-contained review of the classical dislocation's theory following the logic in [23] and [24]. In spite of the well establishment of the classical dislocation theory, we feel such an introduction necessary since this particular classical theory which facilitates the quantization is not commonly introduced in textbooks or articles in material sciences journals. Defining ( ) u R as the atomic lattice displacement at spatial point R, the spatial derivative tensor of u, namely the distortion tenstor, can be written as w º ¶ ¶ u R , ij i j from which we define the strain tensor e ij as are the Cartesian components. The relation between the stress s ij tensor and strain tensor e kl can be found by the generalized Hooke's law as where Einstein's summation convention is adopted. In an isotropic medium, the elastic stiffness tensor c ijkl where λ and μ are 1st and 2nd Lamé constants, respectively. At equilibrium, the internal stress in each direction must balance with the external force f ; i hence the local force equilibrium of the ith component can be written as is a 2nd order linear inhomogeneous differential equation with respect to the displacement field vector component u , k which can readily be solved using the Green's function method. Defining the Green's function of equation (4) as Then the solution of the corresponding inhomogeneous equation (4) can be written from equation (5) as [23,24] ò ò e where i, j, k, l, m=1, 2, 3 are the Cartesian components. The 2nd equality can be obtained by substituting equation (4) to the 1st equality in equation (6), and using integration by parts. This gives the generic displacement field using the Green's function's approach. For the convenience of later computation, the Fourier transformed Green's function is also defined as ij ij k R i 3 which can be obtained by taking the Fourier transform of equation (5) as is the Poisson ratio.
The above theory equations (1)- (7) is valid for all types of lattice displacements within the framework of elasticity. For the case of a dislocation as one special type of displacement, we need to introduce a generic and rigorous definition of the dislocation in order to formulate a quantized theory. In realistic materials, dislocation can either form a self-terminated loop, or form a line terminated at crystal surface [6]. In particular, a line can be considered as a special case of an arbitrary loop with the both ends at ¥ joint together [25]. Therefore, we still could picture this generic dislocation as an arbitrary loop, as shown in figure 1(a) and elaborated in [26]. The arbitrary dislocation loop is denoted as the loop D (black circle), with S is an arbitrary surface (blue surface) whose boundary gives this dislocation loop D, and the local tangent vector of the dislocation loop D is denoted by t. The dislocation is defined as a global shift of the whole surface S by an amount of the Burgers vector b (blue surface shifted to the yellow surface nested above, as indicated by the orange arrows). Defining the coordinate z along the surface normal n (i.e. locally z is always perpendicular to the surface element ¢ S d on the surface S), then we have the distortion w d z on the discontinuity surface S, where n i denotes the projection along the surface normal, b j is the component of the discontinuous shift b, and d z ( ) comes from the fact that the discontinuity caused by the shift of the surface will be located right at and only at the surface S; hence from equation (1), we have Substituting equation (8) back into equation (6), and noticing the fact that since z is defined as the direction perpendicular to the local surface element ¢ S d , the displacement field ( ) u R i caused by a dislocation loop with Burgers vector b can finally be re-written as a surface integral over the surface S as R is a spatial point on the surface S, while R is an arbitrary spatial point which can be well outside the surface S.
To further simplify equation (9), we consider a long, straight dislocation line instead of an arbitrary loop, as shown in figure 1(b) where a long, straight dislocation line extends along the z direction with a core position located at (x 0 , y 0 )=(0, 0). This dislocation line would vibrate within a plane called slip plane, which we have defined it as xz plane. Noticing the fact that the discontinuity surface S now evolves into the slip plane xz within which the discontinuity is generated: for an edge dislocation the discontinuity is created along the x-direction, while for a screw dislocation the discontinuity is created along the z-direction. Such vibration has the form of an atomic motion, similar to phonons but they cannot be described as a collection of propagating plane waves. For an edge dislocation, the slip plane is fixed, i.e. an edge dislocation keeps slip within the same plane, while for a screw dislocation, the slip plane is not fixed, i.e. a screw dislocation can slip along different directions at multiple slip steps. However, the dynamic process we are considering in this study is the local vibrational modes before it starts to slip, with a timescale much faster than an actual slip process which requires the shift of an array of atomic positions. Defining ( ) Q z to be the transverse displacement of the dislocation line within the slip plane, along the x-direction at position z, as in figure 1 and equation (9) can be further rewritten as [24,27] , and º ( ) z R r, are 2D and 3D position vectors, b m is the mth component of the Burgers vector and n is the direction perpendicular to the slip plane with the lth component n l . To understand the significance of the dislocation displacement ( ) Q z , we need to bear in mind that ( ) Q z is not the displacement of the lattice displacement vector ( ) u R , but a displacement caused by the overall movement of the dislocation line. In fact, the dislocation displacement ( ) Q z causes the lattice displacement ( ) u R in the whole crystal. For a vanishing dislocation displacement ( ) Q z 0, the lattice displacement still remains finite due to the topological behavior of a dislocation, and a resulted singular behavior which is discussed in detail at the end of this section. Now mode-expanding the dislocation displacement as a Fourier series where κ is the wavenumber along the z-direction, we can then express the displacement ( ) u R as [25] i is an expansion coefficient to be determined. Substituting equation (11) back into equation (10), and comparing the result with equation (12), we have obtained the coefficients where A is the sample area perpendicular to the dislocation direction, and º ( ) k k s , x y is the 2D wavevector. Substituting the 2nd formula in equation (14) back into equation (12), and comparing the result with the Fourier transform of equation (13), we finally obtain where the 3D wavevector is defined as k º ( ) k s, .Now using equations (12) and (14), the displacement field can then be written in terms of ( ) Now we are ready to encapsulate the classical kinetic and potential energies due to the dislocation displacement field. Substituting equation (16) into the expressions for the classical kinetic energy the classical Hamiltonian can finally be rewritten in terms of a 1D effective Hamiltonian [27], where L is the sample length along the dislocation direction, k ( ) m and k k ( ) K 2 are the classical linear mass density and tension, respectively, and can be written down from a classical theory straightforwardly as was done in [27]. For an edge dislocation, we have the effective mass density and the tension written as where k D is the Debye cutoff in the in-plane xy direction. Before proceeding to the quantized dislocation theory part, we would like to clarify the implications of the classical dislocation Hamiltonian in equation (17). One might be wondering why a dislocation, which is usually considered as a type of quenched defect without excitation, can be written down through a Hamiltonian form as equation (17). In particular, it appears that for a static, quenched dislocation in the long wavelength limit, there is no displacement with ( ) Q z 0, and the dislocation Hamiltonian equation (17) simply vanishes. However, this is not true since a dislocation is a topological defect which cannot be simply canceled by a local variation of ( ) Q z . This can be seen from equation (15). In the long-wavelength k 0 limit, the expansion coefficient Hence in the static limit, despite the vanishing k Q according to equation (11), the divergent expansion coefficient ( ) B k i will compensate and bring the lattice displacement ( ) u R i back to a finite magnitude, according to equation (16). In other words, the Hamiltonian equation (17) simultaneously. To separate the contribution from the static electron-dislocation scattering from the dynamic electron-dislocation scattering and determines the sole contribution from the static dislocation, a different approach using the boundary operator method has been implemented [28]. It is also worth mentioning that, contrary to many would naturally expect, a dislocation is more than a quenched defect. For instance in some materials when considering thermal transport, the dynamic scattering can even dominate over the static scattering [29,30], which have been explained using classical vibration models [27,31].
Canonical quantization of crystal dislocation
After reviewing the classical dislocation theory, we now proceed to the quantization procedure. For a canonical coordinate k Q , we could define its canonical conjugate momentum as = - T U is the Lagrangian. Now imposing the following canonical quantization condition between the canonical coordinate k Q and conjugate momentum k P , that Then the classical dislocation Hamiltonian in equation (17) can be quantized by recognizing k Q and k P as firstquantized quantum mechanical operators satisfying equation (20), instead of the classical dynamic variables. The Hamiltonian equation (17) can now be written as å å To readily study the effect of a dislocation on the electronic properties at a full many-body level, a secondquantized dislocation Hamiltonian is needed. By defining the creation and annihilation of quantized dislocation modes k + a and k a satisfying the canonical commutation relation d = , equation (20) can further be written as the following equivalent form as The first-quantized Hamiltonian equation (21) now can be rewrittng using equation (22) as the following Hamiltonian has a form as a collection of non-interacting Bosonic excitations. Despite the observation that such an excitation shares the similarity with phonon excitation as a type of quantized lattice vibration, the topological constraint here = - leads to a different excitation quantum along the dislocation line and decay away from the dislocation core, which may suitably be called the 'dislon', to distinguish the dislon from a non-interacting phonon. In particular, by imposing the inplane Debye cutoff k D , in xy plane for both an edge dislocation (^= ) x and a screw dislocation the dispersion relation w k ( ) can be written in a closed form as figure 1(c), where the classical shear wave, or equivalently the transverse acoustic phonon mode w k k = ( ) v s (black-dotted line) serves as a pre-factor in quantum-mechanical version of dislocation excitation in equation (24). The higher excitation energy of the edge dislon relative to the screw dislon is reasonable, since even in the pure classical picture, the edge dislocation energy density is higher than that of the screw dislocation by a factor of / n -( ) 1 1 [32]. Substituting equation (22) back into equation (16), the displacement field ( ) u R i caused by a dislocation can finally be written in a second-quantized form as which is the main result of this section 3 and will be used in section 4.
Electron-quantized dislocation interaction
The introduction of the quantized dislocation in section 3 enables us to treat the electron-dislocation scattering at a full second-quantized level by taking advantage the many-body theory as the electron-dislon interaction. We start from a lattice model, where = + R R u, j j j 0 so that R j 0 is the equilibrium position of an ion with label j, and we assume that there are N atomic sites in the system. Assuming the electron charge density is r ( ) R , e the electron-ion interaction Hamiltonian expanding to the 1st-order approximation can be written as [33,34] ò ò ò å å å r r r = - where the 1st term gives the ion potential function which describes the electrons traveling within the periodic potential of a crystal, i.e. Bloch waves, and the 2nd term describes the scattering by a generic displacement field, To further simplify equation (27), we note that the electron charge density r ( ) R e can be written in terms of the number density ( ) n R e as å r where r ( ) q is the Fourier-transformed electron number density. In addition, the ionic potential - can also be expanded in terms of Fourier components by where q is within 1st Brillouin zone, the Fourier component of a screened Coulomb potential gives p = + V Ze q k 4 , q 2 TF 2 in which k TF is defined as the Thomas-Fermi screening wavenumber, and G denotes the reciprocal lattice vectors. Now substituting equations (25) and (29) into the term - where we have used the fact that å where N denotes the total number of atoms. Now we further substitute equations (15), (28) and (30) back into the interacting Hamiltonian equation (27), and moreover by assuming a non-Umklapp normal scattering process (G=0), the electron-dislocation interaction Hamiltonian equation (27) can further be rewritten in a second-quantized form as (supplementary material A) This equation (31) gives a reasonable prediction. In particular, at / n = 1 2, both the dislon excitation equation (24) and electron-dislon interaction equation (31) vanish due to the pre-factor n n -- . This is consistent with the fact that a system with / n = 1 2 corresponds to a purely elastic system without shear modulus (an intuitive example with / n = 1 2 is like rubber), where dislocations simply do not exist. Now noticing the fact that the creation and annihilation operators k which shows an exponential-like decay of the electron-dislon coupling strength at long distances, where the decay constant k = k r 1 2 . The k ( ) r r exp exponential decay behavior is quite reasonable, since the electrondislocation interaction is generally considered as short-range interaction [1], even though the strain field of a dislocation is long-range. Intuitively speaking, an electron is weakly scattered by a dislocation hence the electrical conductivity does not change too much, which is in sharp contrast with the case of the dislocation-phonon interaction, where dislocation can dramatically change the thermal conductivity in a dislocated crystal [35].
At this stage, we have obtained a complete electron-dislocation interacting system at a full second quantization level. In principle, we should be able to compute any electronic properties caused by a dislocation based on the standard many-body approach using finite-temperature Matsubara Green's function formulism [34]. Matsubara formulism is a method by treating time t as a complex number of temperature, allowing one to treat temporal evolution e Ht i and thermal average b e H of a quantum system with Hamiltonian H and at temperature T from equal footing with only one S-matrix expansion. By noticing that a dislon quantized in 1D resembles a phonon as a Bosonic quasiparticle, we could write down the Feynman rules for an electron-dislon interacting system directly by following the same logic used for an electron-phonon interacting system [34], as listed below: (c) Each internal electron-dislon coupling vertex gives where the position-dependent coupling is given in equation (36). Unlike the electron-phonon coupling which is only dependent on momentum transfer, here it depends on the relative position r between an electron and the dislocation's location. When the election is away from the dislocation core, the coupling strength decays accordingly.
where F is the number of closed Fermion loops, K is the diagram order: for electron self-energy, K is the number of internal phonon lines, for dislon self-energy, and K is the half number of vertices. This rule remains the same as an electron-phonon interacting system by noticing the similarity between a dislon and a phonon.
Therefore, to compute the election energy change when an electron is interacting with a dislon to the lowest order, in other words, to compute the election self-energy with the one-loop correction, where an electron emits and re-absorbs a virtual dislon, we could apply the above Feynman rules and write down the position dependent electron self-energy as follows: bunch of electrons forming an electron liquid, here the energy oscillation can emerge when only one single electron is present. Such an energy oscillation does not indicate that the electron energy will constantly vary when traveling nearby a dislocation core. Under the 1-loop correction (supplementary material D), such an oscillation can be understood as an electron-dislon interaction event taking place at a spatial position r, where an electron emits and reabsorbs a virtual-dislon for once. Due to the extended nature of the quantized dislocation, the interaction event can happen when the electron is away from the dislocation core. Such an interaction event has the effect to change electron energy, according to the 1st formula in equation (40). The amount of the energy change, though, depends on the location r of the interaction event, and is a function of r in an oscillatory instead of monotonic way. Therefore, this energy oscillation behavior is indeed an overall spatial pattern away near the dislocation region, or distribution of the energy change of an electron caused by electron-dislon interaction, instead of a single particle trajectory along which the electron energy keeps changing. Another feature is that the oscillation caused by an edge dislocation (figure 2(e)) is much more drastic than that caused by a screw dislocation ( figure 2(f)). This can be understood from the distinct electrostatic effect contributing to the Friedel oscillation. For an edge dislocation there is a finite inhomogeneous lattice dilatation sin , leading to a compensating electrostatic potential to reach a uniformly distributed Fermi energy at equilibrium, while for a screw dislocation, the linear elasticity gives no dilatation and hence no electrostatic effect emerges [1]. In order for such an observation, high-resolution, low-temperature scanning tunneling spectroscopy can be performed, where a single electron can be injected from the tip at different positions away from the dislocation core, with its energy derived indirectly from the measured spectroscopies. The observation of the predicted self-energy's single-electron energy Friedel oscillation may provide strong evidence of the existence of the dislon and thereby the quantum nature of crystal dislocations. In fact, a recent simulation indicates the necessity to incorporate the quantization of the crystal vibrational modes in considering the plastic deformation process [39]. The dislon theory may thus serve as an analytical framework to account for the vibrational modes in a dislocated crystal.
To test the power of this theoretical framework, we compare the relaxation rate t e = S ( ) ( ) p r r p 2 , Im , , p dis from equation (39) to the well-known semi-classical results as reported in [40].
Despite the different methods, our one-loop result shares an identical prefactor t n n µ - The ratio between the modulus of the self-energy real part S | | Re and electron energy e p is plotted on the log scale, as a function of 2D coordinate = ( ) x y r , ,for edge (a), (c), (e) and screw (b), (d), (f) dislocations. The self-energy decays in an exponential way away from the dislocation core, indicating a short-range interaction. Compared with simpler asymptotic exponential decay behavior (a), (b), full coupling constants (c), (d) calculations indeed reveal an exotic Friedel oscillation, which is anisotropic and can occur with only single electron at present. This can be seen more clearly on linear scale waterfall plots (e), (f). The much more drastic oscillation for edge dislocation (e) than screw dislocation (f) is caused by dilatation effect and resulting electrostatic potential. | 6,398 | 2017-01-25T00:00:00.000 | [
"Materials Science",
"Physics"
] |
Handover Skipping for LiFi
This paper studies handover skipping, which enables handovers between two non-adjacent access points (APs), in light fidelity (LiFi) networks. LiFi is an emerging wireless communication technology, which operates in a way similar to wireless fidelity (WiFi) but uses light waves as a medium. Compared with WiFi, LiFi has a relatively shorter range with a single AP. This could possibly cause more frequent handovers, and thus, handover skipping techniques are required. Conventional handover skipping methods rely on information about the user’s trajectory, which is not ready to use at the AP. In this paper, a novel handover skipping scheme based on the reference signal received power (RSRP) is proposed. The new approach combines the value of RSRP and its rate of change to determine the handover target. Since RSRP is already used in the current handover schemes, the proposed method does not require additional feedback. The results show that compared with the standard handover scheme and the conventional handover skipping method, the proposed method can reduce handover rate by up to 29% and 17% and improve throughput by up to 66% and 26%, respectively.
I. INTRODUCTION
Global mobile data traffic will increase sevenfold between 2017 and 2022, reaching 77.5 exabytes per month by 2022, and traffic from wireless fidelity (WiFi) and mobile devices will account for 71 percent [2].Globally, there will be nearly 549 million public WiFi hotspots by 2022, up from 124 million hotspots in 2017 [2].The high-density WiFi deployment would cause sever signal interference due to the limited spectrum resource of radio frequency (RF).
To tackle the looming spectrum shortage in RF, wireless communication technologies based on extremely high frequencies have attracted significant attentions, such as millimetre wave (mmWave) communications [3], massive multiple-input multiple-output (MIMO) [4], and visible light communications (VLC) [5].The wireless networking use case of VLC is termed lightfidelity (LiFi) [6], which operates in a way similar to WiFi but uses light waves as a signal bearer.
Unlike RF communications, the LiFi access points (APs) can be integrated in the existing light infrastructure, e.g.light-emitting diode (LED) lamps, realising a dual purpose system offering illumination and communication.Recent research shows that with a single off-the-shelf LED, LiFi is capable of achieving peak data rates above 10 Gbps [7].Also, LiFi offers many other advantages over WiFi, including: i) a vast and licence-free spectrum; ii) secure communication as light does not penetrate opaque structures; and iii) the availability in RF-restricted areas such as underwater and hospitals [8].
Due to inherently high propagation losses, all wireless communication technologies based on extremely high frequencies, including LiFi, have a relatively short range.Specifically, the LiFi AP has a coverage area of approximately 2-3m in diameter [9].This enables LiFi to achieve a very high area spectral efficiency through frequency reuse [10].However, in such an ultradense network, the handover process becomes challenging mainly due to two issues: i) readily occurring ping-pong effects and ii) relatively short cell dwell time (CDT).The signal strength strategy (SSS) method, which always connects the user to the AP that provides the highest reference signal received power (RSRP), thus becomes hugely suboptimal for LiFi.In order to suppress the ping-pong effect, the standard handover scheme in long term evolution (LTE) [11] uses the idea of hysteresis, which prolongs the handover decision for an amount of time.
However, this handover scheme is not capable of tackling the second issue.
In order to avoid the frequent handovers in ultra-dense networks, the concept of handover skipping is introduced [12]- [14].A topology-aware skipping scheme is proposed in [12], which sets a pre-defined threshold with respect to the chord length of the cell.A similar method is reported in [13], but extended to multiple AP association.The authors in [14] develop a velocityaware handover approach, which performs different skipping strategies according to the user's velocity, including: best connected strategy, femto skipping strategy, femto disregard stratey and macro skipping strategy.However, the above methods are all based on the knowledge of the user's trajectory.As a result, they have the following limitations: i) the measurement of the user's trajectory is less accurate in an indoor scenario due to uncontrollable errors caused by the multiple reflections at surfaces; and ii) extra feedback is required to send this information to the APs.To the best of the authors' acknowledge, no handover skipping method that does not rely on the user's trajectory has so far been proposed.
In this paper, an RSRP-based handover skipping method is proposed.The new method exploits the change in RSRP to reflect whether the user is moving towards the central area of an AP.Through a weighted average of the value of RSRP and the change in RSRP, the novel method is able to determine whether to skip a certain AP.As the change in RSRP is related to the user' velocity, the proposed method is velocity-aware.Unlike the trajectory-based methods, the proposed method does not need extra feedback since RSRP is already used in the standard handover scheme.Therefore, the proposed method can be readily implemented in practice.Also, the performance of the proposed method in terms of handover rate and coverage probability is analysed.Furthermore, the optimal weight coefficient is studied.Simulation results show that against the standard handover scheme, the proposed method can greatly reduce the handover rate and improve the throughput.
The remainder of this paper is organised as follows.In Section II, the system model of an indoor LiFi network and the channel model are described.Section III introduces the standard handover scheme in LTE.The novel handover skipping method is proposed in Section IV.In Section V, the handover rate and coverage probability of the proposed method are theoretically analysed.Simulation results are presented in Section VI.Finally, conclusions are drawn in Section VII.
II. SYSTEM MODEL
Consider an indoor wireless network consisting of a number of LiFi APs.The system is considered to be time division duplex, and we focus on downlink communications.Each LiFi AP is built in a ceiling LED lamp, facing downwards perpendicularly.The LiFi APs use different spectra and therefore do not interfere with each other.A single photodiode (PD) pointing upwards perpendicularly is fitted at the user.Though the issue of random receiving orientaions has been identified [15], the PD can keep facing upwards by using a rotation device to compensate the change in orientation.The user is assumed to move around in the room, following the random waypoint (RWP) model [16].
A LiFi channel is comprised of two components: line-of-sight (LoS) and non line-of-sight (NLoS) paths.Here only first-order reflections are considered since second-order reflections typically contribute little [17].Fig. 1 illustrates the LoS and first-order NLoS paths of a LiFi channel.Let i and u denote the AP and the user, respectively.The LoS path corresponds to the straight-line distance between the AP and the user, which is denoted by d i,u .Let φ i,u and ψ i,u respectively denote the angles of irradiance and incidence.The channel gain of LoS is denoted by LoS , and it is given by [17, eq. ( 10)]: where m = − ln 2/ ln(cos Φ 1/2 ) denotes the Lambertian emission order, and Φ 1/2 is the angle of half intensity; A pd is the physical area of the PD; g f is the gain of the optical filter; the optical concentrator gain g c (ψ i,u ) is given by [17, eq. ( 8)]: where n denotes the refractive index, and Ψ max is the semi-angle of the field of view (FoV) of the PD.
Fig. 1.The LoS and first-order NLoS paths of the LiFi channel [18].
A first-order reflection consists of two segments: i) from the AP to a small area w on the wall, and ii) from w to the user.The Euclidean distances of these two segments are denoted by d i,w and d w,u .The angles of radiance and incidence regarding the first segment are φ i,w and ϑ i,w , and for the second segment they are ϑ w,u and ψ w,u .The channel gain of NLoS is written as follows: where A w is the area of w and ρ w denotes the wall reflectivity.
Adding (1) to (3), the total gain of the LiFi channel can be expressed as follows: At the receiver, the PD converts the captured photons into an electric current: where R pd is the detector responsivity; P opt denotes the transmitted optical power; and ζ is the ratio of P opt to the optical signal power.The signal-to-noise ratio (SNR) of the user is denoted by γ i,u , which can be written as follows: where N LiFi denotes the power spectral density (PSD) of noise at the receiver, including shot noise and thermal noise, while B LiFi is the bandwidth of the LiFi AP.
III. STANDARD HANDOVER SCHEME
In order to tackle the ping-pong effect, the handover scheme in LTE [11] introduces two parameters: handover margin (HOM) and time to trigger (TTT).Fig. 2 shows the principle of this scheme, which is referred to as STD in the remainder of this paper.
The RSRP of the host AP is denoted by P i H , and the RSRP of the target AP is denoted by P i T .Let δ HOM denote the value of HOM.The STD scheme starts counting time when the following condition is satisfied: The time counter continues as long as ( 7) is satisfied, and otherwise is reset.Let t TTT denote the value of TTT.When the time counter reaches t TTT , a handover decision is made to transfer the user from the host AP to the target AP.Fig. 3 exemplifies the movement paths of the user in a LiFi network.The STD scheme can guarantee a minimum connection time equal to t TTT , which is usually limited to hundreds of milliseconds [11].Thus, this scheme is capable of skipping some APs that the user crosses very quickly, such as Path 1.In this case, the user is directly transferred from AP A to AP C, with AP B being skipped.However, this scheme cannot skip the APs where the user stays longer than t TTT , even slightly.Taking Path 2 for example, STD would handover the user from AP A to AP B, and then from AP B to AP C. Also, it is worth noting that the user might experience random light-path blockages [19].This can be deemed as an infinite attenuation for the link between the user and the blocked APs.The impact of random light-path blockages on handover rates will be studied in Section VI-E.
IV. PROPOSED HANDOVER SKIPPING METHOD
The value of RSRP reflects the distance between the AP and the user, and a higher RSRP signifies the corresponding AP is closer to the user.For example, when the user crosses the border between AP A and AP B in Fig. 3 where t 0 denotes the starting point of the time counter; P (t 0 ) i is the RSRP of AP i at t 0 ; λ is the weight coefficient and its optimal value will be studied in Section VI-A; and ∆P i denotes the change in RSRP per time unit, which is expressed as: With the proposed method, the time counter works in the same way as in STD.When the time counter reaches t TTT , the proposed method would select the AP with the largest Γ i to be the target AP.Note that the target AP does not have to be the one that triggers the time counter, e.g.AP B in Fig. 3.At the end of the time counter, a handover will be executed immediately if the target AP already meets the condition in (7).Otherwise, the handover will be held on until the target AP meets the condition.During this period, the target AP could be recalculated if the DRAFT January 9, 2019 direction or speed of the user's movement changes.Let I denote the set of all candidate APs.
The output of the time counter is denoted by t c .The pseudo code of the proposed handover skipping method is given in Algorithm 1.
Algorithm 1 Proposed Handover Skipping Method
Input: i , ∀i ∈ I end while Note that in (8), P
V. THEORETICAL ANALYSIS OF HANDOVER SKIPPING PERFORMANCE
In this section, the theoretical performance of the proposed handover skipping method is analysed for an arbitrary line trajectory.The area covered by the LiFi network is assumed to be boundless.Thus, only LoS paths need to be taken into account.
A. Handover Rate
First, we analyse the handover rate of the SSS method, where there is no handover skip.
We focus on the square deployment of LiFi APs as it is commonly used in practice to provide uniform illumination.The handover rate with the Poisson point process (PPP) deployment can be found in [20].It is assumed that the user enters the coverage area of an AP at an arbitrary point δ with an arbitrary angle θ.Let r denote the length of the side of the coverage area.The length of the user's movement path inside the coverage area is denoted by d path .The average value of d path is denoted by dpath , which is derived in Appendix A. The handover rate in this case is denoted by η, which is equal to the user's speed v divided by dpath : Then we derive the probability of handover skipping.With the proposed method, the user skips an AP when there exists another AP providing a larger Γ i .This event is denoted by X and its probability P(X) can be expressed as follows: DRAFT January 9, 2019 where: With the square deployment, the host AP borders 8 neighbours.Further APs are unlikely to become the handover target due to the much lower RSRP they provide.Let's consider the case that the user leaves AP A and enters AP B, as shown in Fig. 3. AP C and AP D are the only possible candidates for handover skipping, as in comparison with them the remaining neighbours perform worse in terms of both P and ∆P .Since the square deployment is axisymmetric, we assume that the user crosses the right half segment of the border between AP A and AP B. The candidate for handover skipping could only be AP C if θ is less than 90°, and otherwise AP D.
Therefore, P(¬X) can be rewritten as: where: uniformly distributed between 0 and π, the above equation can be rewritten as: As δ is uniformly distributed between 0 and r 2 , we have P(δ) = 2 r .Therefore, (13) can be computed as follows: The handover rate of the proposed method is denoted by η HS , which is the product of η and P(¬X).Combining ( 10) and ( 16), η HS can be expressed as:
B. Coverage Probability
The coverage probability is defined as the probability that a user's SNR is above a certain threshold γ T .This threshold corresponds to a certain horizontal distance between the user and the AP, which is denoted by l T .According to (6), l T can be computed as follows: The user's SNR is larger than γ T when l < l T .Therefore, the coverage probability of the SSS method is equal to P(l < l T ).Assuming the user is randomly located in the square coverage area with an equal probability, P(l < l T ) can be expressed as: It can be found that the coverage probability of the SSS method depends on the size of the coverage area, and is thus denoted by P(r).Regarding the proposed method, its coverage probability is equal to P(r) when no handover skipping occurs.When there is a handover skip, the distance between the host and target APs changes from r to √ 2r.The coverage probability of the proposed method can be estimated as follows: However, the skipped AP is located at one end-point of the border between the host and target APs, making this corner area unlikely to be involved in handover skipping.Therefore, (20) would underestimate the SNR of the user in the lower end.More details will be given in the following section.
C. Validation
Monte Carol simulations are conducted to verify the above theoretical analysis.Here the weight λ is fixed to be 1.In Fig. 4, the handover rate is shown as a function of the user's speed.As can be seen, the analytical results in (17) closely match the simulations.In addition, the handover rate decreases when: i) the distance between the nearest APs increases; or ii) the vertical distance between the user and the AP increases; or iii) the half-intensity angle of the LED increases.
Taking v = 5 m/s as an example, Fig. 5 presents the coverage probability of the proposed method.The impact of the user's speed will be studied in the following section.In general, the estimated expression agrees with the simulations.For lower SNRs, the analytical results are below the simulations with a marginal gap, as explained.Also, it can be found that the noted three situations all result in a decrease in SNR.In summary, the handover rate can be reduced at the cost of a decreasing SNR.
VI. SIMULATION RESULTS
In this section, Monte Carlo simulations are conducted to evaluate the performance of the proposed method.The STD and trajectory-based handover skipping methods are considered as benchmarks.In order to provide a fair comparison, the same HOM and TTT are used in the three methods.Here the values of HOM and TTT are set to be 1 dB and 160 ms [11].In addition, we consider 16 LiFi APs and the separation between the two nearest APs is fixed to be 2m.Other required parameters are summarised in Table I.
A. The Impact of the Weight Coefficient
First, we study the effect of λ on the performance of the proposed method.Note that λ needs to be larger than t TTT , as stated in Lemma A.2. Different speeds of the user in four movement scenarios are considered: 0.1 m/s (slowly moving), 1.4 m/s (walking), 5 m/s (running) and 10 m/s (sprinting).As shown in Fig. 6, for a slowly moving user, the throughput almost remains the same as λ varies in the displayed range.This is because in this case, the change of RSRP is very insignificant in determining the handover target.As the speed increases to 1.4 m/s, choosing a DRAFT January 9, 2019 The physical area of a PD, Apd 1 cm 2 The gain of the optical filter, g f 1 The refractive index, n 1.5 Half-intensity radiation angle, Φ proper λ becomes crucial.On the one hand, a too small λ would disable the function of handover skipping.On the other hand, a too large λ would cause unnecessary handover skipping.For a fast moving user, the throughput is a monotonically increasing function of λ in the displayed range.
The reason is that the of RSRP becomes a dominant factor in this case.Considering the optimal solutions to different speeds of the user, λ is set to be 1 in the following simulations.
B. Handover Rate
Second, the handover rate performance of the proposed method is studied.Fig. 7 presents the decreases in handover rate provided by the proposed method against STD and the trajectorybased method.The following outcomes are observed: i) compared to the baseline methods, the proposed method can effectively decrease the handover rate for different speeds of the user; and ii) as the speed of the user increases, this decrease in handover rate becomes larger.At v = 0.1 m/s, the proposed method achieves a handover rate 2% less than STD.When v increases to 1.4 m/s, this gap increases to 18%.For v = 10 m/s, the proposed method reduces the handover rate over STD by 29%, and compared to the trajectory-based method this gap is 17%.
C. Coverage Probability
Third, the coverage probability for different speeds of the user in shown in Fig. 8.Here the SSS method is considered as a baseline, because its host AP only depends on the user's location, regardless of the user's speed.This method can be deemed as a special case of STD with zero HOM and TTT.As shown, the coverage probability of the proposed method decreases as the user's speed increases, especially for medium SNRs between 14 and 18 dB.High SNRs correspond to the cell centre, where the handover skipping rarely occurs; low SNRs correspond to the cell corner, where the target AP of handover skipping can provide a comparable SNR against the skipped AP.Otherwise, the SNR performance would substantially decrease when the handover skipping happens.Nevertheless, for the 50-th percentile, the SNR of the proposed method is only 2 dB less than that of SSS at most.This means that with the proposed method, the user can achieve an SNR comparable to that of SSS in at least 50% of situations.Also, it is observed that at v = 10 m/s, there is a noticeable gap between the coverage probabilities of the proposed method and the trajectory-based method at lower SNRs.This is because when the user moves very fast, the proposed method might skip more than one AP, leading to a significant decrease in SNR.
D. Throughput
In Fig. 9, the user's throughput is presented as a function of the user's speed.The throughput is mearsured by the modulation and coding scheme in [22], and no data transmission is counted during the process of handover.As shown, the proposed method always achieves a higher throughput than the baseline methods.This gain becomes more significant as the user's speed increases.For v = 5 m/s, the proposed method can improve the throughput over STD and the trajectory-based method by 17% and 5%.When v increases to 10 m/s, the corresponding values increase to 66% and 26%, respectively.
E. The Impact of Random Light-path Blockages
Finally, we study the impact of random light-path blockages on handover rates.In queueing theory [23], the Poisson point process is widely used to model random events such as the arrival of packages at a switch.Here the events of light-path blockages are also assumed to follow the Poisson distribution, and its mean is referred to as the occurrence rate.As shown in Fig. 10, DRAFT January 9, 2019 the handover rates of all involved methods noticeably increase with the occurrence rate in the case of v = 1.4 m/s.While the user's speed increases to 5 m/s, the corresponding handover rate is hardly affected by the change in occurrence rate.This is because for the user moving at a relatively high speed, in comparison to user mobility, the random light-path blockage is an insignificant factor that affects the handover process.
VII. CONCLUSION
In this paper, a novel handover skipping method was proposed for LiFi networks.Unlike the conventional methods using the user's trajectory information, the proposed method is based on RSRP, which has been commonly used in the current handover schemes.Therefore, the proposed method does not require additional feedback and can be readily implemented in practice.Specifically, the change of RSRP is exploited to reflect whether a user is moving towards the AP.The weighted average of this parameter and the value of RSRP is used to determine the target AP for handover.Also, the handover rate and coverage probability of the proposed method is theoretically analysed.Furthermore, the effect of the weight coefficient on the performance of the proposed method is studied.Simulation results show that the proposed method can significantly reduce the handover rate against STD, especially when the user is moving relatively fast.Regarding the system throughput, the proposed method outperforms STD and the trajectory-based handover skipping method by up to 66% and 26%, respectively.Future research will study the issue of handover skipping in hybrid LiFi and WiFi networks.m > 0 for all possible Φ 1/2 .Hence, P (t 0 +t TTT ) B is monotonically increasing.As for F 2 (θ), its derivative F 2 (θ) is expressed as follows: Note that F 2 (θ) is always positive.Also, we have F 2 (0) = −vt TTT r < 0 and F 2 ( π 2 ) = vt TTT (2δ + r) > 0. Therefore there exists one and only one θ meeting F 2 (θ) = 0.This signifies that P (t 0 +t TTT ) C is monotonically increasing until F 2 (θ) = 0 and then monotonically decreasing.
It is worth noting that F 2 (θ) is always larger than F 1 (θ).This means that when P Proof: According to Lemma A.1, Z(θ) is monotonically increasing when F (0) ≥ 0. It is evident that Lemma A.2 is true in this case.When F (0) < 0, Z(θ) is monotonically decreasing first and then monotonically increasing.In this case, Lemma A.2 is true if Z(0) < 0. Substituting θ = 0 into (32), we have: is always non-negative and λ t TTT is assumed to be larger than 1.Hence Z(0) < 0 when F (0) < 0.
The coefficient t TTT is very small in practice, with a typical value of 0.16 s [11].Therefore, the condition λ > t TTT can be readily satisfied.This is also a guideline for the choice of λ.
, AP B offers a higher RSRP than AP C.However, in Path 1 and Path 2, the user passes the outskirts of AP B and moves towards the central area of AP C. As a result, AP C provides a faster increase in RSRP than AP B. With respect to Path 3,
Fig. 3 .
Fig. 3. Different movement paths of the user in a LiFi network.
(t 0
) i depends on the position of the point that the user crosses the border, whereas ∆P i reflects the direction and speed of the user's movement.If the crossing point is very close to the border between two candidate APs, e.g.AP B and AP C in Path 1, the RSRP offered by those APs would be almost the same.In this case, ∆P i is the dominant factor to determine the target AP.On the contrary, the values of RSRP significantly differ when the crossing point is far away from one candidate AP, e.g.AP C in Path 3. In this case, P (t 0 ) i becomes the dominant factor.As for Path 2, AP B provides an RSRP marginally higher than AP C. Meanwhile, the ∆P i of AP C increases with the user's speed.If the user moves fast, it is handed over from AP A to AP C, with AP B being skipped.Otherwise, the user is transferred to AP B due to the insignificant influence of ∆P i .
Fig. 6 .Fig. 7 .
Fig. 6.Throughput versus the weight coefficient for different speeds of the user.
(t 0
+t TTT ) B and P (t 0 +t TTT ) C are both increasing, P (t 0 +t TTT ) B has a larger slope than P (t 0 +t TTT ) C. As a result, F (θ) is monotonically increasing if F (0) ≥ 0. Otherwise, F (θ) is monotonically decreasing first and then monotonically increasing.Lemma A.2: For θ ∈ 0, π2, there is up to one solution to Z(θ) = 0 on condition that λ > t TTT . | 6,234.2 | 2019-03-07T00:00:00.000 | [
"Computer Science",
"Engineering"
] |
Oxidation of Fe-2.25Cr-1Mo in presence of KCl(s) at 400 °C – Crack formation and its influence on oxidation kinetics
Accelerated corrosion of boiler equipment remains a challenge for efficiently utilising biomassand waste for power production. To overcome this challenge a better understanding of the influence of corrosive species present is required. This study focuses on the influence of KCl(s) on corrosion of Fe-2.25Cr-1Mo at 400 °C. This is done by well-controlled laboratory exposures and detailed microstructural investigation with ion and electron microscopy (TEM, FIB, SEM, EDX, XRD, TKD). The scale microstructures are linked to oxidation kinetics. The results indicate that KCl(s) increases the ionic diffusion through the oxide scale as well as introduces cracks and delamination resulting in a rapid periodic growth process.
Introduction
Utilising renewable and CO 2 neutral fuels such as biomass-and waste for power production is an attractive alternative to power plants burning fossil fuels. The combustion of biomass and waste, however, results in the release of corrosive species such as HCl and alkali chlorides [1,2]. This puts high demands on the corrosion resistance of the alloys used for boiler equipment such as waterwalls and superheaters.
In order to limit the corrosion and increase the lifetime of boilers the power plants using renewable fuels are often operated at a considerably lower steam temperature than those using fossil fuels. This results in decreased electrical efficiency, which makes biomass and waste less competitive towards fossil fuels. Another way to limit corrosion of boiler equipment is to use more corrosion resistant materials, such as stainless steels. However, this is costly and in order to make biomassand waste an economically favourable alternative to fossil fuels the use of less expensive materials, such as low alloyed steels (e.g. Fe-2.25Cr-1Mo), as well as higher operating temperatures are interesting goals. To make this possible while maintaining a reasonable lifetime of the boiler equipment it is necessary to increase the understanding of the underlying mechanisms of the rapid corrosion of low alloyed steels.
The influence of alkali chlorides and other chlorine containing compounds on high temperature corrosion has previously been studied extensively on both pure iron [3][4][5][6][7], stainless [2][3][4][5][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and low alloyed steels [2,4,5,8,10,11,13,[21][22][23][24][25][26][27]. While it is well-known that chlorine containing compounds cause corrosion of all these materials, the underlying mechanisms of both chlorine and alkali species are still under debate. The corrosion resistance of stainless steels relies on the ability to form a protective Cr-rich oxide scale ((Cr x Fe 1−x ) 2 O 3 ). Previous studies on stainless steels [12,15,16,18,19] have shown that alkali, specifically potassium, influences high temperature corrosion by depleting the protective Cr-rich scale to form potassium chromates (see reaction (1)). This results in breakdown of the protective Cr-rich oxide and the formation of a less protective iron rich scale. (1) For low alloyed steels the amount of chromium in the alloy is not sufficient to form this protective Cr-rich oxide. Instead the scale formed is iron rich consisting of a Fe 2 O 3 layer on top of an (Fe, M) 3 O 4 (< 570°C). Thus, the depletion of chromium of the oxide does not explain the observed accelerated corrosion of low alloyed steels in presence of alkali chlorides. For low alloyed steels the chlorine is instead considered the most corrosive species and the influence of alkali remains unknown. The so called active oxidation, i.e. the chlorine cycle, initially proposed by McNallan et al. [28] and further developed by Grabke et al. [8], is one mechanism proposed to explain the oxide morphology and microstructure in the presence of chlorine in a wide temperature and material range [2][3][4]6,[8][9][10][11]21,28]. Active oxidation is a cyclic process where chlorine is proposed to be released at the sample surface as Cl 2 molecules (by reaction with O 2 ) and then penetrate the oxide scale to form volatile transition metal chlorides at the scale/metal interface (low pO 2 ). Because of the high vapour pressure of the metal chlorides they will then diffuse outwards through the scale and decompose into a porous metal oxide and Cl 2 (see reaction (2)) closer to the scale surface (high pO 2 ). The released Cl 2 is proposed to partly diffuse back to the scale/metal interface and continue the oxidation process without selfconsumption acting like a corrosion catalyst.
Folkeson et al. [14,24] proposed an alternative to the chlorine cycle, here referred to as the electrochemical mechanism. For low alloyed steels [24] this mechanism proposes KCl to react with O 2 and H 2 O on the scale surface to form potassium hydroxide and release chlorine ions (Cl − ). The Cl − is suggested to diffuse through grain boundaries towards the metal to form metal chlorides throughout the scale (at the grain boundaries and at the scale/metal interface). The accelerated corrosion observed in presence of KCl is proposed to be caused by that FeCl 2 at the grain boundaries facilitates transport of both iron and oxygen ions. Chlorine containing compounds may also form mixtures with low melting points causing rapid spread of corrosive species over the surface and accelerated corrosion due to the liquid phase [4,6,25,29]. Jonsson et al. [25] studied the corrosion mechanisms of a low alloyed steel (Fe-2.25Cr-1Mo) close to the deposited KCl crystals by in-situ ESEM showing that the KCl(s) started to react well below 400°C and proposed that the corrosive species spread over the sample surface by formation of a eutectic mixture (KCl/FeCl 2 ). The study suggested the local corrosion reaction (in the vicinity of the KCl particles) to be initiated by the reaction of KCl with O 2 forming KOH (or K 2 O) and KFeO 2 as well as Cl − ions. The general corrosion, i.e. growth of the base oxide (away from the KCl particles), was proposed to be caused by an increased diffusion rate through the oxide due to the presence of Cl − ions at the oxide grain boundaries, in similarity to Folkeson et al. [24]. However, there was no evidence for formation of iron chlorides or Cl − at the grain boundaries. A recent study by Cantatore et al. [30] showed that chlorine could also permeate the magnetite oxide through lattice diffusion, which could open up for new mechanistic insights on the influence of chlorine on the oxide scale growth.
Several previous corrosion studies performed on the low alloyed steel Fe-2.25Cr-1Mo in presence of KCl(s) [10,24,26,31] showed accelerated corrosion and indications of crack formation and/or delamination. However, the microstructure and the chemical composition of the oxide scale was not studied in detail and the mechanisms for the observed accelerated corrosion and influence on the total growth process is still under investigation. The oxide scales formed on low alloyed steels and pure iron under oxidising conditions at 600°C have been shown to be multi-layered and composed of a thin outward growing Fe 2 O 3 (corundum), a thicker outward growing Fe 3 O 4 and an inward growing spinel oxide [25,[32][33][34][35]. The inward growing spinel formed on iron was pure Fe 3 O 4 while chromium was present in the inward growing spinel ((Fe,Cr) 3 O 4 ) on chromium containing low alloyed steels. Chromium, was suggested to remain at its original position due to the relatively slow diffusivity of Cr 3+ ions in the spinel phase, as compared to iron [36,37]. The influence of a cracked or partly delaminated oxide scale would change the conditions for diffusing species through the scale, affecting the corrosion rate extensively. In order to better understand the reason for the accelerated growth rate observed on low alloyed steels in the presence of alkali chlorides it is of great importance to further investigate the microstructural changes in the oxide scale.
In this study a detailed microstructural investigation in combination with an in-situ oxide growth study aims to link the delamination and scale microstructure to the oxidation kinetics and the observed accelerated corrosion. Explaining the influence of crack formation and scale delamination would contribute with essential information for e.g. the development of reliable kinetic modelling tools for oxide growth such as DICTRA [38] and help to explain the very rapid corrosion rates observed in field studies performed in biomass-and waste fired boilers [39,40].
Sample preparation
The investigated alloy is an Fe-2.25Cr-1Mo steel (see Table 1 for chemical composition). Prior to exposure the steel was cut into coupons (tube furnace exposures: 15 × 15 × 2 mm, TGA: 10 × 8 ×2 mm), ground with SiC (grit size P320), a Largo disc (9 μm) and polished with diamond suspension (3 and 1 μm) until mirror like appearance. The polished steel coupons were degreased and cleaned in acetone and ethanol by using ultrasonic agitation. Both non-coated and KCl(s) coated steel coupons were investigated. KCl(s) was deposited on the coupons before exposure by spraying a solution of KCl (0.1 mg/cm 2 ) solved in ethanol and water (80:20) and subsequently dried in cool air. All samples were stored in a desiccator (drying agent P 2 O 5 ) prior to exposure and awaiting analysis to avoid atmospheric corrosion and hygroscopic effects of chlorine containing species.
Exposures
The exposures were performed in an isothermal horizontal tube furnace as well as a vertical furnace system for recording the oxidation kinetics by thermogravimetric analysis (TGA). The samples were positioned parallel to the direction of the gas flow and all parts of the systems were kept above the dew point of water to prevent condensation. The reference exposure gas consisted of 20%H 2 O + 5%O 2 + 75% N 2 . The exposures were carried out at 400°C for 24 h on both noncoated and KCl(s) coated steel coupons. The exposures in the horizontal tube furnace were made with three samples positioned in a sintered alumina holder during each exposure. The TGA exposures were performed with a single sample at the time, but several exposures were made to ensure reproducibility. The oxidation kinetics were recorded using a Setaram Setsys thermobalance (flow rate of 15 ml/min) humidified with a Setaram Wetsys.
Scanning electron microscopy (SEM)
Surface and cross-sectional characterisation of the samples were performed by an FEI Quanta ESEM 200 and a Zeiss LEO Ultra 55 FEG SEM, both equipped with a field emission gun and a detector for Energy dispersive X-ray spectroscopy (EDX). The microscopes were operated in high vacuum mode with accelerating voltages between 15-20 keV for the chemical analysis, 1.5-2 keV for surface sensitive imaging in the Zeiss LEO Ultra 55 FEG SEM and 10-20 keV for imaging in the FEI Quanta ESEM 200. Both secondary electrons (SEs) and backscattered electrons (BSEs) were used for imaging.
Broad ion beam (BIB)
Wide cross sections of the samples were prepared by Broad ion beam (BIB) milling. The BIB used in this study is a Leica EM TIC 3X BIB with a triple Ar ion gun operated at 6.5 kV. Prior to milling the samples were prepared by application of a 0.5 mm thick silicon wafer glued to the sample with Loctite® 415. The samples were thereafter cut prior to milling by a low speed saw without lubrication. The Si-wafer was used as a protection for the oxide to stay intact during cutting as well as for beam damage during ion milling.
Focused ion beam (FIB)
Site specific cross sections for TEM analysis were prepared using an FEI Versa3D LoVac DualBeam. The instrument is a combined FIB/SEM, equipped with a Ga liquid ion metal source (LMIS), a Gas Injection System for deposition of Pt (used as a protective cap layer to reduce beam damage and ion implantation) and an Omniprobe needle for liftout of thin TEM lamellae. The instrument was operated in high vacuum mode at 30 keV, with varying beam currents (30 pA-15 nA) throughout the lift-out procedure. The FIB was also used for imaging the BIB-milled cross sections with ion induced secondary electrons (iSEs) at 30 keV and 10 pA for enhanced grain contrast to measure the grain size of the oxides. The grain sizes were measured in two dimensions assuming that the most relevant direction for grain boundary diffusion is the growth direction represented in the two-dimensional cross sections.
Transmission electron microscopy (TEM)
Cross sections of the oxides were investigated in further detail using an FEI Titan 80-300 TEM equipped with an Oxford X-sight EDX detector for chemical analysis. The microscope was operated in Scanning TEM mode (STEM), at an accelerating voltage of 300 keV. Both bright field (BF) and High Angle Annular Dark field (HAADF) imaging modes were used. The quantification of oxygen from the STEM/EDX analysis is not reported in this paper due to large errors associated with oxygen quantification in EDX analysis. Instead the cationic percent is reported (in at%) assuming stoichiometric oxides.
X-ray diffraction (XRD)
The crystalline oxide phases formed on the samples were characterised by a Siemens D5000 powder X-ray diffractometer with a CuK α source (λ = 1.5418 Å). The instrument was operated in grazing incidence geometry with an angle of incidence of 2-4°and a measuring range of 10°< 2θ < 85°.
Transmission Kikuchi diffraction (TKD)
Transmission Kikuchi diffraction (TKD) was used in order to locally characterise some of the phases of the oxide scale. The instrument used for the TKD measurements was a Tescan GAIA3 equipped with a NordlysNano Camera for electron backscatter diffraction (EBSD) analysis. The instrument was operated at 30 keV and the FIB-milled thin foil was mounted in a tilted holder at 20°to maintain the Kikuchi diffraction patterns and locally distinguish between corundum and spinel type oxides.
Results
The results below show the influence of KCl on oxidation of a low alloyed steel at 400°C both regarding oxidation kinetics, oxide morphology and scale microstructure by the comparison of a reference exposed sample as well as a KCl exposed sample.
O 2 + H 2 O (reference)
The TGA performed on the reference sample showed slow parabolic kinetics (k p = 7.3 × 10 −14 g 2 cm −4 s −1 ) resulting in a low mass gain (∼0.1 mg/cm 2 ) after 24 h (see Fig. 1). The oxide thickness was estimated to 0.6 μm from mass gain data. The calculation was performed by assuming that the scale consisted of dense Fe 3 O 4 and that all mass gain was related to oxygen uptake from the exposure atmosphere [41].
O 2 + H 2 O + KCl(s)
The KCl(s) coated sample grew with repeated rapid parabolic kinetics resulting in a high mass gain (∼0.9 mg/cm 2 ) after 24 h (see Fig. 1). The growth was parabolic with the parabolic rate constant k p,1 = 4.3 × 10 −12 g 2 cm −4 s −1 for the first 12 h and thereafter disrupted by a short linear growth period followed another rapid parabolic growth (k p,2 = 3.2 × 10 −12 g 2 cm −4 s −1 ). The kinetic transition was, between the first and second parabolic growth, was not always as sharp as shown in Fig. 1 and the time for the kinetic transition varied between samples. However, the kinetic transition occurred at a calculated thickness of at least 3 μm and the final mass gains after 24 h were similar for all samples. The oxide thickness was estimated from mass gain data to 6.5 μm in total, corresponding to 4.2 μm before the kinetic transition (0-12 h) and 2.3 μm after (12-24 h).
Oxide scale
The surface morphology of the reference sample was homogeneous and consisted of blade like whiskers covering all the sample surface (see Fig. 2a Fig. 7) and the composition determined by STEM/EDX analysis of a representative region (see Fig. 3b-d). The STEM/EDX analysis showed that both the outward growing oxides were pure iron oxides while the inward growing spinel contained an average of 10 at% Cr (6.5-19 at%), 2 at% Si (1-4 at%), 1-2 at% Mo, with iron in balance, excluding oxygen from the quantification (see Fig. 3).
The boundary between inward and outward growing oxides, i.e. the original metal surface, was determined from microstructure and the presence of chromium in the inward growing spinel (see the STEM/EDX linescan for chromium in Fig. 3d). The distribution of oxides in the multi-layered scale was approximately 25% Fe 2 O 3 , 50% Fe 3 O 4 and 25% mixed spinel, resulting in an oxide scale consisting of 25% inward growing and 75% outward growing oxide (see Table 2). No depletion zone of chromium was observed in the alloy after 24 h of exposure. A mass balance calculation was performed from the STEM/EDX data indicating that no substantial amount of any alloying element was lost by evaporation or spallation.
The oxide grains in the Fe 3 O 4 layer were columnar with an average grain size of 140 nm × 270 nm (aspect ratio of 0.5) while the grains of the Fe 2 O 3 layer were more equiaxed (aspect ratio 0.7) and approximately 75 nm × 110 nm in size (see Fig. 3b).
O 2 + H 2 O + KCl(s) 3.2.2.1. Surface morphology.
The surface morphology of the oxide scale formed on the KCl(s) coated sample was heterogeneous (see Fig. 4a, b). The surface contained a noticeable amount of remaining, partly unreacted KCl crystals and a variety of oxide morphologies. The remaining KCl crystals covered nearly 20% of the total surface area, both present as isolated crystals and larger crystal agglomerates (see Fig. 4a). A considerable number of the crystals were completely overgrown by iron oxide. Both the corundum (Fe 2 O 3 ), spinel (Fe 3 O 4 ) and rock salt (KCl) phases were detected by XRD (see Fig. 7). The XRD results also indicated the presence of maghemite (γ-Fe 2 O 3 ) which has the same crystal structure as magnetite (Fe 3 O 4 ) but the chemical formula of hematite (Fe 2 O 3 ). The base oxide (i.e. the most common type of oxide region in between the remaining KCl crystals) had a granular surface morphology with a granule diameter of approximately 0.5-1 μm (see Fig. 4b). In contrast to the reference sample the plan view investigation showed that cracks formed on the sample surface (see Fig. 4a). Some cracks were partly overgrown by oxide (see Fig. 5a, b). A one-sided cross section (see Fig. 5c, d), ion milled through a crack, showed the formation of two subscales detached completely to form a new subsurface, covered by whiskers, below the upper subscale.
Scale microstructure.
The base oxide (in between the KCl particles) formed on the KCl(s) coated sample was thick and partly delaminated (see Fig. 6a). The scale consisted of two delaminated, multi-layered oxide subscales with a total thickness of 5.5-7.3 μm (average 6.4 μm) (see Fig. 6b Table 3) based on data from XRD and EDX analysis as well as the oxide microstructure. The STEM/EDX analysis (see Fig. 6d, e) showed that the outward growing oxides consisted of pure iron oxide with small traces of potassium (< 1%) in the top layers of the upper outward growing scale (Fe 2 O 3 + Fe 3 O 4 ) (see Fig. 6d, e). The inward growing spinel in the Fig. 1. Thermogravimetric analysis showing the oxidation kinetics of Fe-2.25Cr-1Mo exposed at 400°C for up to 24 h for both non-coated (reference) and KCl(s) coated steel coupons. Both the reference and KCl(s) coated samples show parabolic kinetics but with different parabolic rate constants. The parabolic rate constants, k p,i , marked in the figure, are calculated from Δm 2 = 2k p,i t, where Δm represent the mass change (y-axis) and t = time (x-axis). A kinetic transition is observed in the curve for the KCl(s) coated sample, with similar parabolic rate constants before and after the transition. upper subscale contained an average of 7 at% Cr (2.5-10%), 1 at% Si (1-2%), < 1 at% Mo, with iron in balance, excluding oxygen from the quantification. The TKD results confirmed that the top oxide layer contained hematite Fe 2 O 3 (corundum), with an average grain size of 190 nm × 330 nm (aspect ratio ≈ 0.6), (see blue regions in Fig. 6c). The thicker oxide below was confirmed to be spinel/magnetite (see yellow regions in Fig. 6c) with columnar oxide grains of average grain size 230 nm × 780 nm (aspect ratio ≈ 0.3). The brighter contrast in the SE image in Fig. 6b appeared to match the indexed corundum in the TKD mapping (see blue regions in Fig. 6c). The SE image in Fig. 6b also showed a band below the pores in the upper subscale with brighter contrast than the surrounding oxide. The difference in contrast in combination with the TKD results indicated that this band was Fe 2 O 3 (average grain size 280 nm × 500 nm) as well as local regions in the mixed (Fe, Cr, Mo, Si)-spinel layer below (see Fig. 6c). However, due to the small area analysed in the TKD, we cannot conclude, but only speculate in, that all brighter regions observed in Fig. 6b were Fe 2 O 3 (corundum).
The lower subscale was concluded to consist of 10% Fe 2 O 3 , 45% Fe 3 O 4 and 45% (Fe,Cr)-oxide (including the fibre structured oxide (35% Fe,Cr) x O y ) (see Table 3) based on data from XRD and EDX analysis as well as the oxide microstructure. The STEM/EDX analysis showed an outward growing pure iron oxide and a mixed inward growing oxide. The oxide grains of the Fe 3 O 4 layer in the lower subscale were 260 nm × 700 nm (aspect ratio ≈ 0.4) while the grains in the top oxide layer (Fe 2 O 3 ) of the lower subscale were equiaxed with an average grain size of approximately 80 nm (see Fig. 6b). This layer was concluded to be Fe 2 O 3 due to the visible contrast in the SE image, the smaller grain size of this oxide layer and the whiskers formation, characteristic for Fe 2 O 3 in exposure to H 2 O, as reported in several studies [17,29,34] (see Fig. 6b). The inward growing oxide could be divided into two different types, separated by a lateral gap. The oxide above this lower gap was suggested to be a dense spinel oxide ((Fe,Cr) 3 O 4 ) while the oxide at the scale metal interface showed a characteristic fibre like microstructure noticeably different from the rest of the oxide scale (see Fig. 6b). Diffraction in TEM (not shown) indicated that this oxide was crystalline showing a spot diffraction pattern in the TEM. However, the diffraction pattern was not recorded and indexed why it cannot be concluded with certainty. The XRD data did only detect Fe 2 O 3 (corundum), (Fe 1−x ,Cr x ) 3 O 4 (spinel) and the alloy (BCC) why it is proposed that the phase is spinel if crystalline. The dense inward growing spinel in the lower subscale contained approximately 3-5 at% Cr with iron in balance and traces of silicon (< 1 at%) and chlorine (< 1 at%) while the fibre like oxide ((Fe,Cr) x O y ) layer, at the scale/metal interface, contained approximately 20 at% Cr (16-21 at%), 3 at% of Mo (2-3 at%), 4 at% Si (4-6 at%) with iron in balance and traces of chlorine (< 1 at%). It should be noted that the porous microstructure made the quantification of this region difficult, why the quantification of this region should be considered as approximate. In addition, since both molybdenum and chlorine were detected in this oxide, there is a risk of overlapping X-ray energies of the K-peaks of chlorine and L-peak family of Mo, which makes the quantification of small amounts of chlorine troublesome. Crack formation is observed on the sample surface (see Fig. 5 for more details). The base oxide (in between the remaining KCl crystals) is heterogeneous but is mainly structured in a granular surface morphology. The plan view images are produced by secondary electrons at an acceleration voltage of 20 keV (a) and 10 keV (b). The microstructure of the base oxide marked in figure (a), is analysed in further detail (see Fig. 6).
Discussion
The present study focuses on the initial stages of the KCl-induced corrosion of Fe-2.25Cr-1Mo at 400°C. The study includes a detailed microstructural investigation of the base oxide scale in combination with in-situ mass gain kinetics.
Oxidation of Fe-2.25Cr-1Mo
The present study shows that the oxide scale formed on Fe-2.25Cr-1Mo in absence of KCl(s) (reference sample) is thin and well-adherent with no indications of scale cracking (see Figs. 2 and 3), corresponding well with previous studies on the initiation of corrosion of low alloyed steels and iron in presence of H 2 O [24,33,34]. The thickness is uniform and in good agreement with the average thickness calculated from mass gain data indicating that no noticeable amount of any species has been lost by spallation or evaporation during exposure (see Table 2). The mass balance performed from STEM/EDX data resulted in the same conclusion.
The slow parabolic kinetics recorded by TGA (see Fig. 1) indicates that the oxide growth is diffusion controlled in good agreement with previous studies [24,25,35]. The parabolic rate constant (k p,Ref = 7.3 × 10 −14 g 2 cm −4 s −1 ) is in the same range as previously reported for low alloyed steels in presence of water vapour at 400°C and 1-2 order of magnitudes lower than pure iron in similar exposure conditions [24,25,32,34]. The difference in parabolic rate constant between iron and Fe-2.25Cr-1Mo observed in this study indicates that the presence of chromium, detected in the inward growing spinel, has an important influence on the overall growth rate at 400°C.
The multi-layered type of oxide scale observed in this study (see Fig. 3) is in good agreement with previous studies performed on low alloyed steel and iron [10,17,25,32,34,35]. The oxide distribution in this oxide scale is concluded to be approximately 25% inward growing and 75% outward growing oxide (see Table 2). The STEM/EDX results show that the mixed inward growing spinel has higher relative levels of Cr, Si and Mo (compared to the original alloy composition. This is proposed to be explained by the rapid outward diffusion of iron to grow the Fe 2 O 3 and Fe 3 O 4 , while chromium remains at its original position due to the relatively slow diffusivity of Cr 3+ ions in the spinel phase [36,37].
Influence of KCl
The present study clearly shows that KCl(s) accelerates and influences the growth process of the oxide scale formed on Fe-2.25Cr-1Mo. Both oxidation kinetics, thickness, surface morphology and microstructure of the base oxide scale changes markedly when KCl(s) is present. In contrast to the reference sample the oxide scale is thick, heterogeneous and decohesive and shows formation of several cracks on the sample surface in good agreement with previous studies on low alloyed steel in presence of KCl(s) at 400°C [24][25][26] or HCl(g) at higher temperatures [13]. The oxide scale is formed by two delaminated multi-layered subscales, composed of Fe 2 O 3 , Fe 3 O 4 and (Fe,Cr,Si,Mo) 3 O 4 . Uusitalo et al. [10] observed a similar, but thicker, microstructure of the oxide scale formed on Fe-2.25Cr-1Mo exposed for 1000 h at 550°C in 500 vppm HCl (g) + 20%H 2 O + 14%CO 2 + 3%O 2 + Ar (bal.). It should be noted that those exposures were interrupted and samples weighted every 100 h, which could result in delimitation of the oxide scale.
Oxide growth
Both the microstructural investigation and oxidation kinetics indicate that the scale growth is diffusion controlled (see Fig. 1). However, the kinetic transition observed suggests that the total growth process of the oxide scale is strongly influenced by microstructural changes during growth. The growth rate is markedly higher compared to the reference sample (k p,KCl ≈ 45-60 × k p,Ref ), supporting that the diffusion rate through the scale is strongly influenced by addition of KCl(s).
The oxidation kinetics are parabolic both before and after the kinetic transition, suggesting that the growth of each subscale is diffusion controlled. However, the parabolic rate constants before and after the kinetic transition (k p,1 = 4.3 × 10 −12 g 2 cm −4 s −1 and k p,2 = 3.2 × 10 −12 g 2 cm −4 s −1 ) are in the same order of magnitude indicating that the first formed oxide does not hinder the diffusing species noticeably (see Fig. 1). Thus, the oxide scale can grow in a repeated parabolic process. The lower value of the parabolic rate constant for the second subscale is proposed to be caused by that not all the surface oxidises simultaneously below the delaminated subscale. The estimated thicknesses, based on the mass gain before (0-12 h) and after (12-24 h) the kinetic transition, provided an estimated thickness of 4.2 μm and 2.3 μm respectively resulting in a total estimated thickness of 6.5 μm. The calculated thicknesses correspond well with the measured thickness of the upper (0-12 h) and lower (12-24 h) subscales as well as the total thickness of the scale (see Table 3). These results suggests that the growth of each subscale is represented by the TG curve before and after the kinetic transition. The results also indicate that the main corrosion product formed is oxide and that evaporation of KCl(s) on Fe-2.25Cr-1Mo exposed at 400°C is low, as reported by Folkeson et al. [24]. The microstructural investigation concludes that the presence of KCl(s) makes the oxide scale susceptible to crack formation and delamination, suggested to explain the global kinetic transition observed in the TG curve (see Fig. 1).
The oxide formed in presence of KCl(s) shows rapid diffusion throughout all of the exposure and no indications of incubation time. Olivas Ogaz et al. [27] showed that Fe-2.25Cr-1Mo exposed under similar conditions at 400°C, but on pre-oxidised samples, had a slight incubation time before the rapid kinetics started. Grabke et al. [8] did however not see much incubation time on pre-exposed Fe-2.25Cr-1Mo, exposed to NaCl at 500°C. The deposited KCl in this study is in contact with the metal from the beginning (no pre-oxidation) and proposed to spread rapidly on the surface as a eutectic melt as proposed by Jonsson et al. [25]. This could explain the instant acceleration of KCl as is observed in this study.
Moreover, the grain morphology of the Fe 3 O 4 layers, of both the upper and lower subscale, correspond well with what has previously been reported for iron oxide at around 400°C while the top Fe 2 O 3 layer (upper subscale) has larger oxide grains compared to previous studies [32,34,42]. However, the grain size of both Fe 2 O 3 and Fe 3 O 4 has increased compared to the reference sample, i.e. the number of grain boundaries has decreased. More grain boundaries are often attributed to increased growth rate of iron oxide at moderate temperatures caused by faster ionic transport through the grain boundaries compared to bulk diffusion [29,34]. This observation therefore indicates that the presence of KCl(s) changes the diffusion rate of ions through the oxide, possibly by lowering the activation energy for diffusion through the bulk and/or grain boundaries, since the number of grain boundaries does not increase.
Traces of potassium (< 1 at%) were detected in the top oxide layers of the outer subscale (both in what is proposed to be the top Fe 2 O 3 and in the Fe 3 O 4 layer). The small amounts of potassium detected may possibly change the conditions for diffusion through this oxide. Jiang et al. [43] proposed that the presence of potassium on iron oxide surfaces could promote the reduction of Fe 3+ to Fe 2+ , which in turn could alter the properties of the oxide scale. This has not been investigated in any detail in this study but could possibly explain the increased relative amount of inward growing scale observed. In this study the phase of the potassium compound is not determined. Previous studies have suggested the formation of KFeO 2 , K 2 O or KOH on Fe 2 O 3 since this would be energetically favourable under similar exposure conditions [24][25][26]30]. However, none of these phases have been detected. Further investigations are ongoing to investigate how potassium is positioned in the oxide, in what phase it is present and how it may influence the bulk and/or grain boundary diffusion.
Crack formation and delamination
In this study both cracks and delamination are observed on the KCl (s) coated sample, in good agreement with previous studies [ the corrosion rate extensively by changing the conditions for diffusion through the oxide scale. Cracks would serve as local highways for the corrosive atmosphere through the scale and delamination would result in the formation of a new reactive surface. Together these two microstructural phenomena could result in a global change in conditions and a sharp kinetic transition. This is supported by the plan view and cross section investigation showing that the base oxide is decohesive on the KCl(s) coated sample and that cracks form in contrast to the reference sample. From this investigation we propose a growth process that includes the delamination and subsequent crack formation as critical parts of the explanation to the microstructural changes and kinetic transitions observed in the TGA. The complete growth process proposed is schematically described in Fig. 8. The process starts with a rapid spread of KCl(s) over the sample surface, explaining the instantly high growth rate observed in the TGA, with subsequent growth of a multilayered oxide scale (upper subscale). The scale grows relatively thick (3.5-5 μm) during the first few hours and then partly delaminates to form a lateral gap and a new reactive surface. The oxide scale cracks at local positions which allows for the oxidising atmosphere to enter and rapidly spread through the lateral gap. The inflow of the oxidising atmosphere subsequently results in new environmental conditions, allowing for a new subscale (lower subscale) to form below the delaminated scale. This results in a global kinetic transition and the beginning of a new growth cycle (see Fig. 1).
In experimental studies it is normally challenging to determine whether observed cracks or delamination are parts of the growth process or if they are formed post exposure during the cooling process or sample preparation. However, in this study some of the cracks were partly overgrown by oxide indicating that the cracks had formed during growth (see Fig. 5a, b). Also, a new subsurface consisting of Fe 2 O 3 had formed under the first formed subscale (upper gap, see Fig. 5c, d) and pure Fe 3 O 4 crystals had grown in the lower gap (see Fig. 6). Formation of Fe 2 O 3 in the middle of the scale is not thermodynamically expected in a dense oxide where we have a gradient in oxygen partial pressure explaining the multi-layered scale. Hence, the uniform layer of Fe 2 O 3 observed in the middle of the scale strongly indicates that the oxygen partial pressure has increased above the dissociation pressure of Fe 3 O 4 (pO 2 > 10 −22 atm at 400°C [29]) to support the transformation of An obvious question that rises is also whether the cracks form as a consequence of delamination or if the delamination caused the crack formation. However, if the cracks formed before the scale detached, we should have a local corrosion attack in the vicinity of the cracks, which is not observed in this study. This suggests that delamination occurred before scale cracking. Also, local acceleration of corrosion would not result in a global kinetic transition as observed in the TGA (see Fig. 1). Hence, scale cracking is proposed to occur after, possibly caused by, the delamination.
Possible explanations to the delamination could be growth stresses, accumulation of vacancies at the decohesive interfaces or formation of metal chlorides. Jonsson et al. [25] observed spallation on Fe-2.25Cr-1Mo in exposure to KCl(s) at 400°C. The spallation was suggested to be caused either by the formation of iron chlorides, decreasing the adhesion of the oxide scale, or due to sample cooling, motivated by that no indications of spallation nor decohesion of the oxide scale was observed during the ESEM in-situ study. In this study the delamination is concluded to occur during growth, why sample cooling can be excluded as the explanation. Bertrand et al. [32] reported decohesion to occur between the inward and outward growing Fe 3 O 4 formed on pure iron after 260 h at 400°C under chlorine absent conditions. This indicates that the delamination is not necessarily explained by formation of metal chlorides. Pilling and Bedworth [44] proposed that volumetric differences between the substrate and the oxides formed result in compressive stresses in the scale. Clarke et al. [45] also suggested grains of larger lateral size to induce less internal stresses in the oxide scale. The origin of growth stresses has not been investigated systematically in this study. However, the larger oxide grain size observed on the KCl(s) coated sample, compared to the reference, either contradicts the theory of reduced internal stresses or indicates that growth stresses are not the only explanation to the delamination. Further investigations are needed in order to understand why the presence of KCl(s) induces oxide delamination and scale cracking. Larsson et al. [26] showed that the presence of 500 vppm HCl(g) (no KCl(s)) resulted in an oxide scale very similar to the reference sample, but approximately three times thicker, indicating that the very rapid growth and scale delamination observed Fig. 7. X-ray diffractogram of Fe-2.25Cr-1Mo exposed at 400°C in 5%O 2 + 20%H 2 O + 75%N 2 for 24 h in absence (lower diffractogram) and presence (upper diffractogram) of KCl(s). The diffractograms suggests that corundum and spinel type oxides are present on the surface after both exposures, interpreted as hematite (Fe 2 O 3 ) and magnetite/mixed spinel (M 3 O 4 ). The diffractogram also detects remaining KCl(s) on the sample exposed in presence of KCl(s) and indications of maghemite (γ-Fe 2 O 3 ), having a spinel type crystal structure, but the same chemical formula as hematite.
in this study is specific for KCl(s) and not general for any chlorine containing compound at 400°C. The thickness corresponded well with the mass gain data reported by Zahs et al. [3] on pure iron exposed at 400°C in presence of 500 vppm HCl(g).
Microstructural changes.
The upper subscale formed on the KCl (s) coated sample is concluded to consists of 30% inward growing and 70% outward growing oxide while the lower subscale consists of 45% inward and 55% outward growing oxide, including the fibre structured oxide, (see Table 2. Thus, the relative amount of inward growing oxide increased in both subscales in presence of KCl(s) compared to the reference exposed sample (compare Tables 2 and 3). This is an indication of that the presence of KCl(s) (chlorine and/or potassium) enhances anion (O 2− ) diffusion more than cation diffusion.
It may also be noted that the composition of the inward growing oxides varies between the two subscales and that the amount of chromium is not uniform in the inward growing spinel but ranged from 2.5-10 at% (avg. 7 at%) for the upper subscale, 3-5 at% for the dense lower subscale and 16-21 at% Cr for the fibre structured oxide. The higher chromium content can be explained by the iron diffusion outwards by that iron depletion results in higher relative levels of other alloying elements in the inward growing oxide. The higher levels of chromium may influence the diffusion properties of the oxide scale, which is another possible explanation to the increased amount of inward growing scale observed. However, this could not be concluded in this study. Further studies are ongoing in order to investigate how chromium doping of the mixed spinel oxide could influence anionic as well as cationic diffusion.
The accelerated corrosion observed in presence of KCl(s) is in literature often explained by the active oxidation process [2,4,6,8,10,11,28]. The active oxidation process would predict increased amount of outward growing oxide when KCl(s) is present due to Fig. 6a). The scale grow relatively thick (3.5-5 μm) during the first few hours and then delaminates from the metal. The oxide scale cracks at local positions and allows for oxygen to enter and rapidly spread through the lateral gap resulting in a global kinetic transition (see Fig. 1). The inflow of oxygen subsequently results in that a new subscale starts to form below the delaminated subscale which is the beginning of the next growth cycle. ). The porous scale was suggested to be caused by active oxidation. By using the same type of interpretation as in this study, the oxide formed in the study by Uusitalo et al. [10] was composed of two delaminated multi-layered scales with approximately 40% inward growing and 60 % outward growing oxides. The comparison between the microstructure of the oxide scale formed without HCl(g) was not the focus of the study by Uusitalo et al. [10]. However, the reference sample in this study, as well as pre-oxidations performed on Fe-2.25Cr-1Mo at 500°C by Olivas Ogaz et al. [27], suggests that the relative amount of inward growing oxide formed on Fe-2.25Cr-1Mo is lower in absence of chlorine. This observation indicates that another or additional process than the active oxidation could be the reason for the accelerating growth of the oxide scale in presence of chlorine. The enhanced inward diffusion of oxygen is predicted by the electrochemical mechanism proposed by Folkeson et al. [14,24] who proposed that iron chlorides at the grain boundaries would facilitate ion, especially anion (e.g. O 2− ), diffusion through the scale. However, no iron chlorides were observed in the grain boundaries in that study. In the present study the STEM/EDX analysis shows traces of chlorine (< 1 at%) in the inward growing oxide in the lower subscale. It is possible that the small amounts of chlorine detected are traces of evaporated metal chlorides that have escaped as a consequence of scale cracking and delamination. However, the performed mass balance and the agreement between calculated and measured thicknesses suggest low levels of evaporated species. The presence of chlorine was qualitatively ensured by comparing the EDX spectra from the KCl(s) coated sample to the reference sample (and the rest of the oxide scale of the KCl(s) coated sample) clearly showing that the chlorine signal is only visible at this position on the KCl(s) coated sample. It should be noted that the amount of chlorine could not be quantified with certainty both due to the porous structure and the overlapping X-ray energies of chlorine and molybdenum present in small amounts in this region. It should also be noted that the chemical detection of STEM/EDX is limited, why minor traces of chlorine could also be present in other regions of the scale. Under the experimental conditions, i.e. the acceleration voltage, the detector limitations and the sample thickness, it would be possible to detect approximately the amount of chlorine corresponding to a decorated oxide grain boundary. Possibly chemical analysis with lower detection limit (e.g. energy loss spectroscopy (EELS) or atom probe tomography (APT)) could be used in order to determine if e.g. any type of metal chloride have formed at the grain boundaries or if chlorine is segregated to other regions.
The scale microstructure observed in presence of KCl(s) in this study is more complex than has previously been reported and consists of a repeated multi-layered scale composed of [46,47]. This could be a possible explanation to the unexpected α-Fe 2 O 3 observed to be incorporated in the upper Fe 3 O 4 (see Fig. 6c.) However, it is also known that spinel type oxides (M 3 O 4 ) containing Fe 2+ ions may be oxidised to γ-Fe 2 O 3 below 300°C [46]. It is therefore possible that the γ-Fe 2 O 3 has formed after the exposure, why no further conclusions about its influence of the overall growth rate will be drawn in this study.
A porous fibre structured oxide is also observed at the scale/metal interface. The fine, porous structure makes it difficult to determine the phase of this layer by TEM diffraction because of movement from the oxide phase to pores when tilting the sample. However, the TEM diffraction (not shown) indicates that it is crystalline by showing a spot diffraction pattern in this region. The diffraction pattern is not indexed since the XRD data (see Fig. 7 only show signal from Fe 2 O 3 (corundum), (Fe 1−x ,Cr x ) 3 O 4 (spinel) and the alloy (BCC) suggesting that this phase is a spinel type oxide if it is crystalline. The STEM/EDX analysis shows that the oxide is enriched in chromium, molybdenum, and silicon, also suggesting that it is an inward growing spinel [35][36][37] highly depleted in iron. It is tempting to conclude that the different microstructure is the reason for the delamination observed in this study and that the traces of chlorine could be remains from evaporated metal chlorides explaining the formation of this structure. However, the structure was observed on Fe-2.25Cr-1Mo exposed without chlorine at higher temperature [27] and not observed at the first delamination (in the middle of the scale). The microstructure has only been observed on relatively thick oxide scales (> 3 μm, grown up to 24 h) formed on Fe-2.25Cr-1Mo, suggesting that the structure is correlated to rapid oxide growth. Further studies are ongoing in order to characterise this structure and understand how it could influence the overall growth process of the oxide scale.
Conclusions
The presence of KCl(s) accelerates corrosion of the low alloyed steel Fe-2.25Cr-1Mo and changes the oxide microstructure markedly at 400°C. KCl also reduces cohesion of the oxide scale formed on Fe-2.25Cr-1Mo and makes the oxide scale susceptible to crack formation. Delamination in combination with local cracks results in a global change in oxidation kinetics. Presence of chlorine and/or potassium is proposed to lower the activation energy for diffusion in bulk and/or grain boundaries resulting in an increased diffusion rate. The microstructure and oxidation kinetics indicate that the oxide growth is diffusion controlled with similar diffusion rate before and after delamination/cracking. Presence of KCl increases the relative amount of inward growing scale indicating that the presence of small amounts of chlorine and potassium detected in the scale may facilitate for oxygen diffusion inwards.
Data availability
The raw and processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations. | 10,847.2 | 2020-02-01T00:00:00.000 | [
"Environmental Science",
"Materials Science",
"Engineering"
] |
Bayesian Effect Selection in Structured Additive Distributional Regression Models
We propose a novel spike and slab prior specification with scaled beta prime marginals for the importance parameters of regression coefficients to allow for general effect selection within the class of structured additive distributional regression. This enables us to model effects on all distributional parameters for arbitrary parametric distributions, and to consider various effect types such as non-linear or spatial effects as well as hierarchical regression structures. Our spike and slab prior relies on a parameter expansion that separates blocks of regression coefficients into overall scalar importance parameters and vectors of standardised coefficients. Hence, we can work with a scalar quantity for effect selection instead of a possibly high-dimensional effect vector, which yields improved shrinkage and sampling performance compared to the classical normal-inverse-gamma prior. We investigate the propriety of the posterior, show that the prior yields desirable shrinkage properties, propose a way of eliciting prior parameters and provide efficient Markov Chain Monte Carlo sampling. Using both simulated and three large-scale data sets, we show that our approach is applicable for data with a potentially large number of covariates, multilevel predictors accounting for hierarchically nested data and non-standard response distributions, such as bivariate normal or zero-inflated Poisson.
Introduction
The flexibility of modern regression methodology is both a blessing and a curse for applied researchers and statisticians alike since, on the one hand, added flexibility enables potentially more realistic models approximating the true data generating process but, on the other hand, poses additional challenges in the model building and model checking process. In this paper, we consider structured additive distributional regression models (Rigby and Stasinopoulos, 2005;Klein, Kneib, Lang and Sohn, 2015) that combine additive predictors consisting of various types of regression effects, e.g. non-linear effects of continuous covariates, spatial effects or random effects (Kammann and Wand, 2003;Ruppert et al., 2003;Wood, 2017) with the possibility to model all parameters of the response distribution (e.g. location, scale or shape parameters) in terms of covariates in a distributional regression approach. As a consequence, an analyst is faced with the challenge of not only choosing an appropriate response distribution, (a task that we will not consider in this paper since both graphical tools for model checking as well as selection criteria are well developed, see for example Klein, Kneib, Lang and Sohn, 2015) but also with determining the most appropriate subset of covariates along with their exact modelling alternative for multiple regression predictors.
As an example, in one of our empirical illustrations on childhood undernutrition in Nigeria with more than 20,000 observations, we analyse a bivariate response variable (y 1 , y 2 ) ′ consisting of two scores for chronic and acute undernutrition. A previous study (Klein, Kneib, Klasen and Lang, 2015) suggests a bivariate normal model in which not only the marginal expectations but also the marginal scale parameters and the correlation parameter depend on covariates. This leads to a distributional regression model with five parameters µ 1 , µ 2 , σ 1 , σ 2 , ρ. In a full model, all of these parameters could be related to a predictor η ik of the form η ik =x ′ i β k + f 1,k (cage) + f 2,k (mage) + f 3,k (mbmi) + f spat ,k (region), k = 1, . . . , 5, i = 1, . . . , n, where i = 1, . . . , n denotes the observation index, k refers to the five distributional parameters, x i contains 13 binary covariates (and an intercept term) with regression coefficients β k , f j,k (·), j = 1, 2, 3, are non-linear smooth functions of age of child (cage), mother's age (mage) and mother's body mass index (mbmi), and f spat ,k are spatial effects based on regional information in the data. While effect selection (deciding which of the different effects should be included in the model) via a full search in the model space would already be challenging in a mean regression framework with only one single predictor, full effect selection in a distributional regression setting with multiple predictors is typically computationally prohibitive. This is even more the case when one is interested in deciding whether the effect of a continuous covariate shall be included in a linear or non-linear form or whether it could be excluded completely from the model. In this paper, we address these challenges and develop a novel spike and slab prior structure that enables Bayesian effect selection within structured additive distributional regression models.
While there has been extensive interest in spike and slab priors for Bayesian variable selection (i.e. the selection of effects in models with purely linear predictors) or function selection (selection of non-linear effects of continuous covariates) in previous years (see for example Clyde and George, 2004;O'Hara and Sillanpää, 2009, for reviews), most research has been restricted to additive mean regression with Gaussian errors, distributions from the exponential family or survival models but also in the context of group variable selection (Zhang et al., 2014;Xu and Ghosh, 2015). Furthermore, most approaches restrict the predictor specification to include either only linear effects or only non-linear effects of continuous covariates but do not enable the consideration of more complex effect types such as spatial effects or the decomposition of non-linear effects in linear and non-linear components.
Classical Bayesian variable selection approaches for linear models based on spike and slab priors include for example Mitchell and Beauchamp (1988), or George and McCulloch (1997). Smith and Kohn (1996) utilise these approaches for function selection in nonparametric regression with Gaussian responses by assigning the variable selection priors to individual basis functions. Approaches that move beyond the framework of Gaussian models but pertain the purely linear predictor structure comprise the approaches of Rossell and Rubio (2017) who propose a Bayesian variable selection approach that allows for skewness and thicker tails compared to the Gaussian distribution, Wang et al. (2017) who consider variable selection after transforming the response, and Chung and Dunson (2009); Kundu and Dunson (2014) who propose nonparametric models where in the former proposal the mean and shape learn the effect of covariates, while the latter assumes symmetric residuals. In all these approaches however, the spike and slab prior is directly imposed on the scalar regression coefficients. In contrast, Ishwaran and Rao (2005) consider a hierarchical specification where the spike and slab structure is not imposed directly on the regression coefficients but, on a higher level of the hierarchy, on their prior variances. This approach also allows to consider situations where selection should take place on blocks of regression coefficients representing for example the coefficients of a basis expansion in nonparametric regression. This leads to function selection approaches for additive models, also considered in Yau et al. (2003); Cottet et al. (2008); Reich et al. (2009), who combine a spike with point mass at zero with a slab that has support only on the positive real numbers. In contrast, Zhu et al. (2010) specify both spike and slab as normal distributions (with very different variance components) and Panagiotelis and Smith (2008) assign a multivariate prior with spike at the origin and normal slab directly to the whole vector of basis coefficients. In either case, one typically observes poor mixing unless sampling from marginalized full conditionals which are only available in closed form for Gaussian models (Yau et al., 2003;Reich et al., 2009;Panagiotelis and Smith, 2008) or models that have a latent Gaussian representation such as the probit model (Zhu et al., 2010). Cottet et al. (2008) address function selection in double exponential regression models, where both the mean and the dispersion parameter are linked to an additive predictor which comprises linear and non-linear effects. The model space is restricted, since functional effects may enter the model only if the corresponding linear effect is included in the model. Our proposal is inspired by the approach of Scheipl et al. (2012) that introduces effect selection in generalized additive models for simple exponential family regression and with only one meanrelated additive predictor. As Scheipl et al. (2012), we rely on a redundant parameter expansion of the vector of the basis coefficients as originally proposed in Gelman et al. (2008), and which allows us to expand the vector of basis coefficients in an importance parameter shared by all basis coefficients on the one hand and standardised basis coefficients on the other hand. Effect selection is then performed by assigning a spike and slab prior to the squared importance parameter. More precisely, our paper makes the following important contributions: • We integrate effect selection based on spike and slab priors in the structured additive distributional regression framework such that selection of general effect types is no longer restricted to mean regression models with responses from simple exponential families.
• The parameter vectors representing the additive effect components in a structured additive predictor are typically assigned partially improper multivariate normal priors. Instead of explicitly reparameterising the vector of basis coefficients to enable the specification of proper priors as in Scheipl et al. (2012), we implicitly remove the partial impropriety by adding a corresponding constraint to the prior distribution. As a consequence, we can retain sparse matrix structures for speeding up computations and show empirically that this has beneficial impact on the mixing behaviour of the MCMC simulations. In particular, when the vector of regression coefficients is large, we do not observe the strong dependence on the dimensionality of the basis coefficient vector identified in Scheipl et al. (2012). This enables us to also include effects of considerable dimension such as spatial effects to truly exploit the benefits of effect selection over function selection and even allows us to further extend the model to hierarchical specifications of the predictors (Lang et al., 2014).
• Formulating the spike and slab prior for the squared importance parameter in the redundant parameterisation yields scaled beta prime marginals which have favourable shrinkage properties (Pérez et al., 2017). We study these properties in detail and provide corresponding theoretical results for our prior structure including conditions for the propriety of the posterior.
• We develop rules for eliciting the hyperparameters of the spike and slab prior based on simple scaling criteria that are easily accessible to applied researchers. Based on the elicited parameters, we find that our new prior structure has similarly favourable shrinkage properties as the approach by Scheipl et al. (2012), while it avoids to arbitrarily fix the hyperparameters.
The rest of this paper is structured as follows: Section 2 summarises the specification of our novel spike and slab prior for effect selection in distributional regression. Properties of the prior, including prior elicitation, shrinkage properties and propriety of the posterior are discussed in Section 3. Section 4 contains details on posterior estimation via Markov chain Monte Carlo simulations and points to software and implementation. Sections 5.1 and 5.2 evaluate the performance of our approach in simulations and three diverse applications. In Section 6 we conclude. Our approach to Bayesian effect selection based on spike and slab priors is developed for the general class of (multivariate) Bayesian structured additive distributional regression (Klein, Kneib, Lang and Sohn, 2015). Let (y i , ν i ), i = 1, . . . , n denote n independent obser-vations on the (not necessarily scalar) response variable y and covariates ν. We then assume that the conditional distribution of y i given ν i is specified in terms of a K-parametric distribution with density p(y i |ϑ i1 , . . . , ϑ iK ), where ϑ i = (ϑ i1 , . . . , ϑ iK ) ′ is a collection of K scalar distributional parameters ϑ ik , k = 1, . . . , K, which depend on ν i . Compared to mean regression models where p(·) is usually assumed to belong to the exponential family and where K −1 parameters are treated as fixed or nuisance parameters, in distributional regression each of the distributional parameters is linked to a structured additive predictor η ik via a suitable one-to-one transformation h k , i.e. h k (η ik ) = ϑ ik and η ik = h −1 k (ϑ ik ).
Structured Additive Predictors
The predictors themselves are specified as where the effects f sel j,k (ν i ) represent various types of flexible functions depending on (different subsets of) the covariate vector ν i that are to be selected via spike and slab priors, while η in ik represents a second additive predictor consisting of all effects f in l,k (ν i ) that are not under selection. The separation into two subsets of effects allows us to include specific covariate effects mandatorily in the model (e.g. based on prior knowledge or since these represent confounding effects that have to be included in the model in any case). In the following, we will only discuss the specification of priors for the effects under selection in detail since the effects η in ik can be handled exactly as in distributional regression models without effect selection, but we will use the differentiation later in Section 3.4 for deriving sufficient conditions for the propriety of the posterior.
Dropping the parameter index k, the function index j and the superscript sel in the rest of this section for notational simplicity, we assume that each effect f (ν i ) can be approximated by a linear combination of basis functions such that where B d (ν i ), d = 1, . . . , D are the basis functions,β = (β 1 , . . . ,β D ) ′ is the vector of (standardised) basis coefficients and τ is an importance parameter. Due to the linear basis representation, the vector of function evaluations f = (f (ν 1 ), . . . , f (ν n )) ′ can be written as f = τ Bβ where B is the (n × D) design matrix arising from the evaluation of the basis functions B d (ν i ), d = 1, . . . , D at the observed covariate values ν 1 , . . . , ν n .
Note that the parameterisation in (M3) is equivalent to the standard specification in structured additive regression but redundant as only the product β = τβ is identified. However, the importance parameter τ allows us to remove effects from the predictor for τ = 0 while effects are considered to be of high importance if τ is large in absolute terms. We will place a spike and slab prior on the squared importance parameter τ to achieve effect selection.
Constraint Prior for Regression Coefficients
Since for many specific types of effects the vector of basis coefficients β is of relatively high dimension, it is often useful to enforce specific properties such as smoothness or shrinkage. In a Bayesian formulation, this can be facilitated by assuming (partially improper) multivariate Gaussian priors where K denotes the prior precision matrix implementing the desired properties, τ 2 is a prior variance parameter and the indicator function 1[Aβ = 0] is included to enforce linear constraints on the regression coefficients via the constraint matrix A. The latter is typically used to remove identifiability problems from the additive predictor (e.g. by centering the additive components of the predictor) but can also be used to remove the partial impropriety from the prior that comes from a potential rank deficiency of the precision matrix K with rk(K) = κ ≤ D.
We specify a prior of exactly the same structure on the vector of scaled basis coefficientsβ, and assume that the constraint matrix A is chosen such that all rank-deficiencies in K are effectively removed from the prior distribution. This can, for example, be achieved by setting where ker(K) denotes the null space of K and span (ker(K)) is a representation of the corresponding basis. This specification effectively restricts the parameter vectorβ to a lower dimensional space of dimension rk(K) and allows us to establish a decomposition of the effect f (ν) into a penalized and an unpenalized part, i.e. f unpen (ν) + f pen (ν) where f unpen (ν) represents parts of the function corresponding to the null space of K which are therefore not affected by the "penalisation" induced by K while f pen (ν) represents the part of the total effect that is associated with the proper, informative prior part. Importantly, we can now put separate spike and slab priors on both parts of f . For instance, in case of penalized splines with second order random walk prior, the space of unpenalized functions contains the linear functions, while the penalized part contains nonlinear deviations from the former. Such a parameterization hence enables the decision whether a continuous covariate should be included purely nonlinearly, whether it is sufficient to assume a pure linear effect or whether the sum of a linear and a non-linear effect is needed. The resulting models are therefore both potentially more parsimonious and easier to interpret.
The specifications (M3), (M4) and (M3 * ), (M4 * ) seem to be equivalent to each other corresponding to rescaling the regression coefficients and the prior distribution as β = τβ. However, this is only true if the prior distribution (M4) is indeed proper. To see this, assume that K is rank deficient and a constant effect is not penalised by the prior precision matrix. In this case, the traditional formulation of structured additive regression models (M3 * ) implies a constant effect if τ 2 approaches zero while the rescaled version (M3) implies an effect equal to zero since the complete function is multiplied by τ .
Note, that both (M4 * ) and (M4) rely on the same precision matrix K and hence the constraint matrix A can be constructed independently of the parametrisation. The traditional way is an explicit mixed model decomposition (Fahrmeir et al., 2004;Wood, 2011) which is used by Scheipl et al. (2012) to perform effect selection for mean regression models. As the mixed model representation yields a penalised component which isβ ∼ N(0, I), this is effectively equivalent to considering our constraint prior by choosing the constraint matrix according to (M5) and by rescaling the individual entries inβ with the eigenvalues of K (see Rue and Held, 2005, Sec. 3.2 for details). However, the explicit mixed model representation used by Scheipl et al. (2012) destroys the sparsity properties of the design matrices (such as band structures for B-splines) and causes full design matrices which in turn increases computation times. In order to keep the sparsity of the design matrices of functional effects (and hence to minimize computation time) we instead implicitly remove the improper part of p(β|τ 2 ) by sampling β directly from the constrained posterior using (M4).
Normal Beta Prime Spike and Slab Prior on Squared Importance Parameter
To achieve function selection in our model, we place a spike and slab prior specification on the squared importance parameter τ 2 . This hierarchical prior relies on a mixture of one prior concentrated close to zero such that it can effectively be thought of as representing zero (the spike component) and a more dispersed, mostly noninformative prior (the slab) and is specified via the hierarchy The scale parameter ψ 2 determines the prior expectation of τ 2 , which is ψ 2 for δ = 1 and rψ 2 for δ = 0 with r ≪ 1 being a fixed small value and hence the indicator δ determines whether a specific effect β = τβ is included in the model (δ = 1) or excluded from the model (δ = 0). The parameter ω is the prior probability for an effect being included in the model and the remaining parameters a, b, a 0 , b 0 and r are hyperparameters of the spike and slab prior. We will discuss prior elicitation for these parameters in detail in Section 3.2.
Marginalising over ψ 2 , both the spike and the slab component p(τ 2 |δ) are scaled beta prime distributions with shape parameters 1/2 and a and scale parameter 2r(δ)b (Pérez et al., 2017). Therefore we call the hierarchical prior on β = τβ specified by (M4) -(M6) the Normal Beta Prime Spike and Slab (NBPSS) prior, see Section 3 for a detailed discussion of the properties of the NBPSS prior. Equations (M1) to (M6) define our complete model specification for effect selection in structured additive distributional regression.
Special Cases
We briefly discuss some of the components of structured additive predictors used later in our empirical evaluations. These include • non-linear effects based on Bayesian P-splines (Lang and Brezger, 2004), where random walk priors are used for the regression coefficients corresponding to D different B-spline basis functions. The i-th row of B then contains the basis functions If not stated otherwise, we will use second order random walk priors and cubic B-splines with 20 inner knots resulting in D = 22.
• spatial effects for a discrete set of geographical regions modelled via Gaussian Markov random fields (GMRFs) with precision matrix given by an adjacency matrix encoding the neighbourhood relation between the regions (Rue and Held, 2005) and a design matrix with entries (i, s) equal to one if observation i is located in region s and zero otherwise. We consider the simplest form of GMRFs and define two regions as neighbours if they share common borders.
• multilevel structured additive regression models as proposed by Lang et al. (2014) that allow for hierarchical prior specifications for regression effects where each parameter vector may again be assigned an additive predictor, i.e. the vector β is decomposed as β = η + ε and the predictor η can itself be of structured additive form.
Properties of the NBPSS prior
In the following, we discuss properties of the NBPSS prior hierarchy, including elicitation of hyperparameters, shrinkage properties and propriety of the posterior. For prior elicitation and shrinkage properties, the marginal distribution of β = τβ plays a crucial role. We will therefore start with deriving this marginal distribution.
Marginal Distribution
The marginal prior for the squared importance parameter τ 2 is given by the mixture of two scaled beta prime distributions BP(1/2, a, 2b) and BP(1/2, a, 2rb) with mixture weight of the slab given by P(δ = 1|a 0 , b 0 ) = a 0 /(a 0 + b 0 ). A modified version of the NBPSS prior can alternatively be derived by assuming a mixture of two scaled t distributions for the importance parameter τ = ± √ τ 2 . Specifying this prior hierarchically, the first equation in (M6) is replaced by τ |δ, ψ 2 ∼ N (0, r(δ)ψ 2 ) and as a consequence posterior sampling would no longer be possible with Gibbs steps as the corresponding conditional posterior would depend on the likelihood function. Marginalising over ψ 2 , δ and ω, the prior p(τ ) is a mixture of two scaled t-distributions with 2a degrees of freedom, location parameter 0, scale parameters b/a and rb/a and mixture weights a 0 /(a 0 + b 0 ) and b 0 /(a 0 + b 0 ), respectively. Thus, the prior on the (signed) importance parameter τ is closely linked to the NMIG prior used in Ishwaran and Rao (2005) when considering scalar regression coefficients β that are conditionally normal given the inverse gamma distributed variance parameter τ 2 (but with one level of hierarchy less) on the one hand, and, on the other hand to the peNMIG specification of Scheipl et al. (2012).
The implied marginal distribution for β = τβ can now be derived as where pβ is given in equation (M4). However no analytical solution exists for this integral such that it has to be approximated numerically.
Prior Elicitation
In the following, we discuss prior elicitation for the NBPSS prior hyperparameters a, b, a 0 , b 0 and r. More precisely, we argue that suitable default values can be suggested for a, a 0 , and b 0 based on theoretical arguments while providing intuitive and user-friendly criteria for the elicitation of b and r. In the literature, default values have often been suggested from simulation-based evidence (e.g. in Scheipl et al., 2012) but we prefer to determine b and r in a more transparent way.
Theoretical properties of the scaled beta prime distribution have been discussed in Pérez et al. (2017). From this, it follows that for both spike and slab moments of order less than a exist and the variance decreases with a. Furthermore, for small values of a, the spike and the slab component will overlap such that moves from δ = 0 to δ = 1 are possible. However to guarantee the existence of moments, a should not be too small either. Fixing a = 5 yielded overall a convincing mixing performance and we therefore use this value also in our real data examples.
For the prior inclusion parameter ω a sensible default is to use a 0 = b 0 = 1 which corresponds to a flat prior on the unit interval. Of course, one can also choose fix values for ω in case strong prior knowledge on the prior inclusion probability of the size of the expected model is available. As the marginal prior inclusion probability is given by P(δ = 1|a 0 , b 0 ) = a 0 /(a 0 + b 0 ), a 0 and b 0 can be chosen to reflect prior assumptions on the inclusion probability of effects.
For the elicitation of b and r, we propose an approach inspired by the principled approaches of Simpson et al. (2017) and Klein and Kneib (2016). More precisely, we consider marginal probability statements on the supremum norm sup ν∈D |f (ν)| over a certain set of covariate values D conditional on the status of the inclusion/exclusion parameter δ. Given δ = 1 (inclusion of the effect), the marginal distribution of f (ν) does no longer depend on r, such that the parameter b can be determined from This is the probability that the supremum norm of an effect is smaller than a pre-specified level c for all design points ν ∈ D, such that α and c should be small. Basically we formulate the prior such that it is unlikely that the supremum norm stays below a pre-specified level if it is indeed an informative effect that should be included. Both the level c and the prior probability α have to be specified by the analyst according to her/his prior beliefs. To derive r, we proceed similarly but consider the probability now conditioning on non-inclusion. Since in this case we would rather be interested in making the probability of not exceeding the threshold c large, the probability is reversed to 1 − α. Note that the absolute value of the effects can be taken without loss of generality due to the centring constraint of each function to ensure identifiability.
The basic idea of these two equations is that such prior statements can be much more easily elicited in applications, in particular in distributional regression where the application of response functions such as the exponential function or the logit transform induce default ranges of plausible effect sizes. Of course, the levels c as well the probability levels α can be chosen to be distinct for the inclusion/exclusion criteria in (3) and (4) but we suppress this possibility notationally both for simplicity and since in most cases it seems plausible to choose the same parameter settings anyway.
To access the probabilities in (3) and (4), we have to derive the marginal distribution of sup |f (ν)| which is not analytically accessible. For a single covariate value ν, the function evaluation is given by denoting the generalized inverse of K) and p(τ 2 ) is given in Equation (1). Note that using the generalized inverse effectively removes the portion of f (ν) that corresponds to the null space of K such that we take the constraint in (M4) into account. The integrals above are scalar integrals for each covariate ν which can be solved numerically. However, obtaining the supremum over a large set D, numerical integration easily becomes computationally intractable. We hence determine the distribution of the supremum based on simulations from the hierarchical NBPSS prior.
In the Online Appendix B, we show how to determine r and b independently of each other. For given design matrix B = (b ′ ν 1 , . . . , b ′ νn ) ′ , precision matrix K, probability level α and threshold c, these can be computed for general functional effects using the R package sdPrior (Klein, 2018).
Shrinkage Properties
Regularisation and shrinkage properties of certain prior settings in regression specifications can be studied by considering the marginal distribution of the regression coefficients and/or functional effects. According to Section 3.1 the marginal densities have to be determined by numerical integration.
Constraint Regions
We compare the prior specified in (M4)-(M6) with a standard NMIG prior applied directly to the coefficients in β and the parameter expanded prior (peNMIG) of Scheipl et al. (2012). Figure 1 shows the univariate marginal log-densities where the most distinct difference is between the standard NMIG prior compared to peNMIG and NBPSS priors. While the standard NMIG prior resembles the shape of a normal distribution with a finite asymptote at zero, both parameter expanded priors feature a spike in zero. As we will show in the next section, this spike is indeed infinite such that advantageous selection behaviour is to be expected for the NBPSS prior. Figure 2 supplements the univariate considerations by bivariate marginal log-densities. We differentiate between two situations: First, we consider two parameters that depend on the same value τ 2 , i.e. parameters belonging to the same function f (ν), while in the second case we consider parameters depending on different importance parameters. This distinction is important since the standard NMIG prior always assumes independent components with separate hyperparameters. As a consequence, the peNMIG and NBPSS priors deviate from the standard situation in two ways: First by the parameter expansion itself and second by making the parameters depend on the same hyperparameter. To disentangle the effect of these two deviations, we rely on the separate presentations. We make the following important observations: • The NBPSS and peNMIG priors share the same qualitative behaviour while deviating considerably from the standard NMIG prior regardless of whether the case of shared or distinct τ 2 is considered.
• The univariate marginal densities qualitatively resemble the ones of the original spike and slab prior of Mitchell and Beauchamp (1988) with tails that are heavy enough to induce a re-descending score function which ensures robustness of the Bayesian estimators (see also the next subsection).
• For the case of distinct parameters, we observe contours similar to the convex shape of L q priors with q < 1 for the peNMIG and NBPSS priors which implies weak shrinkage of large effects while small coefficients are strongly shrunken to zero.
• For the case of shared τ 2 , the shapes of the contours imply simultaneous shrinkage of both parameters instead of the strong shrinkage towards the coordinate axes observed for distinct importance parameters. This is exactly the desired type of shrinkage for parameters belonging to one effect f (ν) to completely remove the effect from the model specification.
• As already noted in Section 2.2, the specification of the prior in Scheipl et al. (2012) differs from ours insofar as they consider the mixed model decomposition of effects. Additionally, Scheipl et al. (2012) use a bimodal prior for the standardized regression effects with modes at +1 and −1. This effectively bounds the coefficients away from zero and thus encourages sampling from one mode of the posterior, while we instead explore the full posterior. Consequently, the conditional posterior ofβ of NBPSS is a standard normal distribution p NBPSS (x) = N(x; 0, 1), while the one of peNMIG is a mixture of two normals with modes, p peNMIG (x) = 0.5 N(x; 1, 1) + 0.5 N(x; −1, 1). Taking the ratio yields p peNMIG (x) p NBPSS (x) > 1 ⇔ |x| > cosh −1 (exp(0.5)) ≈ 1.08, which explains the slightly heavier tails of peNMIG in Figures 1 and 2.
We also study the implied constraint regions for the marginal prior of function evaluations f (ν) = b ′ ν β, which can be derived in complete analogy by utilising that In contrast, the marginal prior for function evaluations for the parameter expanded prior of Scheipl et al. (2012) is not numerically accessible since it involves a complex mixture of 2 D components (where D is the dimension of β) due to the bimodal prior for the elements ofβ. Figure 3 depicts marginal densities for the effect f (ν) evaluated at one (left panel) and two (right hand panel) randomly chosen covariate values of a sequence of n = 100 equidistant values in [−π, π]. The resulting design matrix B is based on cubic Bayesian P-splines with D = dim(β) = 22. Hence, the bivariate plot corresponds to the situation of one shared importance parameter since we are interested in shrinkage of the effect evaluations for the same effect at different covariate values. Qualitatively, the behaviour from the marginal densities of the regression coefficient is translated to the function evaluations, i.e. we observe a peak in zero and simultaneous shrinkage.
Tail Behaviour and Behaviour in the Origin
Visually, the marginal prior for β features a distinct peak as shown in the previous section. We now investigate more closely, whether this spike is finite or infinite by considering the behaviour of p β (β)| β=0 . Using Equation (2) we obtain (0) [log(τ )] 1 0 = ∞, and therefore the marginal prior for β indeed has an infinite spike in zero. Note that we have shown that the multivariate parameter expanded prior has a spike in zero, while Scheipl et al. (2012) have only shown the result for the univariate marginal prior. An infinite spike in zero is considered to induce particularly beneficial shrinkage properties since we obtain heavy penalisation of small effects.
The tail behaviour of the marginal prior for β can be studied by looking at the score function of p(β) which consists of the elements Figure 4 visualizes the resulting score function and compares it to the score function of the NMIG and peNMIG priors. From the graphical representation we find that all three prior structures have heavy tails such that the score functions are re-descending (i.e. they approach zero as their argument tends to infinity) which induces Bayesian robustness of the resulting estimates.
The score functions of the peNMIG and NBPSS priors resemble the shape of L q priors with q close to zero, while the shape of the score function for the NMIG prior shows a more complex non-monotonously shape around zero.
Propriety of the Posterior Distribution
While in Section 2 we do not explicitly change the design matrices to remove the nullspace of the precision matrices K j,k (both effects with NBPSS prior and the ones not under selection), we do derive an explicit mixed model representation of the predictors η k in (M2) in this section as this greatly simplifies the derivation of sufficient conditions for the propriety of the posterior.
As the exact conditions are also dependent on the prior structures employed, we need to be more precise here about η in and will therefore introduce a slightly different notation compared to that in Section 2.
Mixed Model Representation
Assume we have L k effects in η in k and J k effects under selection and let furthermore η k = η in k +η sel k be the complete predictors for k = 1, . . . , K as defined in Section 2.1.2.
We then assume a mixed model type representation (Fahrmeir et al., 2004) for η in The columns of U in l,k are a basis of ker(K in l,k ),Ṽ in l,k forms a basis of the images of K in l,k , such that dim(β in pen,l,k ) = rk(K in l,k ) = κ in l,k and β in pen,l,k |(τ 2 l,k ) in ∼ N(0, (τ 2 l,k ) in I), while β in unpen ,l,k has dimension D in l,k − κ in l,k and a flat prior. As a consequence, we obtain L k variance parameters (τ 2 l,k ) in for the L k penalized vectors of coefficients β in l in η in k . For effects in η sel we proceed similarly but with proper NBPSS priors on both parts of K sel j,k , rk(K sel j,k ) = κ sel j,k representing a basis of the nullspace and the image each. Hence, by construction all effects under selection (after centring) can be assumed to have proper prior distributions. For non-linear effects of continuous covariates with random walk priors of order > 2 for instance, this is achieved by separating the polynomial parts up to order-1 and to include separate NBPSS prior on these, see Section 2 for details. We hence assume that the sub-predictors under selection are of the form This yields J k importance parameters (τ 2 j,k ) sel with hyperparameters ψ 2 j,k , δ j,k , ω j,k in addition to the J k regression coefficients with NBPSS priors after re-parameterisation. We furthermore introduce κ k = L k l=1 κ in l,k + J k j=1 κ sel j,k . Finally, the complete predictor can be written as where we denote β unpen,k ≡ β in unpen ,k , β pen,k = ((β in . Let us in the sequel assume that the matrices U k have full column rank r k , k = 1, . . . , K and define for X k = (U k , V k ) and t k = rk(X k ) − rk(U k ) ≤ dim(β pen ,k ), rk(X k ) = r k + t k . (6) Remark 1. In order to obtain a full column rank matrix of unpenalised effects in the mixed model representation (5), all superfluous columns have to be deleted. In particular, duplicated constant columns representing the levels of the functions are deleted which is a simple way to include the centring restrictions and is equivalent to the centring of functions that we include in our MCMC algorithm. Furthermore, using the one-to-one relationship between original parameterisation and the reparameterised model the restrictions for one presentation can be deduced from the other one. Hence, sufficient rank conditions can be formulated directly for the reparameterised model (5)
Conditional Independence Assumptions
To derive the posterior distribution of model (M1) to (M6), we make the usual conditional independence assumptions (see the Online Appendix A.1, conditions (a.1)-(a.3b)) by labelling for k = 1, . . . K the coefficients β in l,k with variances (τ 2 l,k ) in , l = 1, . . . , L k for effects not under selection; and β sel j,k , (τ 2 j,k ) sel , ψ 2 j,k , δ j,k , ω j,k , ,J = 1, . . . , J k , for the effects with NBPSS prior. In general, they mean that priors for different effects are assumed to be independent, while within an effect they are dependent by construction. In general, prior independence assumptions should be a reasonable working assumption which also does not rule out posterior dependence. Note that we always assume proper NBPSS priors and in particular a j,k > 0, b j,k > 0 in the priors for ψ 2 j,k . This is justified by our considerations on prior elicitation as discussed in Section 3.2 of the main paper. In the following we assume that conditions (a.1)-(a.3b) of the Online Appendix A.1 hold.
Gaussian Mean Regression
Assume in this section a Gaussian mean regression model for y = (y 1 , . . . , y n ) ′ with predictor η from (5) in mixed model representation, i.e.
where we assume for the error variance. Note that k = 1 in this subsection and that J k , L k , κ k are replaced by J, L, κ. Applying the mixed model representation (5) allows us writing (7) as y = U β unpen + V β pen + ε, and with the corresponding rank assumptions from above.
b. Conditions for Gaussian Mean Regression
Condition (b.1) excludes Jeffrey's prior (corresponding to a in l = b in l = 0) for effects not under selection but allows for flat priors on variances and standard deviations (τ 2 l ) in . Conditions (b.2) to (b.4) relate the ranks κ in l and κ sel j of the prior precision matrices of each of the effects to the rank κ of all prior precision matrices. For effects not under selection, the conditions can be ensured by increasing a in l . Condition (b.5) restricts the number of all effects to be smaller or equal to the number of observations but can be relaxed by increasing the hyperparameters values a ε and a in l . Condition (b.7) is always fulfilled for b ε > 0. In case of an improper prior for τ 2 ε , SSE > 0 has to be assured, while b ε > 0 becomes necessary when the number of unknown parameters is greater than n.
Theorem 1. Consider the Gaussian mean regression model (7) with mixed model representation (5) and rank conditions from (6). The proof of Theorem 1 is given in the Online Appendix A.3.
Remark 2. For effects not under selection, additional conditions on the ranks κ l and the number of effects compared to the shape parameters (a l ) in of the priors are required, as the latter can be improper and hence (a l ) in < 0 becomes possible. Consequently, one has to consider the cases t = κ or L = 1 as well as t < κ and L > 1 separately. This is not necessary for effects with NBPSS prior.
Distributional Regression
In order to achieve sufficient conditions for the propriety of the posterior in distributional regression, we define a normalized submodel with Gaussian errors to be able to apply results of Theorem 1. More precisely, we first separate the random effect with largest dimension in each predictor of (5), such that we obtain where V ε,k b ε,k corresponds to the effect with proper prior and with the largest dimension, dim(b ε,k ) = rk(K ε,k ) = κ ε,k , and V k b k contains all remaining effects with proper prior, both the ones with NBPSS prior and the ones not under selection with usual inverse gamma priors. Note that b k is based on J * k = L k + J k − 1 effects in the notation in (5), with κ k denoting the sum of ranks of the J * k precision matrices of predictor k, and where, w.l.o.g. we assume that the effects in the predictors are ordered such that the (J k + L k )-th effect corresponds to the random effect in the mixed model representation with largest dimension. Similarly, the design matrix (V k , V ε,k ) corresponds to the design matrix (V in k , V sel k ). Note also, that b ε,k can originate from an effect not under selection or one with NBPSS prior and we distinguish the two cases in Theorems 2 and 3.
Assume that the set of observations can (after re-ordering) be partitioned such that for n * ≥ 1 . . , n, k = 1, . . . , K. This implies that for at least one observation the density is integrable (with respect to the predictors) and that all remaining densities are bounded. For discrete distributions, all densities are automatically bounded by 1 so that only Condition (c.1) can be an issue in practice. Condition (c.1) is usually fulfilled if certain restrictions apply on specific parameters that exclude extreme values on the boundary of the parameter space, see for a more detailed discussion on count data and binary distributions. For continuous distributions, the densities are sometimes not bounded (e.g. for the gamma distribution). Note that this is not a problem when all observations fulfil Condition (c.1) since n * = n is allowed. Similar as for the discrete distributions, integrability of the densities can be assured by the assumption that none of the distributional parameters is on the boundary of the parameter space (an assumption that would also have to be made to apply standard maximum likelihood asymptotics).
Letñ ε = min{κ ε,1 , . . . , κ ε,K } and assume that we can chooseñ ε observations including at least one observation fulfilling (c.1) to define the submodel with these observations, such that V ε,k,s b ε,k ∼ N(0, τ 2 ε,k V ε,k,s V ε,k,s ′ ). Then the following rank conditions have to be fulfilled: The design matrix U k,s has full rank r k .
(c.5)
To ensure (c.3), superfluous columns arising from the reparameterisation have to be deleted. In particular, duplicated constant columns representing the levels of the functions are deleted, see Klein and Kneib (2016, Remark 2 (iii) for details). Condition (c.4) indicates that the rank of the design matrices in the submodel is the same as in the complete model whereas (c.5) defines a similar restriction for the design matrix of the largest random effect arising from the mixed model representation. Finally, the normalised submodel η k,s =Ũ k,s β unpen,k +Ṽ k,s b k + ε k,s , ε k,s ∼ N(0, τ 2 ε,k Iñ ε ) is obtained by multiplying (8) with M k = (V ε,k,s V ε,k,s ′ ) −1/2 such thatη k,s = M k η k,s ,Ũ k,s = M k U k,s ,Ṽ k,s = M k V k,s , and ε k,s represents an i.i.d. random effect.
The corresponding residual sum of squares for the normalised submodel is To derive sufficient conditions for the propriety of the posterior we have to distinguish two cases: the largest random effect ε k,s corresponds to an effect with a) NBPSS prior and b) not under selection and with the usual inverse gamma priors for the variance τ ε,k .
Above, Conditions (c.·a) each correspond to the case that the largest random effect has a variance with inverse gamma prior, while Conditions (c.·b) each are active when the variance of the largest random effect has an NBPSS prior. Conditions (c.6a),(c.6b) require that if for effects not under selection b in l,k is set to zero, the parameter a in l,k has to be negative. This includes situations corresponding to flat priors for the random effects variance (a in l,k = −1) or standard deviation (a in l,k = −0.5) but excludes Jeffreys prior (a in l,k =0). Conditions (c.7a), (c.7b) and (c.8a), (c.8b) relate the rank of the random effects part of one individual effect to the sum of all rank deficiencies in the corresponding predictor, are similar for effects not under selection and the ones with NBPSS prior and require that the dimensionality is not too small. The condition can be ensured by increasing the shape parameters a in l,k and a j,k , respectively. Conditions (c.9a), (c.9b) restrict the number of effects not under selection and with flat prior to be at most equal to the dimension of the largest random effects part in the model but can again be relaxed by increasing the shape parameters a in l,k . Finally, Conditions (c.10a), (c.10b) require that there is variation in the residual sum of squares in the normalized submodel (implying that not all effects are zero) in situations where the largest random effect has an NBPSS prior and either variation in the residual sum of squares or b ε > 0 when the largest random effect has the usual inverse gamma prior on the variances. The latter requirement can always be ensured in practice but excludes flat priors for the random effects variances or standard deviations.
The proof of Theorem 2 follows from the proof of using Theorem 1 above as we assume that all NBPSS priors are proper.
Posterior Estimation
Update of the Basis Coefficients. Due to the modular structure of Markov chain Monte Carlo (MCMC) simulation algorithms, no changes in the MCMC scheme developed by Klein, Kneib, Lang and Sohn (2015) are required for updating the basis coefficients β when supplementing them with a NBPSS prior instead of the standard inverse gamma prior. We therefore apply iteratively weighted least squares based approximations to the log full conditional and generate proposals from the multivariate normal distribution N(µ, P −1 ) with expectation and precision matrix given by where η − = η − Bβ is the predictor without the effect currently updated and the working observationsỹ and weights W are determined based on first and second derivatives of the loglikelihood with respect to the predictor.
Update of the Smoothing Variance for
Effects not Subject to Selection. For effects not subject to selection, we consider an inverse gamma prior τ 2 ∼ IG(a, b) for the smoothing variances such that the update of τ 2 can be done via a simple Gibbs sampling step drawing from Update of the Squared Importance Parameter for Effects Subject to Selection. The full conditional p(τ 2 |β, δ, ψ 2 ) is a generalised inverse Gaussian distribution GIG(p, q, c), with p = −0.5 rk(K) + 0.5, q = 1/(r(δ)ψ 2 ), c = β ′ Kβ and can be generated efficiently in a Gibbsstep. This has the advantage that τ 2 can be generated independently of the likelihood in an efficient Gibbs step. This is no longer possible when the prior is formulated for the importance parameter τ as in (Scheipl et al., 2012) where a Metropolis-Hastings update is required, see the Online Appendix C.
Updates for the Hyperparameters of the NBPSS prior. For the hyperparameters of the NBPSS prior, we obtain Gibbs sampling steps via the following full conditionals: • Inclusion indicator δ: where ϕ(·; µ, σ 2 ) denotes the density of the normal distribution with mean µ and variance σ 2 and 2ψ 2 (1/r−1) .
• Hyper-variance ψ 2 : Note that it is also possible to use the same ω for multiple effects simultaneously. If ω relates to a total of L effects, the full conditional is then given by Implementation. Spike and slab based effect selection in distributional regression has been implemented in a developer version of BayesX (Belitz et al., 2015) which is available from the authors on request. The software makes use of methods for efficient storing of large data sets and sparse matrix algorithms for sampling from multivariate Gaussian distributions (George and Liu, 1981;Rue, 2001) and also allows us to access existing procedures for example for computing simultaneous confidence bands for nonparametric effects as developed in Krivobokova et al. (2010). Hyperparameter elicitation is integrated in the R-package sdPrior (Klein, 2018).
Simulations
To evaluate the performance of the NBPSS prior for effect selection in distributional regression, we conducted extensive simulations under various settings. We distinguish different scenarios for the predictor complexity, models including and excluding spatial effects, four selected response distributions, varying sample sizes, correlated and uncorrelated covariates and a set of userdefined parameters for hyperprior elicitation. Specifically, • we consider Gaussian responses with effects only on the expectation, a Gaussian location-scale model, Poisson regression and zero-inflated Poisson models.
• we specify four test functions • we distinguish two scenarios in terms of the predictor complexity: low sparsity in which out of 16 included covariates 12 have non-zero influence. The true linear predictor is η = f 1 (x 1 )+f 2 (x 2 )+f 3 (x 3 )+f 4 (x 4 )+1.5 (f 1 (x 5 ) + f 2 (x 6 ) + f 3 (x 7 ) + f 4 (x 8 ))+ 2(f 1 (x 9 ) + f 2 (x 10 ) + f 3 (x 11 ) + f 4 (x 12 ) and we simulate the two cases with additional and without additional spatial effect f spat (s), labeled as 'spatial/non-spatial'. These settings are used for η µ in the homoscedastic Gaussian and the Gaussian location-scale model, as well as for η λ in the Poisson and the zero-inflated Poisson model. high sparsity in which out of eight included covariates four have non-zero influence. The true linear predictor is η = f 1 (x 1 ) + f 2 (x 2 ) + f 3 (x 3 ) + f 4 (x 4 ) and we again simulate the two cases with additional and without additional spatial effect f spat (s). These settings are used for η σ 2 in the Gaussian location-scale model and for η π in the zero-inflated Poisson model.
• we generate covariates either -as i.i.d. realizations from U[−2, 2] or -from an AR(1) process with correlation ρ = 0.7 and standarize x in order to facilitate prior elicitation.
• we simulate 150 replications for each combination of the settings.
• we use six combinations of α and c for the elicitation of the prior hyperparameters b and r arising from the pairwise combination of -α = 0.05, 0.1, 0.2, -c = 0.1, 0.2.
• we consider the sample sizes n = 200; 1, 000 for Gaussian, n = 500; 2, 000 for Poisson, n = 1, 000; 2, 000 for Gaussian location-scale and zero-inflated Poisson responses. The sample sizes have been chosen to reflect a challenging (small sample size) and a relatively informative (large sample size) setting, taking the different complexity of the model structures into account.
As a competitor for the single parameter distributions Gaussian and Poisson, we consider the peNMIG prior of Scheipl et al. (2012) implemented in the R-package spikeSlabGAM (Scheipl, 2016). We refrain from comparison with further variable selection priors mentioned in the introduction as these usually lack applicability beyond the framework of generalized linear models. Hyperparameter elicitation for the NBPSS prior was performed with the package sdPrior (Klein, 2018) and estimation was done with the current developer version of BayesX (Belitz et al., 2015). For both the NBPSS and the peNMIG prior, non-linear effects are based on 20 cubic B-spline basis functions constructed from an equidistant set of knots combined with second-order random walk prior unless stated otherwise.
In the following, we restrict ourselves to the main conclusions, a detailed description about simulation settings and evaluation including complete graphical evidence is provided in the Online Appendix D. As a general outcome, the NBPSS prior results in very good performance for the selection of relevant effects even in challenging distributional regression settings with effect selection on multiple distributional parameters, where no competing Bayesian variable selection approach is available so far. Evidence for that is given in Figures 5 and 6 showing posterior inclusion probabilities and the ratio between predictive NBPSS log-scores and oracle log-scores (i.e. log-scores arising from a model with given, true predictor specification), respectively, in the zero-inflated Poisson model. The log-scores have been computed from independently generated test data sets with 5,000 observations.
In the simple exponential family framework with only one single regression predictor, the NBPSS prior turns out to be a strong competitor to the peNMIG prior (see Figure 7 for overall accuracy results of the Poisson model). Selection of large coefficient blocks such as spatial effects works well for all types of response distributions, while these are particularly problematic with peNMIG due to severe mixing problems. On the other hand, the explicit reparameterisation of non-linear effects used with the peNMIG prior (as compared to the constrained sampling approach that NBPSS is based on) seems to have some advantages in separating the linear and non-linear part of non-linear effects in cases where the true effect is close to linear and at the same time covariates are strongly correlated.
Coinciding with previous evidence on Bayesian effect selection, we find a strong impact of hyperprior parameter choice on the resulting effect selection performance. Our interpretable yet flexible way of eliciting hyperprior parameters equips data analysts with an intuitive approach for choosing these hyperparameters. More precisely, changing the probability α and the threshold c can help to balance between the true positive and false negative rates of effect selection. Choosing α and c smaller, results in more conservative, i.e. sparser models. Based on our simulations, we suggest α = c = 0.1 as default values in our applications.
In summary, our simulations demonstrate that the NPBSS prior provides a promising approach for Bayesian effect selection that extends existing methods to a framework that is applicable in any distributional regression model comprising both multiple hierarchical predictor specifications and high-dimensional coefficient vectors. In addition, our effect decomposition allows to select the linear part and its non-linear deviation for an effect of a continuous covariate separately.
Applications
In this section, we demonstrate the efficacy of a simultaneous selection approach via the NBPSS prior specification and its applicability for non-Gaussian, discrete or multivariate data. Core information about the different data sets Patents, Nigeria and House prices including the type of response distribution, number of observations and effects can be found in Table 1. Estimates shown in the subsequent subsections are all the model-averaged estimates obtained from the MCMC iterates with the NBPSS prior and the covariates have been standardized for prior elicitation reasons.
Number of Patent Citations
The Patents data set contains the number of citations of patents granted by the European Patent Office (EPO). An inventor who applies for a patent has to cite all related, already existing patents his patent is based on. use this data set to illustrate their developed methodology on Bayesian zero-inflated and overdispersed count data and conducted variable selection in a stepwise forward approach based on the deviance information criterion (DIC). In the following, we focus on zero-inflated Poisson (ZIP) models for analysing the number of patent citations. The ZIP model has two distributional parameters, λ, the rate of the count process, and π the probability of observing an excess of zeros. Including all available variables in one of the predictors η k , k = 1, 2 reads as where x contains the continuous variables year (year when patent was granted), ncountry (number of designated states for patent), nclaims (number of patent claims), as well as the binary indicators ustwin (twin patent in the US), opp (oppositions against the patent), biopharm (patent from the biotech/pharma sector), patus (patent holder from the US) and patgsgr (patent holder from Germany, Switzerland or Great Britain), see Table E.1 in the Online Appendix for summary statistics of the variables. Possible non-linear effects of the three continuous variables are captured by the functions f 1 to f 3 . The predictor specifications of the model identified in via stepwise DIC-selection are η λ = β 0,λ + β 1,λ opp + β 2,λ biopharm + β 3,λ patus + β 4,λ patgsgr + f 1,λ (year ) + f 2,λ (ncountry) + f 3,λ (nclaims) η π = β 0,π + β 1,π opp + β 2,π biopharm + β 3,λ patus + β 4,λ patgsgr + f 1,π (year ) + f 2,π (ncountry).
This model is denoted as ZIP DIC in the following.
We compare this model to the model ZIP NPBSS with predictors selected by the NBPSS prior where r and b were determined from α ∈ {0.05, 0.1}, c = 0.1. Table 2 reports predictive log-scores (obtained from ten-fold cross validation) as well as values for the DIC and the widely applicable information criterion (WAIC). From the table, we can conclude, that the ZIP NPBSS model is clearly favoured in terms of the chosen criteria. For the NBPSS model, we report posterior probabilities P(δ|y) in Table 3. Based on the decision to include an effect if P(δ|y) ≥ 0.5 holds, the NBPSS prior coincides with the stepwise approach of ZIP DIC for the effects of the continuous covariates but yields a sparser prediction specification for the effects of binary covariates.
Bivariate Analysis of Undernutrition
The Nigeria data have been extracted from Demographic and Health Surveys (DHS, https://dhsprogram.com/) containing nationally representative information about the population's health and nutrition status in numerous developing and transition countries. Here we use data from Nigeria collected in 2013. Overall there are 23,042 observations after removing outliers and inconsistent observations from the data. We use stunting and wasting as the bivariate response vector, where stunting refers to stunted growth measured as insufficient height of the child with respect to its age, while wasting refers to insufficient weight for height. Hence stunting is an indicator for chronic undernutrition while wasting reflects acute undernutrition. We assume that the two indicators are jointly normally distributed with marginal means, marginal scales and correlation parameter depending on covariates. Specifically, the model equations for all predictors of the distributions are specified as where x i contains 13 binary covariates characterising the household the child is living in as well as the child itself, see Table C.3 of the Online Appendix for a full description of variables. The three non-linear effects f 1 to f 3 of cage (age of the child in months), mage (age of the mother in years), mbmi (body mass index of the mother) are decomposed into their linear and non-linear part as described in Section 2.2. For the scale parameters, we used an exponential response function and for ρ the response function g(x) = x/ (1 + x 2 ). The DIC/WAIC of the full model and model with NBPSS prior are 159,101/159,190 and 159,101/159,173, respectively and hence slightly better for the NBPSS prior model. Figures 8 and 9 show the posterior means together with their 95% posterior credible intervals of linear and non-linear effects for the full model (blue) and the model with NBPSS prior (red).
For the the function estimates f j,k = f j,k,lin + f j,k,nonlin , Figure 9 shows the corresponding nonlinear part f j,k,nonlin separate from the linear part f j,k,lin in Figure 8, while the sum of the two components can be found in the Online Appendix F. We see that both models yield very similar point estimates, however the NBPSS prior results in slightly smoother estimates and more narrow credible intervals and hence more precise predictions -as desired with an effective variable selection approach. Spatial effects of the five distribution parameters with the NBPSS prior are visualized in Figure 10. While we omit the ones of the full model, tendencies are similar as for the remaining effects.
Inclusion probabilities are reported in Table 4. We find that the regional effect is relevant in all distribution parameters, i.e. not only the marginal means but also the scales and the correlation between stunting and wasting. Interestingly, chronic undernutrition measured by stunting seems to be mostly driven by variables describing the life situation of the children. In contrast, besides the region of residence, the mother's nutritional status measured by mbmi has a relevant effect only for acute undernutrition (wasting).
Hedonic House Prices
We apply our methodology to the house prices dataset of n = 98, 354 single family homes in Germany. The data were provided by F+B Research & Consulting for Habitation, Real Estate and Environment Ltd, a business consultancy in Hamburg, Germany. We consider the price per square metre in Euro as the response variable and explain the variation in prices in terms of four continuous covariates representing year of construction (yoc), expert rating (rating), plot area (areapl), living area (arealiv ) and spatial location (dist). We use district-specific averages yoc dist and rating dist as further covariates. We assume a Gaussian hierarchical location-scale model, where both expectation µ and log-variance log(σ 2 ) are related to the following hierarchical predictor.
• Level 1 (houses): 5,k (dist) • Level 2 (districts): 1,k (yoc dist ) + f 2,k (rating dist ) + f 3,k (dist), where f 3,k (dist) follow Gaussian Markov random fields for k = 1, 2 and, as before, we decompose the effects of the continuous covariates in both levels into their linear and non-linear part such that we end up with 26 effects in total. The NBPSS prior is put on all effects and inclusion probabilities are given in Table 5 j,k,nonlin and the estimated spatial effects can be found in the Online Appendix G. In summary, we find that the NBPSS prior demonstrates its effect selection and shrinkage abilities also in hierarchical settings. While on level 1 the full model and the model with NBPSS prior mostly coincide, we see considerable regularisation of some non-linear effects for level 2. The NBPSS prior is clearly able to select the spatial effect and non-linear part of rating dist in both distribution parameters, while the linear part and the effect of yoc dist would be excluded according to the inclusion probabilities.
Summary and Discussion
In this paper, we have developed a novel prior structure for Bayesian effect selection in structured additive distributional regression models thus extending existing approaches in terms of both flexibility of available response distributions and predictor flexibility. We derived shrinkage properties of the NBPSS prior and show its favourable properties. In simulations we demonstrate empirically that the NBPSS prior is applicable even to the selection of high dimensional coefficient blocks in more than one distribution parameter. The method promises wide applicability which we illustrate along three different examples including zero-inflated count data, a bivariate Gaussian model and a hierarchical location-scale specification for hedonic housing priors.
Instead of arbitrarily fixing hyperparameters of the inverse gamma priors we provide an intuitive and interpretable way for hyperprior elicitation which is easily accessible by applied users. This is an important feature since results react sensitively with respect to the actual choices of hyperparameters. Yet, the NBPSS prior controls the flexibility of each effect separately since priors are assumed to be independent and does not allow to control the overall complexity of the predictor. However, the NBPSS prior could be extended to achieve also global shrinkage properties, e.g. by specifying the scale parameter in the prior on τ 2 as a product of a global and a local parameter (Polson and Scott, 2010). As in distributional regression the propriety of the posterior is not trivial, however, care has to be taken with respect to the specific prior choices (Ghosh et al., 2018). Alternatively, if interest is rather in smoothing and shrinkage than in explicit effect selection shrinkage priors like the double gamma prior Bitto and Frühwirth-Schnatter (2018) or penalised complexity priors Simpson et al. (2017) might be used.
Also, it is conceptually straightforward to include Bayesian quantile or expectile regression models into the NBPSS prior framework and we aim to do so in a future work. and of η dist ,µ and η dist ,σ 2 (second row) with the NBPSS prior. Relative mean logarithmic scores Figure 6: Violin plots of relative mean log-scores (i.e. mean log scores obtained with the NBPSS prior divided by mean log scores of the oracle model) in the zero-inflated Poisson model. The log-scores are averaged over 5,000 new test data observations for each simulation replicate. The columns represent the different sample sizes n = 1, 000; 2, 000, rows 1 and 3 belong to the non-spatial scenarios (no spatial effect in the data generating model) and rows 2 and 4 to the spatial ones (the data generating model comprises a spatial effect). Covariates are uncorrelated in rows 1 and 2 and correlated in rows 3 and 4. The different boxplots within a column/row correspond to different combinations of α, c denoted as (α, c) in the labels. | 15,842.4 | 2019-02-27T00:00:00.000 | [
"Mathematics"
] |
Nuclear Magnetic Resonance-Based Metabolomic Analysis of the Anticancer Effect of Metformin Treatment on Cholangiocarcinoma Cells
Metformin is a widely prescribed anti-diabetes drug with potential utilities for cancer therapies. Several studies have related metformin to the reduced risk of cholangiocarcinoma (CCA), highlighting its potentialities for the treatments of CCA. However, the underlying molecular mechanisms remain elusive. Here, we demonstrated that metformin treatment could inhibit proliferations of the human CCA cell lines Mz-ChA-1 and QBC939 in dose-dependent manners. The NMR-based metabonomic analyses showed distinct discriminations between the metformin-treated (Met) and control (Ctrl) groups of both CCA cells. Characteristic metabolites were identified by a combination of multivariate statistical analysis of 1D 1H-NMR spectral data and the pair-wise t-test of metabolite levels. We then identified four significantly altered metabolic pathways based on the characteristic metabolites, including glucose metabolism, oxidative stress-related metabolism, energy metabolism, and amino acids metabolism. Comparing CCA cells with normal human umbilical vein endothelial cells (HUVECs), we found that metformin treatment profoundly promoted glycolysis and specifically increased the levels of BCAAs and UDP-GlcNAc, implying the occurrence of autophagy and cell cycle arrest in metformin-treated CAA cells. This work provides a mechanistic understanding of the anticancer effect of metformin treatment on CAA cells, and is beneficial to further developments of metformin as an anticancer drug.
INTRODUCTION Background
Cholangiocarcinoma (CCA) is the second most common hepatic and biliary malignancy (1). Based on its anatomical location, CCA can be classified into intrahepatic, extrahepatic and distal CCA (1,2). Although CCA is considered as an uncommon tumor and only accounts for 3% of all gastrointestinal tumors, the overall incidence rate of CCA has remarkably climbed in last several decades (3,4). Surgical intervention offers the highest chance to cure for all types of CCA. Unfortunately, individuals with CCA are usually asymptomatic, and most of patients diagnosed with CCA can no longer benefit from surgical resection (4), leading to poor outcomes. Even when surgery is an option for selected patients, the 5-year survival rates are still very low. Both systemic chemotherapy and targeted radiation therapy have been also applied for the treatments of CCA. Nevertheless, these approaches usually fail to efficiently improve the prognosis of CCA (3). Thus, new therapy strategies are urgently needed for CCA.
As the most widely used first-line drug for the treatment of type 2 diabetes, metformin (N, N-dimethyl biguanide) has recently gained interests of investigators for its anticancer potentials. According to recent epidemiological data, cancer risk in diabetic patients taking metformin is significantly reduced relative to patients with other antidiabetic treatments (5)(6)(7)(8). Moreover, numerous studies have reported that metformin has anticancer effects both in vivo and in vitro on various human cancers including CCA (9)(10)(11)(12)(13). These evidences indicate that metformin might have great potentials for CCA prevention and therapy.
As reported recently, metformin treatment can reduce the levels of mitochondrial metabolites, activate multiple mitochondrial metabolic pathways, and increase 18-FDG flux in breast tumors (14). Moreover, metformin can inhibit mitochondrial complex I and disrupt oxidative phosphorylation, thus resulting in alterations in the electron transport chain (ETC) (15,16). The inhibition of complex I also causes energetic stress, then enhancing the activity of AMP-activated protein kinase (AMPK) (17,18). Furthermore, metformin can activate AMPK through the lysosomal pathway, and the anticancer effect of metformin treatment might be not mere a consequence of disrupting metabolic processes such as ATP synthesis through oxidation phosphorylation (19). In addition, previous works also indicate that metformin exerts anticancer capacities by inhibiting the mammalian target of rapamycin (mTOR) through AMPK-dependent and AMPK-independent mechanisms (20,21). However, molecular mechanisms underlying the anticancer effect of metformin treatment on CCA remain to be detailedly clarified.
Metabolomic analysis has been extensively applied to clarify molecular mechanisms of anticancer drugs (22)(23)(24). As metabolites are the final downstream products of gene transcription and translation, variations in metabolite levels reflect systemic changes of biological states. Several complicated signaling pathways could simultaneously bring out alterations in a metabolic pathway. Therefore, a comprehensive metabolomic analysis is of great significance for elucidating the molecular mechanisms of metformin for the treatments of CCA.
As two most efficient detection techniques, mass spectrometry (MS) and nuclear magnetic resonance (NMR) spectroscopy are frequently used in metabolomic analyses. Despite NMR spectroscopy shows lower sensitivities than MS, it offers many unique advantages (25). NMR possesses the capacity of readily identifying and conveniently quantifying absolute levels of compounds present in biological samples, including the compounds which are difficult either to be ionized or are required for derivatization to conduct MS detections. In addition, NMR is a method of choice for the identification of compounds with identical masses, including those with different isotopomer distributions (25,26). Thus, we took advantage of NMR to perform metabolomic analyses.
In the present work, we demonstrated that metformin treatment profoundly suppressed proliferations of two human CCA cell lines (MZ-CHA-1 and QBC939) in dose-dependent manners. By performing NMR-based metabonomic analyses on cellular extracts, we indicated that metformin treatment induced marked variations in metabolic profiles and remarkable changes in metabolite levels as well as significant alterations in metabolic pathways for both CCA cells. Moreover, certain metabolite levels exhibited different changing trends between the CCA cells and normal human umbilical vein endothelial cells (HUVECs) after metformin treatment. These results shed new light on the molecular mechanisms of the anticancer effect of metformin treatment on CCA cells.
Cell Lines and Culture
Two typical human CCA cell lines MZ-CHA-1 and QBC939 were used in this work. MZ-CHA-1 was properly conserved in our laboratory, and QBC939 was obtained from Third Military Medical University. Both CCA cells were cultured in RPMI 1640 supplemented with 10% fetal bovine serum (FBS, Gemini, USA), 100 U/ml penicillin, and 100 U/ml streptomycin. Known as normal epithelial cells, primary HUVEC cells were isolated from the umbilical cord of a neonate as described previously (27), cultured in endothelial cell medium (ECM; ScienCell, USA), supplemented with 5% FBS, 1% endothelial cell growth supplement (ECGS; ScienCell, USA), 100 U/ml penicillin, and 100 U/ml streptomycin. All the cells were cultured in a 5% CO 2 humidified environment at 37°C.
Cell Viability Assay
The cell viability assay was performed on both CCA cells using a CellTiter 96 ® AQueous One Solution Cell Proliferation Assay Kit (Promega, USA) according to the recommendations of the manufacturer. The cells were seeded in 96-well plates (5 × 10 3 per well). After 12 h, the medium was replaced with test medium containing various concentrations of metformin (0.05, 0.5, 2, 5 mM), and the cells were incubated for a further 48 h. Then, 20 ml of MTS solution was added to each well. After 4 h incubation in dark, the absorbance of formazan was measured at a wavelength of 490 nm on a microplate reader (BioTek, USA). Statistical results were presented as the mean ± SEM. To compare cell viabilities between the four metformin-treated (Met) groups and the control (Ctrl) group of the CCA cells, we analyzed the data with ONE-WAY ANOVA followed by multiple post-hoc comparisons (Bonferonni/ Tukeys) using the GraphPad Prism program (Version 6, GraphPad Software, USA).
Colony Formation Assay
Both CCA Cells were planted into 6-well plates at a density of 1,000 cells per well and treated with test medium containing various concentrations of metformin for 7-14 days. Colonies were fixed with 4% paraformaldehyde for 20 min, and stained with 0.5% crystal violet in 20% ethanol for 30 min. The plates were washed with water for 3 times and photographed with camera. The Image J software (Version 1.52a, National Institutes of Health, USA) was used to calculate grey value in each well. The colony formation rates were calculated and analyzed by ONE-WAY ANOVA using GraphPad Prism.
Sample Preparation
Both CCA cells were seeded in 10 cm diameter culture dishes at a density of 1×10 6 per dish and treated with or without 0.5 mM metformin. After 48 h of incubation, the cells reached 80-90% of confluence, and the difference in the number of cells between the Met group and Ctrl group was less than 10%. Before harvest, medium was removed and cells were quickly washed by ice-cold PBS for 3 times. Vacuum suction was used to remove any residual liquid. Then, 3.0 ml of cold methanol was immediately added into the culture dish, and the cells were scraped, collected and transferred into a centrifuge tube. Thereafter, 3.0 ml of cold chloroform and 2.5 ml of water were subsequently added to the tube, and the mixture was fully vortexed. After 30 min of laying aside, samples were centrifuged at 12,000 g for 15 min at 4°C to separate two phase extracts. The aqueous phase was condensed with nitrogen stream and lyophilized by a vacuum freezing dryer.
Nuclear Magnetic Resonance Measurements and Data Processing
NMR experiments were conducted on a Bruker Avance III 850MHz spectrometer equipped with a TCI cryoprobe (Bruker BioSpin, Rheinstetten, Germany) at 298 K. One dimensional (1D) 1 H NOESY spectra were acquired using the pulse sequence (RD-90°-t1-90°-t m -90°-ACQ) with water suppression during the relaxation delay and mixing time (19). RD was the relaxation delay (4 s), t1 was a short delay (4ms), and t m was the mixing time (10 ms). The spectral width was 20 ppm with an acquisition time per scan of 1.88 s (ACQ), and a total of 128 transients were collected into 64 K data points for each spectrum. The free induction delay (FID) signal was processed by a window function with a line broadening of 0.3 Hz, followed by Fourier transformation to obtain 1D 1 H spectra. To assist in resonance assignments of metabolites, two-dimensional (2D) NMR spectra were recorded including 1 H-13 C heteronuclear single quantum coherence (HSQC) and 1 H-1 H total correlation spectroscopy (TOCSY) spectra.
The TopSpin 3.5 software (Bruker Biospin, Germany) was used to perform phase and baseline corrections of the NMR spectra. Chemical shifts were referenced to the CH 3 resonance of TSP at 0 ppm. Peak alignments were further manually carried out with MestReNova Version 9.0 (Mestrelab Research S.L., Espain). Spectral regions of d 9.40-(-0.5) were binned by 0.001 ppm and integrals of the segments were calculated. Regions of residual water resonances at d 5.2-4.6 were removed to eliminate the distorted baselines from imperfect water saturation.
Integrals were normalized by the integral area of TSP to make the data directly comparable between the NMR spectra. Then, probabilistic quotient normalization (PQN) was performed to compensate for dilution-independent effects in MATLAB (Version 2011b, Math Works, USA).
Resonance Assignments of Cellular Metabolites
Resonance assignments of aqueous metabolites were conducted using a combination of Chenomx NMR Suite (Version 8.1, Chenomx Inc., Edmonton, Canada) and Human Metabolome Data Base (HMDB) (http://www.hmdb.ca/) as well as relevant published references. For each cluster of a given metabolite, we compared the shape of the Chenomx preview spectral line (preview line) and the experimental 1D 1 H spectral line (Exp line). Under the condition that the preview line was substantially contributing to the Exp line in the displayed region, and also the Exp line was similar to the standard 1D 1 H spectral lines provided by Chenomx NMR Suite, the metabolite was assigned to be the compound in the Chenomx Compound Table. The resonance assignments were further confirmed based on 2D
Multivariate Statistical Analysis and Identification of Significant Metabolites
The normalized spectral data were scaled by Pareto scaling and objected to the SIMCA-P 14.0 software (Umetrics, Sweden) for multivariate statistical analysis. An unsupervised approach, principal component analysis (PCA) was performed to reveal the trends, highlight outliers, and show clusters among the samples. A supervised approach, partial least-squares discriminant analysis (PLS-DA) was subsequently conducted to improve the classification between the groups of samples. Cross-validation was performed with a random permutation test (999 cycles) to evaluate the robustness of the PLS-DA model. The model is considered credible if all the Q2-values on the left are lower than the original point at the right, and the regression line of the Q2-points intersects the vertical axis below zero. Two criteria derived from the PLS-DA loading plot were used to identify significant metabolites primarily responsible for the metabolic discrimination: variable importance in the projection (VIP), and the correlation coefficient (r) of the variable relative to the first predictive component (tp1). The loading plot was reconstituted in MATLAB. The critical value of the correlation coefficient (r) was defined based on the degree of freedom (df), which were determined as n1+n2-2 with n1 and n2 as the respective number of samples of the two groups in the PLS-DA model. Variables with VIP >1 and |r|> the critical value of p = 0.01 were marked by red color; variables with VIP >1 and |r| between the critical values of p = 0.05 and p = 0.01 were marked by orange; variables with VIP ≤1 or |r| < the critical value of p = 0.05 were marked by blue. Variables colored in red and orange were related to significant metabolites.
Furthermore, hierarchical cluster analysis (HCA) with Pearson distance measure and Ward clustering algorithm was performed on the normalized NMR data to further confirm the metabolic clusters, using the module of Statistical Analysis provided by the MetaboAnalyst webserver 4.0 (http://www.metaboanalyst.ca/). In the HCA approach, each sample acted as a separate cluster initially and the algorithm proceeded to combine them until all samples belong to one cluster.
Univariate Statistical Analysis and Identification of Differential Metabolites
Pair-wise student's t-test was applied to quantitatively compare relative levels of metabolites between the Met and Ctrl groups. Metabolites with p <0.05 were identified to be differential metabolites. Characteristic metabolites were determined by a combination of the identified differential metabolites and the significant metabolites described above.
Metabolic Pathway Analysis and Identification of Significant Pathways
Metabolic pathways were analyzed based on the characteristic metabolites using the module of Metabolites Set Enrichment Analysis (MSEA) provided by MetaboAnalyst 4.0. MSEA is extensively used to identify and interpret patterns of metabolite level changes in a meaningful context (28), which contains 88 metabolite sets functionally related to metabolic pathways. The statistical p value was calculated to evaluate the significance of the metabolic pathway. The metabolic pathway containing at least three enriched metabolites with p <0.05 was identified to be the significantly altered pathway (abbreviated as significant pathways).
Metformin Inhibited Proliferations of Both CCA Cells in Dose-Dependent Manners
To address the anticancer effect of metformin treatment on CCA, we conducted MTS assays and colony formation assays on both human CCA cells (MZ-CHA-1 and QBC939). The CCA cells were treated with various concentrations of metformin for both assays. MTS assays showed that metformin reduced cell viabilities in dosedependent manners ( Figures 1A, B). Moreover, relative cell viabilities were significantly decreased to 80-90% when the two CCA cells were treated with 0.5 mM metformin for 48 h. Such a treatment allowed the difference in the cell number between the Met and Ctrl groups was less than 10%. Our preliminary experiments showed that harvesting the two CCA cells at 48h provided maximum metabolite concentrations with smaller experimental errors. In colony formation assays, additionally, metformin at either 0.5 or 5 mM profoundly decreased the dimensions of colonies ( Figures 1C-F). Thus, we treated the two CCA cells with metformin for 48 h in the following NMR-based metabonomic analyses.
Metformin Markedly Changed Metabolic Profiles of Both CCA Cells
To reveal metabolic distinctions between the Met and Ctrl groups, we performed NMR-based metabonomic analyses on aqueous extracts derived from both CCA cells. The typical 1D 1 H NOEYS spectra are shown in Figure 2. Resonance assignments of cellular metabolites were conducted ( Table 1), and further confirmed by 2D 1 H-13 C HSQC and 2D 1 H-1 H TOCSY spectra ( Figure S1). Totally, 41 metabolites were identified based on the NMR spectra.
Both PCA and PLS-DA of the normalized NMR data were performed to evaluate the effects of metformin treatment on metabolic profiles of the CCA cells. All the samples are situated in the Hotelling's T2 oval of the 95% confidence intervals. In the scores plot of either the PCA model or the PLS-DA model, each point represents a sample, and the distance between points reflects the degree of metabolic distinction. The PCA scores plots show distinct separations of the Met-Mz and Met-939 groups from Ctrl-Mz and Ctrl-939 groups, respectively, suggesting that metformin treatment markedly changed the metabolic profiles of both CCA cells (Figures 3A, B). The PLS-DA scores plots display improved metabolic separations of the Met-Mz and Met-939 groups from the Ctrl-Mz and Ctrl-939 groups (Figures S2A, B). The cross-validation plots indicate the high reliabilities of the PLS-DA models for both CCA cells ( Figures S2C, D). Additionally, we conducted the HCA analyses to confirm the validities of the PCA and PLS-DA models ( Figures S2E, F). The dendrogram plot of HCA illustrates that the Met-Mz group forms a separate cluster, while the Ctrl-Mz group belongs to another cluster ( Figure S2E). The QBC939 cells displayed the similar HCA plot ( Figure S2F). This result well supported those from PCA and PLS-DA.
Metformin Profoundly Changed Metabolite Levels in Both CCA Cells
In the loading plots of the PLS-DA models ( Figures 3C, D), variables colored in red, yellow, and blue are very significant, significant, and insignificant respectively, the upward or downward direction indicates the variable was upregulated or downregulated in the Met group compared with that in the Ctrl group. Expectedly, the levels of metformin were significantly increased in the Met-Mz and Met-939 groups relative to Ctrl-Mz and Ctrl-939, respectively, indicating that extracellular metformin was transported into both CCA cells. Significant metabolites were identified which were primarily responsible for metabolic separations of the Met-Mz and Met-939 groups from Ctrl-Mz and Ctrl-939 groups, respectively. After metformin treatment, 14 metabolites were increased and 18 metabolites were decreased in Mz-ChA-1 cells, while 10 metabolites were increased and 11 metabolites were decreased in QBC939 cells.
Relative levels of metabolites were represented by relative integrals measured from 1D 1 H NOESY spectra. Quantitative comparisons of relative levels of metabolites between the Met-Mz and Ctrl-Mz groups, and between the Met-939 and Ctrl-939 groups were performed by using univariate statistical analysis (pair-wise student's t-test), as shown in Table 2. Metabolites with statistical significances (p < 0.05) were identified to be differential metabolites. Totally, we identified 33 and 30 differential metabolites in Mz-ChA-1 and QBC939 cells, respectively.
Metformin Affected Similar Metabolic Pathways in Both Cholangiocarcinoma Cells
Combining the identified differential metabolites with the significant metabolites described above, we obtained 32 and 29 characteristic metabolites in the Met-Mz and Met-939 cells compared with their controls, respectively. The characteristic metabolites were then subjected to metabolic pathway enrichment analysis. Top 50 enriched pathways are shown in Figure 4. The ranking of enriched metabolic pathways in the Met-Mz cells was highly similar with the Met-939 cells, and the pathways with higher significances were closely related to four major metabolic pathway clusters, including glucose metabolism, oxidative stress-related metabolism, energy metabolism, and amino acids metabolism. Metformin-induced level changes of characteristic metabolites involved in the four major metabolic pathway clusters were quantified for Met-Mz vs. Ctrl-Mz, and Met-939 vs. Ctrl-939 ( Figure 5). Most metabolite levels exhibited consistent changing trends in the two CCA cells. The metformin-treated CCA cells showed upregulated levels of pyruvate, lactate and NAD + , and downregulated levels of glucose, GTP and TCA cycle intermediates (2oxoglutarte; fumarate). Furthermore, most of the detected nonessential amino acids were decreased, and some of the detected essential amino acids (methionine, phenylalanine, valine, leucine, and isoleucine) tended to be increased in the metformin-treated CCA cells. These results suggest that metformin treatment has similar effects on the two CCA cell lines.
Metformin Differently Affected the Levels of Certain Metabolites in Cholangiocarcinoma Cells
To assert the unique effects of metformin treatment on CCA cells, we further assessed metformin-induced level alterations of metabolites involved in the four major metabolic pathway clusters in normal HUVEC cells ( Figure 5). The HUVEC cells shared several metabolite levels with the two CCA cells, including the increased levels of lactate, decreased levels of glutamate, glutamine, asparagine, and b-alanine. After metformin treatment, glucose, fumarate, and alanine were remarkably decreased in CCA cells but increased in HUVEC cells, while NAD + , UDP-GlcNAc, and BCAAs were increased in CCA cells but either decreased or unchanged in HUVEC cells.
To visualize the effects of metformin treatment on the metabolic pathways of the CCA cells, we projected the characteristic metabolites onto a metabolic map ( Figure 6). Both the primarily changed characteristic metabolites and significantly altered metabolic pathways provide new insights into molecular mechanisms underlying the anticancer effect of metformin treatment on CCA cells.
DISCUSSION
As reported previously, metformin is transported into hepatocytes through the organic cation transporter (OTC) family (29).
Particularly, genetic variation in the OTC1 is well correlated to the therapeutic efficacy of metformin treatment (29). In this work, we observed an accumulation of metformin in both CCA cells, implying that metformin was transported into the cells and exhibited its effects. Metformin treatment greatly inhibits the biosynthesis of acetyl CoA which is partly generated by pyruvate dehydrogenase complex (PDC) (30). Moreover, it has been demonstrated that metformin reduces the activity of mitochondrial complex I (12,31) and causes alterations in the ETC. As a result, NADH-contained electrons are not effectively transported through the ETC, thus decreasing the NAD + level (16,32). Consistent with these studies, we detected increased glucose and fumarate, but decreased NAD + in metformin-treated HUVEC cells. It seems that the accumulation of TCA cycle intermediates may facilitate the biosynthesis of alanine and aspartate for normal epithelial cells.
On the contrary, we observed raised levels of NAD + and declined levels of TCA cycle intermediates in metformin-treated CCA cells. This discrepancy might result from the metabolic transformation of cancer cells. Cancer cells produce energy through the aerobic glycolysis, in which high rates of glycolysis and lactic acid fermentation occur in the cytosol regardless of the oxygen level (33,34). Given the enhanced glucose consumption and lactate production, we assume that metformin treatment boosts glycolysis and drains the electrons from NADH for the conversion of pyruvate to lactate, thus aggravating the Warburg effect in cancer cells. It is well known that the regulation of glycolysis is highly associated with AMPK, which can be activated by metformin (19,35,36). Similarly, our results indicate that glycolysis is profoundly affected by metformin in CCA cells, providing independent support for the viewpoint that AMPK is vital for the anticancer effect of metformin treatment on CCA cells.
Biosynthesis of amino acids is tightly linked to the TCA cycle and glutamate metabolism. Our results show that metformin treatment decreases glutamate, glutamine, asparagine and balanine in both CCA cells and HUVECs, indicating that metformin has a significant effect on the synthesis of non-essential amino acids. The lack of substrates in metformin-treated cells potentially leads to insufficient glutathione, thus interrupting the oxidative stress.
We found that the levels of three BCAAs were basically unchanged in HUVEC cells but significantly enhanced in metformin-treated CCA cells. As essential amino acids, BCAAs cannot be synthesized endogenously, and they are catabolized by highly reversible enzymes using all three BCAAs as substrates. Therefore, levels of the three BCAAs display the same changing treads with similar variation amplitudes (37). Moreover, metformin suppresses expressions or activities of BCAAs catabolic enzymes (38,39). Accordingly, we hypothesize that the accumulation of BCAAs in CCA cells might be due to autophagy-induced degradations of proteins. Previous works have well demonstrated that metformin can significantly contribute to the inhibition of mTOR (20,21), directly leading to the activation of autophagy (40,41). Consistently with these works, our results provide independent support for the viewpoint that metformin treatment may exert anticancer effect through activating the process of autophagy. It has been showed that BCAAs (particularly leucine) are potent activators of mTORC1 (42), implying the presence of negative feedback regulation from metformin to mTOR signaling. Future research is needed to better understand the correlation between metformin and BCAAs in CCA. It was previously reported that metformin treatment can induce cell cycle arrest in several other cancer cell lines (43)(44)(45). Interestingly, we observed significantly increased levels of UDP-GlcNAc in metformin-treated CCA cells. To our knowledge, this observation represents the first report that the anticancer effect of metformin is related to UDP-GlcNAc. As is known, UDP-GlcNAc is a common donor substrate for the N-glycosylation of most cell-surface receptors and transporters in eukaryotes (46). Previous works indicate that glycoproteins with few N-glycans are significantly up-regulated in a switch-like response to the increased UDP-GlcNAc level, such as TbR, CTLA-4, and GLUT4 which mediate organogenesis, differentiation and cell cycle arrest (47,48). Contrarily, glycoproteins with high numbers of N-glycans are slowly up-regulated with the increased UDP-GlcNAc level, including EGFR, IGFR, FGFR, and PDGFR which stimulate growth and proliferation of cells (47,48). Thus, the increased levels of UDP-GlcNAc in the CCA cells could potentially induce enhanced surface levels of low-n glycoproteins, and eventually drive to arrest programs and suppress proliferation. Further studies should be conducted in future to mechanistically understand the relevance between metformin and cell cycle arrest. Additionally, in order to identify as many metabolites as possible, we chose to record solution NMR spectra on aqueous extracts derived from the cells. Notably, other powerful NMR The quantitative comparisons were conducted by using student's t-test. Symbols ***, **, *, NS indicate differences between the Met and Ctrl groups were highly significant (p < 0.001), very significant (p < 0.01), significant (p < 0.05), insignificant (p ≥ 0.05), respectively. Red or blue color denotes that the metabolite level was elevated or reduced in the metformin-treated cells relative to control cells. NA, not applicable. techniques are able to provide unique advantages in metabolomic analyses. In particular, the high resolution magic angle spinning (HRMAS) NMR spectroscopy offers a window for the observation of individual metabolites in intact tissues (49), which may facilitate the elucidation of molecular mechanisms underlying the anticancer effect of metformin on CCA in vivo.
CONCLUSIONS
In this work, we have performed comprehensive NMR-based metabolomic analyses to access the anticancer effects of metformin treatment on two CCA cell lines, and address the underlying molecular mechanisms. We identified characteristic metabolites and significantly altered metabolic pathways for metformin-treated CCA cells relative to untreated controls. Through comparing metformin-induced changes of metabolite levels between the CCA cells and normal HUVEC cells, we suggest that metformin profoundly promotes glycolysis and aggravate the Warburg effect in CAA cells. Moreover, metformin specifically increases BCAAs and UDP-GlcNAc, implying the occurrence of autophagy and cell cycle arrest in metformintreated CAA cells. These results extend our understanding on the molecular mechanisms underlying the anticancer effect of metformin treatment on CCA cells, and shed light on the clinical use of metformin for CCA managements.
DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article/Supplementary Materials. Further inquiries can be directed to the corresponding authors.
AUTHORS CONTRIBUTIONS
JZ conducted cell biology and NMR experiments and analyzed metabonomic data. CH, TJ, SY, and WS performed NMR analysis and cell culturing. WL was the initiator of this study. DL and JZ wrote the manuscript. All authors contributed to the article and approved the submitted version. Metabolites colored in red, blue, and black represent increased, decreased, and unchanged by metformin treatment in at least one CCA cell lines (MZ-ChA-1 and/or QBC939 cells), respectively. Metabolites displayed in grey were not detected by 1D 1 H-NMR spectra. Green arrows and red crosses denote potentially promoted and inhibited metabolic pathways in metformin-treated CCA cells relative to their control counterparts, respectively. | 6,353.2 | 2020-11-30T00:00:00.000 | [
"Biology",
"Medicine",
"Chemistry"
] |
Implementation of FxLMS Algorithm Based on Level-2 S-Function and Behavior Analysis
Active vibration control use an active force from secondary path to suppress or attenuate periodic or quasi-periodic vibration and noises, one of the popular control algorithms is filtered-x least mean square (FxLMS) adaptive method. Based on structure of FxLMS algorithm, the paper uses Level-2 S-fun to create a new FxLMS blocks in Matlab/Simulink and apply it on vibration active control system simulator. Results of computer simulation showed the custom FxLMS block’s feasibility and control algorithm’s efficiency. On the condition of stabilization, behavior analysis was also taken out by adjusting the interior parameters, including the number of Weights and the Step size.
Introduction
Rotating machines such as gear boxes, motors, cutting machines, aircrews etc, generate noise and vibration signals that can usually be modeled as sinusoidal signals in additive white noises. Suppressing or reducing these noise signals, especially their lower frequency portion, is of great importance in various engineering and environmental systems [1]- [3] , Recently active vibration control (AVC) systems have been developed to suppress these annoying vibration sources [4] . A large number of AVC systems have been proposed in the literature, and some of them have been implemented in real-life applications [5] . Usually, FIR filters are applied, which are adapted by the filtered-X least-mean square (FxLMS) algorithm or its variants. Other techniques using recursive least squares (RLS) and Kalman filter based algorithms have also been developed for many ANC systems. Normally, a well-designed controller will be able to provide sufficient reduction to achieve the desired response under certain conditions. This paper aims the implementation of FxLMS Algorithm based on level-2 s-function and behavior analysis. Because the Level-2 S-function provides access to a more extensive set of the S-function API and supports code generation that facilitates the next experiments and practical engineering applications. Fig. 1. Block diagram of active vibration control system using the FxLMS algorithm Figure 1 shows the block diagram of the active vibration control system using FxLMS algorithm. The purpose of the control system can divide into two effectively sections: the export of the control signal and the weight adaptation of control filter. p(k) is original vibration to be controlled and ) (z C represents the secondary path, which accounts for the transducer response, including the A/D and D/A converters, and the acoustical or structural propagation. ) (z C′ is a model of the secondary-path transfer function. Error signal e(k) equal to the sum of initial vibration signal p(k) and anti-vibration signal created by control source s(k).
Structure of FxLMS Algorithm
(1) At time k, the output of N orders FIR control filter, y(k), equals to the following convolution: As mentioned above, the signal of feedforward control obtained by FIR control filter, y(k), will doesn't equal to the control source of error signal s(k), for during the active control of noise and vibration, the objective of control is actual signal, including sound interference and vibration disturbance, differ from the electric unit that can use electric signal directly. Therefore, sensors are necessary to transfer between the two states, these sensors (actuators and error sensors) will have characteristic frequency response and transfer functions, that was called the secondary path's transfer function which can be modeled by FIR filters in time domain.
and y(k) is a vector of m×1 order: x (k) is the input of control filter and f(k) is the filtered reference signal.
The update formula of the control FIR filter's weight is: (7) is so called FxLMS algorithm. During the actual applications, if the input signal x(k),the transfer function of secondary path, c, and the error signal e(k) are known, take the initial weight w to 0, then the FxLMS algorithm process could be designed by the following steps: 1. Raise the value of delay chain of FIR control filter to next period and input a new reference sample.
2. Compute a new output of FIR control filter by formula (5).
3. Obtain the anti-vibration components s (k) by formula (4). 4. Obtain the error signal e (k), which equal to the sum of the primary path and the secondary path. 5. Compute the new weight coefficient by formula (7) 6. Repeat the above steps. The Level-2 M-file S-function API defines the signatures and general purposes of the callback methods that constitute a Level-2 M-file S-function. The S-function itself provides the implementations of these callback methods. The implementations in turn determine the block attributes (e.g., ports, parameters, and states) and behavior (e.g., the block outputs as a function of time and the block inputs, states, and parameters). During the course of built the FxLMS block, the following callback methods was necessary.
Create an FxLMS block using level-2 S-functions
1. The setup Method, initializes the instance of the corresponding Level-2 M-File S-Function block, the setup method is similar to the mdlInitializeSizes callback methods implemented by C MEX S-functions. In this paper, the setup method performs such tasks including: Initializing the number of input and output ports of the block, 3 inputs are reference signal, filtered reference signal and error signal, 2 outputs are control signal and weight coefficients. Invoke the run-time object's SetPreCompInpPortInfoToDynamic and SetPreCompOutPortInfoToDynamic methods to indicate that the input and output ports inherit their compiled properties.
Set the run-time object's NumDialogPrms property to 1 to initialize one S-function dialog parameter.
Registering 5. The Output Method, Compute the signals that the FxLMS block emits, and export the results to output ports.
Simulation of FxLMS Algorithm
To examine the custom block of FxLMS algorithm, we apply the block built by the Level-2 S function on the active vibration control. Figure 2shows the simulation with custom FxLMS block used in simulation. In this simulation, the sinusoidal excitation depart 4 part: 90Hz,100 Hz, 110Hz with an amplitude of 1, and a white noise. Both the primary and secondary path were modeled by FIR filters, the transfer function of primary path is: Figure 3 shows the active vibration control results applying the proposed FxLMS algorithm , From the figure, under ideal circumstances(Reference signal and the initial vibration signal is identical, the estimation of secondary path and the actual secondary path is identical), the initial vibration almost be attenuated. Figure 4 show the control results in frequency domain, the blue line is the vibration spectrum without control and the red line is the vibration control with the control turn on. Figure 5 shows the update of the weight coefficient; the weight will turn to be fixed when the vibration sources are a stable period signal. On the condition of stabilization, there are 2 main interior parameters that affect the performance of the FxLMS algorithm: the step size and the number of weights. Reference [6] has pointed out the range of step size to ensure the convergence of the algorithm. To verify the performance of the custom FxLMS block, change the step size and the number of weights, obtain results separately.
Advanced Engineering Forum Vols. 2-3
Firstly, maintain the order equal to 80 and change the step size, the results can be seen in figure 6(a) and 6(b). Secondly, keep step size to 0.0001 and change the number of weights from 80 to 10, then get the result in 6(c). Compare fig. 6 and fig. 3 we can obtained that when the Step size ( µ ) is increased from 0.0001 to 0.001, FxLMS algorithm converges more quickly; when the number of Weights is decrease from 80 to 10, the filter of the algorithm will not remove the noise properly and then the control effect were weakened largely.
Conclusions
1. Uses Level-2 S-functions create a new FxLMS blocks in Matlab/Simulink and apply it on vibration active control system simulator. Results of computer simulation showed the custom FxLMS block's feasibility and control algorithm's efficiency.
2. Conclusions could be drawn that if the number of weights is large, the algorithm will be slow to run, but have better accuracy, if the number of weights is decreased, the filter will not remove the vibration properly. When the Step size is increased, algorithm converges more quickly, when the step-size exceeds a max threshold to ensure stability, the algorithm will be unstable. These results will provide guidance to obtain optimum performance in practical applications. | 1,916.6 | 2011-02-15T00:00:00.000 | [
"Computer Science"
] |
Initial-State Dependence of Thermodynamic Dissipation for any Quantum Process
Herein we provide a new exact result about the nonequilibrium thermodynamics of open quantum systems at arbitrary timescales. In particular, we show that the contraction of the quantum state---towards the minimally-dissipative trajectory---exactly quantifies the excess of thermodynamic dissipation during any finite-time transformation. The quantum component of this dissipation is the change in coherence relative to the minimally-dissipative state. Implications for quantum state preparation, local control, and decoherence are explored. For logically-irreversible processes---like the preparation of any particular quantum state---we find that mismatched expectations lead to divergent dissipation as the actual initial state becomes orthogonal to the anticipated one.
Much recent progress extends Landauer's principle to the quantum regime-affirming that quantum information is physical [1][2][3][4][5]. Associated bounds refine our understanding of how much heat needs to be exhausted-or how much work needs to be performed, or could be extractedto preserve the Second Law of Thermodynamics: Entropy production is expected to be non-negative Σ ρ0 ≥ 0 from any initial density matrix ρ 0 . However, these Landauertype bounds only become tight in the infinite-time quasistatic limit, as entropy production goes to zero. Yet infinite time is not a luxury afforded to quantum systems with short decoherence time. And, even if coherence can be maintained for significant time-length, we want to know the thermodynamic limits of both quantum computers and natural quantum processes that transform quickly. Unfortunately, very few exact general results are known about the finite-time nonequilibrium thermodynamics of open quantum systems. The short list includes quantum generalizations of Crooks' Relation [6,7], the Jarzynski Equality [8,9], and other fluctuation relations [10][11][12][13], which are nonequilibrium equalities that in many ways subsume the inequality of the Second Law of Thermodynamics. More often we must rely on approximations, like the linearresponse and local-equilibrium theories developed many decades ago [14]; and like the weak-coupling, Markovian, and other approximations that lead to quantum Markovian master equations [15,16]. Despite the practical successes of these approximations [17][18][19], further exact results are highly desirable since they could yield new fundamental insight into the interplay among quantum correlations, dissipation, and other aspects of physics.
Here we add to the short list of exact general results for quantum finite-time dissipation. We will show that the thermodynamic dissipation due to alternative initial density matrices is exactly quantified for any finite-time transformation by the contraction of the relative entropy between the actual density matrix ρ t and the minimallydissipative density matrix q t . This generalizes a recent theorem by Kolchinsky and Wolpert, demonstrating that quantum coherence plays a significant role in the quantum extension of this previous classical result [20].
We illustrate some immediate consequences. The first being a thermodynamic risk in overspecialization despite the reward for specialization: To minimize heat dissipation, one should tailor the implementation of a desired quantum operation to particular initial state distributions; but the same optimization can lead to risks of divergent dissipation when input states differ significantly from predictions. The second is the thermodynamic costs of modularity: where quantum operations optimized for thermal efficiency locally can result in unavoidable dissipation beyond Landauer's limit when acting on correlated systems. All of these results are valid over arbitrarily short timescales.
Background To proceed, we consider any quantum system with initial density matrix ρ 0 . We allow a set B of canonical or grand canonical baths to play an active role in the evolution of the system over the duration τ . A control protocol x 0:τ determines the time-dependent interaction H int xt with the thermal and chemical baths (mediating heat and particle exchange) and also controls the time-dependent Hamiltonian H xt of the system to perform work on the system during the protocol.
The initial joint state of the system and baths is assumed arXiv:2002.11425v1 [cond-mat.stat-mech] 26 Feb 2020 to be separable: We furthermore assume each bath is initially in canonical or grand canonical equilibrium: ρ are the chemical potential and the number operator for the bath's th particle type, and Z (b) is the grand canonical partition function for the bath [21]. The baths are assumed to be sufficiently large that their temperature and chemical potentials remain unchanged throughout the protocol.
The driving protocol x 0:τ induces a net time evolution U x0:τ of the system-baths mega-system 1 , so that the joint state is given at the end of the transformation as: We will also consider the reduced density matrices of the system ρ τ = tr B (ρ tot τ ) and baths ρ (b) τ = tr sys,B\b (ρ tot τ ) after the joint evolution. Thermodynamic dissipation is quantified by entropy production Σ ρ0 , which is the effectively-irreversible change in entropy 2 . It is the entropy flow to the environment beyond any reduction in the entropy of the system [11,14,22,23]: The expected entropy flow to the environment over the course of the process is [14,[22][23][24]: where the heat Q (b) is the energy change of bath b over the course of the process: ). The expected change in the thermodynamic entropy of the system is proportional to its change in von Neumann 1 While we only utilize the existence of the net unitary time evolution, we note that it is induced through the time-ordered exponential: Some authors use the term 'dissipation' more loosely, to refer to heat even when it is not associated with entropy production. In either usage, the entropy production quantifies the dissipation beyond the minimal requirements of the Second Law. entropy 3 [11,24]: Since the von Neumann entropy of the joint universe is unchanged under unitary dynamics, entropy production can be viewed as the change in total correlation built up among the system and baths [23,24]-correlations that are too difficult to leverage.
Derivation of Main Result
The initial density matrix ρ 0 can be represented in an arbitrary orthonormal basis as: with c j,k = j| ρ 0 |k . We can consider all possible variations of the initial density matrix via changes in these c j,k parameters.
We aim to expose the ρ 0 -dependence of entropy production. From Eqs. (2) and (5), it is easy to show that [24]: τ . Meanwhile, utilizing the spectral theorem, it is useful to rewrite the change in system entropy as: (9) where Λ ρ0 is the collection of ρ 0 's eigenvalues, and Λ ρτ is the collection of ρ τ 's eigenvalues. We then calculate the infinitesimal perturbations ∂λ0 ∂c j,k and ∂λτ ∂c j,k . As shown in Appendix A, varying a single parameter c j,k of the initial density matrix yields the partial derivative: To consider the consequences of arbitrary variations in the initial density matrix, we construct a type of gradient ∇Σ ρ0 ≡ j,k |k j| ∂ ∂c j,k Σ ρ0 with a scalar product "·" that gives a type of directional derivative: γ · ∇Σ ρ0 ≡ tr(γ∇Σ ρ0 ).
For any two density matrices, (ρ 0 − ρ 0 ) · ∇Σ ρ 0 gives the linear approximation of the change in entropy production (from the gradient evaluated at ρ 0 ) if we were to change the initial density matrix from ρ 0 towards ρ 0 . Notably, using our directional derivative this way allows us to stay along the manifold of density matrices (due to the convexity of quantum states), while inspecting the effect of all possible infinitesimal changes to ρ 0 . Lemma 1. For any two density matrices ρ 0 and ρ 0 : Lemma 1 follows directly from Eqs. (7) and (10). Hence, for any initial density matrix: It is worthwhile to consider the density matrix q 0 that would lead to minimal entropy production under the control protocol x 0:τ . By definition of q 0 ∈ argmin ρ0 Σ ρ0 (11) as an extremum: if (on the one hand) q 0 has full rank, it must be true that: for any density matrix ρ 0 . I.e., moving from q 0 infinitesimally in the direction of any other initial density matrix cannot produce a linear change in the dissipation. Expanding Eq. (12), ρ 0 · ∇Σ q0 − q 0 · ∇Σ q0 = 0, according to Lemma 1 yields our main result: where D[ρ q] ≡ tr(ρ ln ρ)−tr(ρ ln q) is the relative entropy.
If (on the other hand) argmin ρ0 Σ ρ0 has a nontrivial nullspace, then Eq. (13) can be extended by supplementing q 0 with the successive minimally dissipative density matrices on the nullspace. This extension of our main result is derived and discussed in Appendix C.
We see that the information loss D ρ 0 q 0 −D ρ τ q τ generalizes and quantifies the notion of logical irreversibility relevant to physics.
Theorem 1.
Any logically irreversible operation requires dissipation-of at least k B D ρ 0 q 0 −k B D ρ τ q τbeyond Landauer's bound, and cannot simultaneously be thermodynamically optimized for all initial states.
It is interesting to compare to the classical result by Kolchinsky and Wolpert [20], which gives this dissipation in terms of the Kullback-Leibler divergence D KL instead of the quantum relative entropy D. The correspondence is complicated by the fact that q 0 and q τ are not typically diagonalized in the same basis. Nevertheless, we can consider q t 's eigenbasis at each time, and describe ρ t 's coherence in this basis as well as the classical probability distribution that would be induced by projecting ρ t onto q t 's eigenbasis. In particular, the classical probability distribution that would be induced by projecting ρ t onto q t 's eigenbasis is: where each |s is an eigenstate of q t . Since P t and q t are diagonal in the same basis, the relative entropy D P t q t reduces to the Kullback-Leibler divergence D KL P t q t . However the actual density matrix ρ t is typically not diagonalized by q t 's eigenbasis-but rather exhibits coherence there. This coherence is naturally quantified by the so-called 'relative entropy of coherence' [25]: when we take the incoherent basis to be the eigenbasis of the minimally-dissipative density matrix. As shown in Appendix D, the extra dissipation from starting with the density matrix ρ 0 rather than the minimallydissipative q 0 is given for any finite-duration nonequilibrium transformation as: We see that the quantum correction to the classical dissipation is exactly the change of coherence on the minimallydissipative eigenbasis. We now consider several important cases before turning to further general results. Relaxation to equilibrium Let us first consider the simple case of constant weak coupling to a single thermal bath of inverse temperature β = 1 k B T . Suppose the system is undriven, so that it experiences a time-independent Hamiltonian H x . There is zero dissipation if the system starts in equilibrium, so q 0 = π x = e −βHx /Z (where Z is the system's canonical partition function), with Σ πx = 0. The dissipation when starting in state ρ 0 is thus: which is a well known result since F add t = k B T D ρ t π xt is the system's nonequilibrium addition to free energy [11,[26][27][28]. The unharnessed reduction in the nonequilibrium addition to free energy results in entropy production. Furthermore, we see that this dissipation can be decomposed as: , into contributions from the change in probability of the system's energy eigenstates D KL P 0 π x − D KL P τ π x and from the decoherence in the energy eigenbasis: Reset Consider any control protocol x 0:τ that implements RESET to a desired state r τ from all initial quantum states ρ 0 . 4 For example: to erase any number of qubits (or qutrits, etc.) or, similarly, to initialize an entangled Bell state. It is reasonable to desire that the control protocol x 0:τ achieves this erasure with fidelity F (ρ τ , r τ ) ≥ 1 − for all possible ρ 0 , for some allowable error tolerance 0 ≤ 1.
Since D ρ τ q τ = 0 + O( ) for the RESET operation, our Eq. (13) asserts that implementing erasure with the fixed protocol x 0:τ must result in dissipation for any ρ 0 = q 0 . In particular, with fidelity better than 1 − , then: It should be emphasized that this dissipation is distinct and additive to the Landauer cost of erasure [3,4], the latter of which is achieved in the limit of zero dissipation.
For thermodynamic efficiency, the reset protocol must be designed around the expected initial state. But what if the initial state is unknown, or expectations are misaligned? Fig. 1 illustrates the thermodynamic cost of misaligned expectations when the RESET operation is applied to two qubits that the protocol is not optimized for. This exposes the risk of divergent dissipation upon overspecializationwhen the protocol operates on a state that is nearly orthogonal to the anticipated initial state q 0 .
For energetic efficiency in multiple use cases-say in resetting unknown qubits of a quantum computer-it is advisable when constructing such protocols to hedge thermodynamic bets. Bringing q 0 closer to the identity assures that no state is orthogonal to it.
Local control of composite systems Often, only local transformations are applied to globally correlated systems. For example, when computing, it is convenient to apply modular logic gates to implement complicated net transformations. Our main result implies thermodynamic consequences of this local control.
Suppose our system of interest is composed of N subsystems that live on the composite Hilbert space H = Whether preparing a Bell state, erasing quantum memory, or extracting work, no control protocol can be simultaneously thermodynamically optimal for all initial quantum states on which it operates. Inset: A quantum system ρt of two qubits is driven by a time-dependent Hamiltonian Hx t and a time-dependent interaction H int x t with two thermal reservoirs at different temperatures. Main: Suppose the control protocol x0:τ resets the two qubits in finite time, and achieves minimal dissipation when operating on the noisy Bell state: If the reset protocol is designed to be optimal for erasing the Ψ + Bell state (α = 0), then the same protocol approaches infinite dissipation as ρ0 approaches any of the Φ + , Φ − , or Ψ − Bell states orthogonal to it. For 0 < α 1, the dissipation Σρ 0 scales as ln(1/α) near these three Bell states. Whereas if α = 1-i.e., the reset protocol is optimized for erasing completely randomized classical bits-then any quantum state can be erased with no more than 2 ln(2)k B of dissipation beyond Σq 0 (where Σq 0 can be engineered to be arbitrarily small). This dissipation is distinct and additive to the Landauer cost of erasure.
N n=1 H n . The initial state ρ 0 may have both classical and quantum correlations among its constituent parts. Define ρ 0,n = tr H\Hn (ρ 0 ) to be the reduced density matrix of the n th subsystem. For any control protocol that is locally optimized, such that q 0 = N n=1 ρ 0,n and q τ = N n=1 ρ τ,n , the dissipation is the loss in total correlation: In the case of N = 2 subsystems, this is the change in quantum mutual information between them: ∆I[ρ t,1 ; ρ t,2 ].
This will be relevant when only local control is applied to globally correlated systems, when the baths do not further correlate the subsystems [29,30]. This implies dissipation from destroyed correlations during both local measurement and local erasure of entangled systems. And, since computations are often performed modularly, this may be an important contribution to heat generated during a logically irreversible computation. Further dissipation is expected when the system is not locally optimized.
Decoherence The process of decoherence implements the map ρ 0 → m Π m ρ 0 Π m . With minimal physical assumptions, it is plausible that a minimally dissipative initial state would be q 0 = m Π m ρ 0 Π m , since decoherence leaves this state unchanged. In such cases: Discussion We have produced a useful general result that exactly quantifies dissipation in finite-duration transformations of open quantum systems. When the system is initiated in any state other than the minimally-dissipative density matrix, the extra dissipation is exactly the contraction of the quantum relative entropy between them over the duration of the control protocol-the loss of distinguishability.
This has immediate consequences for thermally efficient quantum information processing. Crucially, a quantum control protocol cannot generally be made thermodynamically optimal for all possible input states, creating unavoidable dissipation beyond Landauer's in quantum state preparation. Meanwhile, it imposes extra thermodynamic cost to modular computing architectures, where one wishes to optimize the thermal efficiency of certain quantum operations without pre-knowledge of how they will fit within a composite quantum protocol.
Our results also complement related but distinct results on the initial-state dependence of free energy gain [31]. Appendix I unifies these results, providing a more general theory of state-dependence in energetic computation. Since our results accommodate arbitrary interactions with any number of thermochemical baths, they could be leveraged in future studies to analyze dissipation in relaxation to nonequilibrium steady states (see Appendix G). From a broader perspective, these results extend our understanding of effective irreversibility in quantum mechanics, despite its global unitarity.
Varying a single parameter c j,k of the initial density matrix yields the partial derivative: which leads us to evaluate the infinitesimal perturbations ∂λ0 ∂c j,k and ∂λτ ∂c j,k to the eigenvalues of ρ 0 and ρ τ respectively.
(We could alternatively choose to vary real-valued variables c (r) j,k and c j,k ) |j k| and differentiate with respect to these real variables. However, it conveniently turns out that Σ ρ0 is complex-differentiable in all complex-valued c j,k variables, so we can differentiate directly with respect to c j,k .) Starting with the eigen-relation: ρ 0 |λ 0 = λ 0 |λ 0 , we can take the partial derivative of each side: Left-multiplying by λ 0 |, and recalling that ρ 0 = j,k c j,k |j k|, we obtain: which yields The summations over λ 0 thus become: and Moving on to the slightly more involved perturbation, we use the eigen-relation: ρ τ |λ τ = λ τ |λ τ and again take the partial derivative of each side: Left-multiplying by λ τ |, and recalling that ρ τ = j,k c j,k tr B U x0:τ |j k| ⊗ b π (b) U † x0:τ , we obtain: which yields The summations over λ τ thus become: and λτ ∈Λρ τ Plugging in our new expressions for the λ 0 an λ τ summations in Eqs. (26), (27), (32), and (35), we obtain: so that we arrive at Eq. (10) of the main text.
This allows us to inspect local changes in entropy production (ρ 0 − ρ 0 ) · ∇Σ ρ 0 as we move from ρ 0 towards any other density matrix ρ 0 . By the convexity of quantum states, there is indeed a continuum of density matrices in this direction; so the sign of the directional derivative indeed indicates the sign of the change in entropy production for infinitesimal changes to the initial density matrix in the direction of ρ 0 .
Lemma 2. Dissipation is convex over initial density matrices.
Let ρ 0 = n Pr(n)ρ Eq. (37) is obtained from the recognition that entropy flow ∆S env is an affine function of ρ 0 , and so cancels between Σ ρ0 and n Pr(n)Σ ρ [n] 0 . Each of the square brackets then represents a Holevo information, before and after the transformation, respectively. The non-negativity is finally obtained by the information processing inequality applied to the Holevo information. (Non-negativity can be seen to follow from each n separately: I.e., D ρ with multiplicities inherited from the constituent spectra.
APPENDIX C: GENERALIZED q0 FOR NON-INTERACTING BASINS
It is possible that the evolution acts completely independently on distinct basins of state space. This will generically yield a nontrivial nullspace for argmin ρ0 Σ ρ0 . In such cases, it is profitable to generalize the definition of q 0 so that it includes the successive minimally-dissipative density matrices that carve out the independent basins on the nullspace.
We will show that, within each basin, the extra dissipation due to a non-minimally-dissipative initial density matrix is given exactly by the contraction of the relative entropy between the actual and minimally-dissipative initial density matrices under the same driving x 0:τ .
To make progress in this generalized setting, we must first introduce several new notions.
Definitions
Let P(H) be the set of density matrices that can be constructed on the Hilbert space H. I.e., We will denote the nullspace of an operator ρ as null(ρ). I.e.: null(ρ) = |η : ρ |η = 0 . Furthermore, let H sys be the Hilbert space of the physical system under study (not including the environment).
We can now introduce the successive minimally dissipative density matrices {q In the main text, where q has a nontrivial nullspace, we will also want to consider the minimally dissipative density matrix on the nullspace: q [1] 0 ∈ argmin ρ0∈P null(q Σ ρ0 . If q [1] 0 also has a nontrivial nullspace, then we continue in the same fashion to identify the minimally dissipative density matrix within the intersection of all of the preceding nullspaces. In general, the n th thermodynamically-independent basin has the minimally dissipative initial state: for n ≥ 1.
The n th minimally dissipative basin is the Hilbert space: H 0 \ 0 . We will employ the projector: 0 . Notably, these projectors constitute a decomposition of the identity I on the system's state space H sys : We can now define the minimally dissipative reference state q 0 , as if ρ 0 were minimally dissipative on each of the thermodynamically-independent basins on which it lives: It should be noted that the ρ 0 -dependence is only via the weight tr(Π H [n] 0 ρ 0 ) of ρ 0 on each thermodynamicallyindependent basin, used to linearly combine their contributions.
Generalized dissipation bound
With these definitions in place, let us now reconsider the task at hand.
If q [0] 0 has a nontrivial nullspace (and if Σ ρ0 is finite for all ρ 0 ), then there are thermodynamically isolated basins of state-space. In these cases, q (12) is no longer directly valid. However, for any two initial density matrices ρ 0 and r 0 , such that r 0 has full rank relative to ρ 0 , it is still true that: Indeed q 0 , as defined in Eq. (51), is gauranteed to have full rank, and so Eq. (52) is valid if we set r 0 = q 0 . Alternatively, we can set r 0 = q [n] 0 if we properly restrict ρ 0 .
To proceed, we recognize that ρ 0 can be decomposed via Eq. (50) as: where ρ 0 projects ρ 0 onto the minimally dissipative basins, whereas ρ coh 0 describes the state's coherence between these basins.
Since q [n] 0 is, by definition, the minimally dissipative density matrix on its subspace (and, since it has full rank on that subspace), we have that: As an immediate consequence of their definition, the elements of {q Together with Eq. (55) this leads to: Eq. (58) can be seen as the quantum generalization of the classical result obtained recently in Ref. [32]. The classical version of this result is relevant when the minimally dissipative probability distribution (q 0 ) does not have full support. Dissipation on other 'islands' are then considered. Our derivation points out the nuances of physical assumptions that go into the classical result, and refines the notion of 'islands' (here referred to as 'basins') on a more solid physical grounding. The extension of these results to other optimization problems, as discussed in Ref. [32], is also discussed in one of our later appendices. Crucially, Eq. (58) generalizes the classical result-allowing ρ [n] 0 to exhibit quantum coherence relative to the minimally dissipative state q [n] 0 . In addition to the drop in Kullback-Leibler divergence on the minimally-dissipative eigenbasis, the drop in coherence also contributes to dissipation.
In the quantum regime, there is yet further opportunity for generalization, if we consider the possibility of coherence among the non-interacting basins of state-space. This is the case of non-zero inter-basin coherence: ρ coh 0 = 0. To address this more general case, we recognize that where ∆C ρ t (ρ t ) is the change in inter-basin coherence: from time t = 0 to time t = τ . Meanwhile, is the extra entropy flow due to inter-basin coherence.
APPENDIX D: CHANGE IN RELATIVE ENTROPY DECOMPOSES INTO CHANGE IN D KL S AND CHANGE IN COHERENCES
Our main result, Eq. (13), gave the extra dissipationwhen the system starts with the initial density matrix ρ 0 rather than the minimally-dissipative initial density matrix q 0 -in terms of the change in relative entropies between the two reduced density matrices over the course of the transformation: We now show how this can be split into a change in Kullback-Leibler divergences plus the change in the coherence on the minimally-dissipative eigenbasis.
The classical probability distribution that would be induced by projecting ρ t onto q t 's eigenbasis is: ρ t and P t only differ when ρ t is coherent on q t 's eigenbasis.
The actual state's coherence on q t 's eigenbasis is given by the 'relative entropy of coherence' [25]: Expanding the relative entropy between ρ t and q t at any time yields: where we used the simultaneously-diagonalized spectral representations of ln P t = s∈Λq t ln P t (s) |s s| and ln q t = s∈Λq t ln q t (s) |s s|, and where P t (s) ≡ s| P t |s = s| ρ t |s and q t (s) ≡ s| q t |s are the probability elements of the classical probability distributions P t and q t on the simplex defined by q t 's eigenstates.
(Similar decompositions of the quantum relative entropy appear in recent thermodynamic results of Refs. [33] and [34], although in a more limited context.) Thus, the difference in entropy production can be expressed as: as in Eq. (16) of the main text.
In the classical limit, where there are no coherences, we recover the classical result obtained by Wolpert and Kolchin-sky in Ref. [20]: From Eq. (71), we see that the quantum correction to the classical dissipation is exactly the change of coherence on the minimally-dissipative eigenbasis.
APPENDIX E: JUSTIFICATION FOR APPROACH TO THE GIBBS STATE UNDER WEAK COUPLING
Consider a system in constant energetic contact with a single thermal bath of inverse temperature β = 1 k B T . Suppose the system is undriven (i.e., x t = x t = x for all t, t > 0), so that it experiences a time-independent Hamiltonian H x . From Ref. [35], we can deduce that the system together with part of the thermal bath will together approach a stable passive state under the influence of the remainder of the thermal bath. For large baths, this stable passive state limits to the Gibbs state for the joint system. If we furthermore take the limit of very weak coupling, then this also yields the Gibbs state for the reduced system since e β(Hx⊗I b +Isys⊗H b ) = e βHx ⊗ e βH b . The system-bath interaction H int x can be treated as a small perturbation to the steady state with vanishing contribution in the limit of very weak coupling.
Hence, if this system starts out of equilibrium in state ρ 0 , then it will simply relax towards the canonical equilibrium state π x = e −βHx /Z, where Z is the canonical partition function of the system.
The case of strong coupling is more tricky because of the possibility of steady-state coherences in the system's energy eigenbasis [36]. Nevertheless, there are small quantum systems of significant interest that are rigorously shown to approach the Gibbs state as an attractor, even with strong interactions [37,38].
APPENDIX F: DISSIPATION, WORK, AND FREE ENERGY
Time-dependent control implies work and, in the thermodynamics of computation, entropy production is typically proportional to the dissipated work [4,30]. This appendix relates these quantities.
Since we allow for arbitrarily strong interactions between system and baths, some familiar thermodynamic equa-tions must be revised in recognition of interaction energies. Most of these revisions have already been thought through carefully in Ref. [23]. In this appendix, we spell out some of the general relationships among entropy production, heat, work, dissipated work, nonequilibrium free energy, and so on. This allows our results to be reinterpreted in terms of the various thermodynamic quantities.
Work is the amount of energy pumped into the universe of discourse by the time-varying Hamiltonian. It is the total change in energy of the system and baths: Subtracting the heat yields: which is the First Law of Thermodynamics if the interaction energy is treated as part of the system's energy.
If there is a single grand canonical bath at temperature T , then entropy production is related to the dissipated work and the nonequilibrium free energy. In that case, the dissipated work is: We see that the dissipated work is the work beyond the changes in nonequilibrium free energy and interaction energy. Any work not stored in free energy or interaction energy has been dissipated.
The nonequilibrium free energy always satisfies the familiar relation F t = U t − T S t : where the nonequilibrium addition to free energy is: π xt = e −βHx t /Z xt is the Gibbs state induced by the instantaneous control, and F eq xt = −k B T ln Z xt is the equilibrium free energy of the system, which utilizes the partition function Z xt = tr(e −βHx t ).
Even if the interaction energy is large, we see that we recover the familiar thermodynamic relations, as long as there is negligible net change in interaction energy over the course of the protocol: tr(ρ tot
APPENDIX G: RELAXATION TO NESS
Suppose that the system is in constant contact with at least two different thermal or thermo-chemical baths. We may think, for example, of a stovetop pot of water which is hot at its base and cooler at its top surface. Such a setup famously allows for the existence of nonequilibrium steady states (NESSs), like Rayleigh-Bénard convection [39]. Our concise result-only needing to compare ρ t and q t at times 0 and τ -may be quite useful to circumvent otherwise daunting thermodynamic analyses. 5 At a smaller scale, our results should allow new approaches to analyzing the thermodynamics of biomolecules like sodium-ion pumps or ATP-synthase that reliably break time symmetry in their NESSs via differences in chemical potentials across cellular membranes [41][42][43].
While there is not expected to be a general extremization principle for finding NESSs, the mere existence of minimally-dissipating initial states-or maximally-dissipating initial states 6 -implies the inprinciple-applicability of our results for the thermodynamic analyses of general NESSs. Caveats aside, there is an obvious opportunity to apply our results to systems with NESSs that do extremize entropy production, like certain steady states in the linear regime [14,21].
APPENDIX H: RELATION TO ERROR-DISSIPATION TRADEOFFS
Under control constraints-like time-symmetric drivingwhere fidelity costs significant dissipation [44], we find that q 0 may be forced to have eigenvalues of order and thus D ρ 0 q 0 can diverge as ln (1/ ). This is consistent with the generic error-dissipation tradeoff recently discovered for non-reciprocated computations in Ref. [44], but only explains the error-dissipation tradeoff for logically irreversible transitions like erasure. For logically reversible but nonreciprocal transitions, all initial distributions suffer the same error-dissipation tradeoff. In those cases, the error-dissipation tradeoff is not a consequence of the contraction of the relative entropy discussed here, but rather follows more generally from the theory laid out in Ref. [44].
With unrestricted control, arbitrarily high fidelity can be achieved with bounded dissipation.
APPENDIX I: RELATED OPTIMIZATION PROBLEMS
Our result appears superficially similar to a recent result by Kolchinsky et al. [31], which describes the initial-state dependence of nonequilibrium free energy gain. The results are nevertheless distinct since the initial state that leads to maximal free energy gain is typically not the same as the initial state that leads to minimal dissipation. Yet the similarity of the two results suggests a more general overarching result. Indeed, we have found a general theorem that contains these results as important cases.
Let the initial joint state of the universe be a product state of the system and environment: ρ tot 0 = ρ 0 ⊗ ρ env 0 , and suppose that the joint system evolves according to some unitary time evolution, such that the reduced state at time τ is given by: ρ τ = tr env Uρ 0 ⊗ ρ env 0 U † . We can consider any function of the initial density matrix: and its minimizer: Proof. If a(ρ) is an affine function, then it can be written as a(ρ) = (ρ) + c, where where (ρ) is a linear function of ρ and c is a constant. Representing the initial density matrix in an orthonormal basis as ρ 0 = j,k c j,k |j k|, and differentiating f (ρ 0 ) with respect to the matrix elements of ρ 0 , we find: = (|j k|) + tr |j k| ln ρ 0 − tr tr env U |j k| ⊗ ρ env 0 U † ln ρ τ .
If q 0 has a non-trivial nullspace, then Thm. 2 can be extended as done in App. C.
The classical limit of Thm. 2 is closely related to a result recently derived in Ref. [32,Thm. 1].
Another possibility is obtained if we simply let a(ρ) = 0. Then we find a new result about the initial-state dependence of entropy change: where q 0 ∈ argmin ρ0 S(ρ τ ) − S(ρ 0 ).
A simple example reveals that these optimization problems indeed have different solutions (i.e., different q 0 s). Consider a double-well energy landscape. The right well is raised in a very short duration τ in which the system cannot fully relax. The initial distribution that minimizes dissipation primarily occupies the left well. The initial distribution that maximizes free energy gain primarily occupies the right well.
We obtain further interesting results when a is a nonlinear function-which indicates the growth of other physically relevant quantities-and we will report on these elsewhere.
APPENDIX J: AN OBSERVATION ABOUT RELATIVE ENTROPIES
It is interesting to compare our main result with an expression for entropy production that can be derived (following Ref. [23]) from Eq. (4): It is an interesting mathematical observation that: when q 0 ∈ argmin ρ0 D ρ 0 ⊗ b π (b) U † x0:τ ρ τ ⊗ b π (b) U x0:τ . This seems related to the Pythagorean theorem of information geometry, which utilizes the information projection [45], but nevertheless appears to be distinct. It would be interesting to understand under what circumstances a similar mathematical relation holds. Given the prevalence of relative entropies in thermodynamics and quantum information, perhaps that understanding would lead to further physical insights. | 8,303.4 | 2020-02-26T00:00:00.000 | [
"Physics"
] |
Cosmological perturbations from stochastic gravity
In inflationary cosmological models driven by an inflaton field the origin of the primordial inhomogeneities which are responsible for large scale structure formation are the quantum fluctuations of the inflaton field. These are usually computed using the standard theory of cosmological perturbations, where both the gravitational and the inflaton fields are linearly perturbed and quantized. The correlation functions for the primordial metric fluctuations and their power spectrum are then computed. Here we introduce an alternative procedure for computing the metric correlations based on the Einstein-Langevin equation which emerges in the framework of stochastic semiclassical gravity. We show that the correlation functions for the metric perturbations that follow from the Einstein-Langevin formalism coincide with those obtained with the usual quantization procedures when the scalar field perturbations are linearized. This method is explicitly applied to a simple model of chaotic inflation consisting of a Robertson-Walker background, which undergoes a quasi-de-Sitter expansion, minimally coupled to a free massive quantum scalar field. The technique based on the Einstein-Langevin equation can, however, deal naturally with the perturbations of the scalar field even beyond the linear approximation, as is actually required in inflationary models which are not driven by an inflaton field such as Starobinsky's trace-anomaly driven inflation or when calculating corrections due to non-linear quantum effects in the usual inflaton driven models.
I. INTRODUCTION
Inflation has become the paradigm for our understanding of the origin of the primordial inhomogeneities which are responsible for large scale cosmic structure. The typical inflationary scenario assumes a period of accelerated expansion in the early universe, usually driven by a scalar inflaton field, which provides a natural explanation for the homogeneity, isotropy and flatness problems of the standard big-bang cosmology [1,2,3,4,5]. The generation of structure is explained by the back-reaction effect of the quantum fluctuations of the inflaton field on the gravitational field which translate, after quantization, into non-trivial two-point correlation functions of the primordial gravitational fluctuations. These correlations give an approximate Harrison-Zeldovich spectrum for large scales [6,7,8,9,10,11]. The remarkable success of this scenario to explain the observed anisotropies of the cosmic microwave background [12,13,14,15] is today the most compelling reason which supports the inflationary paradigm [16,17], in spite of some interpretational problems such as the transition from quantum to classical fluctuations [18,19,20,21,22,23,24,25].
Semiclassical gravity is a mean field approximation that describes the interaction of quantum matter fields with the gravitational field, which is is treated as a classical geometry, and provides a suitable framework for the study of macroscopic black holes as well as scenarios in the early universe after the Planck time. In particular it accommodates the different inflationary models. The key equation in semiclassical gravity is the semiclassical Einstein equation where the expectation value of the stress tensor operator of the quantum matter fields is the source of the spacetime metric. In cosmology this is usually assumed to be a spatially homogeneous and isotropic Robertson-Walker spacetime. However, since this theory relies only on the expectation value, it completely misses the fluctuations of the stress tensor operator. Thus, when the back reaction of the inhomogeneous fluctuations of the inflaton field around the homogeneous background are relevant, as in the generation of primordial inhomogeneities, the semiclassical equation is insufficient.
In recent years a stochastic semiclassical gravity, or stochastic gravity, approach has emerged as an extension of semiclassical gravity which accounts for the quantum fluctuations of the stress tensor [26,27]. These fluctuations are characterized by the noise kernel, which is defined as the symmetrized two-point quantum correlation function of the stress tensor operator. The extension is based on the so-called Einstein-Langevin equation, which is a stochastic equation for the linearized gravitational perturbations around a semiclassical background. A Gaussian stochastic source with a correlation function determined by the noise kernel is the key ingredient of this equation. From the solutions of the Einstein-Langevin equation, the two-point correlation functions for the metric perturbations can be obtained.
Stochastic gravity provides an alternative framework to study the generation of primordial inhomogeneities in inflationary models. Besides the interest of the problem in its own right, there are also other reasons that make this problem worth discussing from the point of view of stochastic gravity. The Einstein-Langevin equation is not restricted by the use of linearized perturbations of the inflaton field. This may not be very important for inflationary models which are driven by an inflaton field which takes a non-zero expectation value, because the linear perturbations will give the leading contribution; although the need to consider higher-order corrections (from one-loop contributions) has recently been emphasized [28,29] (see also [30]). These contributions are in any case important in models such as Starobinsky's trace anomaly driven inflation [31], which rely on conformally coupled scalar fields with a vanishing expectation value. The corresponding Einstein equation is quadratic in these fields and the linear approximation becomes trivial.
In this paper we prove that the usual quantization for linear perturbations of both the metric and the inflaton field is equivalent to using the Einstein-Langevin equation when the latter is restricted to linearized inflaton perturbations, in the sense that the same results for the relevant correlation functions of the metric perturbations are obtained.
The plan of the paper is the following. In Sec. II a brief description of stochastic gravity is given. This is done in an axiomatic way by showing that the semiclassical Einstein equation can be consistently generalized in a perturbative way by including a Gaussian stochastic source with vanishing expectation value defined through the noise kernel. The dynamical equation for the metric perturbations is the Einstein-Langevin equation. An alternative derivation of this equation, reviewed in Appendix C, is based on the influence functional method due to Feynman and Vernon, which is generally used to describe the dynamics of open quantum systems, i.e., systems interacting with an environment [32,33]. Here the gravitational field plays the role of the system and the quantum matter fields play the role of the environment.
In Sec. III we discuss the linearized perturbations around a cosmological Robertson-Walker background coupled to a free massive scalar field minimally coupled to the curvature. This corresponds to the simplest model of chaotic inflation. The linearized Einstein-Langevin equations is then used to obtain an expression for the correlation function of the scalar-type metric perturbations. We concentrate on metric perturbations of scalar type because they are the only ones that couple to the inflaton perturbations in the linear approximation. Next, we use the standard linear theory of cosmological perturbations, quantize them and derive an expression for the symmetrized quantum correlation function of the scalar metric perturbations. This expression is then employed to show the equivalence between this correlation function and that derived from the Einstein-Langevin equation. An alternative proof of this equivalence is provided in Appendix E.
Note that whereas in stochastic gravity the metric is treated as a classical but stochastic field, in the usual approach to linear cosmological perturbations both metric and inflaton perturbations are quantized. Nevertheless, the correlation functions derived within the Einstein-Langevin approach agree with the symmetrized quantum correlations, similarly to what happens in simpler open quantum systems [34]. More specifically, the stochastic correlation functions derived from the Einstein-Langevin equation agree with the symmetrized quantum correlation functions of the theory of gravity interacting with N matter fields to leading order in 1/N [35]; this was shown in Refs. [36,37] for perturbations around a Minkowski background. In this sense the Einstein-Langevin equation can be regarded as a useful intermediary tool to compute the quantum correlations of metric fluctuations in the large N approximation. It should also be noted that there are situations for open quantum systems where, for a sufficient degree of environmentinduced decoherence that guarantees the absence of relevant interference effects, the temporal correlations of some actual properties of the system (corresponding to suitably smeared projectors) can be described in terms of classical stochastic processes governed by a Langevin equation [38]. In those cases the stochastic correlation functions obtained from the Langevin equation also describe such quasi-classical correlations of the system dynamics.
It is, however, important to stress that when one linearizes with respect to both the scalar metric perturbations and the inflaton perturbations, as in the case discussed here, the system cannot be regarded as a true open quantum system. The reason is that Fourier modes decouple and the dynamical constraints due to diffeomorphism invariance link the metric perturbations of scalar type with the perturbations of the inflaton field so that only one true dynamical degree of freedom is left for each Fourier mode.
In Sec. IV we explicitly compute the correlation functions for the scalar metric perturbations in a simple model of chaotic inflation using the Einstein-Langevin approach as described in the previous section. A quasi de Sitter expansion for the background is assumed and an almost Harrison-Zeldovich spectrum at large scales is obtained. We comment on the different approximations that one is naturally lead to consider within the two approaches.
Finally in Sec. V we conclude by summarizing our results and briefly discussing the changes that one would encounter when using the Einstein-Langevin equation if the inflaton perturbations were treated exactly, that is, beyond the linear approximation. We note in particular that the scalar, vectorial and tensorial metric perturbations are dynamically related in that case since they all couple to the inflaton perturbations. The metric perturbations can then be considered a true open quantum system.
Throughout the paper we use the (+, +, +) convention of Ref. [39]. We also make use of the abstract index notation of Ref. [40]. The Latin indices (a, b, c . . .) denote abstract indices, whereas Greek indices are employed whenever a particular coordinate system is considered [Latin indices such as (i, j, k . . .) are used instead when referring only to spatial components].
II. STOCHASTIC GRAVITY FORMALISM AND EINSTEIN-LANGEVIN EQUATION A. Stochastic gravity. General formalism
There are a number of situations, especially in black hole physics and cosmology, in which regarding spacetime as classical whereas the remaining matter fields are quantized has proved very fruitful. This is often considered a reasonable approximation as long as the typical length scales involved are much larger than the Planck length. A first step in that direction is to consider the evolution of quantum matter fields on spacetimes with non-vanishing curvature. The consistent formulation of quantum field theory on general globally hyperbolic spacetimes is nowadays well established for free fields [41,42], and significant progress has been made for interacting fields as well [43,44,45]. Up to this point the quantum matter fields are regarded as test fields evolving on a fixed geometry which is unaffected by their presence.
A second step is to consider the back reaction of quantum matter fields on the spacetime geometry by including the expectation value of the stress tensor operator of the quantum fields as a source of the Einstein equation for the spacetime geometry, which becomes then the so-called semiclassical Einstein equation. The expectation value of the stress tensor is divergent and a non-trivial renormalization procedure is required even for a free field in order to preserve general covariance. This can be achieved by using, for instance, dimensional regularization or point splitting and introducing suitable local counterterms, which are quadratic in the curvature, in the bare gravitational action. Any renormalization method can be used provided Wald's axioms [41,42] are satisfied, since this guarantees equivalent results.
The semiclassical Einstein equation was derived in Ref. [46] by considering the large N limit of N free scalar fields weakly interacting with the gravitational field so that the product of the gravitational coupling constant times the number of fields N remains constant as N tends to infinity; see also Ref. [47] for a related result concerning fermions. However, the semiclassical Einstein equation is most often introduced in an axiomatic way. The basic aspects of this framework, commonly known as semiclassical gravity [42,48], can be summarized as follows. Let us consider a manifold M with a Lorentzian metric g ab which is globally hyperbolic. Let us also consider a linear matter field evolving on that manifold. In the Heisenberg picture the scalar field operatorφ [g] satisfies the Klein-Gordon equation where ∇ a means covariant derivative with respect to the metric g ab , and the state of the scalar field, which is characterized by a density matrixρ [g], is assumed to be physically acceptable in the sense of Ref. [42]. This means that it is of the so-called Hadamard type, so that the expectation value for the stress tensor operator can be consistently renormalized. The set (M, g ab ,φ [g] ,ρ [g]) constitutes a self-consistent solution of semiclassical gravity if the following semiclassical Einstein equation is satisfied: where G ab is the Einstein tensor, T ab [g] ′ ren is the suitably renormalized expectation value of the stress tensor operator corresponding to the scalar field operatorφ [g] and α, β, Λ and κ are renormalized parameters (the prime in the expectation value is used to distinguish it from the expectation value introduced below). We considered natural units in which = c = 1, and introduced the notation κ = 8πG = 8π/m 2 p for the renormalized gravitational coupling constant where m p is the Planck mass. The local tensors A ab and B ab are obtained by functionally differentiating with respect to the metric terms in the action that correspond to the Lagrangian densities proportional to C abcd C abcd and R 2 , respectively, where C abcd and R are the Weyl tensor and the scalar curvature. These terms correspond to the finite part of the counterterms introduced in the bare gravitational action to cancel the divergences arising in the expectation value of the stress tensor [41].
From now on, and despite their purely geometric character, we will consider for notational simplicity that the last three terms on the left-hand side of Eq. (2) have been reabsorbed in the renormalized expectation value of the stress tensor operator, which we write now without the prime; this can be done consistently because ∇ a A ab = 0 = ∇ a B ab . Taking this into account, the semiclassical Einstein equation becomes where we should now keep in mind that the expectation value depends on the renormalized parameters Λ, α and β.
There are, however, situations in which the fluctuations of the stress tensor operator are important [49,50,51]. In Refs. [52,53] it was shown that the semiclassical Einstein equation (2) could be consistently extended to partially account for the fluctuations of the stress tensor operator by introducing a Gaussian stochastic source. More precisely, given a self-consistent solution of semiclassical gravity one can introduce the following equation for the metric perturbations h ab around the background metric g ab : where the whole equation should be understood to linear order in h ab . Note that throughout this paper indices will be raised and lowered using the background metric. The renormalized expectation value is computed with the scalar field operator satisfying the Klein-Gordon equation on the perturbed metric g ab + h ab and the Gaussian stochastic source ξ ab is completely determined by the following correlation functions: where we used . . . ξ to denote the expectation value with respect to the stochastic classical source ξ ab [g]. The operatort ab [g] is defined ast ab [g] ≡T ab [g] − T ab [g] and the bitensor N abcd (x, y), which determines the correlation function of the stochastic source, is computed using the scalar field operator satisfying the Klein-Gordon equation for the background metric g ab . The bitensor N abcd (x, y) is called the noise kernel, it describes the quantum fluctuations of the stress tensor operator and is positive-semidefinite. Strictly speaking, the previous definition for the operator t ab only makes sense when some kind of regulator is employed since both the operatorT ab [g] and the expectation value T ab [g] are divergent. However, the operatort ab is finite in the sense that one can compute any matrix element of this operator using a regularized version of the two terms that define it, and one finally gets a finite result when removing the regulator because the divergences coming from both terms cancel out exactly [53]. Hence, the noise kernel requires no renormalization whereas the divergences of the expectation value T ab [g + h] appearing in Eq. (4) are canceled by the counterterms whose finite contribution corresponds to the last three terms on the left-hand side. Furthermore, since ξ ab [g] ξ = 0, Eq. (4), which is called the Einstein-Langevin equation, reduces to the semiclassical Einstein equation for the metric perturbations h ab around the background metric g ab when taking the expectation value with respect to the stochastic source ξ ab . 1 This framework, in which the metric perturbations are regarded as a stochastic process satisfying the Einstein-Langevin equation, is usually referred to as stochastic gravity.
Similarly to what was done for the semiclassical Einstein equation, we will assume that the last three terms on the left-hand side of Eq. (4) are reabsorbed in the renormalized expectation value of the stress tensor operator, so that the Einstein-Langevin equation will be written from now on as where the superindex (1) means that only terms linear in the metric perturbations h ab are kept. This follows straightforwardly from the fact that Eq. (4) was considered only to linear order in h ab (the stochastic source ξ ab is regarded to be of the same order as h ab ) and that the zero order contribution is identically satisfied, since the background configuration was assumed to be a solution of semiclassical gravity. A necessary condition for the integrability of the Einstein-Langevin equation, via the Bianchi identity, is the conservation of the stochastic source. Hence, one must make sure that the stochastic source ξ ab [g] is covariantly conserved so that Eq. (7) is a consistent extension of the semiclassical Einstein equation (3). That the stochastic process ∇ a ξ ab (x) vanishes is a consequence of the stress tensor conservation on the background metric [52,53]. Furthermore, it can also be checked that the Einstein-Langevin equation is compatible with the gauge symmetry corresponding to infinitesimal diffeomorphisms. In fact, both the stochastic source and the remaining terms of the Einstein-Langevin equation are separately invariant under gauge transformations for the metric perturbations of the form h ab → h ab + ∇ a ζ b + ∇ b ζ a corresponding to infinitesimal diffeomorphisms generated by any arbitrary vector field ζ defined on the background spacetime [52,53].
We finish this general introduction to the Einstein-Langevin equation by briefly mentioning that there are derivations of the Einstein-Langevin equation in different cosmological settings making use of functional methods [54,55,56,57,58] or a derivation using arguments based on the renormalization group [59]. In Appendix C we sketch a derivation of the Einstein-Langevin equation (7) for the case of a general globally hyperbolic background spacetime using the influence functional formalism [53,60]. The Einstein-Langevin equation has also been applied to the study of fluctuations in black hole spacetimes [61,62,63].
B. Einstein-Langevin equation for cosmological perturbations
In this paper we will study small perturbations around a Robertson-Walker background when the matter source is a minimally-coupled scalar field with a quadratic potential. In fact, this corresponds to the simplest model of chaotic inflation with the scalar field playing the role of the inflaton field, but it is sufficient for our purpose of illustrating the relationship between the usual treatment of cosmological perturbations and those approaches based on the Einstein-Langevin equation within the framework of stochastic gravity. Furthermore, taking into account the assumptions made throughout the forthcoming sections, the generalization of our main conclusions and results to non-linear potentials should be rather straightforward as long as we keep to quadratic order in the scalar field perturbations when considering the potential.
Recall that the form for the line element of a general Robertson-Walker metric is where a (t) is called the scale factor and γ ij is the induced metric for the homogeneous spatial sections, which are maximally symmetric hypersurfaces. The line element of the spatial sections can have the three following forms γ ij dx i dx j = {dχ 2 + sin 2 χdΩ 2 , dr 2 + r 2 dΩ 2 , dχ 2 + sinh 2 χdΩ 2 } depending on whether the curvature is positive, zero, or negative, respectively. In terms of the conformal time coordinate η = dta −1 (t) the metric (8) becomes Before proceeding further it is convenient to introduce the following decomposition for the scalar inflaton field, which will be used throughout:φ where φ(η), which corresponds to the expectation value φ [g; x) of the inflaton field on the background metric, is a homogeneous classical-like (as an operator it is proportional to the identity) solution of the Klein-Gordon equation which is compatible with the background metric through the semiclassical Einstein equation (3). The operatorφ(x), which will be referred to as the inflaton field perturbations, corresponds to the quantum operator for a minimallycoupled massive scalar field whose expectation value vanishes on the background spacetime, i.e., φ[g; x) = 0. We will consider a Gaussian state for the inflaton field and, thus, for the inflaton field perturbations; see Appendix A for the definition and the basic properties of pure Gaussian states and the relationship between the state of the inflaton field and the inflaton field perturbations. It should also be stressed that there are many situations (e.g., in the context of stochastic inflation) in which the classical background configuration of the inflaton field will not be homogeneous over the whole spacetime. Nevertheless, this will not have observable consequences at present provided that the scale of the inhomogeneities is larger than the horizon before the last 60 e-folds of inflation. In fact, when studying models of eternal inflation [64,65,66] using the formalism of stochastic inflation [67], the expectation value of the inflaton field is no longer the relevant object. One should consider instead the amplitude of a given realization of the inflaton field smeared over scales slightly larger than the horizon radius right before the region that had left the self-regenerating regime and would eventually give rise to our visible universe underwent the last 60 e-folds of inflation. It has been argued that in those circumstances the smeared inflaton field behaves as a classical stochastic process. (This is closely related to the quantum to classical transition problem for the inflaton fluctuations [18,19,20,21,22,23,24,25].) If that is the case, one can use a particular realization of the smeared inflaton right before the last 60 e-folds of inflation as the classical background configuration φ(η) and treat it in the same way in which one would have dealt with a quantum expectation value.
Let us begin by discussing the semiclassical Einstein equation (3) for the background metric g ab defined by Eq. (8). The right-hand side of Eq. (3) is the properly renormalized expectation value for the stress tensor of the inflaton field operator, which satisfies the Klein-Gordon equation (1) on the background spacetime.
If we consider the general expression for the stress tensor operator of a minimally-coupled massive scalar field and use the decomposition of the scalar field introduced in Eq. (10), the expectation value for the stress tensor operator can be separated into three different contributions: where the subindices φφ, φϕ and ϕϕ are used to denote the contributions to the stress tensor operator which are respectively quadratic in φ(η), linear in both φ(η) andφ(x), and quadratic inφ(x). The first term depends just on the homogeneous solution φ(η), the second term vanishes since it is proportional to φ[g; x) and the third term, which is completely independent of the homogeneous part φ(η), is quadratic in the inflaton field perturbationsφ(x) and needs renormalization. The first term on the right-hand side of Eq. (12) will be denoted by T ab ≡ T ab [g] φφ ; see Appendix B for further comments on this notation. Taking into account the special form of the Robertson-Walker metric, in the basis associated with the conformal time and comoving spatial coordinates these components can be rewritten as where primes denote derivatives with respect to the conformal time η. In this coordinate system the time-time and space-space components of a −2 (η)T µν can be respectively identified with the energy density ρ(η) and the isotropic pressure p(η) of a perfect fluid. The components of Eq. (3) become then the usual Friedmann equations where H = a ′ /a and ǫ = 0, 1, −1 depending on whether the homogeneous spatial sections of the Robertson-Walker geometry are respectively flat, with positive curvature or with negative curvature. The third term on the right-hand side of Eq. (12), T ab [g] ren ϕϕ , will in turn have a similar structure to that of Eqs. (13) and (14) with diagonal non-vanishing components which can be regarded as corrections ∆ρ(η) and ∆p(η) to the energy density and pressure. This structure is necessary so that the solutions of Eq. (3) are of Robertson-Walker type, but there is a family of quantum states of the scalar field which gives rise to such a structure for T ab [g] ren ϕϕ . They can be characterized as follows. Since the Lie derivatives of the six spacelike Killing vectors which characterize a Robertson-Walker metric commute with the Klein-Gordon operator satisfying Eq. (1), one can introduce a unitary operator which implements at the quantum level the symmetries corresponding to the six Killing vectors and is preserved by the dynamical evolution. Consequently, the Hadamard function (the quantum expectation value of the anticommutator of the field) employed to compute the renormalized expectation value of the fieldφ(x) will respect the symmetries of the Robertson-Walker geometry provided that one considers a quantum initial state which is kept invariant, up to a phase, by the unitary operator associated with those symmetries. Throughout this paper we will consider this class of states (spatially homogeneous and isotropic). Nevertheless, being quadratic in the inflaton perturbations, which are considered in general to be much smaller during the inflationary period than the homogeneous background solution φ(η), the contribution from the last term in Eq. (12) and, hence, the corrections ∆ρ and ∆p, will in general be small compared to those from Eqs. (13) and (14) during the inflationary period. The usual treatments which keep to linear order in both the metric perturbations and the inflaton perturbations directly discard them. This is actually the situation that we will be interested in here. Therefore, the background solution for the scale factor a(η) is completely determined by Eqs. (15) and (16) without considering the corrections that come from the third term on the right-hand side of Eq. (12), which is approximated to linear order by T ab [g] ren ≈ T ab .
In addition, either from the conservation of the stress tensor, ∇ a T ab = 0, or by taking the expectation value of Eq. (1), the homogeneous background solution φ(η) is seen to satisfy the following Klein-Gordon equation on the background Robertson-Walker metric: Let us now consider the objects which appear in the Einstein-Langevin equation (7) and particularize them to the case addressed here. The geometric part, i.e., the components of the Einstein tensor for a linear perturbation h ab of the metric will be discussed in the next section. The contribution to the expectation value of the stress tensor which is linear in the metric perturbation, T (1) ab [g + h] ren , can be decomposed according to Eq. (10) as: where the whole inflaton field satisfies now the Klein-Gordon equation on the perturbed metricg ab = g ab + h ab , and∇ a means the covariant derivative with respect tog ab . The first term on the right-hand side of Eq. (18), T (1) ab φφ , depends on the scalar field only via the homogeneous background solution φ(η), which was already fixed by Eq. (17) together with Eqs. (15) and (16), and therefore the metric perturbations enter only through the explicit dependence of the stress tensor on the metric. Contrary to what happened in Eq. (12), the second term on the right-hand side of Eq. (18), T (1) ab φϕ , no longer vanishes since it is now proportional to φ[g + h] and the Klein-Gordon equation satisfied byφ[g + h] on the spacetime with the perturbed metricg ab , given by Eq. (19), has an inhomogeneous source term proportional to the metric perturbation h ab and the homogeneous background solution φ(η) which in general prevents its expectation value φ[g + h] from vanishing. Hence, the only non-vanishing contributions to the second term are those which depend implicitly on the metric perturbations through the quantum operator for the inflaton perturbationsφ[g + h].
Finally, the third term, T (1) ab ren ϕϕ , which requires renormalization, will have contributions with either explicit or implicit dependence on the metric perturbation. Not only the contributions which depend on the metric perturbations explicitly, but also those which depend implicitly viaφ[g + h] are ultimately quadratic in the inflaton perturbationŝ ϕ[g] [after solving Eq. (19) perturbatively in the metric perturbations]; otherwise they would vanish, as follows from the fact that φ[g] = 0.
Similarly to what was said concerning the last term in Eq. (12), the last term in Eq. (18) is not taken into account by usual approaches to cosmological perturbations, which keep to linear order in the inflaton perturbations as well as the metric perturbations. We will not consider these terms either in the next two sections, but some general remarks on how to deal with them, and possible implications, will be made in Sec. V.
Let us now briefly concentrate on the noise kernel, which accounts for the stress tensor fluctuations and characterizes the correlations of the stochastic source ξ ab . It is proportional to t ab [g],t cd [g] wheret ab =T ab − T ab , and is evaluated on the background metric. Using Eqs. (10) and (11) it can be separated into the following non-vanishing terms: where the first and second terms on the right-hand side are, respectively, quadratic and quartic in the inflaton perturbationφ[g]. We used a notation similar to that introduced in Eq. (12) since the first term on the right-hand side of Eq. (20) comes entirely from those contributions to the operatorst ab andt cd which are proportional to both φ(η) andφ[g], whereas the last term in Eq. (20) comes from the contributions to the stress tensor which are quadratic inφ [g]. The contribution to the noise kernel which depends on the background homogeneous solution φ(η) but not on the inflaton perturbationφ vanishes since, being proportional to the identity, the corresponding stress tensor operator coincides with its expectation value. The terms linear inφ[g] also vanish because φ[g] = 0. Finally, since we will be considering Gaussian quantum states for the inflaton perturbations (see Appendix A for a definition and a brief description of some basic properties of Gaussian states), the 3-point quantum correlation functions φ[g]φ[g]φ[g] are proportional to the expectation value φ[g] and, therefore, the contributions which are cubic inφ[g] vanish as well.
It is important to note that both the quadratic and the quartic contributions to the noise kernel are separately conserved since both φ(η) andφ[g; x) independently satisfy the Klein-Gordon equation (10) on the background geometry; recall that φ(η) = φ [g] . Due to this fact, we can consistently consider a pair of independent stochastic sources ξ 1 ab and ξ 2 ab associated with each term so that ξ ab = ξ 1 ab + ξ 2 ab with ξ 1 ab ( The integrability of the Einstein-Langevin equation with any of the two sources is then guaranteed because both sources are separately conserved. In the next section we will show that keeping only ξ 1 ab , which can be thought to be of the same order asφ, the results obtained using the Einstein-Langevin equation and those from the usual treatments which quantize the linearized theory for both the metric and the inflaton perturbations are equivalent. On the other hand, some of the main features and consequences of the source ξ 2 ab , which can be regarded as being of quadratic order inφ, will be briefly discussed in Sec. V and studied in more detail in Ref. [35]. Of course, when considering the stochastic source ξ 2 ab , the last term on the right-hand side of Eqs. (12) and (18) should also be considered since their contribution is of the same order as that of ξ 2 ab .
A. Gauge invariant formalism for linearized cosmological perturbations
Let us consider small metric perturbations around a fixed Robertson-Walker background geometry. It can be shown [68] that the most general expression for the components of metric perturbations in some particular coordinate system can be written as which depends on ten functions:φ, ψ, B and E, the two independent components of each transverse vector S i and F i , and the two independent components of the traceless and transverse symmetric tensor h ij . The vectors S i and F i as well as the tensor h ij are tangent to the isotropic and homogeneous spatial sections of the Robertson-Walker spacetime, but depend in general on the conformal time η which labels each spatial section. Furthermore, the notation |i is used to denote the covariant derivative associated with the metric γ ij induced on these spatial sections. The transversality condition for the vectors and tensor is then written as S i |i = 0, F i |i = 0 and h i j|i = 0. The global factor a 2 (η) is introduced for later convenience, but could be reabsorbed. The metric perturbations will henceforth be treated linearly.
Four functions describing the metric perturbations are of scalar type, four more are of vector type and finally there are two which are of tensor type, according to their transformation properties on the three-dimensional spatial sections [68,69,70]. These types are preserved by time evolution provided that the perturbations of the matter sources around the configuration generating the background Robertson-Walker geometry are also treated linearly. Those ten functions do not characterize in a unique way non-equivalent perturbed geometries since they may arise not only due to real perturbations of the geometry but also to changes of the mapping from the background manifold to the perturbed one. Hence, a diffeomorphism generated by a vector field ζ, considered to be of the same order as the metric perturbations, would give an extra contribution L ζ g ab to the metric perturbation h ab , where g ab is the background metric. These local diffeomorphisms do not preserve in general the scalar, vectorial or tensorial nature of the metric perturbations.
There are different approaches to overcome the difficulties derived from this gauge freedom. One approach is to fix the gauge [71] so that further changes on the metric perturbations resulting from coordinate changes, are not allowed. This can be achieved by fixing some of the ten functions characterizing the components of the metric perturbations either directly specifying some components of h ab or imposing relations between them. A second approach, first used by Bardeen [69], is based on the introduction of so-called gauge-invariant variables which corresponds to using linear combinations of those ten functions which remain invariant to linear order under diffeomorphisms generated by any vector field ζ. One can always argue that those gauge-invariant variables coincide with the value taken by the functions appearing in Eq. (21) (or some linear combination of them) in some particular gauge, as follows from the remark that the components of any tensorial object referred to a particular and fixed coordinate system do not change when are reexpressed in terms of some new coordinates [72].
From now on we will consider spatially flat Robertson-Walker metrics, i.e. γ ij = δ ij in Eq. (8), and concentrate on scalar-type metric perturbations. The motivation for the latter is that scalar-type metric perturbations are the only ones which couple to matter sources characterized by scalar functions when both metric perturbations and matter perturbations (the inflaton perturbations in our case) are treated linearly. Only two true kinematical degrees of freedom (i.e., before imposing the Einstein equation) exist for this type of perturbations, in the sense that from the four arbitrary functions characterizing scalar metric perturbations, the equivalence classes invariant under local diffeomorphism transformations are completely characterized by two arbitrary functions [68,73,74,75]. A particular example corresponds to the following two linear combinations of the four functionsφ, ψ, B and E, which are invariant under local diffeomorphisms: These gauge-invariant variables were first introduced by Bardeen [69] with the notation Φ A = Φ and Φ H = −Ψ.
One can also define a gauge-invariant version of the linear perturbations of the Einstein tensor, (G inv ) b a , which depends only on the gauge-invariant functions Φ and Ψ, and is invariant under the same kind of local diffeomorphism which preserve the scalar nature of the metric perturbations characterized by Φ and Ψ; see Ref. [74,75] for details. In fact, the gauge-invariant perturbations (G a of the Einstein tensor coincide with the actual components of the linear perturbations of the Einstein tensor in the so-called longitudinal gauge, which corresponds to taking E = B = 0. Similarly, one could also define a gauge-invariant version of the stress tensor linear perturbations and write a version of the Einstein equation for the metric perturbations with both sides explicitly invariant; recall that the whole linearized Einstein equation is itself gauge invariant. We will follow an alternative procedure which yields equivalent results. The idea is to consider the components of the Einstein equation in the longitudinal gauge and notice, as will be explicitly shown below, that all the geometric dependence can be written entirely in terms of the gauge invariant variables Φ and Ψ since the only non-vanishing scalar contributions to the metric perturbations in the longitudinal gauge,φ and ψ, coincide with Φ and Ψ. In the longitudinal gauge the expression of the perturbed metric for scalar type perturbations on a spatially flat Robertson-Walker background in terms of the two gauge-invariant functions Φ(x) and Ψ(x) is and the components of the linear perturbation of the Einstein tensor are where H = a ′ (η)/a(η), D = Φ − Ψ, ∇ 2 = δ ij ∂ i ∂ i and, as we mentioned above, primes denote derivation with respect to the conformal time η. The Einstein equation for the linear perturbations of the metric is where the right-hand side corresponds to those terms which are not included in the background stress tensor T b a and are at most linear in the metric perturbations (some terms from the stress tensor on the background geometry, T (0) b a , are present because the scalar field is also perturbed). Note that at the classical level one should simply substitute the unperturbed stress tensor T b a for T a has non-trivial additional components in stochastic gravity or when quantizing both the metric perturbations and the scalar field; see the last paragraph of Appendix B for additional discussion on the notation and related points. Furthermore, from now on we will only consider terms which are linear in either the metric perturbations or the inflaton field perturbations ϕ, which are both assumed to be of the same order. The contribution to the stress tensor of these linear perturbations will be denoted by δT b a . Hence, taking all this into account, the components of the Einstein equation for linear scalar perturbations of the metric become Let us remember that the expression for the stress tensor of the free massive field ϕ, which is minimally coupled to the spacetime curvature and evolves on the perturbed metricg ab = g ab + h ab , is The components for the linear perturbations of the stress tensor, δT b a , in the basis associated with the conformal time and comoving spatial coordinates are then straightforwardly obtained: Taking into account the fact that δT j i is diagonal, one can use Eq. (27) [see also Eq. (25)] with i = j to conclude that Φ and Ψ are equal [74,75], except for a possible homogeneous component (independent of the spatial coordinates), which should be included in the background scale factor. Alternatively, the same conclusion can also be reached by considering the sum of all the diagonal elements of the ij-components of Eq. (27) together with Eqs. (30) and (31) to substitute ϕ in terms of Φ and Ψ, which yields ∇ 2 (Φ − Ψ) = 0 and hence Ψ = Φ provided that they vanish at infinity.
From the Friedmann equations (15) and (16) for the background solution, we have and we can use this equation to reexpress the terms in Eqs. (29)-(31) which are linear in Φ. Substituting these terms into the perturbed Einstein equations, given by Eq. (27), we finally get Similarly, the Klein-Gordon equation for the inflaton perturbations can be obtained by linearizing in both the metric perturbations Φ and the inflaton perturbations ϕ the exact Klein-Gordon equation for the whole inflaton field φ(η) + ϕ(x) on the perturbed geometry, Eq. (19), and making use of the fact that the homogeneous background solution φ(η) satisfies the Klein-Gordon equation on the background spacetime, Eq. (17). It can also be obtained from the conservation equation, to linear order in the metric perturbations, of the linearly perturbed stress tensor. The result is where we have already taken into account that Ψ = Φ.
B. Einstein-Langevin equation for linearized cosmological perturbations
Using the results of the previous subsection, the Einstein-Langevin equation (7) can be particularized to the case of scalar-type metric perturbations around a Robertson-Walker background geometry with the following result: where we have used Eqs. (23)- (25) for the linearized Einstein tensor and we have considered the stress tensor operator δT b a , which results from keeping terms linear in either the inflaton perturbations or the metric perturbations. The notation δT b a Φ is equivalent to δT b a [g + h] for the particular case of scalar metric perturbations that we are considering. Note, in addition, that all the contributions to δT b a Φ are, explicitly or implicitly, proportional to the metric perturbations since otherwise they would be proportional to φ[g] , which vanishes. In fact, this turns out to be important so that , which is the object that appears in the Einstein-Langevin equation, when one keeps to linear order in the inflaton perturbations, i.e., when only the first two terms on the right-hand side of Eq. (18) are considered.
The three equations corresponding to the spatial components with equal indices of the Einstein-Langevin equation are equivalent due to the symmetries of the Robertson-Walker metric and those of the Gaussian state of the inflaton perturbations being considered, which was chosen to be compatible with those symmetries. On the other hand, the equation for the spatial components with different indices can be used in a similar way to that of the previous subsection in order to show that the gauge invariant functions for the scalar metric perturbations Φ(x) and Ψ(x) coincide. In this case it is also necessary that the spatial components of the stochastic source ξ ij (x) with indices i = j vanish identically. Indeed, since ξ ab (x) is a Gaussian stochastic process with zero mean, ξ ij (x) will vanish provided that ξ ij (x)ξ cd (y) ξ = 0, which can be argued as follows. The correlation function for ξ ab is defined by the noise kernel and, as we are keeping to linear order in the inflaton perturbations, only the first contribution in Eq. (20), vanishes for i = j since δT ij = 0 in that case, as follows from Eq. (31) with the inflaton perturbation promoted to a quantum operator. Hence, from now on we will take Ψ = Φ. Eq. (39) is then trivially satisfied for i = j and for i = j it reduces to (no summation should be understood over the repeated index i) It is clear that Eqs. (37)- (39) are redundant since we have three equations but only two variables to be determined: the function Φ characterizing the metric perturbations of scalar type and the expectation value of the quantum operator for the inflaton perturbations on the spacetime with the perturbed metric, φ[g + h] , which will also be denoted in this case by φ Φ . However, despite the apparently excessive number of equations, the system is integrable and solutions can be found. This fact is guaranteed by the Bianchi identity provided that the source of the Einstein-Langevin equation is conserved. This is indeed the case: the averaged and stochastic sources are separately conserved. On the one hand, the conservation of δT ab Φ is equivalent to the Klein-Gordon equation for the expectation value φ Φ , which is completely analogous to Eq. (36): On the other hand, the conservation of the stochastic source is a consequence of the conservation of the noise kernel, which in turn relies on the fact that the quantum operator for the inflaton perturbationsφ[g] satisfies the Klein-Gordon equation on the background spacetime, ∇ a ∇ a − m 2 φ(x) = 0. Taking all these considerations into account, the Klein-Gordon equation (41) can be used to obtain the expectation value φ Φ in terms of Φ. We can then easily write the expectation value of the stress tensor linear perturbations δT b a Φ in terms of Φ and use any of the constraint equations, Eq. (37) or (38) to express Φ entirely in terms of the stochastic source ξ ab ; to be specific, in this subsection we will consider Eq. (38). The spatial derivatives can be easily handled by working in Fourier space. Hence, in the rest of this section we will work with Fourier transformed expressions in the spatial coordinates. A subindex k will denote the three-dimensional comoving momentum vector k that labels each Fourier mode in flat space, i.e., Thus, the Fourier-transformed version of Eq. (38) is where k i is the comoving momentum component associated with the comoving coordinate (43) is a first order linear integro-differential equation with an inhomogeneous term corresponding to the 0i component of the stochastic source ξ b a . Therefore, one can always write the solution to Eq.
where Φ ret is the retarded propagator associated with Eq. (43). The correlation function for the scalar metric perturbation regarded as a solution of the stochastic differential equation (43) corresponds to where . . . ξ denotes the average over all possible realizations of the stochastic source, as previously defined. From now on we will concentrate solely on the last term, which comes entirely from the solutions of the inhomogeneous equation; see Appendix D for a discussion on the role of the initial conditions and the contributions of the homogeneous solution to the correlation function. The correlation function has then the following form: where we used the notation A T (η, η ′ ) = A(η ′ , η) and A · B = ∞ η0 dη A(η)B(η), and the factors a 2 (η ′ 1 ) and a 2 (η ′ 2 ) were simplified when lowering the spatial indices with the background metric in the last equality. Since we are linearizing in the inflaton perturbations, only the first term on the right-hand side of Eq. (20) should be considered. The expression for the Fourier-transformed version of the noise kernel then becomes where δt ab = δT ab − δT ab , as defined earlier, and . . . Φ=0 is the expectation value for the product of quantum operators δt ab with the fieldφ evolving on the background metric. We finally obtain the following expression relating the correlation function for the metric perturbations and the fluctuations of the stress tensor operator: A detailed example of this kind of computation is given in the next section, where the correlation function of scalartype metric perturbations will be computed for the particular case in which the background solutions for φ(η) and a(η) correspond to a period of slow-roll inflation. We end this subsection by working out the explicit expression for the 0i component of the expectation value δT b a Φ . From Eq. (30) we get and everything reduces to compute the expectation value φ k (η) Φ . One way of obtaining it is by regarding Φ k as an external source of the Fourier-transformed version of the linearized Klein-Gordon equation (41) and solving the corresponding inhomogeneous equation perturbatively so that is the solution of the inhomogeneous equation with vanishing initial conditions, which is proportional to the metric perturbation Φ k and can be written as (41) with Fourier-transformed spatial coordinates is given bȳ Substituting Eq. (51) into Eq. (50) and the result into Eq. (49) one gets the following result for the expectation value (δT i 0 ) k Φ : Note that this expression for the expectation value of the stress tensor operator requires no renormalization because we linearized with respect to the scalar field perturbations; see Appendix C for further comments on this point. Furthermore, in Appendix C we also show that the expectation value obtained above is in agreement with the general expression for the expectation value of the stress tensor which follows from the approach to the Einstein-Langevin formalism based on functional methods.
C. Equivalence with the usual quantization methods
In this subsection we will show that the result for the correlation function of the metric perturbations obtained in the previous subsection using the Einstein-Langevin equation and linearizing in the inflaton perturbations coincides with the result which follows from the usual quantization procedures in linear cosmological perturbation theory; see for instance Refs. [73,74,75].
Let us promote the scalar-type metric perturbations Φ and the inflaton perturbations ϕ to quantum operators. Eqs. (33)-(35) then become equations for the operators in the Heisenberg picture. In particular, we will concentrate on the temporal components of the Einstein equation where the quantum operator for the inflaton perturbationsφ[g + h], on which δT ab |Φ depends, satisfies the linearized Klein-Gordon equationφ The situation is completely analogous to that of the previous subsection except for the fact that the metric perturbation Φ(x) is now a genuine quantum operator instead of a stochastic c-number. Thus, taking the Fourier transform for the spatial coordinates and proceeding in a similar fashion to the previous subsection, the Klein-Gordon equation (55) can be solved with the following result: Taking into account Eq. (56), one could use any of the constraint equations (53) or (54) to express the quantum operator for the metric perturbationΦ entirely in terms of the operator for the inflaton perturbationsφ (0) [g] (in addition to the scalar functions φ(η) and a(η) characterizing the background solution), which satisfies the Klein-Gordon equation on the unperturbed geometry. However, before proceeding further it is convenient to discuss some useful expressions relating δT ab and its expectation values on both the background spacetime and the perturbed geometry. The stress tensor operator δT ab |Φ, which is linear in bothφ[g + h] andΦ, can actually be written as a linear combination of terms proportional toφ (0) [g], the inflaton perturbations on the background metric, and terms proportional toΦ. The latter correspond to terms coming either from the explicit dependence of the stress tensor on the metric, which give a local contribution, or from the dependence ofφ[g + h] on the metric perturbations according to Eq. (56). In fact, since Eq. (56) is identical to Eq. (50) when substituting the stochastic function Φ k (η) by the operatorΦ k (η), it is clear that all the terms proportional toΦ in δT ab |Φ are identical to the terms proportional to Φ in the operator δT ab [g + h] considered in the previous subsection. Furthermore, since φ (0) [g] = 0, those terms were identical to δT ab Φ , where δT ab Φ should be understood as the result of replacing Φ withΦ in the expectation value δT ab Φ of the previous subsection. Hence, we have where we used in the last equality the fact that δT ab Φ =0 actually vanishes. Eq. (57) can be written as where δt ab = δT ab |Φ =0 − δT ab Φ =0 . It should be remarked that taking the expectation value with respect to some quantum state of the field ϕ should be considered with caution here since, due to the constraint equations (53) and (54), the operatorsφ andΦ are not independent. Thus, strictly speaking, δT ab Φ should be regarded in this context merely as a notation for those terms of δT ab |Φ which are proportional toΦ, in contrast to those proportional toφ (0) [g]. Substituting Eq. (58) into any of the constraint equations (53) or (54), one could easily obtain the metric per-turbationΦ in terms of the operator δt ab constructed with operators for the inflaton perturbations evolving on the background metric. In order to compare in detail with the result of the previous subsection, where the Einstein-Langevin equation was used, we will explicitly consider the case in which the constraint equation (54) is used. Having substituted δT ab |Φ by δt ab + δT ab Φ into the Fourier-transformed version of Eq. (54), we have Taking into account that δT i 0 Φ is linear inΦ, one can obtain the following expression forΦ in terms of k is a solution of the homogeneous version of Eq. (59) and where G k . Using Eq. (61) and concentrating on the inhomogeneous contribution (a discussion of the homogeneous solution and its relationship to the initial conditions is given in Appendix D), the symmetrized two-point quantum correlation function for the metric perturbation operatorΦ can be written as Thus, we can see that the result for the symmetrized quantum correlation function of the metric perturbations coincides with the stochastic correlation function (48) obtained in the previous subsection using the Einstein-Langevin equation. We end this section by making a few remarks concerning the issue of the normalization of cosmological perturbations. In principle, one could differentiate Eq. (54) with respect to the conformal time (the spatial derivatives can be easily eliminated by working in Fourier space) and combine it with Eq. (53) to obtain a linear second order differential equation for the metric perturbation operatorΦ. However, when trying to quantize a theory beginning with the equations of motion instead of an action, one faces a normalization ambiguity which stems from the fact that, although any pair of actions that differ in a constant factor yield the same equations of motion (either classical or for quantum operators in the Heisenberg picture), their corresponding quantum theories are not completely equivalent. In particular, the quantum correlation functions for a given state (e.g. the fundamental state) do not coincide. For a linear theory they actually differ by some power of a constant factor which is precisely the square root of the proportionality constant between the two actions. This is the reason why in Ref. [74], when quantizing the theory for linear perturbations, the final action was obtained from the original linearized action for a scalar field evolving on a metric perturbed around a given background geometry together with the linearized Einstein-Hilbert action for the perturbations of that metric. That was done by using the constraint equations to reduce the whole action to that for the only true dynamical degrees of freedom. It was precisely in order to avoid the normalization ambiguity explained above that such a procedure, which turns out to be rather cumbersome, was used instead of working directly with the equations of motion and finding at the end an action which corresponds to the equation of motion for the true dynamical degree of freedom.
On the other hand, the method employed in this section is not affected by such a normalization ambiguity because, as can be seen from Eqs. (54) and (30), the constraint equation relates the operator for the metric perturbations to the operator for the inflaton perturbations on the background metric. The normalization of the latter operator is already determined by the usual procedure of quantization starting from the action of a scalar field on a fixed spacetime geometry. Hence, the key point was to separate the inflaton perturbation operatorφ satisfying the Klein-Gordon equation (55) into a contributionφ (0) [g] which can be regarded as the inflaton perturbation evolving on the fixed background spacetime plus a contribution proportional to the metric perturbation operatorΦ, and use then the constraint equation to expressΦ entirely in terms ofφ (0) [g]. In contrast with the approach of Ref. [74], this procedure does not give an explicit expression for the reduced action or even the equation of motion for an isolated true dynamical degree of freedom, but it is rather useful (and sufficient) in order to compare with the results obtained in the previous subsection by means of the Einstein-Langevin equation.
IV. PARTICULAR EXAMPLE: COMPUTATION OF THE POWER SPECTRUM FOR LARGE SCALES IN A SIMPLE INFLATIONARY MODEL
In this section we will apply the method developed in Sec. III B to studying the particular example of metric fluctuations induced by the quantum fluctuations of the inflaton field in the context of a simple model of chaotic inflation corresponding to a free minimally-coupled massive scalar field. In order to carry out explicit computations, we will assume that the Robertson-Walker background geometry is close to the de Sitter geometry. For models with exponential inflation, as the one being considered here, this approximation is reasonable during the inflationary period, in which the so-called slow-roll parameters controlling the deviations from de Sitter geometry are small, but not for later times. One can, nevertheless, obtain useful results from a cosmological point of view because those scales which are of cosmological interest at present correspond to scales which left the horizon during the inflationary period. This can be understood as follows. On the one hand, the evolution of gravitational perturbations outside the horizon is fairly simple, as can be understood from causality arguments [11,74], and rather independent of the particular dynamics of the matter sources. On the other hand, the evolution when the scale reenters the horizon later on during the radiation and matter dominated eras has been widely studied using the Newtonian approximation [76,77].
We stress that the results obtained in this section, which are based on the use of the Einstein-Langevin equation, are not new. They are basically in agreement with most of the literature based on the simultaneous quantization of gravitational perturbations and inflaton perturbations when both are treated linearly 2 . Of course, this fact ultimately follows from the equivalence between both approaches established in Sec. III C (as well as in Appendix E). Thus, the purpose of this section is to illustrate with a simple but relevant example how the Einstein-Langevin equation can be useful to obtain explicit results concerning cosmological perturbations.
Let us start by recalling the expression for the 0i component of the Einstein-Langevin equation which was obtained in Sec. III B working in Fourier space for the spatial components: The expectation value of the linearized stress tensor operator is given by Eq. (52) and is non-local in the conformal time. In general, this fact makes it difficult to find an analytic expression for the solution of the Einstein-Langevin equation.
One possible approach is to realize that there is a certain linear combination of the different components of the Einstein-Langevin equation for which all the contributions from the non-local terms cancel out, as well as those from the stochastic source (a detailed proof and discussion is provided in Appendix E). In that case the equation that one needs to solve, Eq. (E5), is a linear second-order ordinary differential equation. In fact, this equation has the same form as one often considered in standard treatments of linearized cosmological perturbations (see Eq. (6.48) in Ref. [74]), and one can take advantage of the existing methods and approximation schemes for solving it. Nevertheless, for illustrative purposes we will not follow this approach in this section. We will directly consider Eq. (63), neglect its non-local part and concentrate on the fluctuating part (neglecting the non-local term is not necessary, but it simplifies the problem considerably for a quick calculation). 3 Eq. (63) then becomes from which we can obtain the metric perturbation Φ k in terms of the stochastic source (ξ 0i ) k . We need the retarded propagator for the gravitational potential Φ k , i.e., the required Green function to solve the inhomogeneous first order differential equation (64) with the appropriate boundary conditions: where f (η, η ′ ) is a homogeneous solution related to the chosen initial conditions. In particular, if we take f (η, η ′ ) = −θ(η 0 − η ′ ) a(η ′ )/a(η), we have G ret k (η, η ′ ) = 0 for η ≤ η 0 , which gives the stochastic evolution of the metric perturbations for η > η 0 due to the effect of the stochastic source after η 0 . The correlation function for the metric perturbations is then given by the following expression: The correlation function for the stochastic source is, in turn, connected with the stress tensor fluctuations: where the delta function follows from spatial translational invariance and G } is the kmode Hadamard function for a free minimally-coupled scalar field which is in a state close to the Bunch-Davies vacuum 2 More specifically, we will obtain a Harrison-Zeldovich spectrum for the scalar metric perturbations with an amplitude which has the right dependence on the parameters of the problem (the Planck mass and the mass of the quadratic inflaton potential). However, our simple calculation does not give the right result for the spectral index: it gives a spectral index whose value is exactly one (rather than slightly smaller than one). In fact, one can explicitly check that the three main approximations that will be employed in this section (namely, neglecting the non-local terms, considering a de Sitter background and computing the quantum correlation function for the inflaton field using the massless approximation) all contribute to a comparable deviation from the exact result for the spectral index, whereas the correct result is obtained when none of the approximations are made. (All this can be checked by proceeding analogously to the calculation in Sec. 8.2.2 of Ref. [75].) 3 One can see from our derivations in Sec. III that neglecting the non-local term is equivalent to neglecting the terms proportional to the metric in Eq. (41).
The result to lowest order in the mass m of the inflaton field and the slow-roll parameters is: where we used the lowest order approximation forφ(t) during slow-roll:φ(t) ≃ −m 2 p (m/m p ); overdots denote here derivatives with respect to the physical time t. We considered the effect of the stochastic source after the conformal time η 0 . Notice that the result (68) is rather independent of the value of η 0 provided that it is negative enough, i.e., it corresponds to an early enough initial time. This weak dependence on the initial conditions is fairly common in this context and can be qualitatively understood as follows: after a sufficient amount of time, the accelerated expansion for the quasi-de Sitter spacetime during inflation effectively erases any information about the initial conditions, which is redshifted away. The actual result will, therefore, be very close to that for η 0 = −∞: One remark concerning the massless approximation for the computation of the Hadamard function of the inflaton perturbations is needed. It is clear from the equation for the scalar field modes that when one considers scales much smaller than the Compton wavelength of the inflaton field, i.e., k/a(η) ≫ m, the effect of the mass term can be neglected. On the other hand, for scales larger than the Compton wavelength one could object that the mass term should no longer be negligible. However, it can be argued that the mass term can also be neglected for large scales provided that the Compton wavelength is much larger than the horizon (the Hubble radius H −1 ), i.e., H ≫ m. The argument goes as follows. For a massless minimally-coupled scalar field in de Sitter spacetime the modes become effectively frozen after leaving the horizon: k/a(η) < H. On the other hand, for a massive scalar field, the modes decay approximately like exp(−m 2 ∆t/3H) outside the horizon, but this decay will not be important if m 2 /H 2 is small enough. In particular, if 3H 2 /m 2 60, the decay factor exp[−(m 2 /3H 2 )H∆t] will not be too different from one for those modes that left the horizon during the last sixty e-folds of inflation (H∆t = 60 with ∆t being the time between horizon exit and the end of inflation), which includes all the relevant cosmological scales since the scale that left the horizon sixty e-folds before the end of inflation corresponds to the size of the visible universe at present; any feature with a scale larger than the visible universe appears to us as observationally indistinguishable from a homogeneous one. Hence, due to the special behavior of the modes outside the horizon, even when considering scales which became much larger than the Compton wavelength before the end of inflation, k exp(−H∆t) < m, it is reasonable to approximate a massive scalar field with a massless one as long as H ≫ m, which happens to be the case in most slow-roll inflationary models and in particular for the simple example considered in this section [5].
Let us consider the cosmological implications which can be extracted from Eq. (69), especially those related to large-scale gravitational fluctuations. These fluctuations are believed to play a crucial role in the generation of the large-scale structure and matter distribution observed in our present universe [77]. They are also closely connected with the anisotropies in the CMB radiation, which decoupled from matter about 4 × 10 5 years after the Big Bang and provides us with very valuable information about the early universe [75,76].
From the analysis of our final result in Eq. (69) two main well-known facts can be concluded. First, an almost Harrison-Zeldovich scale-invariant spectrum is obtained for large scales. Indeed, for scales clearly outside the horizon at the times η and η ′ , i.e., kη, kη ′ ≪ 1, the right-hand side of Eq. (69) becomes proportional to k −3 δ( k + k ′ ) with negligible extra dependence on k, η and η ′ . Second, since we get Φ k (η)Φ k ′ (η ′ ) ξ ∝ (m/m p ) 2 in agreement with the usual results [22,74,75], the small value of the CMB anisotropies first detected by COBE imposes a severe bound on the gravitational fluctuations, characterized by Φ k (η)Φ k ′ (η ′ ) ξ , which implies the following restriction (fine tuning) for the inflaton mass: m/m p ∼ 10 −6 .
Some comments on the mechanisms considered in earlier related work [78,79,80,81] which allowed a significant relaxation on the fine tuning of that kind of parameters are in order here. In those studies either a self-interacting scalar field or a scalar field interacting non-linearly with other fields were considered. The modes of the inflaton field corresponding to scales of cosmological interest were regarded as an open quantum system with the environment constituted either by the short-wavelength modes in the case of self-interaction or else by other fields interacting with the inflaton field. Therefore, one can introduce a stochastic description based on a Langevin equation, as explained in Ref. [34], to study the dynamics of the inflaton field modes. In fact, Langevin-type equations or related stochastic tools were employed in the references cited above. Furthermore, it was shown in Ref. [34] that the validity of the results, such as the correlation functions, obtained by those methods is independent of the existence of enough decoherence to guarantee the presence of a semiclassical regime for the system dynamics. However, it was also shown that the two-point quantum correlation function for the system had two separate contributions (see Eq. (4.9) in Ref. [34]): one related to the dispersion of the system's initial state and another one which was proportional to the noise kernel and accounted for the fluctuations of the system induced by the interaction with the environment. For natural states in de Sitter spacetime such as the Bunch-Davies vacuum (in fact, any reasonable state in de Sitter space tends asymptotically to it [82]) the dispersion is proportional to H 2 . This contribution is actually several orders of magnitude larger than that coming from the term proportional to the noise kernel for the situations considered in Refs. [78,79,80,81]. Thus, the two-point quantum correlation function for the inflaton perturbations is dominated by the contribution connected to the dispersion of the initial state. This point has been confirmed by a detailed analysis in Ref. [23]. Moreover, this contribution essentially coincides for the cases of an interacting and a free scalar field. The latter is the case being considered throughout this paper and exhibits no noise term for the inflaton dynamics because there is no environment for the inflaton perturbations (this should not be confused with the noise kernel for the fluctuations of the metric perturbations induced by the quantum fluctuations of the inflaton). One could try to choose the initial state, as argued in Ref. [81], so that the contribution from the dispersion of the initial conditions were smaller than the fluctuations induced on the modes of the inflaton field, but that would require a great amount of fine-tuning for the initial quantum state of each mode, which would become highly unstable due to the large dispersion in momentum implied by Heisenberg's uncertainty principle [22] and quickly tend to the de Sitter invariant Bunch-Davies vacuum; or even have no inflation at all due to the back reaction on the evolution of the background geometry generated by such a highly excited state.
V. DISCUSSION
In this paper we have studied linearized metric perturbations around a Robertson-Walker background interacting with a quantum scalar field and we have shown that, when linearizing the perturbations of the scalar field around its background configuration, the Einstein-Langevin equation yields a result for the correlation function of the metric perturbations equivalent to that obtained in the usual approach based on the linearization and quantization of both the metric perturbations and the perturbations of the scalar field around its expectation value. Although for the sake of concreteness we have mostly concentrated on the case of a spatially flat Robertson-Walker metric and a minimally-coupled scalar field with a quadratic potential, the main result can be generalized rather straightforwardly to Robertson-Walker metrics with non-flat homogeneous spatial sections, as well as to general potentials for the scalar field and arbitrary coupling to the spacetime curvature. Considering Robertson-Walker metrics with homogeneous spatial sections of positive or negative curvature would imply, respectively, the use of three-dimensional spherical or hyperbolic harmonics rather than simple Fourier transforms for the spatial coordinates, but that would not substantially change the procedures and the main conclusions since the basic properties of Fourier transforms employed in the text have analogous counterparts for these harmonics [83,84,85]. On the other hand, the use of a general potential should not imply major differences since after all we would linearize with respect to the scalar field perturbations around the background configuration.
In addition, we also provided in Sec. IV a particular example illustrating how the Einstein-Langevin equation can be used in practice to compute the correlation function at large scales for scalar metric perturbations in cosmological inflationary models. In doing so we made use of slightly oversimplified approximations, namely, use of a de Sitter background geometry, calculation of the Hadamard function for a massless scalar field and neglecting a non-local term, because the result has already been computed in a number of references, see for instance Refs. [5,73,74,75], and our primary concern was simply to show how the Einstein-Langevin equation can be used to obtain an explicit result for cosmological perturbations.
Throughout the article we have concentrated on scalar-type metric perturbations. The reason for this is that, when linearizing with respect to both the metric perturbations and the scalar field perturbations, the vectorial and tensorial metric perturbations decouple from the matter scalar field. In this case the metric perturbations do not constitute a true open system since the dynamics of the scalar and vectorial perturbations is completely constrained by the temporal components of the Einstein equation; in fact, the vectorial ones actually turn out to vanish and the scalar ones cannot be regarded as a degree of freedom independent of the scalar field perturbations. Moreover, the only true dynamical degrees of freedom, the two tensorial ones, do not couple to the matter field. On the other hand, an even more interesting situation corresponds to the case in which the scalar field is treated exactly, at least for quadratic potentials. Then the scalar field also couples to the metric perturbations of tensorial type and the metric perturbations become a true open system with the scalar field corresponding to the environment.
The main features that would characterize an exact treatment of the scalar field perturbations interacting with the metric perturbations around a Robertson-Walker background as compared to the case addressed in this paper are the following. First, the three types of metric perturbations couple to the perturbations of the scalar field, as already mentioned above. Second, the corresponding Einstein-Langevin equation for the linear metric perturbations will explicitly couple the scalar and tensorial metric perturbations. Furthermore, although the Fourier modes (with respect to the spatial coordinates) for the metric perturbations will still decouple in the Einstein-Langevin equation, any given mode of the noise and dissipation kernels will get contributions from an infinite number of Fourier modes of the scalar field perturbations (see Ref. [86] for an explicit calculation of the noise kernel for a massless and minimally-coupled scalar field in de Sitter). This fact will imply, in addition, the need to properly renormalize the ultraviolet divergences arising in the dissipation kernel, which actually correspond to the divergences associated with the expectation value of the stress tensor operator of the quantum matter field evolving on the perturbed geometry.
The importance of considering corrections due to one-loop contributions from scalar field perturbations, beyond the tree level of the linear cosmological perturbation theory, has recently been emphasized [28,29]. In the present context this means treating the scalar field perturbations exactly in the Einstein-Langevin equation. Furthermore, in Ref. [34] it was explained how a stochastic description based on a Langevin-type equation could be introduced to gain information on fully quantum properties of simple linear open systems. In a forthcoming paper [35] it will be shown that, by carefully dealing with the gauge freedom and the consequent dynamical constraints, the previous result can be extended to the case of N free quantum matter fields weakly interacting with the metric perturbations around a given background (here weakly interacting means that the gravitational coupling constant times the number of fields remains constant in the limit of large N ). In particular, the correlation functions for the metric perturbations obtained using the Einstein-Langevin equation are equivalent to the leading order contribution in the large N limit to the correlation functions that would follow from a purely quantum field theory calculation. This will generalize the results already obtained on a Minkowski background [36,37]. These results have important implications on the use of the Einstein-Langevin equation to address situations in which the background configuration for the scalar field vanishes, so that linearization around such a configuration is no longer possible. This includes not only the case of a Minkowski background spacetime, but also the remarkably interesting case of inflationary models driven by the vacuum polarization of a large number of conformal fields with vanishing expectation value [31,87,88], where the usual approaches based on the linearization of both the metric perturbations and the scalar field perturbations and their subsequent quantization can no longer be applied.
A pure state is called Gaussian if its wave functional in the Schrödinger picture is a Gaussian functional: with a suitable normalization constant. The fundamental property of Gaussian states is the fact that the cumulants of order higher than two associated with the quantum expectation values of products of the field operatorφ vanish, i.e., for n ≥ 3 and where we introduced the notation Ô Ψ ≡ Ψ|Ô|Ψ . This implies that the connected part of any quantum correlation function Ψ|φ( x n ) . . .φ( x 1 ) |Ψ with n ≥ 3 vanishes or, equivalently, that any quantum correlation function Ψ|φ( x n ) . . .φ( x 1 ) |Ψ can be written as a linear combination of products involving the expectation values Ψ|φ( x i ) |Ψ and two-point functions Ψ|φ( x j )φ( x k ) |Ψ . Furthermore, if the Hamiltonian of the field under consideration is quadratic, this property can be generalized for different times to quantum correlation functions in the Heisenberg picture of the form H Ψ|φ(t n , x n ) . . .φ(t 1 , x 1 ) |Ψ H , which follows from Wick's theorem [89]. Finally, given a field operatorφ and a Gaussian state |Ψ with non-vanishing expectation value φ Ψ , it is always possible to introduce a new fieldφ =φ− φ Ψ so that the wave functionalΨ[ϕ] for the state |Ψ in the basis associated with the fieldφ becomes a Gaussian functional with vanishing expectation value and independent of the expectation value φ Ψ . This can be immediately seen by rewriting the expression for the wave functional in Eq. (A1) as and then change to the basis associated with the fieldφ: It is precisely in this sense that the state for the inflaton field perturbationsφ introduced in Sec. II B follows immediately from the state of the inflaton fieldφ. It should be emphasized that any of the vacuum states commonly considered for free fields in curved spacetimes are Gaussian states. Furthermore, as stated in Sec. II B, in this paper we concentrate on states which are invariant under the symmetries of the Robertson-Walker metric. In particular, for the case of Robertson-Walker metrics with flat spatial sections this implies φ Ψ (t, x) = φ Ψ (t) and A( x, x ′ ) = A(| x − x ′ |).
APPENDIX B: CONVENTIONS AND NOTATION FOR THE LINEARIZED STRESS TENSOR
Here we explain the notation concerning the linearized stress tensor employed in this article and clarify some related subtle points.
Let us begin with the objects which appear in the Einstein-Langevin equation (7). The tensors G ab can be raised using the background metric [from now on everything that will be said for G (1) ab applies exactly in the same way to T (1) ab ]. On the other hand, one could perturb the background object G (0) ab with the indices already raised, and reach a different result for G (1) ab : it would differ by the terms G (0) cd h a c + G (0) ac h b c . Our notation (and those commonly employed) is ambiguous in the sense that it does not distinguish between both possibilities. In order to remove such an ambiguity it is necessary (and sufficient) to specify a priori which objects are going to be perturbed. In particular, in Sec. II it is G ab . Hence, if one deals with equations involving tensorial objects rather than with isolated objects, everything is independent of the particular choice provided that the same choice is made for all the objects in the equation.
The previous ambiguity does not affect the stochastic source of the Einstein-Langevin equation, which is completely defined on the background spacetime (the noise kernel is evaluated on the background geometry). Furthermore, the argument given in Sec. III to show that Ψ = Φ is not affected by such an ambiguity either. The reason is that the ambiguous extra terms for δT ij with i = j vanish because both T (0) µν ren (or T µν ) and the scalar metric perturbations in the longitudinal gauge are diagonal. Similarly, each one of the terms appearing in the 0i component of the Einstein-Langevin and the quantum version of the linearized Einstein equations considered in detail in Secs. III B and III C, respectively, do not suffer from the ambiguity either.
The tensors G (1) ab and T (1) ab , which are discussed above, result from linearizing just the metric perturbations. On the other hand, in the usual treatment of cosmological perturbations in inflationary models not only the metric perturbations, but also the inflaton perturbations are simultaneously linearized. Therefore, we introduced the notation T ab for the contribution to the expectation value of the background stress tensor T (0) ab ren which is quadratic in the background solution φ(η) and independent of the inflaton perturbations, i.e., the first term on the right-hand side of Eq. (12): T ab = T (0) ab φφ . As we already explained in Sec. II B, the expectation value T (0) ab ren has also a contribution which is quadratic in the inflaton perturbations, but it is neglected when linearizing in those. We also introduced the notation δT ab for the perturbed stress tensor operator obtained when linearizing with respect to both the metric perturbations and the inflaton perturbations. Its expectation value δT ab [g + h] is, thus, equivalent to linearizing also with respect to the inflaton perturbations the expectation value T (1) ab [g + h] ren . Similarly, the operator δT ab [g + h] corresponds to linearizing in the inflaton perturbations the expressionT ab . This expression, which appears (after raising one index) in Eq. (26), might seem a bit awkward at that point, but this is just because the notation generally employed for the Einstein-Langevin equation, where one linearizes only with respect to the metric perturbations, is no longer the most natural when one also linearizes with respect to the inflaton perturbations. The expression is appropriate either when quantizing both the metric perturbations and the scalar field perturbations or when considering a stochastic version of it, namely the Einstein-Langevin equation. In the latter case one takes the expectation value ofT (1) ab plus a stochastic source that accounts for the quantum fluctuations of the operator t ab =T ab , whose expectation value vanishes. Finally, the notation δt ab is used for the result of linearizing the operatort ab with respect to the inflaton perturbations, which coincides with δT ab evaluated on the unperturbed metric. The Einstein-Langevin equation for metric perturbations around a given background and interacting with quantum matter fields has been formally derived using functional methods [53,54,55,56,57,58,60]. This was achieved by regarding the metric perturbations as an open quantum system with the environment corresponding to the quantum matter fields, and using the influence functional formalism for open quantum systems introduced by Feynman and Vernon [32,33]. In this appendix we briefly review some basic aspects of the functional approach to the Einstein-Langevin equation and explain how an alternative derivation of Eq. (52) for the expectation value of the linearized stress tensor operator evaluated on the perturbed metric can be obtained.
When considering derivations of the Einstein-Langevin equation using functional methods, one begins by computing the influence functional for the metric perturbations by integrating out the quantum matter fields (we will only consider free fields) as follows: where ρ [ϕ i , ϕ ′ i ; t i ) is the density matrix for the initial state of the matter field, ϕ, which is assumed to be initially uncorrelated with the metric perturbations (moreover, asymptotic initial conditions with t i → −∞ are usually considered) and S [ϕ, g + h] is the action for the matter field evolving on a spacetime with metric g ab + h ab . Furthermore, only terms up to quadratic order in the metric perturbations h ab around the fixed background metric g ab will be considered. In that case the action for the matter field can be written as where T ab [ϕ, g ′ ab ; x) = 2 (−g (x)) −1/2 δS [ϕ, g] /δg ab (x) corresponds to the stress tensor for the matter field, whose functional derivative (−g (y)) −1/2 δT ab [ϕ, g ab ; x) /δg cd (y) is a local object, i.e., proportional to the covariant delta function (−g (y)) −1/2 δ (4) (x − y). The influence action to quadratic order in the metric perturbations, which can be obtained by integrating out the matter field ϕ as explained in Refs. [53,60], exhibits a structure analogous to that of a linear open quantum system: where A · B denotes d 4 x −g (x)A ab (x) B ab (x) and we introduced the average and difference variables Σ ab = (h ab + h ′ ab )/2 and ∆ ab = h ′ ab − h ab . The expressions for the kernels are the following: where the functional derivative in Eq. (C6) should be understood to account only for the explicit dependence on the metric, whereas the implicit dependence through the field operatorφ[g] is not included. The notation T * appearing in Eq. (C5) means that the matter field operators must be temporally ordered before applying any derivatives acting on them. Thus, we have, for instance, T * ∇ x aφ (x)∇ y bφ (y) = ∇ x a ∇ y b Tφ(x)φ(y) . Note that although the background geometry is non-trivial in general, the notion of temporal ordering is well defined because we are restricting the possible background geometries to globally hyperbolic spacetimes, which are time orientable; moreover, the microcausality condition of the quantum field theory for the matter fields under consideration guarantees that [Ô 1 (x),Ô 2 (y)] = 0 ifÔ 1 (x) andÔ 2 (y) are local operators and x and y are spacelike separated points. It should also be noted that the first term on the right-hand side of Eq. (C5) is symmetric under interchange of x and y, whereas the second one is completely antisymmetric. On the other hand, the term on the right-hand side of Eq. (C6) is local and symmetric under interchange of x and y.
The noise kernel N abcd (x, y) requires no renormalization, as explained in Sec. II A, whereas the kernels Z ab (x), H abcd (x, y) and K abcd (x, y) contain divergences [some regularization procedure is implicitly understood in Eqs. (C4)-(C7)] that can be canceled out by adding suitable counterterms, quadratic in the curvature, to the bare gravitational action. These are precisely the same counterterms which are introduced in semiclassical gravity so that, when functionally differentiating with respect to the metric, they cancel the divergences from the expectation value of the stress tensor. This fact should not be surprising at all since the kernel Z ab (x) corresponds to the expectation value of the stress tensor operator on the background metric and the kernels H abcd (x, y) and K abcd (x, y) are closely related to the expectation value of the stress tensor operator on the perturbed metric, as follows straightforwardly from the following relation, valid up to linear order in h ab : where we introduced the kernel M abcd (x, y) defined as follows: which results from adding to the kernel K abcd (x, y) the term −(−g(x)) −1/2 (δ −g(x)/δg cd (y))Z ab coming from the contribution to the factor 2[−(g + h)(x)] −1/2 that is linear in h ab . When the counterterms introduced in the bare gravitational action are included in the influence action, so that the divergences cancel out and the bare kernels H abcd (x, y) and M abcd (x, y) get renormalized, Eq. (C8) becomes which can be rewritten as where, as mentioned above, the functional derivative appearing in the kernel M abcd (x, y) should be understood to account only for the explicit dependence of the stress tensor on the metric, whereas the implicit dependence through the field operatorφ[g] is entirely contained in the first term on the right-hand side of Eq. (C11). Taking into account the previous results, the Einstein-Langevin equation can then be obtained from the CTP effective action for the metric perturbations by using a formal trick described below. Such a CTP effective action for the metric perturbations has the following form at tree level (note, however, that the matter fields, which have already been integrated out, were treated beyond the tree level): IF . On the other hand, using the following mathematical identity for the imaginary part of the influence action: and interpreting ξ ab as a stochastic source with vanishing expectation value and correlation function ξ ab (x)ξ cd (y) ξ = N abcd (x, y), one can define a stochastic effective action, such that exp(iΓ stoch ) ξ = exp(iΓ (0) CTP ). The Einstein-Langevin equation can be immediately obtained by functionally differentiating with respect to the metric perturbation h ab and letting h ′ ab = h ab afterwards: It is worth discussing the issue of causality in Eq. (C15), which basically amounts to considering the second term on the right-hand side of the equation since the remaining terms are local. The right-hand side of Eq. (C5) can be formally rewritten as where η x and η y can be any pair of well-behaved time coordinates for the points x and y, and the star index in the theta function was used to indicate that the derivative operators acting on the scalar field which appear in the stress tensor operator should also act on the theta function. Thus, all the terms in expression (C16) are either proportional to θ(η x − η y ), δ(η x − η y ) or δ ′ (η x − η y ), and, being proportional to a commutator, expression (C16) vanishes for spacelike separated points because of the microcausality condition of the quantum field theory for the matter fields. Furthermore, since both the divergences and the counterterms are local (proportional to delta functions or derivatives of them), the contribution to Eq. (C15) from the term (H ren · h) ab (x) is causal, i.e., it only depends on the metric perturbations h cd (y) at any point within the past lightcone of x. Finally, taking into account Eq. (C11), Eq. (C15) becomes where the indices have been lowered using the background metric. It should be noted that, in contrast to Sec. II A, the tensors appearing in Eq. (C17) correspond to perturb the background tensors with both indices already raised. However, as pointed out in Appendix B, the resulting equations in both cases are equivalent because the unperturbed tensors satisfy the semiclassical Einstein equation. Therefore, Eq. (C17) is in complete agreement with Eq. (7), keeping in mind that the finite contributions of the counterterms, corresponding to A ab and B ab in Eq. (4), have been reabsorbed in the renormalized expectation value of the stress tensor operator. After this brief review of the functional approach to the Einstein-Langevin equation, let us now see how Eq. (C11) gives a result for δT i 0 Φ which is equivalent to that obtained in Sec. III B. To begin with, it should be pointed out that the ambiguity mentioned in Appendix B does not affect the 0i component of δT b a Φ since both the background stress tensor and the scalar metric perturbations in the longitudinal gauge are diagonal. Furthermore, it can be seen that for a diagonal perturbed metric the 0i component of the second term on the right-hand side of Eq. (C11) vanishes. Thus, we can concentrate on the first term.
Fourier transforming the spatial coordinates as done in Sec. III, the expectation value for the 0i component of the perturbed stress tensor becomes where the kernel H abcd (η, η ′ ; k) corresponds to the Fourier transform of the two terms on the right-hand side of Eq. (C5). Using the equivalent expression in Eq. (C16), the kernel H abcd (η, η ′ ; k) is given by the following expression, which already takes into account that the Fourier transform of the expectation value t ab [g; η, x),t cd [g; η ′ , x ′ ) is proportional to a Dirac delta function due to the existing translation invariance in the spatial coordinates, where the star in the theta function had been introduced earlier to indicate that the derivatives appearing int ab and t cd should also act on the theta function. Performing a similar decomposition to that introduced for the noise kernel in Eq. (20), we obtain two non-vanishing contributions to the expectation value t ab [x; x),t cd [g; x ′ ) [g]: where the first contribution is quadratic in the quantum operatorφ[g] for the inflaton perturbations evolving on the unperturbed geometry, whereas the second contribution is quartic inφ [g]. As already pointed out for the separation of the noise kernel, the fact that the conservation of the stress tensor, which is the source of the Einstein equation, is necessary to guarantee its integrability implies that both contributions to the expectation value must be separately conserved if we want to discard one of them keeping the consistency of the Einstein equation at the order that we are working, which is linear in the metric perturbations. This is indeed the case as follows from the fact that both the background homogeneous solution φ(η) and the operatorφ[g] satisfy the Klein-Gordon equation on the background spacetime.
If we keep only the first term on the right-hand side of Eq. (C20), i.e., if we take H abcd (x, , which corresponds to considering the contributions tot ab [g] that are linear in the inflaton perturbations and is consistent with the linearization of the inflaton perturbations that was considered in Secs. III and IV, we obtain where we used the explicit expressions for the components H 0i00 and H 0ijj . In this case, there is actually no need for the * prescription in θ * (η, η ′ ), which implies that the derivative acting onφ(η ′ ) should also act on the theta function, since it yields a term proportional to [φ(η),φ(η)]δ(η − η ′ ), which vanishes identically. Integrating by parts the first term in the integrand and using the Klein-Gordon equation for the background solution φ(η), given by Eq. (17), we finally get where the factor a −2 (η) comes from raising the index i with the background metric and we have substituted the expectation value for the commutator of the field operators simply by the commutator since for a linear theory they are c-numbers, whose expectation value is independent of the state. This result for the expectation value of the stress tensor coincides with Eq. (52), found in Sec. III B. It should be noted that the contribution from the boundary term at η ′ = η which results from the integration by parts vanishes because [φ(η),φ(η)] = 0. On the other hand, there is a non-vanishing contribution from the boundary term at η ′ = η 0 : It might seem that the existence of this term would imply a conflict between the result for the expectation value of the linearized stress tensor operator obtained in Sec. III B using the equations of motion for the quantum operators in the Heisenberg picture and the result based on the influence functional formalism derived in this appendix. However, this is not the case. The reason for the apparent discrepancy is the following. When computing the expectation value of the stress tensor operator, there are terms proportional to φ[g; η) , where the operatorφ[g; η), which satisfies the Klein-Gordon equation, can be written as a linear combination of a term proportional toφ[g; η 0 ) and a term proportional toφ ′ [g; η 0 ). In particular, in Sec. III we chose a state for which both φ[g; η 0 ) and φ ′ [g; η 0 ) vanished. On the other hand, in the approach based on the influence functional formalism the operators which naturally determinê ϕ[g; η) in terms of the initial state areφ[g; η 0 ) and its conjugate momentumπ[g; η 0 ). Since the coupling between the metric perturbations and the inflaton perturbations involves terms proportional to the time derivative of the inflaton perturbations,π[g; η 0 ) will differ fromφ ′ [g; η 0 ) by a term proportional to the metric perturbations at the initial time. This is precisely the origin of the term in expression (C23). Thus, the apparent discrepancy is just a consequence of the fact that in the influence functional approach it has been implicitly assumed that the initial state has vanishing π[g; η 0 ) rather than vanishing φ ′ [g; η 0 ) . It is important to stress that the expression in Eq. (C22) for the expectation value of the stress tensor operator needs no renormalization. This fact can be easily understood because we are dealing with the linearized theory. Therefore, the terms involved in the computation of the expectation value of the stress tensor operator are proportional to φ[g + h; x] , whereas the divergences that arise in an exact treatment (without linearizing with respect to the scalar field) are a consequence of taking the coincidence limit x ′ → x in terms involving products of the field operator, i.e., proportional to φ[g + h; x]φ[g + h; x ′ ] . Alternatively, when considering Eq. (C8) together with Eq. (C16), the need for renormalization can be understood as follows. The expectation value of the commutator is finite as long as one restricts to x = x ′ , but it diverges when one considers the coincidence limit. Nevertheless, it is still meaningful as a distribution. In this context, the divergences arise because the product of distributions in Eq. (C16) is ill defined in general although each factor is well defined as a distribution; see Ref. [90] for a detailed discussion on this point. In fact, the terms in Eq. (C16) involve terms proportional to the imaginary part of the product of two Feynman [57,91,92]. Working in Fourier space for the spatial variables, this product becomes d 3 qG F (η, η ′ ; k − q)G F (η, η ′ ; q), which exhibits an ultraviolet divergence when performing the integral d 3 q over all possible momenta. On the other hand, when linearizing with respect to the scalar field, the Fourier transformed version of the terms in Eq. (C16) is simply proportional to G F (η, η ′ ; k), with no integral over momenta and, hence, no ultraviolet divergence.
APPENDIX D: INITIAL CONDITIONS
In this appendix we will explain why, strictly speaking, a homogeneous solution Φ (h) k (η) with some particular initial conditions must be added to the purely inhomogeneous solution Φ It is well known that the Bianchi identity guarantees the integrability of the Einstein equation provided that the stress tensor of the matter sources is covariantly conserved. Let us, however, discuss this point in some more detail. The ten components of the Einstein equation for a globally hyperbolic spacetime, which can be foliated with a set of Cauchy hypersurfaces, can be formulated as an initial value problem with time corresponding to some continuous variable labeling the Cauchy hypersurfaces. In particular for the cosmological problem that we are considering we can choose the homogeneous spatial sections labeled by the conformal time η as the set of Cauchy hypersurfaces. The four temporal components of the Einstein equation can then be regarded as a set of dynamical constraints at any given instant of time. Thus, the integrability of the Einstein equation as an initial value problem can be understood in the following way: using the Bianchi identity and the conservation of the matter sources, the constraints can be shown to hold at any time provided that the spatial components of the Einstein equation are satisfied for all times and the four constraint equations are fulfilled on the Cauchy hypersurface corresponding to some initial time [40]. Obviously, the previous discussion can be extended to the case of the Einstein-Langevin equation since the stochastic source is also covariantly conserved.
Let us recall the temporal components of the Einstein-Langevin equation for scalar metric perturbations after Fourier transforming with respect to the spatial coordinates: In Secs. III and IV the constraint equation (D2) was solved to find Φ k (η). However, one should make sure that the remaining components of the Einstein-Langevin equation are also satisfied. According to the discussion in the previous paragraph, to make sure that this is indeed the case it is sufficient to demand that the Eq. (D1) holds at the initial time η 0 for every k. The solution of Eq. (D2) can always be written as Φ k (η) = Φ where we took into account that (δT i 0 ) k (η 0 ) Φ vanishes, as can be immediately seen from Eqs. (52), or (C21), because the limits of integration coincide. We also used the fact that (δT 0 0 ) k (η 0 ) Φ = a −2 (η 0 )[φ ′ (η 0 )] 2 Φ k (η 0 ): in this case the second term on the right-hand side of Eq. (C8) vanishes for the same reason as with (δT i 0 ) k (η 0 ) Φ , but there is a non-vanishing contribution from the last term in Eq. (C8), which corresponds to the first term on the right-hand side of Eq. (29).
Since Eq. (D2) is a first order integro-differential equation, the result for Φ k (η). The situation will be completely analogous when linearizing and quantizing both the metric perturbations and the inflaton perturbations, as done in Sec. III C, with the quantum operator for the metric perturbationsΦ(x) replacing the stochastic scalar field Φ(x) and the operator δt b a instead of the stochastic source ξ b a (x). Hence, the argument concerning the equivalence between the quantum correlation function for the metric perturbations and the stochastic correlation function can be straightforwardly extended, following the same line of reasoning as in Sec. III C, to the case in which the contribution from the homogeneous solution is also taken into account.
Nevertheless, in Secs. III and IV this homogeneous solution was not considered when giving the final result for the correlation function of the metric perturbations. Therefore, we end this appendix arguing why it is justified to neglect the contribution from the homogeneous solution when computing the correlation functions for scalar metric perturbations at large scales in the context of cosmological inflationary models. In other words, the contribution from the first three terms on the right-hand side of Eq. (45) is much smaller than the contribution from the fourth term when considering a situation similar to that addressed in Sec. IV. This can be qualitatively understood in the following way. Since Eq. (D2) is a linear first order differential equation, the solution of the homogeneous equation, Φ (h) k (η), will be proportional to the expression for Φ (h) k (η) given by Eq. (D3). Thus, the first term on the right-hand side of Eq. (45) is proportional to the correlation functions for the stochastic source at the time η 0 , and the second and third terms are proportional to the correlation functions at different times: η 0 and a time η ′ which is integrated from η 0 to η 1 or η 2 [see Eq. (44)]. The value of the noise kernel is small when one or both the two arguments are η 0 provided that η 0 is negative enough so that the scales of interest were well inside the horizon at that time. This is in contrast to the contribution from the last term in Eq. (45) when the relevant scales are well outside the horizon at η 1 and η 2 , since the two arguments of the noise kernel in that term are integrated from η 0 to η 1 or η 2 . Hence, the reason for neglecting the first three terms on the right-hand side of Eq. (45) in this context is actually rather similar to the reason for the weak dependence on η 0 of the result obtained in Sec. IV when the scale k is well outside the horizon at η 1 and η 2 , and η 0 is negative enough so that k is well inside the horizon at that time.
The previous argument can be made more precise if we concentrate on the particular model considered in Sec. IV. In that case, if we neglect the non-local term corresponding to δT i 0 Φ , as done in Sec. IV, the expression for the homogenous solution is The contribution form the first three terms on the right-hand side of Eq. (45) can then be explicitly computed and compared to the last term, taking into account that kη 1 , kη 1 ≪ 1 and kη 0 ≫ 1. In particular, the first term on the right-hand side of Eq. (45) is proportional to (κ/2)(m/m p ) 2 (2π) 3 k −3 δ( k − k ′ )a 2 (η 0 )/a(η 1 )a(η 2 ) and a sum of terms of order 1, (1/kη 0 ) 2 and (m/H)(1/kη 0 ) 2 . The factor a 2 (η 0 )/a(η 1 )a(η 2 ), which is of order kη 1 kη 2 /(kη 0 ) 2 , as well as (1/kη 0 ) 2 and m/H are much smaller than 1. It is thus clear that those contributions can be safely neglected as compared to the last term, which was found to be of order (κ/2)(m/m p ) 2 (2π) 3 k −3 δ( k − k ′ ) in Sec. IV. Similarly, the second and third terms on the right-hand side of Eq. (45) are proportional to (κ/2)(m/m p ) 2 (2π) 3 k −3 δ( k − k ′ )a 2 (η 0 )/a(η 1 )a(η 2 ) and a sum of terms of order 1 and 1/kη 0 . Therefore, they can also be neglected as compared to the last term.
APPENDIX E: ALTERNATIVE PROOF OF THE EQUIVALENCE BETWEEN STOCHASTIC AND QUANTUM CORRELATION FUNCTIONS
In this appendix we provide an alternative proof of the equivalence between stochastic and quantum correlation functions whose key step is to show that the Einstein-Langevin equation for linearized cosmological perturbations implies Eq. (6.48) of Ref. [74].
Let us consider the Einstein-Langevin equation for scalar metric perturbations when one also linearizes with respect to the inflaton field, whose different components are given by Eqs. (37)- (39). We will take Ψ = Φ, as justified by the discussion before Eq. (40), and work in Fourier space for the spatial coordinates. Next, we add Eq. (37), the i = j component of Eq. (39) and Eq. (38) multiplied by F ≡ 2m 2 a 2 (φ/φ ′ )(k i /k 2 ), which leads to the following result: with no summation over the repeated i indices. In deriving Eq. (E1) we made use of the following two relations which follow from the Klein-Gordon equation (17) for the background field φ. The final step is to show that the right-hand side of Eq. (E1) vanishes. In order to do so, it is convenient to consider first the Fourier-transformed version of Eqs. (29)-(31) for the linearized stress tensor. It is then straightforward to show that with no summation over the repeated i indices. The same conclusion applies when ϕ is promoted to a Heisenberg operatorφ, which implies that the first three terms on the right-hand side of Eq. (E1) cancel out. On the other hand, since ξ 0 0 + ξ i i + F ξ i 0 k is a Gaussian stochastic process with vanishing mean, in order to prove that it vanishes it is sufficient to see that ξ 0 , which is proportional to δt 0 0 + δt i i + F δt i 0 k (η), δt ν µ k ′ (η ′ ) , vanishes. Indeed, taking Φ = 0 in Eq. (E4) and promoting ϕ to a Heisenberg operator, it follows that δt 0 0 + δt i i + F δt i 0 k = 0. Thus, the right-hand side of Eq. (E1) vanishes and one is left with which coincides with Eq. (6.48) in Ref. [74]. Several remarks about Eq. (E5) are in order. First, the non-local terms associated with δT b a Φ are not present so that, when working in Fourier space for the spatial coordinates, one is left with an ordinary differential equation rather than an integro-differetnial one. Second, the equation exhibits no dependence on the stochastic source. However, the solutions of the Einstein-Langevin equation should also satisfy the constraint equations at the initial time in addition to Eq. (E5). According to the results in Appendix D, this | 25,478.6 | 2007-09-12T00:00:00.000 | [
"Physics"
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Using AlphaFold to predict the impact of single mutations on protein stability and function
AlphaFold changed the field of structural biology by achieving three-dimensional (3D) structure prediction from protein sequence at experimental quality. The astounding success even led to claims that the protein folding problem is “solved”. However, protein folding problem is more than just structure prediction from sequence. Presently, it is unknown if the AlphaFold-triggered revolution could help to solve other problems related to protein folding. Here we assay the ability of AlphaFold to predict the impact of single mutations on protein stability (ΔΔG) and function. To study the question we extracted the pLDDT and metrics from AlphaFold predictions before and after single mutation in a protein and correlated the predicted change with the experimentally known ΔΔG values. Additionally, we correlated the same AlphaFold pLDDT metrics with the impact of a single mutation on structure using a large scale dataset of single mutations in GFP with the experimentally assayed levels of fluorescence. We found a very weak or no correlation between AlphaFold output metrics and change of protein stability or fluorescence. Our results imply that AlphaFold may not be immediately applied to other problems or applications in protein folding.
Introduction
AlphaFold is widely claimed to have revolutized protein 3D structure prediction from protein sequence, a 50-years long-standing challenge of protein physics and structural bioinformatics [1]. The fourteenth round of CASP, a blind competition on protein 3D structure prediction [2], demonstrated that AlphaFold, a newcomer to the field, significantly outperforms all other methods. Crucially, AlphaFold models showed an accuracy of their predicted structures that was comparable to structures solved by experimental methods, like X-ray crystallography, NMR, and Cryo-EM [3]. 'It will change everything', said Andrei Lupas in an interview to Nature [3]. One of the primary changes may be that AlphaFold may also solve other problems related to protein folding. These problems include the prediction of various protein interactions, such as protein-protein, protein-ligand and protein-DNA/RNA, and the prediction of the impact of mutations on protein stability. AlphaFold proved to be useful for experimental determination of protein structures with molecular replacement phasing [4,5] and already facilitated elucidation of SARS-Cov2 protein structures [6,7]. Next, AlphaFold in collaboration with EMBL-EBI constructed the structure models for the whole protein sequence space [8]. The database of freely available structures of all proteins, is attributed to "revolutionize the life sciences" [3]. A pool of high-quality predicted structures is a plus for 3D-based prediction of mutation influence on protein stability since 3D-based prediction is more accurate than 1D-based one [9][10][11]. Furthermore, AlphaFold is expected to bring new insights into our understanding of the structural organization of proteins, boost the development of new drugs and vaccines [12]. Researchers in the field are already actively testing AlphaFold performance in various bioinformatics tasks, for instance, in peptide-protein docking [13,14].
Guided by the expected immediate impact of AlphaFold for the solution of a wide range of problems in structural bioinformatics, we explored the capacity of AlphaFold predictions to serve as a proxy for the impact of mutations on protein stability change (ΔΔG). Although AlphaFold provides a disclaimer that it "has not been validated for predicting the effect of mutations" (https://alphafold.ebi.ac.uk/faq), the expectations of AlphaFold are so high that we judged it prudent to check how well AlphaFold predictions could work for estimation of ΔΔG values. Therefore, given that pLDDT score reflects confidence of the location of the residue in the structure, it may be expected that this measure correlates with ΔΔG or protein function. We found that the difference between pLDDT scores, the only local AlphaFold prediction metric reported in the output PDB file, had a very weak correlation with experimentally determined ΔΔG values (Pearson correlation coefficient, PCC = -0.17). The difference in the global AlphaFold metric-the pLDDT averaged for all residues-shows no correlation, both isolated and in combination with the mutated residue's pLDDT score. Similarly, the same AlphaFold metrics had a very weak correlation with the impact of single mutations on protein function, fluorescence, of GFP. Recent results [15] show that the use of AlphaFold models instead of template structures does not improve ΔΔG prediction. Taken together, so far we failed to find a use for AlphaFold to predict the impact of a mutation on protein stability. The availability of AlphaFold models allows applying more accurate 3D protein structure-based ΔΔG predictors rather than sequence-based ΔΔG predictors; the bottleneck still seems to be the accuracy of current 3D protein structure-based ΔΔG predictors.
Dataset of experimental mutations
The data on experimentally measured effects of mutations on protein stability were taken from ThermoMutDB [16] (version 1.3). From 13,337 mutations in the database we extracted singlepoint mutations with data on ΔΔG measured in the experimental conditions of pH between 3 and 9, and temperature between 293 to 300 Kelvins. We also put the restriction on protein length for it to be less than 250 amino acids. Since stabilizing mutations have to have negative ΔΔG while in ThermoMutDB they are positive, all ΔΔG values from ThermoMutDB were multiplied by −1.
The filtered dataset resulted in 1779 mutations in 80 proteins. We have done the analysis for randomly chosen 1154 mutations in 73 proteins. The final dataset and computed metrics are given in S1 Table.
Dataset of GFP mutants fluorescence
We took data on fluorescence levels of GFP mutants from [17]. From the original dataset we randomly extracted 796 single mutants for our analysis. The list of the chosen mutations is given in S2 Table. Protein structure modeling with AlphaFold The wild type protein structures were retrieved from the AlphaFold Protein Structure Database (AlphaFold DB) [8] by their UniProt accession code. The structures of original proteins that were absent in the AlphaFold DB as well as structures of mutant proteins were modeled by the standalone version of AlphaFold [1] using the fasta file with UniProt sequence of a protein as the only input in the '-fasta_paths' flag.
Prediction metrics
The per-residue local distance difference test (pLDDT) confidence scores for the protein structure models downloaded from the AlphaFold DB were retrieved from the B-factor field of the coordinate section of the pdb file. The pLDDT confidence scores for the protein structure models that we predicted by standalone AlphaFold were extracted from the pickle file, from "plddt" array. By default, AlphaFold produces five models. The differences in pLDDT and <pLDDT> were statistically significant within the group of five produced models (both for wildtype and mutant); we used in our analysis only the best one, i.e., having the highest value of <pLDDT>.
Sequence identity of proteins within the dataset of mutations
To identify the sequence identities between the proteins in the dataset of mutations we performed protein BLAST [18] search of protein sequences against themselves.
We divided the dataset into training and test sets for linear regression model based on the arbitrary sequence identity threshold of 50%. Mutations in proteins above the threshold comprised the training set, and the rest of mutations were used as the test set. The training and test sets resulted in 423 mutations in 50 proteins and 731 mutations in 23 proteins, respectively.
Linear regression analysis
Multiple linear regression fit with two parameters was performed using the linear_model module of Sklearn library with default parameters.
Properties of mutated amino acid residues
Mutated amino acids were annotated by relative solvent accessibility, effect of mutation on stability, hydrophobicity, polarity, and side chain size.
Information on solvent accessibility was taken from Stride [19]. The relative solvent accessibility (RSA) of an amino acid residue was calculated according to the equation: where ASA is the solvent accessible surface area and maxASA is the maximum possible solvent accessible surface area of an amino acid [20]. Following [21] we used the solvent accessibility threshold of 25% to classify residues as exposed or buried. The rest of the properties were assigned according to http://www.imgt.org/ IMGTeducation/Aide-memoire/_UK/aminoacids/IMGTclasses.html. The side chain sizes were annotated as very small (1), small (2), medium (3), large (4), very large (5). We defined 'no', 'small', and 'large' change in size chain volume equal to difference of 0, 1 or 2, and 3 or 4 in absolute values, respectively.
All correlations were adjusted for multiple hypotheses testing by Benjamini-Hochberg correction [22].
Data set of mutations
We used experimental data on protein stability changes upon single-point variations from ThermoMutDB Database [16]. After the filtering procedure (see Materials and methods) we performed analysis for 1154 mutations in 73 proteins. For the multiple linear regression analysis, the dataset was split into two sets, a training and a test set. The split was based on BLAST [18] results, such that the mutations were assigned to the test set if corresponding proteins had <50% sequence identity to any other protein in the entire dataset (see Materials and methods). All of the other mutations were assigned to the training set.
AlphaFold prediction metrics
Along with coordinates of all heavy atoms for a protein, AlphaFold model contains "its confidence in form of a predicted lDDT-Cα score (pLDDT) per residue" [1]. LDDT ranges from 0 to 100 and is a superposition-free metric indicating to what extent the protein model reproduces the reference structure [23]. The pLDDT scores averaged across all residues designate the overall confidence for the whole protein chain (<pLDDT>). The distributions of Alpha-Fold prediction metrics for wildtype and mutant structures statistically significantly differ from each other, both for pLDDT (p-value = 7 � 10 -10 ) and <pLDDT> (p-value = 3 � 10 -3 ). For each mutation in the dataset, we calculated the difference in pLDDT between the wild type and mutated structures in the mutated position as well as the difference in <pLDDT> between wild type and mutant protein structure models. By checking ΔpLDDT and Δ<pLDDT> values as potential proxies for the change of protein stability we explored the hypothesis that the change of protein stability due to mutation is somehow reflected in the difference of AlphaFold confidence between wild type and mutant structures.
Correlation between ΔΔG and ΔpLDDT values
First, we studied the relationship between the effect of mutation on protein structure stability and the difference in the accuracy of protein structure prediction by AlphaFold for the wild-type and mutant proteins. We did not observe a pronounced correlation between the mutation effect and the difference in confidence metrics (Fig 1). The correlation coefficient is -0.17 ± 0.03 (p-value = 10 -8 ) for ΔpLDDT and 0.02 ± 0.03 (p-value = 0.44) for the Δ<pLDDT>.
Relationship of ΔpLDDT and amino acid properties
We explored the outliers with high absolute values of ΔpLDDT in Fig 1A. Expectedly, the destabilizing effect of mutations was associated with decreasing pLDDTs: 87% of destabilizing mutations had negative ΔpLDDT (p-value = 10 −22 ). However, there was no correlation between ΔpLDDT and ΔΔG for that 87% of mutations with negative ΔpLDDT.
We explored the correlation between AlphaFold prediction metrics and ΔΔG for different categories of mutations (see Methods, Properties of mutated amino acid residues). The correlation remained poor (|PCC| being less than 0.19 and 0.07 for ΔpLDDT and Δ<pLDDT>, respectively, see S3 Table) for mutations stratified by their effect on polarity, hydrophobicity, charge upon mutation and relative solvent accessibility of mutated residue (S3 Table).
The difference in pLDDT score distributions was significant for positions with the different secondary structures of mutated residue (Kruskal-Wallis p-value = 4 � 10 −10 ) and for mutations changing the side chain size (Kruskal-Wallis p-value = 0.04). However, the correlation between ΔpLDDT or Δ<pLDDT> and ΔΔG for different types of mutations within these categories was not strong (|PCC| < 0.38 except for 29 mutations having a large increase in size showing correlation of -0.67 for ΔpLDDT, see S3 Table).
Correlation between GFP fluorescence and ΔpLDDT values
Protein stability is intimately coupled with protein functionality. Thus, a reasonable hypothesis holds that the loss of protein functionality due to mutations in most cases results from reduced stability [24]. Therefore, along with testing correlation of AlphaFold metrics with ΔΔG, it is reasonable to test the correlation of AlphaFold metrics with protein function. Furthermore, the change of pLDDT scores may contribute directly to protein functionality without contributing to protein stability. We checked the correlation between ΔpLDDT values and the fluorescent level of 796 randomly chosen single GFP mutants from [17]. The correlation coefficient is 0.17 ± 0.03 (p-value = 3 � 10 -6 ) for ΔpLDDT and 0.16 ± 0.04 (p-value = 10 -5 ) for the Δ<pLDDT> (Fig 2).
Discussion
Extraordinary success of AlphaFold in predicting protein 3D structure from protein sequence may lead to temptation to apply this tool to other questions in structural bioinformatics. Here we checked the potential of AlphaFold metrics to serve as a predictor for the impact of mutation on protein stability and function. We found a weak correlation of -0.17 ± 0.03 between ΔpLDDT and ΔΔG associated with specific mutations. Although the correlation was statistically significant (p-value < 10 -8 ), it is so weak that it cannot be used for accurate ΔΔG predictions (Fig 1) and it is unclear how such predictions can be used in practical applications. Clearly, ΔpLDDT would show a better correlation with ΔΔG if it was measured across bins of averaged ΔΔG. Alternatively, ΔpLDDT could be a separate term in a multiple linear regression model. The averaged metric Δ<pLDDT> shows correlation with ΔΔG, which is statistically indistinguishable from zero. However, a linear combination of the two metrics, ΔpLDDT and Δ<pLDDT>, does not greatly improve the correlation. As for the loss-of-function prediction, the correlation with the impact of mutation on GFP fluorescence showed similar results: PCC was 0.17 ± 0.03 and 0.16 ± 0.04 for ΔpLDDT and Δ<pLDDT>, respectively (Fig 2).
Taken together, our data indicate that AlphaFold predictions cannot be used directly to reliably estimate the impact of mutation on protein stability or function. But why should we have expected such a correlation in the first place? Indeed, AlphaFold was not designed to predict the change of protein stability or function due to mutation. In the words of the authors "AlphaFold is not expected to produce an unfolded protein structure given a sequence containing a destabilising point mutation" (https://alphafold.ebi.ac.uk/faq). However, the only reason for a protein to fold into the distinct native structure is the stability of this structure, so the protein 3D structure and its stability are closely connected. Logically, an algorithm predicting protein 3D structure from sequence should search for the most stable 3D state under the native (or standard) conditions. If a compact structure becomes unstable (for example, due to mutation) then we might expect that the algorithm shifts its predictions toward an unfolded state. Evidence in favor of this point of view is the successful prediction of natively disordered protein regions by AlphaFold and the correlation between the decrease of pLDDT and propensity to be in a disordered region [25]. Thus, it is not unreasonable to expect a decrease in the confidence score of the mutated residue or the whole native structure.
Indeed, it was reported many times that 3D-based predictors perform better than 1D-based [9][10][11], so the availability of a pool of high-quality 3D predicted structures could be a plus.
Our results show that AlphaFold repurposing for ΔΔG prediction did not work for the proteins we studied. AlphaFold 3D models can be used to predict the impact of a mutation on protein stability or function by 3D-structure-based ΔΔG predictors. However, the performance of the resulting predictions is going to be far from perfect: the 3D-structure based ΔΔG predictors show modest performance even using 3D structures from PDB [26], with correlation of 0.59 or less in independent tests [27]. Thus, using AlphaFold models instead of PDB structures does not make ΔΔG predictions more accurate [15], so availability of AlphaFold models is expected to show an approximately 0.59 correlation with predictions of ΔΔG, which may be too low for many applications.
The deep learning approach demonstrated by AlphaFold may be an inspiring example to develop a deep learning ΔΔG predictor. However, we see the dramatic difference between the situations with 3D structure prediction and ΔΔG prediction that may impede this development. The difference is in the amount of available data. For protein structure prediction AlphaFold used PDB with �150,000 files, and each file contained a wealth of information. In contrast to PDB, the number of experimentally measured ΔΔG values are of the order of 10,000 and these are just numbers without accompanying extra data. To make a rough comparison of information in bits, PDB structures occupy 100 Gb, while all the known experimentally ΔΔG values occupy about 10 kb. Neural networks are very sensitive to the amount of information in the training set so the ability of deep learning to tackle the ΔΔG prediction task at present looks hindered mostly by the lack of experimental data.
Overall, we explored the capacity of direct prediction of ΔΔG by all AlphaFold metrics reported in the standard deafault mode: (i) the difference in the pLDDT score before and after mutation in the mutated position, (ii) the difference in the averaged pLDDT score across all positions before and after mutation. We found that the correlation was weak or absent, and, therefore, AlphaFold predictions are unlikely to be useful for ΔΔG predictions. Taken together with our recent result that AlphaFold models are not better for ΔΔG predictions than best templates [15], we see no straightforward way to use AlphaFold advances for solving the task of prediction of ΔΔG upon mutation. The task of ΔΔG prediction should be solved separately and it will face the problem of limited amount of data for training neural networks.
Supporting information S1 Table. List of studied mutations with ΔΔG values. The list of 1154 mutations in 73 proteins randomly chosen for ΔΔG analysis as described in Materials and methods). (XLSX) S2 Table. List of studied single mutations in GFP. The list of 796 single mutants of GFP randomly chosen for our analysis as described in Materials and methods). (XLSX) S3 | 4,165 | 2021-09-20T00:00:00.000 | [
"Biology"
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Assembly and comparative analysis of the complete mitochondrial genome of Brassica rapa var. Purpuraria
Background Purple flowering stalk (Brassica rapa var. purpuraria) is a widely cultivated plant with high nutritional and medicinal value and exhibiting strong adaptability during growing. Mitochondrial (mt) play important role in plant cells for energy production, developing with an independent genetic system. Therefore, it is meaningful to assemble and annotate the functions for the mt genome of plants independently. Though there have been several reports referring the mt genome of in Brassica species, the genome of mt in B. rapa var. purpuraria and its functional gene variations when compared to its closely related species has not yet been addressed. Results The mt genome of B. rapa var. purpuraria was assembled through the Illumina and Nanopore sequencing platforms, which revealed a length of 219,775 bp with a typical circular structure. The base composition of the whole B. rapa var. purpuraria mt genome revealed A (27.45%), T (27.31%), C (22.91%), and G (22.32%). 59 functional genes, composing of 33 protein-coding genes (PCGs), 23 tRNA genes, and 3 rRNA genes, were annotated. The sequence repeats, codon usage, RNA editing, nucleotide diversity and gene transfer between the cp genome and mt genome were examined in the B. rapa var. purpuraria mt genome. Phylogenetic analysis show that B. rapa var. Purpuraria was closely related to B. rapa subsp. Oleifera and B. juncea. Ka/Ks analysis reflected that most of the PCGs in the B. rapa var. Purpuraria were negatively selected, illustrating that those mt genes were conserved during evolution. Conclusions The results of our findings provide valuable information on the B.rapa var. Purpuraria genome, which might facilitate molecular breeding, genetic variation and evolutionary researches for Brassica species in the future. Supplementary Information The online version contains supplementary material available at 10.1186/s12864-024-10457-1.
Introduction
Purple flowering stalks (Brassica rapa var.purpuraria) is widely distributed in the middle regions of the Yangtze River that belongs to the Cruciferae family [1].B. rapa var.Purpuraria is an important and popular vegetable for consumers due to its bright color and delicious taste with abundant anthocyanidins, carotenoids, proanthocyanidins, vitamin C and mineral elements [2,3].Mitochondria (mt) is important organelles that involve in many metabolic processes related to the synthesis of these nutritional components of amino acids, lipids and vitamins and energy production [4][5][6].The mt genome of angiosperm Arabidopsis thaliana was first reported in 1997 [7].Subsequently, the mt genomes of some field crops and fruits, including rice (Oryza sativa L.) [8], rape (Brassica napus L.) [9], corn (Zea mays L.) [10], grape (Vitis vinifera) [11], apple (Malus domestica) [12], and kiwifruit (Actinidia chinensis) [13], have been successively published.The mt genomes have the characteristics of integrity, polymorphism, and semi-autonomy with a unique expression system, they contain a few genes and limited the types of proteins.Therefore, they need to be coordinated with nuclear genes to maintain normal biological functions [14].The number, arrangement and composition of genes are conserved in the chloroplast (cp) genomes of higher plants [15].However, Mt genomes have highly conserved characteristics and evolutionary rates that are different from nuclear genes.Therefore, the mt genome is relatively large, which could provide a large amount of genetic information and solve the problem of classification, identification and evolution of related species [14,16].
The mt genome has significant differences in length, gene sequence, and gene content in different species, and even varies in different cultivars in the same species [17][18][19].The length of mt genome in plants varies from 66 Kb to 11.7 Mb [18,20].The plant mt genomes mainly contain 50-60 conserved genes, which involved in oxidative phosphorylation and protein translation, and many unknown function open reading frames (ORFs) [21].In addition, Some of ORFs in the mt genome play a key role in cytoplasmic male sterility of species [22][23][24].Except for the unknown function ORFs, the differences in the number of complex II subunit, ribosomal protein genes, tRNAs and multi-copy genes were the main reason for the difference in the number of mt genes in different species [25].With the development of sequencing technology and the decreasing of sequencing costs, a variety of mt genomes have been reported.The mt genome of Brassica species including A. thaliana [26], Raphanus sativus L. [27], and B. napus [28] have been reported.In addition, the mt genomes of several varieties of B. rapa species have also been addressed.The mt genomes in the varieties of B. rapa developed with close full length from 219,736 bp to 219,775 bp, with same number of tRNA (18) and rRNA (3); and exhibited minor differences for gene numbers between 54 and 99, and PCGs ranged from 34 to 78 [29][30][31].The characterized mt genome could help to observe structural variations in the evolutionary history of Brassica species or varieties.Therefore, assembling and analyzing the mt genomes is important to better understanding of their genetic characteristics and for molecular breeding research.
In this work, the whole mt genome of B. rapa var.Purpuraria was sequenced and assembled using the Illumina and Nanopore sequencing platforms.The genomic features, repeat sequences, codon usage, RNA editing sites, and comparative genomics were analyzed.We also conducted phylogenetic analysis to understand the genetic variations in B. rapa var.Purpuraria more effectively.This study enhances our understanding of B. rapa var.
Purpuraria genetics and provides useful information for future researches on identification, molecular breeding and system evolution of mt genomes of Brassicaceae species.
Plant materials, DNA extraction and sequencing
The B. rapa var.Purpuraria seeds were provided by Peng Li (Xiangtan Agricultural Science Research Institute), and cultivated at the Xiangtan Agricultural Science Research Institute (Yuhu District, Xiangtan, Hunan, China; 27°52 N, 112°50E) under natural conditions.Fresh young leaves were collected and quickly frozen in liquid nitrogen, and then stored at 80 °C.Plant specimens were conserved in the Hunan University of Humanities, Science and Technology (accession number: 20231218BRP02).The total DNA isolation from the young leaves was performed using CTAB method [32] and purified using Plant DNA Mini Kit (D311, Genepioneer Biotechnologies, Nanjing, China) according to the manufacturer's protocol.The qualified DNA samples was sequenced with 500 bp paired-end (PE) library construction using the VAHTS Universal DNA Library Prep Kit for IlluminaV3 (Vazyme Biotech Co., Ltd, Nanjing, China).About 29,356,547,400 raw data from B. rapa var.Purpuraria were generated with PE150 sequencing strategy.Subsequently, the qualified DNA was cut into 20-kb fragments using a Covarisgtube (Covaris) and purified with AMPure beads.The samples were sequenced with Oxford Nanopore library construction.
Mitochondrial genome assembly and annotation
We used the Fastp 0.23.4 ( https:// github.com/ OpenG ene/ fastp) software to filter the second-generation raw data.The parameters were set as follows: (1) Cut off the primer and adapters sequences; (2) Filter out the reads with average quality value lower than Q5.(3) Delete the reads with the number of uncertain bases more than 5.Then, the original tri-generational data was filtered using filtlongv0.2.1 (https:// link.zhihu.com/?target= https% 3A// github.com/ rrwick/ Filtl ong) with parameters set as:-min_length 1000 and -min_mean_q7.The highly quality tri-generational data were aligned with the plant mt gene database (https:// github.com/ xul96 2464/ plant_ mt_ ref_ gene) using min-imap2 [33].The size of sequence more than 50 bp, containing multiple core genes and higher alignment quality was selected as the seed sequence.Then, the original tri-generational data were compared with the seed sequences using minimap2, and the sequences with overlap more than 1 kb were screened and added to the seed sequences.The original data were compared to the seed sequence iteratively, and all the third-generation sequencing data of the mt genome were obtained.All the third-generation sequencing data were performed self-correction and assembled using the canu v2.0 program [34], and Bowtie2 (v2.3.5.1) was used to align the second-generation data to the corrected sequence.The second-generation data were compared to stitch the corrected third-generation data using Unicycler (v0.4.8) software with default parameters, followed by using Bandage ( v0.8.1) software to visualize and manually adjust the stitching results.The corrected third-generation sequencing data were aligned to the conting obtained by the second step of Unicycler using minimap2, and the branch direction was manually determined to obtain the final assembly result.
The encoded proteins and rRNAs were aligned to reported plant mt sequences using BLAST, and further manually adjusted according to closely related species.The tRNAs were annotated using tRNAs-canSE online tool [35] (http:// lowel ab.ucsc.edu/ tRNAs can-SE/).ORFs were annotated using Open Reading Frame Finder (http:// www.ncbi.nlm.nih.gov/ gorf/ gorf.html) with a minimum length of 102 bp.The map of B. rapa var.Purpuraria mt genome was drawn using OGDRAW (https:// chlor obox.mpimp-golm.mpg.de/ OGDraw.html) software.A single nucleotide polymorphism (SNP) was detected among six Brassica mt genomes using MUMmer and BLAT v35 softwares.
Relative synonymous codon usage (RSCU) analysis.
The codon composition of the mt genome of B. rapa var.Purpuraria was analyzed using a Perl script written by ourselves, to select for a unique coding sequences (CDS) and calculate the RSCU of synonymous codons.
Gene transfer between the cp genome and mt genome
The B. rapa var.Purpuraria mt genome was aligned with its cp genome (PP191173) by blast and the selected parameters were set as the matching rate ≥ 70%, E-value ≤ 1e −5 and length ≥ 30 bp [38].
Ginkgo biloba (NC_027976) was used as the outgroup in this analysis.
Characteristics of the B. rapa var. Purpuraria mt genome
In this study, the mt genome of B. rapa var.Purpuraria was sequenced 29,356,547,400 raw data and 97,855,158 bp clean data (Q20 = 97.11%and Q30 = 91.81%)were obtained using the Illumina platform (Table S1).Regarding the Nanopore sequencing, a total of 17,960,842,101 bases and 1,417,067 reads were obtained using the Nanopore sequencing platform.The subreads with N50 and the mean read were 27,413 bp and 12,674 bp, respectively (Table S2).The whole mt genome of B. rapa var.Purpuraria was 219,775 bp in length with a typical circular structure (Fig. 1).The nucleotide composition of the whole B. rapa var.Purpuraria mt genome contains 27.45% of A, 27.31% of T, 22.91% of C, and 22.32% of G, with GC and AT contents accounted for 45.23% and 54.77%, respectively (Table S3).PCGs and cis-spliced introns occupied 13.22% and 12.86% of the complete mt genome, whereas tRNA and rRNA genes only made up 0.79% and 2.34%, respectively.A total of 59 genes, comprising 33 PCGs, 3 rRNAs, and 23 tRNAs, were found 2).Six genes, namely, ccmFc, cox2, rpl2, rps3, trnI-AAT , and trnT-GGT included one intron, genes of nad1, nad2, nad5, and nad7 contained four introns, and one gene of nad4 had three introns.Three tRNA genes were identified in two or three copies (trnH-GTG , trnM-CAT and trnY-GTA ) (Fig. 1 and Table 1).
Plant mt genomes have significantly different in size, gene order and content [42].We selected six Brassica mt genomes to compare genome characteristics and determine variability of the mt genome of B. rapa var.Purpuraria (Table 2).The size of selected mt genomes varied from 219,736 bp (B.rapa ssp.rapa) to 232,145 bp (B.nigra).The smallest number of genes (53) S4).
Codon preference analysis of PCGs
The total size of PCGs in B. rapa var.Purpuraria was 35,927 bp.Except for nad1 gene with ACG as the start codon, ATG was the start codon for other PCGs, which might be the result of C-to-U RNA editing of the second site (Table 1).Four types of stop codons, including TAA, TGA, TAG, and CGA, were detected, and the C to U for RNA editing phenomenon was discovered in ccmFc gene.We also calculated the RSCU of 33 PCGs in the B. rapa var.Purpuraria mt genome (Fig. 2).The 33 PCGs made up 29,055 bp encoding 9685 codons including termination codons.Leucine (Leu) was the most frequent amino acid, with a total of 1053 codons, accounted for 10.87%, followed by serine (Ser), with a total of 856 codons, accounting for 8.84%, and termination codon (Ter) was the rarest with a total of 33 codons, accounting for 0.034%.We discovered that 30 codons of RSCU value were greater than 1, of which 27 codons (90%) ended with A or U, two codons (6.67%) ended with G, and only one codon (3.33%) ended with C. It illustrated that the A / U preference at the third codon was positioned in the B. rapa var.Purpuraria mt genome (Table S5).
The prediction of RNA editing
RNA-editing sites are widely distributed in the mt genome of plants.In this study, 379 RNA editing sites within 33 PCGs (Table 3) were predicted in the mt genome of B. rapa var.Purpuraria using PmtREP tool (Figure S1).Among these PCGs, atp6 had one RNA-editing site, whereas the highest was in nad4 with 379 RNAediting sites (33), of which 30.34% (115 sites) occurred with the first position of the triplet codes, 68.07%(258 sites) located at the second base of the triplet codes.In addition, the first and second bases of the triplet codes were edited, leading to an amino acid change from proline (CCC) to phenylalanine (TTC).There were 45.64% (173 positions) of amino acids hydrophobicity remained unchanged after the RNA editing.Besides, 45.38% (172 positions) of the amino acids were varied from hydrophilic to hydrophobic, while 8.71% (33 positions) were ranged from hydrophobic to hydrophilic.Furthermore, only one amino acid was varied from arginine to stop codon (Table 3).The findings in our study showed that most amino acids were changed from serine to leucine (24.01%, 160 sites), proline to leucine (22.69%, 86 sites), and serine to phenylalanine (12.40%, 47 sites).
In addition, we compared the RNA editing sites of B. rapa (AP017996), B. nigra(AP012989), and B.oleracea (AP012988) with representatives from Brassica species (Fig. 3).The highest edited transcripts were ccmB with 32 editing sites in B. nigra, and nad4 with 33 editing sites in B. rapa, B.oleracea and B. rapa var.Purpuraria.From the comparison results of RNA editing sites, we found that B. rapa var.Purpuraria is highly similar to other three closely related Brassica species.
Repeat sequences analysis
Simple sequence repeats (SSRs), also known as microsatellites, are DNA stretches composing of short unit sequence repeats of 1-6 base pairs in length [43].In this study, a total of 55 SSRs were detected in the mt genome of B. rapa var.Purpuraria, containing 20 (36.36%) monomers, 11 (20.00%)dimers, 5(9.09%) trimers, 18 (32.73%)tetramers, and 1 (1.82%) pentamers (Table 4).No hexanucleotide repeats were detected.Among the 55 SSRs, monomer and tetramer were the main type of SSR motifs, accounting for 69.09% of all detected SSRs.In addition, 90.00% of monomers had A/T contents, and 36.36% of dimers were AT/TA (Table S6).The abundant AT content of SSRs supported with the high AT content (54.77%) of the whole mt genome of B. rapa var.Purpuraria.Tandem repeats (satellite DNA) are core repeating units about 1-200 bases [44].As shown in Table 5, 17 tandem repeats with a matching degree over than ≧84% and length varying from 3 to 39 bp were obtained.A total of 252 dispersed repeats (≧28 bp), of which 144 palindromic (57.54%) and 108 forward repeats (42.46%) were observed, and no reverse and complementary repeats were found (Fig. 4).The total length of the dispersed repeats was 16251 bp, which occupied 7.39% of the whole mt genome.Most repeats were 25 repeats, 67.06%), while only one was over than 1 kb being 2427 bp (Table S7).
Ka/Ks and Pi analysis
The Ka/Ks ratio was used to evaluate selective pressures during the evolutionary dynamics of PCGs among similar species.In this work, B. rapa var.Purpuraria was used as a reference to calculate the Ka/Ks value of 33 PCGs in the B. rapa var.Purpuraria mt genome (Fig. 5).The Ka/ Ks values of most of PCGs were less than one, demonstrating that these genes may undergo negative selections during evolution.However, the Ka/Ks value of the atp4 and ccmB genes between B. rapa var.Purpuraria and Cucurbita pepo, the ccmB gene between B. rapa var.Purpuraria and Glycyrrhiza uralensis, the atp4, ccmB, and mttB genes between B. rapa var.Purpuraria and Helianthus grosseserratus, the ccmB gene between B. rapa var.Purpuraria and Solanum lycopersicum were higher than one, implying positive selection for these genes during evolution.Our findings further indicated that these mt genes might be highly conserved during the evolution process in higher plants.
The nucleotide diversity (Pi) values of 36 PCGs were accounted and varied from 0.01790 to 0.14222, with an average of 0.04417 (Fig. 6 and Table S8).The Pi value of gene3.rpl10region was largest among these regions being 0.1422, and 0.07436 in gene4.rps4,0.07195 in gene6.atp8, 0.07182 in gene29.rpl2and 0.0709 in gene21.atp9were found The lower Pi values revealed that the mt genome sequences of B. rapa var.Purpuraria were highly conserved.
Analysis of homologous fragments of mitochondria and chloroplasts
The total length of homologous sequences on chloroplasts was 13,153 bp, accounting for 8.57% of the whole cp genome.While the total size of homologous sequences on mitochondria was 8961 bp, accounting for 4.08% of the whole mt genome (Table S9).As shown in Table 6, twenty-two homologous fragments with a total length of 13,325 bp were found.The transfer route of the fragments may occur firstly from the chloroplast to nucleus, and then to the mitochondrion in B.rapa var.Purpuraria, accounting for 6.06% of the whole mt genome.Eight annotated genes, namely, trnL-CAA , trnN-GTT , rrn18, trnW-CCA , trnD-GTC , trnM-CAT , ccmC, and trnI-AAT , with high similarity to the mitochondria likely originated from the mt genome.While 17 genes, being rpoB, ycf2, ycf15, trnL-CAA, rbcL, trnN-GUU, ycf1, psaA, rrn23, rrn16, psaB, trnW-CCA, trnD-GUC, trnP-UGG, trnM-CAU, trnI-CAU, and trnI-GAU with high similarity to the cp genes, might be transferred from cp genome, and only partial sequences of those genes were identified in the mt genome (Table 6).Most of transferred genes were tRNA genes, of which those genes were much more conserved in the mt genome than PCGs during the evolution.
Discussion
Mitochondria is the core of energy source in cells, which exhibited more complex in plant than animals due to its size variations and repetitive sequences [45][46][47].In this study, we analyzed the characteristics of mt genome in B. rapa var.Purpuraria.The total length of the mt genome of B. rapa var.Purpuraria was similar to that of B. juncea [48], being moderate in genome length compared with other reported mt genomes [49].The GC content in the In addition, the PCGs occupied 13.22% might be due to the result of increasing sequence repeats during evolution.PCGs usually encoded from initiation codon (ATG) to stop codons (TGA, TAA, and TGA), and the distribution of amino acids compositions was consistent with Acer yangbiense [55] and A. thaliana [56].The nad1 gene using ACG as start codon in consistent with Salix suchowensis and Phaseolus vulgaris might be induced by RNA editing [46,47].
Codon usage bias refers that synonymous codons exist in a non-random manner in different species [57].The analysis of codon usage patterns is helpful to understand the molecular mechanism of biological adaptation and explore the evolutionary relationship among species [58].Previous studies have shown that codons prefer to use A / U endings in the plant mt genomes [44][45][46][47].In total of 30 high-frequency codons were detected in the B. rapa var.Purpuraria mt genome, of which 90% codons ended with A or U, which might be the result of natural selection, mutation pressure and genetic drift [59].In addition, we found that leucine was the most frequently used amino acid, which was consistent with S. glauca [44] and Acer truncatum Bunge [60].
The number of RNA editing sites varies among different plants, and occurred commonly in gymnosperm and angiosperm mt genomes.We obtained 379 RNA editing sites within all the 33 PCGs in the B. rapa var.Purpuraria mt genome, which exhibited much less than those in Diospyros oleifera (515) [61], Bupleurum chinense DC (517) [38], Macadamia integrifolia (688), M. ternifolia (689) and M. tetraphylla (688) [62], and higher than those in S.glauca (261) [44] and Pereskia aculeata (362) [63].The selection of RNA editing sites in the B. rapa var.Purpuraria genome exhibited a high degree of compositional bias.Most of the RNA editing sites were the C-T editing type, being similar as in other plant mt genomes [64][65][66].
Previous studies showed that about 50% of RNA editing generated at the second bases of the triplet codes [44,65].About 68.07%(258) RNA editing sites occurred at the second codon position in the B. rapa var.Purpuraria mt genome, greater than that at the first codon position (115, 30.34%).In addition, 1.58% (6) RNA editing sites occurred at both of the first and second codon position.The similar phenomenon was observed in the D. oleifera mt genome [61].There is no RNA editing sites predicted at the third codon position in B. rapa var.Purpuraria mt genome [44,66].The repeat sequences, including SSR, tandem and dispersed repeats, were widely distributed in the plant mt genomes [8,67].Previous studies have reported that repeat sequences were important for intermolecular recombination, which play a vital role in forming the mt genome [68].Because of its high variability and recessive inheritance, SSR has been widely used to confirm phylogenetic relationships, genetic diversity studies and species identification [69].The mt genome of B. rapa var.Purpuraria contained 55 SSRs, of which 90.00% of monomers being A or T, resulting 54.77% of AT in the B. rapa var.Purpuraria mt genome.The high AT content in mt genome were also detected in Scutellaria tsinyunensis [70].and Magnolia biondii [71].In addition, 252 dispersed repeats were discovered in this study, which was much greater than B. oleracea var.Italica in the genus Brassica [72].
The ratio of Ka/Ks provides useful information for reconstructing phylogenetic relationships, and contributes to understand the evolutionary dynamics of PCGs among closely related species [73].Most of mt genes with Ka/Ks ratios < 1 exhibited negative selections, and a few genes with Ka/Ks ratios > 1 showed positive selections during the evolution in plants [44,61].The Ka/Ks ratio of ccmB gene was greater than 1 in S. glauca mt genome exhibited positive selection [44], whereas Five genes, namely, atp4, nad1, ccmC, mttB, and rpl2, showed positive selections in Capsicum pubescens Ruiz & Pav mt genome [74].Two genes, being mttB and rpl5 exhibited positive selections in European-Asian species [75].However, three genes with Ka/Ks ratios > 1, including atp4, ccmB, and mttB, exhibited positive selections in our study in consistent with previous studies [44,74,75], illustrating that these genes might be selected for future researches on the gene selection and phylogenetic of Brassica species.Changes in the size and structure of the plant mt genomes have been obviously observed, whereas the functional genes are still conserved [76].
Previous studies indicated that Pi could reveal the variation of nucleic acid sequences in different plants, and the highly variable regions might be selected as potential molecular markers for population genetics [77,78].Pi analysis reflected the variation of nucleotide sequences among different species (Fig. 6).Our results revealed that the Pi value of rpl10 gene was the largest in these regions, illustrating that rpl10 gene might be used as molecular markers for the mt genome analysis in B. rapa var.purpuraria.Except for Reclinomonas, plants are the only group of eukaryotes that still remain the rpl10 gene in their mt genomes [48,49].However, the mt rpl10 gene has been missed in some Brassicaceae species, and replaced by an additional copy of the nuclear gene that normally encodes cp RPL10 protein [79].Five highly variable regions, being ccmB, ccmFC, rps1, rps10, and rps14, might be used as molecular markers in Phaseolus vulgaris mt genome.In addtional, the overall low Pi values showed that the mt genome sequences of B. rapa var.Purpuraria were highly conserved.Phylogenetic analysis of plants have developed to use the complete genome data to construct the relationship among different species [44][45][46][47][48]. Here, the phylogenetic tree was constructed according to the mt genomes of 25 species.B. rapa var.Purpuraria was well clustered with the species of genus Brassica and stayed closely to B. rapa subsp.Oleifera and B. juncea, suggesting that B. rapa var.Purpuraria belongs to the Brassica species in the Cruciferae family.Shao et al. (2021) found that B. oleracea stayed a closely relationship with B. rapa subsp.Campestris with 100% support rate [80].Brassicaceae is a superfamily containing over 3800 species, in which Brassica is the most important genus as having many important vegetables and oil crops.It has been mentioned that based on cp genome, B. napus always clustered with B. rapa morphotypes, but did not cluster into a monophyletic group, and were distantly separated by B. juncea and B. oleracea.The obtained phylogenetic tree revealed a clear phylogenetic relationship among the species.B. rapa var.Purpuraria as a local vegetable planted around Yangtze River, may also develop some different characteristics in mt genome to regulate the biosynthesis in anthocyanin, and other nutritional compounds.Therefore, assembling and analyzing the mt genomes with those difference genome information will help to better understand their genetic characteristics and selecting their differences for further investigation.DNA sequence transfer between cp and mt genomes has been frequently discovered in plant mt genomes [81].In higher plants, the total size of transferred DNA ranges from 50 kb (A.thaliana) to 1.1 Mb ( O. sativa subsp.japonica)depending on the plant species [82].In total, 13,325 bp of cp DNA has been transferred into the mt genome of B. rapa var.Purpuraria, accounting for 6.06% of the B. rapa var.Purpuraria mt genome.In comparison, the proportion in M. integrifolia, Liriodendron tulipifera, and Nicotiana tabacum is 5.4%, 3%, and 2.5%, respectively [38,71,83].About 22 fragments transferred from the cp genome to the mt genome, containing eight annotated genes, with six tRNA genes (trnL-CAA , trnN-GTT , trnW-CCA , trnD-GTC , trnM-CAT , and trnI-AAT ), rrn18, and ccmC.The tRNA genes transferred from cp to mt genomes has been commonly discovered in angiosperms [44,84,85].These results were consistent with the previous study, which showed much more conserved for tRNA genes than the PCGs during the evolution, and tRNA genes played indispensable roles in mt genome [46].
Gong and Hua Huang wrote and revised the manuscript.All authors read and approved the final manuscript.
Fig. 1
Fig. 1 The circular map of the B. rapa var.Purpuraria mt genome
Fig. 3
Fig. 3 The distribution and comparison of RNA-editing sites in the PCGs of B. rapa var.Purpuraria mt genome and three closely related Brassica mt genomes
Fig.Fig. 7
Fig. Nucleotide diversity of B. rapa var.Purpuraria mt genome was found in B. nigra, and the largest (106) in B. napus.The number of tRNA genes ranged from 17 in B. napus, B. nigra, and B. oleracea to 23 in B. rapa var.Purpuraria.In addition, all the selected mt genomes included 3 rRNA genes (Table 2).Combing our present results, it revealed that B. rapa var.Purpuraria has a high degree of similarity to the mt genome sequences to B. rapa, B. nigra, and B. oleracea.Furthermore, to identify sequence variations in the known genes, SNPs were detected between B. rapa var.Purpuraria and B. juncea, B. napus, B. rapa, B. nigra and B. oleracea.A total of 202 SNPs were found among six mt genomes.135 SNPs were identified between B. rapa var.Purpuraria and B. rapa ssp.rapa, followed by 62 SNPs in B. rapa var.Purpuraria vs B. nigra group, 4 SNPs (cox2, atp1, and two cox1 genes) in B. rapa var.Purpuraria vs B. napus group, and only one SNP (atp1 gene) in B. rapa var.Purpuraria vs B. oleracea group.But there were no SNPs identified in B. rapa var.Purpuraria vs B. juncea and B. rapa var.Purpuraria vs B. rapa (Table
Table 1
Gene profile and organization of the B. rapa var.Purpuraria mt genome
Table 2
Comparison of gene content among Brassica mt genomes
Table 3
Prediction of RNA editing sites in the B. rapa var.
Table 4
Frequency of identifed SSR motifs in the B. rapa var.Purpuraria mt genome
Table 5
The tandem repeats anaysis of B. rapa var.Purpuraria mt genome
Table 6
Fragments transferred from cp to mt in B.rapa var.Purpuraria a Represents the partial sequence identified in mt genome | 6,326.6 | 2024-06-01T00:00:00.000 | [
"Biology",
"Environmental Science"
] |
Modeling Wireless Mesh Networks for Load Management
—Developing a simulation model for multi-hop multi-gateway wireless mesh networks (WMNs) is a challenging task. In this paper, a multi-hop multi-gateway WMN simulation model is developed in a step-by-step approach. This paper presents a MATLAB Simulink-based simulation model of Wireless Mesh Network (WMN) designed for easy optimization of layer 2. The proposed model is of special utility for the simulation of scheduling of GateWay (GW) and packet within a multi-hop multi gateway wireless network. The simulation model provides the flexibility of controlling the flow of packets through the networks. Load management among the GWs of WMN is performed in a distributed manner wherein the nodes based on their local knowledge of neighborhood beacons optimize their path to a GW. This paper presents a centralized Load Management Scheme (LMS). The LMS is based on the formation of Gateway Service Sets (GSS). The GSS is formed on basis of equal load distribution among the GWs. The proposed LMS is then analyzed for throughput improvement by leveraging the MATLAB Simulink model developed in the paper. A throughput improvement of almost 600% and a 40% reduction in packet loss was observed through simulations thus indicating the efficacy of the proposed LMS. The uniqueness of the simulation model presented in this paper are its scalability and flexibility in terms of network topology parameters.
I. INTRODUCTION
Nearly always good research methodology is supposed to culminate with performance analysis and simulation study. Research in wireless networks carries no exception. In this paper, a system model is presented to simulate the WMNs. The model is designed in a manner such that it supports the flexibility to increase or decrease the number of GateWays (GWs) within the mesh as well as supports the increase and decrease in the number of hops for a particular router. This results in providing a very simple lightweight model for the optimization of layer 2. This model can be applied easily for GW scheduling in a very quick and efficient manner.
Designing a multi-hop multi gateway WMN model is a tough challenge. In such a mesh network there are multiple parameters to be handled. A very popular example is the IEEE 802.11s mesh architecture [1]. Another example is the Zigbee mesh architecture [2]. In a mesh architecture, the model has to be developed in such a way that the simulations can be performed on a wide variety of scenarios. Specifically, the model should be able to generate scenarios wherein the number of gateways can be varied. At the same time, the model should also have the capability to increase/decrease the number of Mesh Routers (MRs). The model should also be able to depict the three-level hierarchy of a WMN as presented in Fig. 1 and Fig. 2 of this paper. In this paper, a WMN model is developed which comprises all the aforesaid properties efficiently. Such a model can be used by researchers to apply their solutions easily. The contribution of this paper is to provide a platform and insight which can be used by the scientific community to build their WMN models in a better and more efficient manner using Simulink.
In this paper, a load management technique is applied to reduce congestion in GWs of WMN. In multi-GW WMNs, there is no mechanism available to schedule a fixed set of MRs to GWs. This causes either contention or congestion of GW [3,4]. In this paper, a GW scheduling technique is applied by creating a fixed Gateway Service Set (GSS). GSS is defined as assigning an equal number of MRs to each GW. This will result in avoidance of delay due to repeated computation of nearest GW by MRs. This will also reduce GW congestion by avoiding unfair allocation of MRs to GWs. Such an LMS is then used to analyze the performance of load sharing in various scenarios of WMN. The pertinent point is that the simulations to analyze the proposed LMS could be performed with ease due to the flexibility provided by the proposed simulation model.
II. LITERATURE REVIEW
Most of the research about WMNs generally opts for the ns2 [5] simulator which is an unlicensed open-source simulator. Among the licensed simulators, the top choices are Qualnet and Simulink [9]. Simulations are of two types -Discrete events and continuous ones. Discrete event simulations are suitable for models where parameters do not change until the occurrence of some event. Continuous event simulations are suitable for models where parameters change continuously and do not require the occurrence of any event for the occurrence of change [6]. In [7], the authors have defined and compared different types of simulation models based on event and time. A characteristic feature of a good model is its scalability. The model of WMN should allow flexibility in changing the network topology quickly and easily. An analysis of different types of network simulators is presented in [8].
The model of a WMN comprises three types of nodes -GWs, MRs, and End Nodes/client nodes. GWs provide Internet access to MRs and end nodes. There can be multiple GWs that connect the network to the Internet. The difference between MRs and End nodes is that MRs can redirect traffic to GWs, whereas End nodes just connect to the nearest available MR. Unlike MRs, the End nodes cannot connect to a far-off node www.ijacsa.thesai.org that is out of communication range of a GW. Most of the WMNs follow the generic architecture recommended by the IEEE 802.11s standard [1].
An abundance of literature is available on wireless network simulations using Simulink [9,10,19]. But in most of these papers, the researchers are unable to consider multi-hop multigateway WMNs such that the number of GWs is more than 5 and the number of routers more than 20. In [9], the authors have simulated multi-gateway mesh networks. Although the authors of [9] analyze multi-GW association in WMNs, the simulation model comprised only two GWs and 14 MRs. The authors in [10] have simulated WMN with 100 MRs but have not considered more than one GW. This limits their analysis to WMNs with only a single GW. In [11], the authors have used the ns2 simulator to simulate a network with 50 nodes but with only a single GW. The authors in [12] have considered WMN with up to 5 GWs and 50 MRs. But the topology of WMN has not been modified throughout the simulation process.
In this paper, a step-by-step process is presented to develop a WMN on Simulink. Thereafter, the model is used to analyze the performance of the WMN when there is an increase in the number of GWs and MRs systematically. In the process, there is an attempt to achieve a balanced approach for ensuring a fair allocation of MRs among multiple GWs. Therefore, to each GW an equal number of MRs is assigned. The uniqueness of the model presented in this paper is that it is scalable and flexible in terms of network topology parameters. In this model, very easily the number of MRs can be increased and decreased. The same applies to GWs wherein the number of GWs can be increased and decreased with ease. Finally, this model is applied to analyze a fair GW scheduling technique. This paper proposes to allocate a fixed set of MRs to a GW thus forming a GSS. The GWs are deployed such that each GW receives an equal number of MRs which is in its wireless coverage area. These MRs assigned to a GW might be directly within its communication range or through another MR as mesh topology [1]. This will result in the mitigation of delay in the computation of the path to a GW. Since most of the traffic is to or from the Internet, GWs become a major source of traffic within WMN. This results in congestion of the wireless links to GWs and congestion due to queuing delays in GWs. This occurs since some GWs might have a larger number of MRs associated with them compared to some other GWs in WMN, which might be idle due to no traffic through them. In [13], the authors have identified that the available capacity of a GW reduces by O(1/n) where n is the number of users. The presence of many users results in GW bottleneck and was termed as a "bottleneck collision domain" in [13]. In [14,16] the authors have attempted mitigation of GW bottleneck with a proposal of performing cooperative caching among the MRs to avoid packet loss. Most of the load balancing techniques focuses on route optimizations. Since most of the time routes are formed on basis of the information about the neighborhood of a node, these are not very optimal techniques. It is also observed by [15] that such techniques consume network resources and bandwidth due to repeated attempts for route requests and route response packets. A very recent paper in this direction is by [17]. In this paper, the authors have attempted to balance load by optimizing the Adhoc On-Demand Distance Vector (AODV) Routing Protocol. AODV is a very popular routing protocol in WMNs. This is because most of the optimization techniques in WMN are derived from the adaptations of MANET technologies. In the case of MANETS, assigning a fixed service set to GW is not possible due to peer-to-peer routing. But in the case of WMNs, especially IEEE802.11s WMNs, such an assignment is possible because WMNs are a hybrid of fixed and mobile infrastructure. Therefore, this paper proposes a mechanism in which each GW can be assigned its own GSS thereby reducing the network traffic for route determination. This technique also results in a fast and efficient delivery mechanism because the MRs do not have to keep computing the shortest path to a GW when there are multiple GWs in the vicinity. In [18] the authors have performed a detailed survey and have concluded that the WMNs are here to stay for a long time. In [18] the authors also note that the WMN model should become more and more flexible in a manner that allows for the nodes to move from one gateway to another seamlessly. This paper attempts to provide such flexibility while performing the load sharing among gateways through a fair assignment of MRs to GWs. Fig. 1 presents a conventional WMN with three levels of nodes. For more details on WMN and its architecture one may refer to [19] in which authors have explained in detail different types of WMNs based on various IEEE standards. At the first level is the GW node which connects to the Internet. In IEEE802.11s standard [1], it is called the Mesh Portal Point (MPP). But in this paper, a more generic term called the GW node is used. The GW node is connected to many routers which are called the Mesh Points (MPs) in IEEE 802.11s. But to keep the term generic, it is called the Mesh Router (MR). Finally, the end nodes are the client devices, for example, a laptop, smartphone, or a sensor. These are called the Mesh Clients in IEEE 802.11s. In this paper, they are referred to as End nodes.
III. NETWORK ARCHITECTURE OF WMN
The WMN architecture in Fig. 1 is extended further to a real-world scenario in Fig. 2. The difference between Fig. 1 and Fig. 2 is that in Fig. 1 none of the GWs have a fixed Gateway Service Set (GSS) whereas in Fig. 2 each GW has been assigned a fixed number of MRs. In Fig. 2, the MRs and the GWs are connected through wireless links and there are wired connections between the GWs and the core router. Each GW locally maintains an Active Passive Routing (APR) table which is explained later in this section. It is important to note that there might be many WMNs connected and served by the same Internet Service Provider (ISP). To illustrate this, there are two labels indicating WMN-1 and WMN-2 in Fig. 2. Both the WMNs are shown connected to the same ISP and core router. Fig. 2 depicts a dashed line that separates the ISP space and the edge space. The edge space marks the beginning of the WMN space or the Local Area Network (LAN) space.
The next section presents how this model can be used to implement fair scheduling of GWs within a WMN. The proposed scheduling of GWs through the judicious management of the routing table is called Load Management Scheme (LMS). The usage of the term LMS is justified because the scheduling of GWs aims at the reduction of processing load on GWs. A particular GW can hand off its extra load to a neighboring GW by simply changing the MR entry from active to passive, in its routing table. At the same time, the GW receiving the load will change the entry of the MR from passive to active. Therefore, by managing and changing the routing table, a fair allocation of GW to MRs can be maintained.
IV. COMPONENTS OF WMN
The core router is a router that connects the edge network to the Internet. The major functionality of the core router is to streamline the Internet traffic as per the bandwidth demand without a loss in performance [16]. In this paper, the core router is entrusted with the main functionality of meeting the bandwidth demand at the edge routers (GWs in this case). Fig. 2 depicts the Core Router sub-block. The major components of a core router are Internet Service Provider (ISP), Core Router, Authentication, Authorization, and Accounting (AAA) server, Billing server, Network Management System (NMS) Server, Voice, and Video data services, DHCP Server, Global Active/Passive Routing (APR) Table and Intelligent Middle Ware (IMW).
Although the APR Table and IMW may not be a part of the core router in conventional WMN, the proposed LMS requires this additional software to be installed at the core router. The IMW and its components are discussed in more detail in a later section. The components of Edge Space define the components of WMN and are described next.
A. GW
This is the connection point to provide Internet connectivity through the Core router. The GW is connected to the core router through a wired medium or high bandwidth.
B. MRs
The GW is associated with a set of MRs labeled from R 1 to R 6 . Each MR has a wireless connection to either another MR or the GW. An MR is connected to another MR or GW if they are within transmission range of each other. If an MR is not in the transmission range of the GW, it can still reach the GW through multiple hops by using another MR which is within the transmission range of GW. An MR is not allowed to send a packet to GWs other than its associated GW even if there are other GWs that are in its transmission range. The MR-GW association is decided through the APR table depicted alongside each GW in Fig. 2.
C. Local APR Table
This is the most important data structure of the proposed LMS residing at the GW. This table facilitates mapping the GSSs of WMN. Each GW has two main columns in its APR table namely, the active column and the passive column. The active column contains the list of all those MRs that are associated with the GW whereas the passive column keeps the list of all those MRs that are in the transmission range of the GW but are not associated with it. While configuring the WMN, the GW routing table is configured such that the GSSs obtained from the Greedy Graph Partitioning Algorithm (GGPA) are mapped onto the routing table of each GW. This means all those MRs that belong to a GSS are made active in the routing table of GW. Table I, the active column contains MRs labeled R 1 , R 2 , R 3 , R 4 , R 5, and R 6 . The MRs labeled R 7 and R 11 are associated with GW 2 as shown in Fig. 2. But because they are within the transmission range of GW 1 , R 7 and R 11 are listed under the passive column of Table I. TABLE I. APR Initially, the APR table of GW1 appears like Table I and after offloading of MRs labeled R7 and R11 to GW1, the modified APR of GW2 is depicted in Table II. Interestingly, the transition process at the core router involves only updating the entry of the APR table of receiving and sending GWs.
D. The Intelligent Middle Ware
The core router shown in Fig. 2 executes an IMW explained in this section. The IMW residing on the Core router of Fig. 2 has two modules namely load monitoring and load sharing. The load monitoring module periodically estimates the load demand of each GW. Based on this estimation, the module decides whether the load on GW is excess or not. The basis of this calculation is based on comparing load demand to the capacity of GW. A discussion on computing the capacity of GW is presented in [16,20]. If the load demand exceeds the capacity of GW, then a particular GW is overloaded. Demand at each GW is computed by the load monitoring module by recording the number of MRs connected through the GW and the applications that they are executing.
The load sharing module has two components to support load sharing with neighboring GWs. Load sharing with wireless GWs is invoked when the load monitoring module raises an overload alert. The load sharing module checks the stability condition (whether any neighboring GW is having less load and is willing to receive MRs from the overloaded GW). If the stability condition is satisfied, then from an overloaded GW, an MR with a high bandwidth demand is shifted to a neighboring GW with a nominal load. Accordingly, the APR tables are updated.
V. SIMULATION MODEL OF THE PROPOSED LMS OF WMN
Since this research is focused on routing optimization for load balancing, this study requires simulation to be built around the multi-hop routing mechanism of mesh. In this paper, the Simulink blocks are developed to suit the requirement of IEEE 802.11s MAC which is the main module of interest to this paper. To develop this model, the network architecture evolved in the previous section is used. The coming sections explore this process and after the explanation of the individual blocks, the complete integrated model is presented. Fig. 3 represents the sub-blocks required for the implementation of the proposed LMS. The simulation model has the following four major modules namely Packet Generator, Core router, MR Mobility, and MPP GW. These blocks follow the network architecture depicted in Fig. 2. It can be recalled that in the network architecture of Fig. 2, the core router routes packets to the respective GWs. Thereafter the GWs forward the packets to the destined MR through multiple hops. Finally, the destined MR forwards the packet to the client/customer device. The simulation model uses a packet generator to generate traffic and this traffic constitutes the input to the core router. Each packet has a destined MR identified by an IP address. The core router module maintains a global APR table for each of the GWs of WMN.
The MR-mobility module simulates the transition of MRs from one GW to another. Since the MR transition effect percolates to the core router, this block is kept located between the GW and the core router block in the hierarchy. For this, the MR mobility block receives signals from the GW about the completion of the transition. It must then send a signal to the core router to resume packet flow from the packet generators, in case the MR transition is complete. The core router in turn issues a signal to the packet generator to resume packet generation.
The MPP GW module defines the operations of GW. The GW model also has a sub-model that simulates the enduser/customer device which operates on the normal IEEE 802.11x [21] standard. This simulation also comprises the client hand-off/handover process between two MRs. A detailed discussion of the layout of each block is presented in the coming sub-sections. The block layout is followed by a screenshot of the actual Simulink model used in the simulation. More details on the process of designing the Simulink block are presented in [22].
A. Packet Generator Module
A packet generator is modeled as a random packet generator that generates packets with labels for specific GWs. The packet generator has five major blocks as depicted in Fig. 4, namely, Set Attribute, Free running counter, Repeating Sequence Stair, Time based entity generator, and FIFO Queue. Set attribute block gets packet generated. The free-running counter block is for data generation. Repeating sequence block is to define the length of the data block. Time-based entity generator defines the rate at which packets are generated. Finally, packets are delivered to the core router through the FIFO queue. A screenshot of the final packet generator Simulink block comprising these sub-blocks is shown in Fig. 5. The output of the packet generator is fed to the core router. This module is explained in the next subsection.
B. Core Router Module
The function of a core router is to route the packet coming from the packet generator to respective GWs. From its global APR table, the IMW checks for the destination MR and the GW associated with the destination MR. Then the packet is routed to the associated GW of destination MR. The core router has six major blocks as depicted in Fig. 6. 1) GW server receives packets from respective "packet generators" which are to be fed to "path selector".
2) A reverse traffic block is used to model traffic from GWs and MRs to the core router.
3) Path selector sorts all the GW packets along with power line packets and reverses traffic packets.
4) The service time function computes the time taken for path selection (routing) to respective GWs. The referred service time is computed by dividing the length of the packet by the capacity of the core router. For example, if the length of the packet is 512 bits and the capacity of the core router is assumed to be 100 Mbps, then the service time for each packet is 512 ns. 5) Core GW server serves each packet in-service time defined by the service time function. The health of the core router is monitored in the "core GW server" by analyzing Channel Utilization, Average delay, Number of packets departed, Number of packets dropped, Average wait time, and packet delay. 6) Output switch sends packets to their destined GWs: The functionality of the Core router block along with these components is depicted through a Simulink model shown in Fig. 7.
C. MR-Mobility Module
MR Mobility module simulates the MR hand-off and handover from one MR to another MR just like client mobility in an IEEE 802.11x network. When an MC moves out of an MR access area, the MR hands over the MC traffic to the MR which is accessible to the MC. This delay is added to the total packet response time. A Simulink model of MR mobility is shown in Fig. 8. It can be observed that the MR mobility module has two major blocks. MR delay model. GW Channel model.
1) MR delay model:
The MR delay block simulates delay due to the transfer of MR from one GW table to another. This is an atomic process involving a delay in updating the global APR table at the core router and the local APR tables at the sending and receiving GW involved in MR transition. This block consists of a packet generator sub-block as shown in Fig. 9. The packet generator block induces reverse traffic from the GW towards the core router. In this paper, the word "traffic" indicates the traffic from the Internet (packet generator) to the MRs whereas "reverse traffic" is defined as packets from the
MR Delay
Packet generator www.ijacsa.thesai.org MR towards the Internet. This reverse packet, when generated by the packet generator module of the MR delay block, indicates invoking of load sharing. When the reverse traffic packet reaches the main packet generator module through the core router, it blocks the packet generator till the time the MR transition takes place (delay in updating the local and global APR table). Once the MR transition is over, another reverse packet is generated from the MR delay block towards the core router and the packet generator resumes the forward traffic. Fig. 10 depicts the MR delay block comprising the packet generator sub-block. The packets generated by the MR delay block are forwarded to the "GW Channel Model", explained in the next section, which incurs channel processing delay.
2) GW channel model of the MR mobility block:
The GW Channel block of the MR mobility module models the channel between the GW and Core router. The sub-blocks of the channel model are depicted in Fig. 11. b) Signal latch: Path selector uses "Probabilistic signal latch model" to select packets. c) Attribute: The service time in processing packets in a single server is calculated by the "Attribute Function" block. d) Packet sink: The data packets are routed to the respective GW or core router in case of backward traffic using the "Packet sink" block. e) Output switch: The packets are sorted by "Output switch" which checks the packet header and routes the packets to the respective destination GW or routes the packet back to the core router if it is a backward packet requesting a traffic block. Fig. 12 depicts the final Simulink block of the channel model representing all the above-listed sub-blocks.
3) The final MR mobility Simulink block: The final MR mobility Simulink block comprising its major sub-blocks the MR delay block of Fig. 10 and channel model of Fig. 12 is shown in Fig. 13.
D. GW Module
The GW module segregates and routes the packet destined to a particular MR. The structure of the GW module is depicted in Fig. 14. This block has four major sub-blocks: a) Wireless GW: This model has a "set attribute" block that receives packets from the core router and forwards them at a pre-defined data rate (bandwidth) to the channel model through the "FIFO queue" block. b) Power Line GW: The power line GW gets the packets directly from the core router. It uses the same "set attribute" block to define the data rate. The "FIFO queue" www.ijacsa.thesai.org block gets input about the MRs chosen to transit to the power line. This block is attached to the core router and it routes the traffic from the core to the MRs specifically attached to the power line. The MRs attached to the power line GW can be identified using the global APR table at the core router. c) Mesh Client Mobility delay: This block has two parts. One part simulates the end-user device, and the other part simulates the mobility of the client. The end-user device acts as either a source or a sink for the traffic flow. Therefore, the end-user device is modeled as having two parts-the packet generator part which is the source, and the sink which consumes the packets which are received through its connected MR. The mobility of the client is modeled by introducing a handoff-handover delay whenever the mobile client moves from one MR transmission range to another.
d) MR Channel model: This model simulates the channel between the GW and the MRs. The channel model is responsible to induce the client's mobility delay. This is the delay involved in hand-off and hand-over when an end-user moves from one MR to another MR. This is different from the MR mobility delay which involves delay incurred during the transition of MRs for load sharing. The sub-blocks listed in Fig. 15 are shown in the final Simulink block of the MPP-GW model block in Fig. 16.
2) Multi-Hop MR of GW:
The "multi-hop MR" sub-block receives packets from the MPP-GW block and records variation in-service time due to the increasing number of hops. This block consists of two sub-blocks as depicted in Fig. 17. b) Backend traffic delay: This block simulates the processing delay incurred by the mesh management traffic. Although this traffic does not contain the actual data packets, mesh management packets are also important. The Simulink block of multi-hop MR simulation is shown in Fig. 18 which depicts the "get attribute" and "delay" sub-blocks listed in Fig. 17.
3) Display block:
Since this is the final and the last block of the simulation model, it displays parameters such as "number of packets departed", "Average waiting time", and "service time". Fig. 19 depicts the final GW simulation block comprising the MPP-GW and the MR multi-hop simulation blocks.
F. System-Level Simulation Block
The system-level simulation model is shown in Fig. 20. This model depicts the packets generator module, the core router module, the MR mobility module, and finally the GW module. The process flow can be mapped onto the final simulation model in Fig. 20. This model will be used in the next section to derive various performance results and to investigate the various system parameters. The framework of this model follows the schematic architecture proposed in the network architecture diagram in Fig. 2. The next section presents the results obtained through the system-level simulation block of LMS shown in Fig. 20.
VI. ASSUMPTIONS AND PARAMETERS FOR MATLAB MODEL
In the previous sections, a simulation model of the proposed LMS was developed using MATLAB, and Simulink blocks. This model is used to analyze the performance of the proposed LMS. Various test cases for performance analysis are created to compare the performance of the WMN with the proposed LMS and the conventional WMNs with no load management feature. Throughout the simulation process, the simulation parameters are chosen as per Table III. The traffic flow is assumed to be Markov distributed. The core router is assumed to be connected through a high-speed wire link. Therefore, its capacity is 100 Mbps which is the usual capacity of a high-speed fiber backhaul. The communication range of 250 m and carrier sensing range of 550 m is the most used value in the simulation of the IEEE 802.11 standard. This assumption is based on the ns2 [5] and Qualnet"s physical layer adaptation of the IEEE 802.11 standard and 914 MHz Lucent WaveLAN DSSS wireless card [23]. Initially, a formulation is derived to compute the throughput from the simulation results. Thereafter this formulation is applied to obtain the throughput in the following section. First, a simple WMN is simulated without load management or GW scheduling. The throughput of this WMN is recorded. Thereafter the GW scheduling is performed, and the throughput is computed again. The performance of a conventional WMN is compared with a WMN with GW scheduling on basis of throughput, packet delay, and packet dropped parameters.
VII. ANALYSIS OF THE THROUGHPUT OF A WMN WITH THE PROPOSED LMS
This section investigates the throughput of WMN after applying each step of the proposed LMS. To compare the performance, it is necessary to create two WMN models namely Conventional WMN without LMS and WMN with proposed LMS. It can be observed that both these models can be derived from the system-level simulation model in Fig. 20 by making slight modifications in the IMW block.
A. Creation of a Simulation Model for Conventional WMN without LMS
To create a model of such a WMN, the simulation model of Fig. 20 is modified slightly. The IMW block as well as the Global APR table as explained in previous sections is disabled. The MRs are assigned to the GWs randomly and the respective APR tables of GWs are created accordingly. Thereafter, there is neither load monitoring nor load adjustments throughout the simulation period. This is the closest approximation to the conventional model of WMN without LMS.
B. Creation of Simulation Model of Load Management with
Load Sharing To obtain this model, the IMW block is modified such that all the blocks are enabled, and load monitoring is performed. Whenever the steady-state load condition is violated, the WMN performs load-sharing as explained in the IMW earlier. Since one of the major comparison parameters is the system throughput performance, the next subsection explains how throughput is calculated from the system utilization graph obtained through the simulation.
C. Process of Throughput Computation from the System Utilization Graph
This section explains how the throughput is calculated using the system utilization graph obtained from the MATLAB simulation. The system utilization graph is a part of the results displayed by the display block of the System-level simulation model in Fig. 20. It represents the average channel utilization of the entire WMN. The throughput computation is based on the following system parameters.
D. Throughput Analysis with Load Sharing
This section presents the analysis of a WMN having the capability of load sharing incorporated in it. For uniformity and ease of comparison, the same scenarios of the previous section are reconsidered. For the simulation, the maximum capacity of GWs is assumed to be 2 Mbps. The first simulation on a WMN with load-sharing features pertains to the studies on the variation of throughput as a function of the number of MRs. As can be seen from the results of Fig. 21, initially the throughput improves with the increase in the number of MRs. The improved throughput is due to the fair scheduling of WMN. Regarding the throughput performance, it is interesting to note that the performance profiles exhibit a steep rise and slow decay characteristics.
It is worth mentioning here that a very similar trend was observed in [24] when they performed a similar study on fifthgeneration cellular networks. It was observed by them that increasing the number of devices resulted in a decrease in data rates. They concluded that until better technology is devised, this decrease is bound to continue. This indicates that when a WMN gets congested and when all its GWs are utilized to their full potential, the throughput shall begin to drop. The relationship between the capacity of a WMN and the capacity of GW can be written as: The capacity of a WMN= (Capacity of GWs) x (Number of GWs).
E. Comparison of a Conventional WMN and a WMN with
Proposed LMS This section compares the throughput obtained in a conventional WMN without LMS with the throughput obtained in a WMN with the proposed LMS feature. The simulations have been performed keeping the total number of MRs fixed to 100 in each of the WMN scenarios but the number of GWs has been varied. This helps to study the effect of increasing the number of GWs on the throughput of WMN, keeping the number of MRs constant. The results in Fig. 22 depict a continuous increase in the throughput after the application of the proposed LMS. The percentage increase in throughput of a WMN with 5GW 100MR after load sharing is 869%. In the case of a WMN with 10 GW 100 MR, the percentage increase is 893% after load sharing. For a WMN with 15GW 100 MR, the percentage increase in throughput is 1000% after load sharing!!! The only difference in the simulation scenario between the Fig. 22 and Fig. 23 is the change in the total number of MRs to 200. Additionally, Fig. 23 also compares the throughput of a WMN obtained with a total number of 5 GW and 100 MRs.
The results of Fig. 23 reveal that a WMN with the same number of GWs but with a relatively larger total number of MRs exhibits better throughput performance. The throughput improvement of a WMN with 15GW 200MR is 1036% after load sharing. For a WMN with 10GW 200MR, the throughput improvement is 811% after load sharing. For a WMN with 15GW 200MR, the throughput improvement is 102.7% after load sharing. It can be noticed that if the number of MRs is fixed and only the number of GWs is increased, the gain in throughput is not as significant after performing load sharing. This is because when the number of GWs is increased but the number of MRs is fixed, then the GSS of every GW gets a lesser number of MRs. This results in a smaller number of MRs per GW and thus implying a relatively lesser gain in throughput. (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 13, No. 5, 2022 250 | P a g e www.ijacsa.thesai.org The next section compares the parameter of packet drop before and after applying load sharing.
F. Analysis of Packet Loss
Since the proposed LMS relieves the congestion of GWs, it results in a reduced packet loss thereby leading to overall improved performance of a WMN. For the simulation, a WMN of 100 MRs is considered. Fig. 24 presents a comparative summary of the results obtained for the packet loss parameter. For the simulation results showed in Fig. 24, the total number of MRs remains constant at 100 while the number of GWs is varied from 5 to 15. The results of Fig. 24 depict an average 40% reduction in the packets dropped after applying the proposed LMS. This confirms the progressive improvement attributed to each constituent process of the proposed LMS thereby demonstrating the best performance.
VIII. CONCLUSIONS AND FUTURE WORK
This paper has demonstrated the step-by-step process in the development of a simulation model of WMN using Simulink. The proposed simulation model was used to analyze the performance of the LMS proposed in this paper. It was found that there was an average 600% increase in the throughput of WMN after applying the LMS. The model also depicts a reduction of 40% in the number of packets dropped. The model is designed to facilitate the flexibility to increase or decrease the number of GWs within the mesh to support the increase and decrease in the number of hops for a particular router. The presented model will be helpful for researchers to analyze proposed techniques that involve many variations in the topology of WMN. The proposed model is also useful for the simulation of scheduling of Gateway and packet within a multi-hop multi gateway wireless network. This paper discusses the MATLAB model of conventional WMN and the implementation of the Load Management Scheme (LMS) on it. Using the proposed model, this paper has presented a comparative analysis of the throughput performance of WMN with and without the LMS. The uniqueness of the model presented in this paper is that it is scalable and flexible in terms of network topology parameters. | 9,018.8 | 2022-01-01T00:00:00.000 | [
"Computer Science",
"Engineering"
] |
Comparing Partial and Full Return Spectral Methods
An analysis on the arithmetic complexity of recently proposed spectral modular arithmetic – in particular spectral modular multiplicationis presented through a step-by-step evaluation. Standart use of spectral methods in computer arithmetic instructs to utilize separated multiplication and reduction steps taking place in spectrum and time domains respectively. Such a procedure clearly needs full return (forward and backward) DFT calculations. On the other hand, by calculating some partial values on-the-fly, new methods adopt an approach that keeps the data in the spectrum at all times, including the reduction process. After comparing the timing performances of these approaches, it is concluded that full return algorithms perform better than the recently proposed methods.
INTRODUCTION
Spectral techniques for integer multiplications have been known for over a quarter of a century (Schönhage and Strassen, 1971).These methods are extremely efficient for applications using large size integer multiplications.The technique starts with transforming the encoded integers to the frequency domain (possibly via FFT), which is followed by a point multiplication in the spectrum.After this computation, an inverse transform and a decoding is applied to send the result back into the time domain as seen in Figure 1.Pamukkale University, Journal of Engineering Sciences, Vol. 18, No. 2, 2012 After the RSA proposal (Rivest et al., 1978), modular arithmetic-in particular modular reduction-attracts more and more interest.Perhaps, a method (Montgomery, 1985) described by P. Montgomery in 1985 is the most notable presentation among several other methods.Montgomery reduction carries numbers into n-residues, in which modular multiplication is more effective if consecutive multiplications are performed.
Saldamli proposed a new method for integer modular reduction (Saldamli, 2005;Saldamli and Koc, 2007).This method performs reduction on spectral domain rather than the time domain.
In fact the method is an adaption of the redundant Montgomery algorithm to the spectral domain.Based on this reduction, he further proposed spectral modular multiplication, and spectral modular exponentiation.However, in their work, the authors did not conduct a true comparision with the existing literature.In this study, our main objective is to give a regirous comparision between the usual redundant Montgomery algorithm and proposed methods.
Going back again to the history: RSA altered the history of cryptography by bringing up the public key cryptography notion.Later in late 80s, Koblitz and Miller independently introduced the elliptic curve cryptography-ECC, (Miller, 1986;Koblitz, 1987).Because of its efficiency, short key lengths and mature mathematics ECC is recently adopted by the U.S. Government as the basic technology for key agreement and digital signature standard (NIST, 2009).
The security of the ECC depends on the well known discrete logarithm problem.To setup the system one has to compute exponentiations in the elliptic curve group, requiring several calculations (especially multiplications) with in a finite field.As the ECC over binary and prime fields are standardized (IEEE, 1999;ANSI, 2001), one can argue that the practical (i.e.implementation) aspects of these systems are fairly mature.On the other hand, the arithmetic in medium size characteristics extension fields (i.e.GF (p k ) for some positive integer k and a prime p such that 0 < p < 2 128 ) is still a very active research topic.Recently, some researchers proposed and evaluated the spectral modular reduction over the medium size characteristics fields (Baktir et al., 2007;Baktir, 2008).Moreover, he successfully applied the method to ECC.
In this study, we compare the performance of the standard modular FFT multiplication and spectral modular multiplication.To be more specific, FFT multiplication combined with the redundant Montgomery reduction and recently proposed spectral algorithms given by Saldamli and Baktir et al. (Saldamli, 2005;Baktir et al., 2007).We believe, developers in particular cryptographic engineers would benefit the outcomes of this work as it would give them a fair foreseeing before doing their design work.
The presentation of our study is organized as follows.
In the next section, after giving the preliminary definitions, we state the standard modular FFT multiplication as a combination of Schönhage and Strassen's integer multiplication algorithm (SaSIMA) and redundant Montgomery reduction.Our spectral modular multiplication presentation follows the notation and terminology given in (Saldamli, 2005).
In Section 3, we present our evaluation results for the prime fields showing that SaSIMA performs much better than the spectral modular multiplication.In Sections 4 and 5, we turn our attention to multiplication over the medium size characteristics fields; present an adaption of SaSIMA to GF (p k ) and report a similar result when it is compared with the algorithm proposed in (Baktir et al., 2007).Finally, we conclude our work in the last section.
SPECTRAL MODULAR REDUCTION
We briefly give the basic terminology needed for the presentation of the spectral modular operations.
= a for some a Є Z than we say x(t) is a polynomial representation of a with respect to base b.
1. Discrete Fourier Transform (DFT)
The definition and properties of DFT in a finite field setting is slightly different from the Pamukkale Üniversitesi, Mühendislik Bilimleri Dergisi, Cilt 18, Sayı 2, 2012 common use of this transform in engineering.
In order to suppress on this distinction we start with a formal definition of DFT over finite fields.
Definition 2 Let ω be a primitive d-th root of unity in Z q and, let x(t) and X (t) be polynomials of degree d − 1 having entries in Z q .The DFT map over Z q is an invertible set map sending x(t) to X (t) given by the following equation; (1) With the inverse, for i, j = 0, 1, . . ., d − 1.We say x(t) and X (t) are transform pairs, x(t) is called a time polynomial and sometimes X (t) is named as the spectrum of x(t).
Remark 1 In the literature, DFT over a finite ring spectrum is also known as the Number Theoretical Transform (NTT).Moreover, if q has some special form such as a Mersenne or a Fermat number, the transform named after this form; Mersenne Number Transform (MNT) or Fermat Number Transform (FNT).
Note that, unlike the DFT over the complex numbers, the existence of DFT over finite rings is not trivial.In fact, Pollard mentions that the existence of primitive root d-th of unity and the inverse of d do not guarantee the existence of a DFT over a ring (Pollard, 1976).He adds that a DFT exists in ring R if and only if each quotient field R/M (where M is maximal ideal) possesses a primitive root of unity.
To simplify our discussions, throughout this text we take q as a Mersenne prime and the principal root of unity as ω = −2 without loss of generality.According to Saldamli and Baktir et al., such a preference reflects the best performance for DFT computations, spectral multiplications and eductions among other choices (Saldamli, 2005;Baktir et al., 2007).
SaSIMA Combined with Redundant Montgomery Reduction
To be consistent, we adopt the previous section's notation and state the standard modular FFT multiplication as a combination of SaSIMA and redundant Montgomery reduction.
Let r, b, u Є Z, b = 2 u and n i (t) be the polynomial representation of an integer multiple of modulus n such that the zeroth coefficient of n i (t) satisfies Now, we write a β multiple of n(t) as (2) Where b > β Є N and β i represents the binary digits of β.
Algorithm 1 Spectral multiplication with time reduction
Suppose that there exist a d-point DFT map for some principal root of unity ω in Z q , and X (t) and Y (t) are transform pairs of x(t) and y(t) respectively where x(b) = x and y(b) = y for some x, y < n.Let N T = {n 1 (t), n 2 (t), . . ., n u (t)} be the set of special polynomials as described above; Input : X (t), Y (t) and a basis set
3. Modified Spectral Modular Product (MSMP)
On the other hand, MSMP describes a partial return algorithm originally described by Saldamli (Saldamli, 2005).Let r, b, u Є Z, b = 2 u and n i (t) be the polynomial representation of an integer multiple of n such that the zeroth coefficient of n i (t) satisfies (n i ) 0 = 2 i−1 for i = 1, 2, . . ., u (note that n(t) = n 1 (t)).We can now write β • N (t) as Where β i is a binary digit of β and N i (t) = DFT d ω (ni(t)) for i = 1, 2, . . ., u.Note that β < b and β i = 0 for i > u.
Algorithm 2 MSMP algorithm Suppose that there exist a d-point DFT map for some principal root of unity ω in Z q , and X (t) and Y (t) are transform pairs of x(t) and y(t) respectively where x(b) = x and y(b) = y for some x, y < n and b > 0. Let N F = {N 1 (t), N 2 (t), . . ., N u (t)} be the set of special polynomials as described above; Input: X (t), Y (t) and a basis set N F Output: Z (t) = DF T (z(t)) where z xy2 −db mod n and z(b) = z,
COMPARING SaSIMA AND MSMP
Notice that both of the algorithms perform their multiplication in the spectral domain.However, they employ different reduction process.To be more informative; the reduction in Alg. 1 takes place in time whereas Alg. 2 computes the modular reduction in spectral domain.Therefore, we particularly probe this difference to compare the arithmetic and ASIC performances of these algorithms through a step-by-step evaluation.
1. Arithmetic Performance
In order to perform the Montgomery reduction, the least significant word of the partial sum has to be known in advance at each iteration.Therefore, Alg. 2 requires partial returns to time domain to determine the least significant words.With the help of these partial returns, reduction calculations are performed in spectral domain.
On the other hand, Alg. 1 performs the Montgomery reduction in time domain.
Naturally, such a reduction needs a full return of the multiplication result to the time domain.
Once the reduction is completed using redundant Montgomery method, a forward DFT transform is applied to grasp the spectral coefficients.
At first glance, the partial return of the Alg. 2 seems advantageous over Alg. 1 requiring full forward and backward DFTs.However, if the arithmetic requirements of both algorithms are evaluated step-by-step (i.e.given in Tables 1 & 2) and further summed up in Table 3, it is easily seen that full return algorithm needs less additions and hence behaves better than the partial return one.
Another comparison concern is the memory requirements of both algorithms.As both algorithms enjoy the performance gain comes with the high radix Montgomery reduction, one has to pre-compute and store the basis sets.
Observe that Alg. 1 and Alg. 2 require u and q sized words respectively for such allocations.If the relation 2u<q is considered (see "Saldamli, 2005" for the exact ratio), one sees that Alg. 1 is advantageous over Alg. 2.
2. ASIC Performance Evaluation
Since spectral methods exploit massive parallelism, ASIC architectures are utmost suitable for their employments.In this respect, precise ASIC analysis for both algorithms have to be given for a healthy comparison.As the complexity of the multiplication for both algorithms is same, we exclude its cost from our analysis.Alg. 1 consists of three stages, namely; iDFT, reduction steps and DFT.Among those three, DFT and iDFT can be calculated with the same FFT hardware, preferably with a butterfly network taking logarithmic time with respect to the operand size.
If Alg. 1 is considered, it has a single stage, consists of reduction steps and partial return embeddings.This stage loops d times and calculates a single reduction step in one clock cycle as seen in Figure 2. On the other hand, the loop of Alg. 2 contains a partial return, which calculates the value z0.As mentioned before this single word computation takes the same logarithmic time as the full iDFT calculation.Since this partial return is computed at every iteration of the loop as it can be seen in Figure 3, the rest of the remaining steps in both algorithms have similar complexities.Above analysis demonstrates a fair comparison of both algorithms.In fact, one can equipped Alg. 1 with more features that one can not do that with Alg. 2. For instance; better parameters on the encoding and decoding can be chosen while transforming to the non-redundant form.With these parameters, Montgomery reduction requires less values to store and can be calculated faster as described by some references (Tenca and Koc, 1999;Todorov et al., 2001;Bunimov and Schimmler, 2003).
As a last remark, we remind that in our analysis we reference the worst case DFT and iDFT computa-tion.The analysis of fast Fourier transform algorithms are beyond the scope of this text.However; in real world applications one should benefit the fruits of this mature methods.We refer the reader to textbook presentations for such discussions (Nussbaumer, 1982;Blahut, 1985).
SPECTRAL MODULAR ARITHMETIC FOR FINITE FIELD EXTENSIONS
In this section, we turn our attention to the arithmetic in the extension fields and revisit two methods of multiplication including an adaption of Schönhage and Strassen's algorithm and the algorithm of Baktir et al. (Schönhage and Strassen, 1971;Baktir et al., 2007).
Abstractly, a finite field consists of a finite set of objects together with two binary operations (addition and multiplication) that can be performed on pairs of field elements.These binary operations must satisfy certain compatibility properties.There is a finite field containing q field elements if and only if q is a power of a prime number, and in fact for each such q there is precisely one finite field denoted by GF (q).When q is prime the finite field is called a prime field whereas if q = p k for a prime p and k>1, the finite field GF (pk) is called an extension field.The number p is named as the characteristic of the finite field and in case of p = 2, the extension field is called a binary extension field.
The extension field GF (p k ) can be represented by the set of polynomials with polynomial addition and multiplication modulo an irreducible polynomial f (t) over GF (p) having degree k.The degree of the polynomial f (t) is also referenced as the degree of the extension.In fact, the defining polynomial f (t) characterizes the structure of the mathematical object consist of the polynomial congruent classes.Since for every prime power q there exists a unique finite field, the structure of the finite field does not depend on the choice of the defining polynomial as long as it is an irreducible having degree k.
Being a polynomial ring, the arithmetic in extension fields is the familiar modular polynomial arithmetic.Since the characteristic is p, addition is performed by adding polynomials modulo p whereas multiplication involves a polynomial multiplication and a reduction with respect to the defining irreducible polynomial f (t).
We assume that the parameter p and f (t) can arbitrarily be chosen without concerning about the security of a cryptosystem defined over the extension field.Certainly, our first choice for p would be a Mersenne prime enjoying the one's complement arithmetic.Similarly we would tend to choose f (t) as a low hamming weight polynomial such as a binomial or a trinomial.Moreover, we would insist on fixing the coefficients of f (t) to powers of two, so that multiplications on the coefficients enjoys shifts instead of full multiplications.
Obviously, the above extension field selection exploits the spectral algorithms built over it.If this is furnished with the selection of DFT parameter ω as a power of 2, one would utilize the best performing spectral algorithm setup.For instance, in a study, such a selection is presented by choosing f (t) = t k − 2, ω = −2 and p a Mersenne prime such as 2 13 − 1 or 2 19 − 1 (Baktir et al., 2007).
2. ASIC Performance Evaluation
The ideas of Section 3.2 discussing the ASIC performance evaluation can be applied in here also.In the light of these ideas, the simple reduction of the Alg. 3 gives much better performance.
Putting these in a more formal setting gives the following analysis.Suppose that T sRed and Tred are the time of the reductions of Algorithms 3 and 4, respectively.Let T DF T and T iDF T be the times of DFT and inverse DFT to be performed, respectively, then and Clearly, the above analysis shows the superiority of the Alg. 3 over Alg. 4.
CONCLUSIONS
In this study, we compare partial and full return modular multiplication algorithms proposed for ring of integers and finite field extensions.
Our comparison is based on a step-by-step evaluation of their arithmetic operations and ASIC performance.
Our arithmetic performance calculations shows that although Alg. 1 requires full return to time domain, it is better choice over Alg. 2 for integer modular multiplication.When multiplication over medium size characteristic fields is taken into account, Alg. 4 is better choice over Alg.
3. Due to the zero memory requirements, Alg.
3 may become a suitable choice over Alg. 4 for some processing environments.Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 11 Step 12 Step 13 Step
NT Output: Z (t) = DF T (z(t)) where z xy2 −db mod n and z(b) = z, Observe that Alg. 1 requires a full return computation (i.e.Step 2) right after the Pamukkale University, Journal of Engineering Sciences, Vol. 18, No. 2, 2012 component-wise multiplication.Moreover, Steps 4 through 9 perform the reduction in time domain implementing the so called redundant Montgomery reduction.
İ. H. Akın, G. Saldamlı, M. Aydos Pamukkale Üniversitesi, Mühendislik Bilimleri Dergisi, Cilt 18, Sayı 2, 2012 reduction taking t k = 2 and simple adding at once has better approach in time domain.The next algorithm presented under this consideration.Therefore; it does not includes a Montgomery reduction step.Algorithm 3 Standard DFT modular multiplication for GF (p k ).
Table 6 . Arithmetic performance of Alg. 3 & Alg. 4.
If the ASIC performance comparison is considered Algorithms 1&3 do not have better performance.Interestingly, although Alg. 4 has better arithmetic performance over Alg. 3, its ASIC performance is worse than its rival.As a final remark, we conclude that all algorithms are evaluated have inputs with frequency coefficients and complete the result in spectral domain.However, when ASIC implementations are considered there must be some DFT implementations which would give further stress on these deployments. | 4,299.4 | 2012-01-01T00:00:00.000 | [
"Computer Science"
] |
Investigation of glucose-dependent insulinotropic polypeptide-(1-42) and glucagon-like peptide-1-(7-36) degradation in vitro by dipeptidyl peptidase IV using matrix-assisted laser desorption/ionization-time of flight mass spectrometry. A novel kinetic approach.
The incretins glucose-dependent insulinotropic polypeptide (GIP1-42) and glucagon-like peptide-1-(7-36)-amide (GLP-17-36), hormones that potentiate glucose-induced insulin secretion from the endocrine pancreas, are substrates of the circulating exopeptidase dipeptidyl peptidase IV and are rendered biologically inactive upon cleavage of their N-terminal dipeptides. This study was designed to determine if matrix-assisted laser desorption/ionization-time of flight mass spectrometry is a useful analytical tool to study the hydrolysis of these hormones by dipeptidyl peptidase IV, including kinetic analysis. Spectra indicated that serum-incubated peptides were cleaved by this enzyme with only minor secondary degradation due to other serum protease activity. Quantification of the mass spectrometric signals allowed kinetic constants for both porcine kidney- and human serum dipeptidyl peptidase IV-catalyzed incretin hydrolysis to be calculated. The binding constants (Km) of these incretins to purified porcine kidney-derived enzyme were 1.8 +/- 0.3 and 3.8 +/- 0.3 microM, whereas the binding constants observed in human serum were 39 +/- 29 and 13 +/- 9 microM for glucose-dependent-insulinotropic polypeptide and glucagon-like peptide-1-(7-36)-amide respectively. The large range of Km values found in human serum suggests a heterogeneous pool of enzyme. The close correlation between the reported kinetic constants and those previously described validates this novel approach to kinetic analysis.
Incretins are hormones of the enteroinsular axis, which potentiate the actions of glucose on the endocrine pancreas (1). The most potent known incretins are glucose-dependent insulinotropic polypeptide (GIP 1-42 ) 1 and truncated forms of gluca-gon-like peptide-1 (GLP-1 7-36 -amide and GLP-1 7-37 ); both are members of the glucagon family of hormones sharing considerable N-terminal sequence homology (2,3). Both hormones are released from the gut in response to ingested nutrients and were recently shown to be substrates of the circulating exopeptidase dipeptidyl peptidase IV (DP IV, EC 3.4.14.5) (4,5). This enzyme is a highly specific protease, preferentially hydrolyzing peptides with N-terminal Xaa-Pro and Xaa-Ala motifs (6). Hydrolysis of GIP and GLP-1 7-36 by DP IV yields GIP and GLP-1 9 -36 and the dipeptides Tyr-Ala and His-Ala, respectively. Activation or inactivation of biologically active peptides is frequently associated with DP IV catalysis. Work by ourselves and others (7,8) has demonstrated that GIP and GLP-1 9 -36 are biologically inactive, and it has been hypothesized that serum degradation of GIP and GLP-1 7-36 by DP IV is the primary step in the metabolism of these hormones in the circulation (4,5,9).
In 1993 Mentlein and co-workers (4) reported on the kinetics of enzymatic degradation of GIP and GLP-1 7-36 by purified human placental DP IV, as determined by high performance liquid chromatography (HPLC), and suggested that this may be a physiologically important pathway for the degradation of these hormones. This proposal was supported by Kieffer et al. (5) who administered physiological concentrations of intravenous 125 I-GIP and 125 I-GLP-1 7-36 into anesthetized rats and monitored the fate of the injected label. HPLC analysis of purified plasma revealed that over 50% of both incretins were hydrolyzed into DP IV reaction products in less than 2 min (5).
The present study describes further investigations on serum degradation of GIP and GLP-1 and clarifies the role of DP IV in the breakdown of these hormones. Currently used methods for studying the degradation of peptides rely on radioimmunoassay and/or measurement of radioligand metabolites by HPLC, or capillary electrophoresis, all of which are labor-intensive and require the extensive use of controls. Since these approaches offer only limited information on incretin metabolites, this study was designed to use matrix-assisted laser desorption/ionization-time of flight mass spectrometry (MALDI-TOF MS) to investigate incretin degradation in human serum, and to study the kinetics of GIP and GLP-1 hydrolysis by human serum and purified porcine kidney DP IV.
Since MALDI-TOF MS is tolerant of heterogeneous samples (buffers, salts, and contaminants), this technology is ideally suited for analysis of biological fluids such as serum and is able to accurately resolve all analyte metabolites on the basis of their m/z, thereby overcoming a significant limitation of other approaches.
Instrumentation and General Procedures
Matrix-assisted laser desorption/ionization mass spectrometry was carried out using a Hewlett-Packard G2025 mass spectrometer with a linear time of flight analyzer. The instrument was equipped with a 337-nm nitrogen laser, a high-potential acceleration source (5 kV), and a 1.0-m flight tube. Detector operation was in the positive-ion mode, and signals were recorded and filtered using a LeCroy 9350 M digital storage oscilloscope linked to a personal computer. The spectrometer was externally calibrated using the low molecular weight standard Hewlett-Packard (G2051A).
The DP IV used in this study was purified from porcine kidney according to a previously described method (10) (this enzyme was kindly prepared by C. Krü ger, Hans-Knöll-Institute of Natural Product Research Jena, Halle-Saale, Germany). The specific activity measured using H-Gly-Pro-4-nitroanilide as a chromogenic substrate was 45 units⅐mg Ϫ1 .
To obtain mass spectra of GIP 1-42 (Peninsula) and GLP-1 7-36 (Bachem), in the presence or absence of DP IV, substrate was incubated at 30°C with 0.1 mM Tricine buffer, pH 7.6, and either enzyme or water in a 2:2:1 ratio. Samples (4 l) of the incubation mixture were removed at various time intervals and mixed with equal volumes of 2Ј,6Ј-dihydroxyacetophenone as matrix solution (Aldrich). A small volume (Ͻ1 l) of this mixture was transferred to a probe tip and immediately evaporated in a vacuum chamber (Hewlett-Packard G2024A sample prep accessory) to ensure rapid and homogeneous sample crystallization. All spectra were obtained by accumulating data generated by 250 single shots with laser power between 1.5 and 4.5 J.
Dependence of MALDI-TOF MS Signal on the
Concentration of GIP and GLP-1 Various concentrations of synthetic porcine GIP 1-42 (Peninsula) and synthetic human GLP-1 7-36 (Bachem) were mixed with buffer and water as described above, and 1-l samples ranging from 0.5 to 6 pmol/ sample of GIP 1-42 and 3.75 to 10 pmol/sample GLP-1 7-36 were analyzed by MS in order to determine the relationship between concentration of hormone versus MS signal intensity. Spectra for each peptide concentration were generated in triplicate. Quantification of GIP 1-42 and GLP-1 7-36 signals was accomplished by dividing the peak intensity by the base-line intensity resulting in a signal intensity normalized to spectra base lines.
Incubation in Human Serum-In order to study proteolytic degradation of GIP 1-42 (30 M) and GLP-1 7-36 (30 M) in serum, peptides were incubated in buffer containing 20% human serum under standard conditions. Serum was pooled from three individuals and obtained from the Medical Science Division (courtesy of Dr. S. Heins, Department of Child Diseases), Martin-Luther University, Halle-Wittenberg, Germany. Samples of the respective peptides (15 pmol) were removed from the incubation mixture at hourly intervals for 15 h and analyzed using the MS.
Kinetic Analysis of DP IV-mediated GIP and GLP-1 Hydrolysis Using MALDI-TOF MS Hydrolysis with Varying Concentrations of DP IV-In order to determine the feasibility of studying the time dependence of an enzymatic reaction using MALDI-TOF MS and to establish a convenient DP IV concentration for subsequent kinetic analysis, GIP 1-42 (5 M) and GLP-1 7-36 (15 M) were incubated under standard conditions with varying concentrations of purified DP IV (ranging from 0.29 to 5.8 nM for GIP 1-42 incubations and from 1.5 to 12 nM for GLP-1 7-36 ). Samples were removed at various time intervals after the start of the reaction and analyzed by MS. The relative amounts of GIP 1-42 and GLP-1 7-36 were calculated from net substrate peak intensity divided by the sum of the net substrate and net product peak intensities and plotted versus time. Net peak height was defined as peak intensity minus base-line intensity. Before transferring to the probe for MS analysis, these samples were diluted so that the final amount of peptide on the probe tip was 2.5 pmol for GIP 1-42 metabolites and 7.5 pmol for GLP-1 7-36 metabolites. The linearity between rate of hydrolysis and enzymatic concentration was determined from a plot of the initial slopes of substrate turnover (mol/l/min) versus enzyme concentration.
Determination of Kinetic Constants-The kinetic constants of DP IV-catalyzed GIP 1-42 and GLP-1 7-36 hydrolysis were determined by introducing a specific and kinetically characterized DP IV inhibitor into the incubation mixture and observing the relative reaction rates of inhibited and uninhibited substrate hydrolysis as described by Crawford et al. (11). Both are specific, competitive inhibitors of DP IV synthesized in our laboratory (12,13). Similarly, GIP 1-42 (30 M) and GLP-1 7-36 (30 M) were incubated with 20% human serum in the presence or absence of inhibitors. Samples were appropriately diluted and assayed by MS. Quantification of relative amounts of substrate after various time intervals was calculated as described in the previous section. The initial slopes of peptide turnover with purified DP IV or human serum DP IV activity in the presence and absence of inhibitors were used to calculate reaction velocities. To validate this approach, two different competitive inhibitors, exhibiting fairly different K i values (more than one order of magnitude different), were used. The K m of DP IV-catalyzed peptide hydrolysis was calculated according to Equation 1: where v o and v i are the uninhibited and inhibited relative reaction rates, respectively; S is the substrate concentration; I is the inhibitor FIG. 1. Concentration dependence of signal intensity relative to base-line intensity. A, GIP 1-42 and B GLP-1 7-36 in 0.1 mM Tricine buffer, pH 7.6, at 30°C were analyzed by MALDI-TOF MS using 2Ј,6Јdihydroxyacetophenone as matrix. GIP 1-42 concentrations ranged from 1 to 12 M and correspond to 0.5-6 pmol per MS analysis, whereas GLP-1 7-36 concentrations ranged from 7.5 to 20 M corresponding to 3.75 to 10 pmol. 250 single spectra were accumulated for each of three trials at each concentration. Signal intensity relative to spectrum baseline intensity was calculated as described under "Experimental Procedures." concentration; and K i is the inhibition binding constant. V max was then calculated according to Equation 2: Values for k cat were calculated using M ϭ 110 kDa per catalytically active subunit as the molar mass of DP IV. To estimate these kinetic constants for serum DP IV activity, it was necessary to determine the concentration of purified DP IV equivalent to human serum DP IV activity. A standard curve of DP IV activity versus DP IV concentration was generated by incubating 50 l of various DP IV concentrations (ranging from 29.3 to 293 pM) in 0.04 M HEPES buffer, pH 7.6, at 30°C and monitoring the rate of H-Gly-Pro-4-nitroanilide hydrolysis. Data acquisition was carried out using a Kontron 930 Uvicon uv-visible spectrophotometer at 390 nm (⑀ ϭ 11,500 M Ϫ1 ⅐cm Ϫ1 ) equipped with thermostated cells. An equivalent volume of serum was assayed under identical conditions allowing the purified DP IV concentration equivalence of serum DP IV activity to be determined using the standard curve. It was assumed that the major serum DP IV isoenzyme has M ϭ 110 kDa per catalytically active subunit.
Confirmation of MS-derived K m Values Using a Spectrophotometric Competition Assay
To confirm the kinetic constants determined using MALDI-TOF MS, the inhibition constant of GIP 1-42 as a competitive substrate of the DP IV-catalyzed hydrolysis of a chromogenic substrate was determined spectrophotometrically. Three concentrations of H-Gly-Pro-4-nitroanilide corresponding to K m /2, K m and 2K m (5.0⅐10 Ϫ5 , 1.0⅐10 Ϫ4 , and 2.0⅐10 Ϫ4 M) were incubated in 0.04 M HEPES buffer, pH 7.6, at 30°C in the presence of a range of GIP 1-42 concentrations (1.0⅐10 Ϫ7 to 1.0⅐10 Ϫ5 M). Hydrolysis of the chromogenic substrate was monitored using the Kontron 930 Uvicon uv-visible spectrophotometer as outlined above. Data were analyzed using nonlinear regression (Graphfit 3.01) yielding an inhibition binding constant (K i ) for GIP . Since GIP 1-42 is simultaneously an inhibitor to DP IV-catalyzed H-Gly-Pro-4-nitroanilide hy-drolysis, as well as a substrate of DP IV, this inhibition binding constant should be an approximation to the K m for DP IV-catalyzed GIP 1-42 hydrolysis. and GLP-1 7-36 on MS Signal Intensities-Polypeptide concentration was plotted versus GIP 1-42 and GLP-1 7-36 signal intensities normalized to spectral base lines (Fig. 1). This simple approach resulted in graphs indicating the concentration range of polypeptide during which signal intensity increased with increasing concentration of substance without the necessity of internal standards. By knowing this unique concentration window, bound by the limit of detection and the highest normalized signal intensity, the optimum analyte to matrix ratio for subsequent sample dilution was chosen. The molar GIP 1-42 :matrix ratio was optimum at 2.5:10 5 , whereas the GLP-1 7-36 to matrix optimum was 7.5:10 5 .
Concentration Dependence of GIP
In Vitro Degradation of GIP and GLP-1 7-36 by DP IV- Fig. 2 shows the MS spectra of GIP 1-42 and GLP-1 7-36 and their DP IV reaction products at various time intervals during incubation with purified DP IV. The relative heights of the substrate signal (GIP 1-42 and GLP-1 7-36 ) decreased as the relative heights of the peaks corresponding to the DP IV hydrolysis products (GIP and GLP-1 9 -36 ) increased. The average m/z of GIP for GLP-1 7-36 and GLP-1 9 -36 was 0.05 and 0.06%, respectively.
In order to gain insight into the identity of the major metab- (Table I). olites found in the circulation, GIP 1-42 and GLP-1 7-36 were incubated in human serum. The MS spectra generated at the stated time intervals are shown in Fig. 3. Metabolites were identified on the basis of their m/z ratio. were Ͼ0.20%. Over a 15-h period, serum-incubated GIP 1-42 showed a consistently gradual decrease in the relative peak height of the intact peptide with a complementary increase in the relative peak height of a degradation product having m/z corresponding to GIP . Only after approximately 3 h, by which time more than half of the GIP 1-42 was already converted to GIP 3-42, were minor peaks due to secondary stepwise degradation by other serum proteases observed. These results support the hypothesis that DP IV is the primary serum protease acting on GIP .
Similarly, serum-incubated GLP-1 7-36 was degraded by serum DP IV activity to GLP-1 9 -36 . The serum degradation spectra for GLP-1 7-36 at different times are illustrated in Fig. 3B and show doublet peaks for both GLP-1 7-36 and GLP-1 9 -36 . The m/z difference between these doublets was consistently 29, a mass corresponding to an ethyl group most likely attached as a protecting group to a glutamate residue during peptide synthesis of the commercial product. As the incubation time increased, the heights of the mass peaks corresponding to [M ϩ H] ϩ of a metabolite of GLP-1 7-36 -ethyl ester decreased relative to the height of the mass peak of the unesterified GLP-1 7-36 metabolite. This suggests that nonspecific serum esterases remove the ethyl group over time. Parallel studies of GLP-1 7-36 , using the same commercially available substance, with purified DP IV did not result in doublet peaks but only the mass peak of GLP-1 7-36 -ethyl ester (Fig. 2.). Presumably this occurs because the purified enzyme preparation is free of contaminating nonspecific esterases.
Kinetic Analysis Using MALDI-TOF MS-Under normal circumstances increasing the concentration of an enzyme while maintaining a constant substrate concentration results in an increased rate of product formation. Fig. 4 illustrates that MALDI-TOF MS analysis of DP IV-catalyzed GIP 1-42 and GLP-1 7-36 hydrolysis can be used to demonstrate this relationship. Peptide turnover varies linearly with increasing concentrations of DP IV (Fig. 4, inset; R 2 ϭ 0.9986 and 0.9849 for GIP and GLP-1 7-36 hydrolysis, respectively).
MALDI-TOF MS was used to demonstrate that GIP 1-42 and GLP-1 7-36 turnover was attenuated by Ala-thiazolidide and Ile-thiazolidide inhibition of purified DP IV and serum DP IV as predicted by the inhibitor binding constants (K i ) (Fig. 5.). These results lend more credibility to MALDI-TOF MS as a feasible method for quantitative kinetic analysis, as well as allowing the K m values for purified porcine kidney-catalyzed GIP 1-42 and GLP-1 7-36 hydrolysis to be calculated. These results are summarized in Table II expressed as a range derived from the two inhibitors.
Serum DP IV was determined to have the equivalent activity of 1.3⅐10 Ϫ5 mg⅐ml Ϫ1 of purified porcine kidney, as measured by the rate of H-Gly-Pro-4-nitroanilide hydrolysis using the standard curve in Fig. 6. The kinetic constants (k cat ) for GIP 1-42 and GLP-1 7-36 hydrolysis by serum DP IV activity were calculated and compared in Table II. The binding constant of GIP 1-42 derived from the competitive inhibition of porcine kidney DP IV-catalyzed hydrolysis of H-Gly-Pro-4-nitroanilide was found to be 54 Ϯ 8 M (mean Ϯ standard error). DISCUSSION With the introduction of electrospray ionization (14,15) and MALDI (16) as soft ionization methods that greatly decrease the fragmentation of fragile biomolecules, mass spectrometry has become an important tool in biological research. Subsequent to the development of these techniques, mass spectrometry has been used to analyze a wide range of substances including polypeptides, proteins, oligonucleotides, polysaccharides, and other bio-organic compounds. An important feature of mass spectrometry is the high sensitivity and excellent resolution, allowing detection of picomole to femtomole amounts of substance up to molecular masses of 300 kDa with an accuracy of 0.1 to 0.01% (17). In the present study, MALDI-TOF MS, a particularly versatile and easily used method of mass spec-trometry, was used to monitor the in vitro degradation of GIP 1-42 and GLP-1 7-36 in human serum, as well as to investigate the kinetics of DP IV catalysis of these peptides.
It was observed by ourselves in this study and others (17) that absolute quantification of MALDI signals is extremely difficult due to inconsistent shot to shot and sample to sample reproducibility. Although several studies have tried to address this issue (18 -20), laser beam heterogeneity and irradiance, as well as inconsistent sample preparation and crystallization, are still cited as the most significant problems in obtaining consistent results. Fig. 1 illustrates the MALDI-TOF MS signal profile over a range of GIP 1-42 and GLP-1 7-36 concentrations. As previously observed, signal intensity does not continue to increase but rather plateaus or decreases as the relative amount of analyte increases with respect to matrix (21). The observation that diluting analyte results in a more intense signal is not uncommon. One explanation is that decreasing the amount of analyte relative to matrix results in a more optimum analyte:matrix ratio (22). Tang and colleagues (21) suggest this nonlinearity is likely due to changes in the number of analyte layers that the laser can penetrate in order to produce intact ions that ultimately can reach the detector. This conclusion was based on their finding that increasing the number of analyte molecules while maintaining a constant analyte:matrix and GLP-1 7-36 degradation products of serum protease activity GIP 1-42 and GLP-1 7-36 were incubated with 20% human serum in 0.1 mM Tricine buffer, pH 7.6, at 30°C for 10 and 15 h, respectively. MALDI-TOF MS analysis after this incubation period showed serum degradation products identified on the basis of their m/z ratios. The peptide sequence plus cation adducts are indicated where observed. Sequences with the additional ϪCH 2 CH 3 on a glutamate residue (found in the commercial GLP-1 7-36 ) are also identified. Where more than one possible sequence of similar m/z is possible, alternatives are given. GIP does not improve the linearity of analyte concentration versus signal intensity. For GIP and GLP-1 7-36 , the concentrations yielding signals of greatest intensity were 5 and 15 M, respectively, and subsequent incubations using higher peptide concentrations were diluted to these concentrations prior to MS analysis. MALDI-TOF MS proved a highly sensitive technique to confirm the removal of N-terminal dipeptides from GIP 1-42 and GLP-1 7-36 due to DP IV catalysis, on the basis of the mass difference between substrate and product. Equally significant was the observation that monitoring the time course of peptide hydrolysis was an appropriate application of this analytical tool (Fig. 2). However, methodologically, the great advantage of MALDI-TOF MS over other approaches, and even over other types of mass spectrometry, is the tolerance of impurities in the analyte solution. An objective of this study was to analyze the metabolism of GIP 1-42 and GLP-1 7-36 in serum, without prior purification, to test the hypothesis that DP IV is the principal protease responsible for serum inactivation of these hormones. This study clearly affirms that more than 50% of GIP 1-42 and GLP-1 7-36 was converted to GIP 3-42 and GLP-1 9 -36 , respectively, before significant secondary degradation was observed (Fig. 3). Addition of specific DP IV inhibitors (Fig. 5.) reduced this conversion as predicted by inhibitor binding constants (K i ), suggesting that the serum protease responsible for the initial hydrolysis was DP IV. The data presented in Table I suggest that secondary degradation of GIP 1-42 may include stepwise N-terminal removal of amino acids due to serum amino peptidases, resulting in m/z corresponding to GIP 8 -42 , GIP 11-42 , GIP 12-42 , GIP 13-42 , GIP 15-42 , GIP 18 -42 , GIP , and GIP 22-42. This does not preclude the possibility that GIP metabolites are susceptible to hydrolysis by other serum proteases resulting in other sequences listed in Table I. Regardless of interpretation, however, serum DP IV is unquestionably the primary enzyme responsible for serum inactivation of GIP . Analysis of GLP-1 7-36 degradation is complicated by the fact that the commercially available peptide (Bachem) had a mass of 29 Da greater than its theoretical mass. This is postulated to correspond to an ethyl group attached to a glutamate residue as a protective ester during commercial synthesis. Despite this, data presented in Fig. 3 indicate that DP IV is the primary enzyme responsible for GLP-1 7-36 metabolism in serum as well.
Although mass spectrometry has been used extensively for analyzing protein degradation products, Hsieh and colleagues (23) combined mass spectrometric analysis of enzymatic degradation with quantitative mass spectrometry to demonstrate the feasibility of studying enzyme kinetics in real time using HPLC-coupled electrospray mass spectrometry. Classical methods for investigating enzyme kinetics such as refractive index monitoring, radioimmunoassay, HPLC, or capillary zone electrophoresis are time consuming, use large amounts of substrate, and are often insensitive. In the case of colorimetric assays, chromogenic substrates must often be synthesized, and many of these do not adequately parallel the kinetics of the substrate they were designed to mimic. Mass spectrometry offers a rapid, accurate and easy approach to study enzyme kinetics. This is especially relevant for analyzing large biomolecules such as proteins. In order to study the kinetics of DP IV-catalyzed GIP 1-42 and GLP-1 7-36 hydrolysis, protocols were developed for the quantification of MS signals. This typically involves the incorporation of an internal standard to the sample mixture, allowing an unknown quantity of analyte to be normalized relative to the standard (21, 24 -26). When measuring the activity of protein kinase and phosphatase, however, Craig et al. (27) avoided the use of an internal standard by quantifying substrate and product peaks relative to each other. Essentially, these peaks served as their own internal standards. The approach of relative quantification was used in the present study. The feasibility of this method is demonstrated in Fig. 4 which shows the relationship between the rate of DP IV-catalyzed peptide hydrolysis and enzyme concentration. As expected, the initial reaction rates increased linearly as a function of DP IV concentration providing convincing evidence that our approach to MS quantification was valid.
Incubation of GIP 1-42 and GLP-1 7-36 with purified porcine kidney DP IV or human serum in the presence and absence of two known specific DP IV inhibitors (Fig. 5) allowed the kinetic constants for peptide hydrolysis to be calculated. The K m values calculated for purified DP IV correspond well to those previously reported for GIP and GLP-1 7-36 hydrolysis by purified human placental DP IV (Table II) (4). The error in the MS-derived constants for GIP and GLP-1 7-36 , as determined using only single trials of two DP IV inhibitors, was 17 and 7.9% respectively. This compared with errors of 8.8 and 13% as determined by seven HPLC-analyzed trials (4). Although MS-and HPLC-generated kinetic analysis result in were also incubated in 20% human serum under the same experimental conditions. Samples of analyte (15 pmol) were removed from the incubation mixture for MS analysis. Spectrum peaks were quantitatively analyzed as outlined under "Experimental Procedures." Squares represent substrate turnover in the absence of inhibitor, whereas triangles and circles represent turnover in the presence of alanine-thiazolidide and isoleucine-thiazolidide, respectively.
TABLE II
Kinetic constants for the degradation of GIP and GLP-1 7-36 by DP IV as determined by quantitative MALDI-TOF MS All assays were carried out in 0.1 mM Tricine buffer, pH 7.6, at 30°C. K m values were calculated using the Michaelis-Menten equation for competitive inhibition from the substrate/inhibitor/DP IV incubation experiments (Fig. 5). Ala-thiazolidide has a K i of 3.4 M and Ile-thiazolidide has a K i of 0.126 M. Values for k cat were calculated using M ϭ 110 kDa as the molar mass of DP IV. Where appropriate, results are expressed as the range of the results obtained using the two inhibitors. comparable variability, this study demonstrates that MS offers some considerable advantages. Significantly fewer trials mean that MS is less time consuming and labor-intensive, and since MALDI-TOF MS can detect picomole amounts of analyte, complete kinetic analysis can occur with only minimal amounts of substance, making this approach much less expensive.
The fact that MALDI-TOF MS is tolerant of sample impurities also makes it an ideal tool to study the kinetics of serum proteases without prior purification. The rate specificity constants (k cat /K m ) for GIP and GLP-1 7-36 hydrolysis by human serum DP IV were between 10 5 and 10 7 , suggesting that DP IV-mediated peptide hydrolysis is significant at physiological concentrations of these hormones. The large variability in the K m values of peptide hydrolysis by human serum DP IV is likely due to the presence of a distinct DP IV isoenzyme in serum. In this regard, a novel 175-kDa soluble form of DP IV was recently identified and purified from human serum (28). Inhibitor binding constants (K i ) of Ala-thiazolidide and Ilethiazolidide, the DP IV inhibitors used to estimate the kinetic constants of peptide hydrolysis in human serum, were evaluated using purified 105-110 kDa membrane-derived porcine kidney DP IV. Presumably, inhibitor interaction with the serum DP IV is not identical to that with the membrane-associated enzyme, resulting in the disparate K m values of GIP and GLP-1 7-36 hydrolysis. Thus, these experiments support the findings of Duke-Cohan and colleagues (28,29) that human serum DP IV is a unique protease having similar, yet distinct kinetic properties as compared with the insoluble form.
The close correlation between MALDI-TOF MS-derived kinetic constants and those previously reported, or determined using a spectrophotometric competition assay, validate MS as a reliable method for kinetic analysis.
The serum degradation experiments combined with the serum kinetic experiments provide considerable evidence that DP IV plays a significant role in GIP 1-42 and GLP-1 7-36 hydrolysis. Although this in vitro study may model the physiology of DP IV degradation of incretins in vivo, one important limitation must be considered. Membrane-associated DP IV is found on the surface of T-lymphocytes, endothelial cells of the vasculature, epithelial cells of the intestine, renal brush border membranes, as well as in most other tissues (30). Thus, it is likely that the inactivation of circulating biologically active peptides is much more rapid than predicted by the kinetics of serum DP IV alone. This underscores the importance DP IV plays in incretin physiology. DP IV catalysis of GIP 1-42 and GLP-1 7-36 to GIP 3-42 and GLP-1 9 -36 renders these hormones biologically inactive. Subsequent evidence has suggested that this hydrolysis represents the first step in hormone metabolism. MALDI-TOF MS was used in the present study to test this hypothesis and investi-gate the kinetics of DP IV-catalyzed incretin hydrolysis, thereby introducing a novel application of MALDI-TOF MS: kinetic analysis. In vitro experiments indicate that DP IV acts rapidly on GIP 1-42 and GLP-1 7-36 , converting more than 50% of either peptide before significant secondary degradation was observed. On the basis of this and previous studies, in vivo inhibition of DP IV is predicted to have a profound effect on the enteroinsular axis. An exaggerated incretin response would be expected in response to an increased half-life of endogenously released GIP 1-42 and GLP-1 7-36 . This is currently under investigation. | 6,658.4 | 1996-09-20T00:00:00.000 | [
"Biology",
"Chemistry"
] |
Simulations of Rayleigh ’ s Wave on Curved Surface
Impulsive line load in a half-space (Lamb’s problem) can be solved with a closed form solution. This solution is helpful for understanding the phenomenon of Rayleigh’s waves. In this article, we use a boundary element method to simulate the solution of an elastic solid with a curved free surface under impact loading. This problem is considered difficult for numerical methods. Lamb’s problem is calculated first to verify the method. Then the method is applied on the problems with different surface curvatures. The method simulates the phenomenon of Rayleigh’s wave propagating on a curved surface very well. The results are shown in figures.
Introduction
The phenomenon of surface wave is interesting and important for many engineers and scientists.Impulsive line load in a half-space can be solved by analytic methods [1].Herewith scientists and engineers may get understanding with Rayleigh's wave.When the free surface is not flat the phenomenon of surface wave should be similar, but some detail can be different.On the case of curved surface, analytic solutions are no longer available.Therefore numerical methods become an alternative way to understand the phenomena.These problems are considered difficult for numerical methods.To the best of our knowledge, there are no related reports on this problem.
Simulating transient wave in elastodynamics needs mass computing time and huge memories.Boundary element methods are efficient for simulating elastodynamics [2,3].Recently personal computers (PC) become much more powerful and are equipped with more rams then ever.Practical problems can be simulated with a PC precisely.
In this article, we use a boundary element method to solve two dimensional elastodynamic problems with curved surfaces.The curved boundary is assumed to be an arc.The loading is an impulse.The numerical method is implemented with fortran programs and a PC.In Section 2, the mathematical problem is described.In the following section, we formulate the numerical method briefly.The results are shown in Section 4.
The Problem
Because our goal is to simulate the Rayleigh wave on a smooth surface near the loading point, the boundary of the 2D domain is modeled as a arc with curvature . The loading is a single line impact at the surface.
The schematic diagram is shown in Figure 1.
Boundary value problems with zero initial conditions and absent body force for 2D elastodynamics in plane strain condition are considered.The material is homogeneous, isotropic and linear elastic.
where and are the Lame constants an d is the mass density of the elastic material.
,
The boundary conditions are where is the stress tensor, is the outward normal vector on , s is the coordinate on the boundary, is the Dirac delta function, and s x presents the map from coordinate s to 2D spatial coordinates . The time-varied displacements on the curved surface are Rayleigh's waves.
The Method
We use a boundary element method to calculate the surface displacements.The boundary is approximated as a polygon.
There are two families of particular solutions of Navier's equation, Using Hooke's law, we have stress bases,
, , , , , Note that are vector fields and The bases have been derived in a close form [4].The the coefficients, and , will determined with the boundary condition (2).
x ik a y ik a Then, the approximated stress field is When a collocation method apply on Equation (7), the coefficients x n are as many as .It is difficult to calculate a precise elastodynamic solution on a personal computer with this formulation.Therefore we take the advantage of the symmetry of the boundary.
and cos sin sin cos sin cos Substituting Equations ( 8) and ( 9) into (7), we have Then, we decomposite the traction into normal and tangent directions. .Then apply the semicollocation method [4] to Equations (15) and (16).Rearranging the equations for and , we have the stepping equations. where and 1 if 0 and 0 0 e l s e 0.
The where H is the Heaviside step function.
In formulae ( 17) and ( 18), the coefficients , ik j take the form of ,00 . The usage of computer memory is enormously deduced to 2Nm.
Then the time-stepping technique is applied on Equations (17) and (18) to solve and on th step.
After solving the coefficients, and , the numerical displacement may be calculated by and the numerical interior stress by
The Results
In order to verify this method, we calculate the problem with very large first.For , the problem becomes Lamb's problem in which the exact surface displacements are available.The elastic half space The solutions for problems of a line impulse load on an elastic half plane were derived by Lamb.A modern treatment with integral transform technique was given by De Hoop, but the results were in complex function form.Nevertheless explicit form for surface displacements are available.The analytic solution for surface displacement can be found in page.614-626 of [1].
The schematic diagram of the geometry of the problem is shown in Figure 1.
In this example Poisson's ratio 0.25 . Therefore the shear and Rayleigh's wave speeds are and respectively, where is the dilatation wave speed. .Even though this problem is considered difficult for numerical methods, our results are precise.This example shows the method is applicable for impact problems.When 5 R , the results are shown in Figure 3.In this case tangential displacement is almost the same with Lamb's problem, but the normal displacement is changed much.The normal displacement has a strong and short peak at the shear wave front and the head wave is enlarged.The head wave is the wave beyond the shear wave front [5].The dashed line is the displacement for R .Figure 4 shows the displacements for 3 R .The phenomenon is similar to the case of .5 R
Conclusion
We use the boundary element method and write a fortran program running on a personal computer.In order to simulate the phenomenon of Rayleigh's wave propagating on a curved surface, the free surface is assumed to be a constant, 1 R .The method is verified by the problem of 1000 R . Two examples, R = 5 and R = 3, calculated to demonstrate the phenomenon.On the shear wave front, the wave is very different from that of Lamb's problem.
Figure 1 .
Figure 1.The schematic diagram of the geometry of the problem.
Figure 2
Figure 2 shows the displacements with vertical loading when 1000 R .The dashed line shows exact displacement when R .There is a Dirac delta function at the Rayleigh wave front in the exact solution.The vertical line indicate the arriving time of Rayleigh's wave.For this figure, 1 600 s .Even though this pro-
Figure 2 .
Figure 2. The displacements with vertical loading when R = 1000.The dashed line shows exact displacement when R = ∞.The vertical red lines indicate the arrival time of Rayleigh's wave.There is a Dirac delta function at the Rayleigh wave front in the exact solution.In this figure, 1 600 s is used.
Figure 3 .
Figure 3.The displacements when R = 5.The dashed line shows exact displacement when R = ∞.The vertical red lines indicate the arrival time of Rayleigh's wave.In this figure, 1 400 s is used.
Figure 4 .
Figure 4.The displacements when R = 3.The red line shows exact displacement when R = ∞.The vertical dashed lines indicate the arrival time of Rayleigh's wave.In this figure, 1 400 s is used. | 1,754.2 | 2013-06-03T00:00:00.000 | [
"Engineering",
"Physics"
] |
An Exploration of the Alignment of Learning Theories with eTools at the University of the Western Cape ( UWC )
The impact of emerging technologies on authentic learning in higher education remains a core concern in the South African context. Learning Management Systems (LMSs) must include emerging technologies to support innovative teaching and learning practices, given their importance in expanding student access to learning materials, and the facilitation of student development. At the University of the Western Cape (UWC), the Centre for Innovative Education and Communication Technologies (CIECT) has championed the adoption of innovative eLearning practices for over 10 years. This study explores the infusion of learning theories aligned to eTools in service of national higher education imperatives. The authors discuss the value of learning theories in the eLearning field, and deliberate on the development of the main learning theories. Original Research Article Stoltenkamp et al.; ACRI, 8(1): 1-9, 2017; Article no.ACRI.34133 2 The study also discusses the application of learning theories in online environments, and this issue is explored by way of six cases, providing examples of how various learning theories can be aligned to eTools. These were gathered from CIECT’s marketing blog, which constitutes a research repository of practitioner experiences and reflections of the institutional LMS and innovative teaching and learning practices. The aim is to explore and emphasize the importance of grounding emerging eTools use in theory and pedagogy to promote student development, as well as the application of learning theories, specifically when designing learning environments to support traditional teaching and learning practices. The qualitative study is primarily exploratory and descriptive. It also includes a brief discussion of the results of a student questionnaire (179 respondents from across faculties and departments) exploring how and why students use eTools at UWC. This exploration of broader student eTools use will help create the foundation for a followup study to explore the use of learning theories in promoting more focused eTools adoption.
INTRODUCTION
At the University of the Western Cape (UWC), the Centre for Innovative Education and Communication Technologies (CIECT) is responsible and accountable for the delivery and infusion of emerging technologies across campus.This accountability includes exploring the impact of learning technologies and interventions (on staff and students) and providing evidence thereof, which is instrumental to promoting the iKamva (Sakai) Learning Management System (LMS), and which facilitated the migration to iKamva from KEWL, a home-grown LMS [1].This exploration of impact is also in line with UWC's Institutional Operating Plan White Paper (2016-2020), which emphasizes this provision of evidence, especially in relation to teaching and learning.It is necessary to continuously review the impact of authentic online activities undertaken for student development across disciplines.As Elliot argues, the introduction of new learning environments necessitates a continuous revision of the methods of teaching and learning [2].To this end, this study explores how various learning theories are used by CIECT in designing eTools at UWC.The authors present examples of the impact of authentic teaching and learning online activities for student development, across faculties and disciplines, thus highlighting the importance of the meaningful impact of trustful relationships and networks of support over time.These qualitative examples are drawn from CIECT's marketing blog, which constitutes a research database recording evidence of various interventions (including training), and novel use of eTools.In addition to exploring the impact of learning theories on the design of eTools, this paper includes a brief exploration of what eTools students make most use of, and for what purpose, at UWC.This will help guide future thinking towards better aligning learning theories to eTools.This is in line with Engelbrecht, who argues that eLearning constitutes more than mere "delivery of traditional learning content via the Internet" [3].
The results support the view that "new technology -as an educational tool, [is not] entirely separate from pedagogy" [2].Transforming lecturers' mindsets regarding the importance of sound ePedagogy and student development requires CIECT team members to be more than mere trainers, and to remain at the forefront of theory and the broader professional development project.Effective eLearning implementation requires pedagogical and didactic proficiency [4].This view is also reflected nationally through the White Paper on e-Education, which positions the challenge in relation to the alignment of learning activities and objectives [5].Additionally, the White Paper for Post-School Education and Training highlights that Information and Communications Technology (ICT) integration must be determined by pedagogical strength [6].For this reason, the researchers explore the use of learning theories in the application of eLearning practices, and their value.Hence, the authentic examples (deliberated in Section 3.4) expand on this in relation to the engagement within online teaching and learning interventions, such as: contribution to group tutorials; discussion forums and related articles; self-directed assessment tasks; journal writing; active problem-based case studies; and assessment activities addressing lower and higher cognitive skills.
The researchers aim to explore examples of online teaching and learning practices within a complex higher education environment.Furthermore, the study explores how important learning theories are when selecting eTools.There is still a need within higher education to explore the application of learning theories to enhance design and development processes and how well-designed, interactive teaching and learning environments promote student engagement.The researchers argue for the consideration of learning theories in the effective use of institutional LMSs to promote pedagogical benefits.
The researchers explain the need for a higher education institution to explore the use of educational technologies aligned to global trends.This is also pertinent for UWC, a member of the Sakai consortium, which includes other South African and global institutions, such as the University of South Africa (Unisa), North-West University (NWU), University of Cape Town (UCT) and University of the Witwatersrand (WITS).Lecturers and students still want to see contextualized examples of good practices, whilst thinking of adoption.Hence, the researchers have illustrated cases from the marketing blog, which promotes a continuous awareness of innovative technologies to support traditional teaching and learning practices.The following section presents a brief word on methodology.
METHODOLOGY
This study is a combination of exploratory and descriptive qualitative research.In the discussion of the employment of learning theories in practice, it also makes use of various short cases collected from the marketing blog, which serves the purpose, as Neuman argues, of "connect[ing] the micro level, of the actions of individual people, to the macro level" [7].This act of connecting learning theory with learning practice is important in ensuring that CIECT's mission to infuse emerging technologies into its higher education setting continues to serve and promote student development and staff needs.
An online survey was also designed and shared with students to explore broader eTools use.This will help create the foundation for a follow-up study to explore the use of learning theories in promoting more focused eTools adoption.It was distributed via various channels, eliciting a total of 179 responses.A purposive sampling method, and a mix of open and closed questions was used.While learning theories and sound pedagogy are vital, the aim here was to establish how and why students use eTools, allowing CIECT to better focus its efforts to support student development, and identify further opportunities to infuse learning theories in the design of learning environments.This creates the foundation for the follow-up study, which will develop this further.
INTERRELATED LEARNING THEORIES UNDERPIN ELEARNING
This section briefly outlines the value of learning theories for teaching and learning purposes, the development of the main learning theories, and their application within online learning environments.This review is of value because these learning theories are used on a daily basis within the operations of CIECT.It can also remind other eLearning professionals of the value of learning theories and to prompt them to consider how they use eTools within their teaching and learning, and to enhance their effect.
The Value of Learning Theories
Learning theories provide a structure for teaching and learning practices, and influence learning processes and student development.More importantly, the principles and associated pedagogies which arise from various learning perspectives have a profound impact on practical applications [8].This impact extends to eTools and eLearning interventions as well.Theory should underpin curriculum design and pedagogy.
It enables critical program examination to reveal "structuring principles and to develop insights into the knowledge and practices that enable effective courses" [9].
As Subject-Matter Experts and Academic Developers, it is valuable for us to investigate learning theories, as they enable us to engage more effectively with lecturers across disciplines.As Quinn argues, these make "explicit the underlying principles" of conceptualization and structure, as well as enabling analysis of curricula and pedagogy [9].Furthermore, the understanding of learning theories provides a structure for "organizing thinking and making sense" [8].This investigation of learning theories will enable the researchers to highlight the application and implications of the adoption of emerging technologies to support teaching and learning.First however, a brief discussion of the development of the main learning theories will be presented.
The Development of Learning Theories
Learning theories stem from multiple disciplines including education, psychology, pedagogic studies, sociology and neuroscience [8].The application of each theory led to necessary constructive criticism around learning processes, and the development of later theories.For example, initial behaviorist principles, focusing on "learning as observable changes in behavior", were criticized as being too teacher-centered, ignoring the discourse around thinking and understanding [8].
This constructive criticism gave rise to cognitivist and constructivist theories (while not completely rejecting behaviorism), which reflected a "more holistic view of behavior and the mind".These perspectives influenced the main discourse contrasting passive learners with more active learners who are involved in the "primary construction of knowledge".However, further criticism of these perspectives focused on the underlying assumption that all students are able to engage successfully in "unguided methods of instruction", and called for more "structured learning activities" [8].
This gave rise to social and situated learning perspectives, as social psychologists and sociologists emphasized the "effects and influences of social and cultural interaction" on individual learning [8].Hence, (i) social constructivism emphasizes the importance of the educator who develops the potential of the learner and provides "scaffolding support" interventions; (ii) social learning theory emphasizes that learning occurs through observation and imitation; (iii) situated learning emphasizes that learning also occurs in informal settings, is contextually situated and success thereof is determined by individual situational competence.These too were critiqued, in relation to how much influence social interactions have on behavior, and for assumptions of communities of practice being stable environments that students easily adapt to.
Recently, the focus has been on socioconstructivism, also referred to as 'communal constructivism'.This learning theory emphasizes a process whereby people construct their own knowledge (constructivism) as a result of social learning (social constructivism), and actively contribute their learning to the creation of a communal knowledge base for other learners [10].Importantly, ICTs present tools whereby a social constructivist environment can realize its goals, and "online learning affords individuals the linked community, the knowledge bases, the knowledge-creation tools and the facility to provide their learning to others" [11,12].
The recognition of ever-changing environments has given rise to self-theories and humanistic perspectives, focusing on experiential learning, personal growth and the importance of selfperceptions in determining learning processes.However, these theories have been criticized as too 'optimistic', and for ignoring that many students will not be able to make positive choices on their own [8].Being knowledgeable regarding these learning theories is important, and the researchers will reflect on the value of learning theories for an impactful teaching and learning agenda in the next section.Cases providing examples of how various learning theories can be aligned to eTools were gathered from CIECT's reporting and marketing blog, which is briefly introduced next, after which these cases are explored in more detail.
Application of Learning Theories in Online Environments
As a result of an ongoing non-coercive approach to eLearning since November 2008, CIECT employs a marketing strategy via campus-wide email, further linked to a blog (https://ciect.wordpress.com/),which constitutes a valuable research repository of practitioner experiences [13].Over the longer term, email is not the "ideal medium" for storing and sharing "snippets, or information nuggets", however, blogs "make an ideal tool for this kind of information management", especially for an online community [14].This marketing strategy is a crucial facet of fostering a community of practice around eLearning, as it provides a platform for "enculturation", in relation to the sharing of experiences, especially for newcomers [15].Observations by the CIECT team over time have shown that lecturers across disciplines who read these blogs have contacted CIECT for the creation of interactive online environments and training sessions for both the lecturers and their students.
The blogs convey each initiative in an impactful way, including the particulars of the lecturer, the eTools used for their pedagogical value in structured activities or assessment tasks, and ultimately the impact on student development [13].The blogs entail substantive theoretical engagement aligned to practice, since it is best to assist teachers in improving their teaching by making use of theory to reflect on their practices [16].This strategy has contributed to the "evergrowing recognition of eLearning as an important role-player in the effective delivery and decisionmaking of teaching-and-learning at UWC" [13].The next section presents the discussion of examples of how various learning theories have been aligned to eTools.
Notable
Examples of Learning Theories in Practice (In the Use of eTools) This section highlights underlying learning theories of CIECT's emerging technologies.Six examples from the blog are used to explore and emphasize the importance of grounding emerging eTools use in theory and pedagogy to promote student development.
First, it is possible to showcase behaviorist perspectives in the growth of emerging technology adoption and effective eTools use.The CIECT team assisted a lecturer in creating a video for an online chemistry course, which demonstrated the use of a specific apparatus in a laboratory setting, allowing students repeated attempts to practice and reinforce their learning.
Second, the design of an online environment can also showcase a cognitivist and constructivist perspective.A discussion forum, with an attached reading, can encourage students to engage with the topic prior to a face-to-face tutorial.A lecturer from the English Department set up an interactive online environment for a large class of 600 first-year Law students, who accessed their online term test, and which they completed during vacation (regardless of location).This resulted in student engagement and reflection on the subject by allowing unlimited attempts, with the highest mark being recorded.Also, students learning in an 'academic way' used this opportunity to attend the lecture better equipped, forming a "keystone for a particular arch of knowledge", aligned to a deep learning approach (Marton and Saljo in [16]).
Third, a lecturer is not in control of all factors that impact students' development, such as a surface approach to learning, and mere note collation for assessment.A more active problem-based teaching method can bridge this gap considerably [16].The CIECT team assisted a lecturer from the Interdisciplinary Teaching and Learning Unit (ITLU) to create a structured, interactive online environment, aligned to Salmon [17], who emphasizes the creation of spaces entailing guiding roles and a skills approach.These first steps of "familiarisation and socialisation" to eTools and environments contribute to the critical stages of achieving effective online communication and knowledge creation.To this end, a Facebook group ('Inter-Professional World Café') was created to supplement the online course, enabling the students to post comments related to their group case-studies, and to share related media, to which the lecturer was able to comment in realtime.Thus, meaning was not imposed by the lecturer, but created by the students' learning activities, allowing them to structure the information and make sense of it -referred to as conceptual change [16].This environment enabled students with a surface approach to learning, to "question, speculate, generate solutions, and use higher-order cognitive skills" [16].
Fourth, the design of an online environment can showcase social and situated learning perspectives.A collaborative online course was created (UWC/University of Missouri), organizing students in groups related to specific topics.A debate initiated by the lecturer took cognizance of different cultures, and a guest speaker (champion) was invited.Furthermore, a 'Multidisciplinary University Traditional Health Initiative (MUTHI) Clinical Trials' online course was designed and developed by the CIECT team and shared among eight universities in Africa and Europe.Students could navigate the structured course that consisted of manageable units of work which contained various interactive media and assessment activities.This becomes a community of practice, whereby clinical trial investigators in the herbal science and medicine field, registered in the course, can join.
Fifth, the design of an online environment can also showcase the influences of humanistic and self-theories.The delivery of a digital inclusion course for eCentre Managers from rural and urban areas demonstrated the importance of mindsets in the achievement of eSkills.The CIECT team designed a scaffolded learning pathway, engaging with the learners through self-directed activities and instructional material.Surprisingly, deep-rural learners with fewer resources successfully completed both the faceto-face and online phases, whilst some wellresourced urban learners did not receive their Certificates of Competence.CIECT's monitoring and tracking throughout the phases revealed a high work ethic and positive mindset of some learners, despite their challenges.
Finally, lecturers in Physics used emerging LMSintegrated eTools, namely Doctopus and Goobric, in a project aligned to socioconstructivism.The co-designers (lecturers and CIECT Instructional Designer) customized an eAssessment environment to manage large classes.This entailed the co-creation of a scientific report template which was shared (Doctopus) with students to build and strengthen their own.The template was aligned to an online rubric (Goobric), enabling students to meet specific assessment criteria.This assisted lecturers with assessment and provided constructive feedback online.These assessment processes enabled the lecturer to identify bottlenecks within the module.Students could monitor and track their progress online, through the rubric.Socio-constructivist principles are evident here, but "[a]lthough a resource may be both appropriate and useful, students may require some guidance or scaffolding in the procedures and uses of the resource" [18].
These qualitative examples presented the adoption and implementation of eTools for teaching and learning, underpinned by, and aligned with, theory.The following section will provide an exploration of broader student eTools use via an online survey.This will help create the foundation for a follow-up study to explore the use of learning theories in promoting more focused eTools adoption.
STUDENT USE OF ETOOLS
As part of CIECT's delivery and infusion of emerging technologies across campus, it is important not only to ensure the proper alignment of learning theories and ePedagogy with eTools, but to explore and review how and why students are using various eTools.In this way, it becomes possible to ensure that attention is given to those tools and functions that are most useful for students.In this section, we briefly explore what eTools students are making use of, how, and for what purpose.The ultimate aim is to reflect on where learning theories can be better aligned, and to help focus future efforts and identify new learning theories.This is linked to follow-up research, but serves the purpose of providing at least a cursory overview of student eTools use at UWC.
In June/July of 2015 an online student survey was conducted to explore precisely this issue of student eTools use (see Appendix).It was distributed via various channels, including CIECT training workshops, student visits to the Centre, and email, resulting in a total of 179 responses, despite coinciding with student examinations and vacation.A purposive sampling method, based on the "judgment of an expert in selecting cases", was deemed appropriate given the direct contact between students and CIECT's SMEs [7].A mix of open and closed questions was used.
All respondents indicated that they and their friends make use of the iKamva LMS to access learning material.It was then explored how many modules students were accessing via iKamva, and results reflected access to multiple modules.A majority of responses indicated 11 modules (20.1%, n=36), three modules (16.2%, n=29), and eight modules (10.6%, n=19).The responses overall ranged from one to 15 modules, but were concentrated between three and 11 modules (84.9%, n=152).Students are able to access previous years' modules for revision purposes or as part of a scaffolded structure.
Further results, related to engagement with emerging eTools embedded within iKamva, reflected that 64.2% (n=115) used iKamva only to download class or learning material.Apart from retrieval of learning material, 35.8% of students used additional functions, including assessment activities: (i) Assignments 71.6%, n=63; (ii) Tests and Quizzes 86.4%, n=76; (iii) Discussion Forums, 30.7%, n=27; (iv) and Other 21.6%, n=19 (Personal Learning Environments including videos, digital stories, blogs, Google Applications -used as stand-alone interventions or embedded in iKamva).This reflects that lecturers are recognizing the underlying pedagogical value of eTools, and use them to encourage social learning.This concurs with Garrison and Anderson in [2], who emphasize the need to rethink pedagogy in order to overcome passive-information-transfer approaches.
Student iKamva access responses revealed that the majority of students have access via laptops (60.9%, n=109), followed closely by campus computer labs (58.1%, n=104).Another major avenue is via smartphones (49.7%, n=89) and the final response indicated that some students use tablets (23.5%, n=42).Importantly, 92.7%, (n=166) believed that the eTools they used served to develop their overall eSkills.
The final, optional, open-ended question strived to explore LMS improvement.Feedback indicated five general groups of responses.Fourteen responses were received providing only positive feedback.Five requested email notification updates.Three requested an app to access iKamva on their smartphones.Two requested the creation of assignment groups and related communication.Finally, four had a diverse range of requests (for online textbooks, Wi-Fi accessibility, educational videos, and video chats).Some of these requests made by students regarding specific features are already embedded and available in the iKamva LMS.Lecturers are making use of the announcement feature, which is directly linked to student Gmail, group assignments, and related discussions.Additionally, lecturers across disciplines are creating and retrieving educational videos.Regarding the request for eBooks, the CIECT team has to collaborate with faculty members and the Library, especially with regards to copyright issues.Regarding the Wi-Fi request, UWC has since expanded its information infrastructure on campus.Additionally, the CIECT team has successfully launched its mobile 'Student Toolkit Application', which includes a link to iKamva and other student services.Thus, these requests are afforded full consideration to help improve the student experience at UWC.
A follow-up study, to capture the student voice with regards to the use of the LMS for student development, can provide a valuable insight into changing patterns of use by students.A special focus on whether learning theories and their use can promote the adoption of wider eTools use beyond retrieval of learning material from the LMS will be especially insightful.
CONCLUSION
This study explored some of the ways in which CIECT aligns the design of learning environments and eTools with learning theories in order to promote student development and contribute to UWC's graduate attributes.The research used a framework of learning theories to explore impactful eLearning application.The value, development, and application of learning theories in online environments were discussed.Six cases were drawn from the marketing blog, which constitutes a research repository of practitioner experiences.The authors argue that these cases showcase good practices, and prompt other eLearning professionals to enter into a debate on how eTools may better serve student development in light of the insights presented by various learning theories.The authors also contend that blogs are excellent tools for other practitioners to adopt, since our blog reflects the collaborative efforts of the CIECT team and the lecturers within the broader teaching and learning milieu, representing "evidence-based learning" and the "learning organisation" culture (UWC) [19].The efforts demonstrated in this research are also aligned to the National e-Skills Plan of Action, which calls for an "appropriate 'enabling environment' for eskills development" [20].Ultimately, this environment aims to make UWC students more successful future workers and citizens.
Learning theories thus remain critical in the design of learning environments.This is equally true for online learning environments supporting both traditional and innovative teaching and learning practices.CIECT's grounded research, going back more than a decade, has also demonstrated the continuing need for familiarization and socialization, linked to the effective use of eTools aligned to learning theories.Students will also continue to demand access to online modules.The creation of online modules takes place via a collaborative partnership between the CIECT Instructional Designers and the lecturers.Furthermore, by reflecting on how and why students use eTools, both in the institutional LMS and in PLEs, the CIECT team is prompted to continue efforts, and to recognize the fundamental importance of learning theories in (e)learning practice.
CONSENT
Consent was obtained from all participants in the online survey.See Appendix for full consent information.
ETHICAL APPROVAL
All authors hereby declare that this study and the student survey have been examined and approved by the UWC Humanities and Social Sciences Ethics Committee.
APPENDIX Student Survey (2015)
You are kindly invited to participate in a research study, which focuses on the impact of eTools, You are kindly invited to participate in a research study by the Centre for Innovative Education and Communication Technologies (CIECT), which focuses on the impact of the use of eTools, specifically iKamva, on student development.Completing the questionnaire should take no more than 10 minutes.Participation is voluntary and you may withdraw at any time.
This research is being conducted by Dr Juliet Stoltenkamp, Mr Andre Siebrits and Mr Valentino van de Heyde of CIECT.We believe there are no known risks associated with this research study, which means you should not experience it as any more troubling than your normal daily life.If you have any questions or concerns, please direct them to the researchers at 021-959-3068, or via email to<EMAIL_ADDRESS>or<EMAIL_ADDRESS>effort will be made by the researchers to keep your responses confidential and all data will be stored in a password protected electronic format.
By completing the questionnaire, you agree that: -Participation in this study is entirely voluntary.-You will not be penalised if you refuse to participate.
-The researcher(s) may quote your responses for the purposes of the study.
-The findings of this research project may be published.
-Your identity and that of all other participants will be protected.
By clicking on the "Submit" button, you agree that you have read and understood the above information, that you voluntarily agree to participate, and that you are at least 18 years old.Peer-review history: The peer review history for this paper can be accessed here: http://sciencedomain.org/review-history/19760 1. Do you use the iKamva platform to access your class notes/material?If you answered NO, what are the reasons for this? 2. Are your friends/fellow students making use of iKamva? 3. How many modules do you have in iKamva? 4. Do you only use iKamva to download class/learning material?If you answered NO, please explain how else you use it?5. How do you access iKamva?6. Do you think the eTools used on iKamva have developed your eSkills? 7. If there is anything else that you would want to do or see in iKamva, please add it here.© 2017 Stoltenkamp et al.;This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. | 6,221.6 | 2017-01-10T00:00:00.000 | [
"Education",
"Computer Science"
] |
Bisphenol A Causes Liver Damage and Selectively Alters the Neurochemical Coding of Intrahepatic Parasympathetic Nerves in Juvenile Porcine Models under Physiological Conditions
Bisphenol A (BPA) is an extremely common polymer that is used in typical everyday products throughout the world, especially in food and beverage containers. Within the last ten years, it has been found that the BPA monomer tends to leach into foodstuffs, and nanogram concentrations of it may cause a variety of deleterious health effects. These health problems are very evident in developing children and in young adults. The aim of this study was to expose developing pigs to dietary BPA at both legally acceptable and ten-fold higher levels. Livers that had been exposed to BPA showed vacuolar degeneration, sinusoidal dilatation, vascular congestion and glycogen depletion that increased with exposure levels. Furthermore, the livers of these models were then examined for irregularities and double-labeled immunofluorescence was used to check the innervated hepatic samples for varying neuronal expression of selected neuronal markers in the parasympathetic nervous system (PSNS). It was found that both the PSNS and all of the neuronal markers showed increased expression, with some of them being significant even at recommended safe exposure levels. The implications are quite serious since these effects have been observed at recommended safe levels with expression increasing in-line with exposure levels. The increased neuronal markers studied here have been previously correlated with behavioral/psychological disorders of children and young adults, as well as with childhood obesity and diabetes. However, further research must be performed in order to develop a mechanism for the above-mentioned correlations.
Introduction
Currently, bisphenol A (BPA) can be found throughout our environment. It is a chemical compound commonly used as an epoxy resin in typical everyday products, such as the lining inside canned foods and beverages, pre-packed foodstuffs, packaged baby formula, baby bottles, and containers used for food-storage in the home. Also, it may be found in dental prosthetics, and sales receipts that use thermal paper [1,2]. Unfortunately, some of this resin may leak from the polymer and enter into the human body, mainly through the contamination of food and beverages. The United States Environmental Protection Agency (EPA) has declared that BPA is the third highest priority environmental hazard [3,4]. BPA has been used for many years, because it was originally thought to be a safe chemical that showed very little chemical toxicity during standard testing. However, bisphenol is not a typical toxin. Instead, it is an EDC (endocrine disrupting compound), and behaves like estrogen in vivo. Therefore, BPA is blocking and/or interfering with the normal functioning of estrogen within the human body. It has been implicated in the disruption of thyroid hormone receptors, androgen receptors, and other endocrine system signaling pathways [5]. Meanwhile, many studies have shown that nanogram levels of bisphenol may be significantly affecting biological systems because of the disruption of normal hormonal signaling pathways. The main clinical manifestations that have been associated with BPA in the literature include reproductive disorders in adults, psychological and metabolic disorders in children, and neoplasms resulting from a weakening of the immune system [5][6][7].
There have been a handful of studies that have associated BPA exposure with abnormal brain development, but usually with limited mechanistic details. There have been no studies (to the best of our knowledge) concerning BPA exposure and the development of innervation in hepatic tissue. Unfortunately, bisphenol exposure is such a new area of research that most of the mechanisms involved have yet to be described.
However, there are a few key studies that have begun to bring these mechanisms to light. Hajszan and Leranth found that "BPA completely negates the ∼70-100% increase in the number of hippocampal and prefrontal spine synapses induced by both estrogens and androgens" [8].
Synaptic loss of this magnitude may have significant consequences, potentially causing cognitive decline, depression, and schizophrenia, according to the authors [8]. These studies were mainly performed on primates. Unfortunately, a molecular basis for these findings has not yet been determined. A study of zebra fish noted that very low-dose bisphenol exposure caused significant abnormal neurogenesis of the hypothalamus which is "a highly conserved brain region involved in hyperactivity" [9]. Again, the molecular mechanisms for this are not clear. Further research using rodent models has attempted to make some of the molecular mechanisms clearer [10,11], but the researchers could only conclude that BPA exposure changes the developing brain, but the mechanisms are still unknown. In terms of a mechanism for how bisphenol is changing neuronal architecture in the brain, and perhaps in the peripheral nervous system as well, one study has found that BPA may cause neuronal changes by inhibiting the proper functioning of T-type calcium channels. The authors have suggested that BPA may act as a modifier of channel gating and may directly plug conductive channel pores [12]. Other authors have found that the biologically active from of bisphenol can bind directly to DNA [13]. However, a mechanism for how that binding would affect neuronal expression is not yet available.
Despite a reasonable amount of recent literature concerning the effects of BPA on the central nervous system (CNS), there are scant articles concerning the effects of BPA on the PNS (peripheral nervous system). Articles concerning the effects of BPA on hepatic tissue are limited to pathophysiological analyses of hepatic tissue at recommended safe levels [14,15]. Some studies have gone a bit farther and have developed a few mechanisms for the hepatic injury. For example, one study found that rats after moderately long-term exposure had hepatocyte damage that was mediated by mitochondrial apoptosis [16]. Another study found that BPA induced DNA damage in human hepatocytes in vitro and in rat hepatocytes in vivo [17]. Unfortunately, there are no articles to date that have examined the pattern of innervation in the nerve fibers of hepatic tissue after BPA exposure, to the best of our knowledge.
The aim of this study was to examine the effects of low and high doses of bisphenol A on the innervation of porcine hepatic tissue, namely, the parasympathetic nervous system (PSNS). Co-localization of vesicular acetylcholine transporter (VAChT), a specific marker for the PSNS [18,19] with cocaine and amphetamine regulated transcript (CART), galanin (GAL), calcitonin gene regulated peptide (CGRP), substance P (SP), and pituitary adenylate cyclase activating polypeptide (PACAP), was studied using standard double-immunofluorescence.
The choice of using the domestic pig for this experiment is not accidental. Due to neurochemical similarities in the organization of the nervous system between human and pig [20][21][22], this mammal species seems to be a good animal model of the processes connected with the influence of various pathological stimuli on the human nervous system. So, the results obtained during the present study may be an animal model of BPA, but they have similarities to the innervation of human liver.
Histopathological Examination and Biochemical Blood Study
The histological appearance of porcine liver subjected to 0.05 mg/kg bw/day of BPA was characterized as having central vein and hepatic sinusoid dilatation, as well as vascular congestion. Moreover, those samples subjected to 0.5 mg/kg bw/day BPA showed remarkable vacuolar degeneration. All other components of the liver, such as the lobules, appeared normal. The histopathology of the porcine liver control samples displayed unremarkable liver lobular structure with normal hepatocytes and sinusoids. Liver sections of the high dose BPA experimental group showed hepatocytes with marked vacuolar degeneration, and staining showed changes consistent with glycogen depletion. Representative images of the histopathological samples are shown in Figure 1. Moreover, during the present study, significant changes in the levels of serum hepatic biomarkers (alanine aminotransferase (ALT) and aspartate aminotransferase (AST)) between the control group and both experimental groups were observed. Under physiological conditions, the concentration of ALT amounted to 43 ± 2.4 U/L, and that of AST was 48 ± 5.8 U/L. Low dose BPA caused an increase in the levels of these biomarkers to 69.8 ± 0.8 U/L (ALT) and 66.8 ± 3.4 U/L (AST). In animals that received high doses of BPA, the levels of ALT and AST were even higher and achieved 83.2 ± 3.5 and 87.2 ± 4.1 U/L, respectively.
Neurochemical Characterization of Intrahepatic Nerves
Both doses of BPA studied during the present investigation caused an increase in the number of VAChT-positive nerves (Table 1), but the observed changes were not statistically significant. At suggested safe levels, the number of VAChT + fibers was elevated by 8.8%, and was elevated by 27.0% at a BPA exposure ten times higher than the recommended safe level when compared to the control samples. At suggested safe-levels, the number of CART + /VAChT + fibers was 45.3% higher than that of the control samples, but was not statistically significant. At an exposure of ten times higher than recommended safe levels, the density of CART + /VAChT + nerves was 190.6% higher than that of the control samples, and was statistically significant. Also, at suggested safe-levels, the number of nerves simultaneously immunoreactive to SP and VAChT was 41.9% higher than that of the control samples, and at an exposure of ten times higher than recommended safe levels, the density of SP + /VAChT + fibers was 43.5% higher than that of the control samples. However, neither result was statistically significant.
There was an increase of 13.3% in the percentage of CGRP + /VAChT + fibers at recommended safe levels, but it was not statistically significant. At ten times the legally recommended safe level, there was a statistically significant increase of 70.0% as compared to that of the control samples. Furthermore, at the suggested safe-level, the number of GAL + /VAChT + nerves was 167.6% higher than that of the control samples, and at an exposure of ten times higher than recommended safe levels, the expression of nerves immunoreactive to GAL and VAChT was 258.8% higher than that of the control sample. Both of these results were statistically significant. Finally, the number of PACAP + /VAChT + nerves at suggested safe-levels was 49.2% higher than that of the control samples, and at an exposure of ten times higher than recommended safe levels, the expression of PACAP + /VAChT + nerves was 64.4% higher than that of the control samples. Unfortunately, these results were not statistically significant. The results above are tabulated in Table 1
Discussion
There are several articles dealing with hepatic damage. Quite often, the damage takes the form of central vein and hepatic sinusoid dilatation, vascular congestion, and vacuolar degeneration [23,24]. These particular histopathologies are typical of hepatic changes commonly observed after chemical exposure, with much of the literature centering on the effects of long-term ethanol or narcotics usage [25,26]. However, there are several toxins other than ethanol or narcotics that cause hepatic damage. Since, ethanol and narcotics are most often intentionally abused; they tend to get more attention in the scientific literature. However, there are other chemicals that may cause similar changes to the hepatic tissue. For example, acetaminophen (paracetamol) is a common over the counter pain reliever, which may cause extensive hepatic trauma even after only a single over-exposure [27]. Environmental exposure to industrial toxins such as carbon tetrachloride (CCl4) has also been shown to cause vascular congestion and vacuolar degeneration [28,29]. Exposure of endogenous wildlife to a popular insecticide also caused observable hepatic damage in a similar way to that of CCl4 [30]. Furthermore, life-saving drugs such as the antiretroviral HIV treatment azidothymidine (AZT) and popular anti-cancer chemotherapy medications have been shown to cause similar hepatic trauma [31,32]. What all of these potentially hepatotoxic compounds have in common is vascular congestion, vacuolar degeneration, and quite often oversized mitochondria, which is a sign of mitochondrial damage [25]. Very often, this hepatic damage is not only observed in microscopic tissue samples, but is also recorded in specialized markers found in the blood serum.
The types of hepatic injury mentioned above are very often measurable with the use of serum alanine aminotransferase (ALT) as well as aspartate aminotransferase (AST) levels. ALT and AST are transaminases widely used to assess hepatic trauma. AST is not a specific hepatic marker since it is often released when other cellular damage occurs, for example, during a heart lesion, over-exertion of skeletal muscle, or some erythrocyte based diseases [27]. ALT is far more specific than AST in detecting damaged hepatocytes, and also remains in the serum for longer. However, both are normally reported together in the literature, and increased levels are considered to be an indicator of hepatic damage.
One of the main ways that hepatocytes are damaged is via mitochondrial enlargement and vacuolar degeneration, which are both caused directly by excessive water retention. This leads to interference with aerobic adenosine triphosphate (ATP) production, mitochondrial mediated apoptosis, and eventually the destruction of the plasma membrane as the hepatocytes lyse from the excessive hydration [16,25]. The transaminases are released from the cytoplasm and become detectable by way of testing for ALT and AST in blood serum.
Our histopathological examination also showed staining that was consistent with glycogen depletion at high levels of BPA exposure. The glycogen depletion may be a symptom of only hepatic trauma [30], it may be a consequence of neuropeptide upregulation, or it may be a combination of both. From the available data, we can report the glycogen depletion, but can only speculate about what may be causing it.
It is quite possible that BPA may damage hepatocytes in a similar way to that of the toxins mentioned above. Our results have shown significantly increased ALT and AST levels when compared to the control group at both low dose and high dose exposure. In the high dose BPA group, the AST and ALT levels were nearly double that of the control group. Other studies have shown increased ALT levels in rat models after moderate duration BPA exposure [16]. Since the potential dangers of BPA exposure have only come to light within the last ten years, there is a limited amount of literature with regards to the effects of BPA on hepatocytes and hepatic tissue in general. However, some recent studies have shown that BPA exposure caused hepatic trauma by way of oxidative stress as well as mitochondria-mediated apoptosis [16,33]. Other studies have shown that high and low dose BPA exposure caused genomic damage as well as alterations in liver enzyme levels [15,17]. All of the in vivo studies were carried out using rat models. To the best of our knowledge, our study is the first in vivo study to use an animal model (porcine) that more closely approximates human physiology.
Although the BPA exposed liver samples in our study showed no changes in the hepatic lobular structure, they did show observable levels of vacuolar degeneration, sinusoidal dilatation, and vascular congestion. At high BPA exposure levels, vacuolar degeneration was also observed. These findings are consistent with the literature cited above. Therefore, it is reasonable to hypothesize that BPA exposure in developing children may also be causing similar hepatic trauma depending on the level of exposure. Our results have shown observable hepatic injury in a large animal model that approximates human development after only 28 days of BPA exposure. The histopathology presented in the figures taken together with the increased ALT and AST levels, plus the previous literature based on earlier rodent models, is highly suggestive of BPA inducing hepatocyte damage after only short-term exposure at currently suggested safe-levels. The mechanism of how this may be happening is currently not well-understood. Since the first major organ that ingested materials come into contact with is the liver, BPA could be causing liver damage in developing children who are exposed to this common endocrine disruptor, but future research is needed.
Knowledge of the anatomy and physiology of the intrinsic innervation of hepatic tissue is relatively recent, with the first detailed articles concerning hepatic intrinsic nerves published within the last thirty-five years [18,34,35]. More recently, neural markers have been used to study hepatic innervation by immunofluorescence. These studies are often specialized into examining the nerve-fibers of the sympathetic nervous system or the parasympathetic nervous system. For the parasympathetic nervous system (PSNS) markers such as acetylcholinesterase (AChE) and VAChT are most often used [19,36]. This study made use of VAChT in order to specifically investigate the hepatic PSNS. Although there are several studies which have investigated neural "gut-brain" markers, to the best of our knowledge, this is the first study to investigate changes in hepatic neural markers after BPA exposure.
VAChT is an enzyme important for the proper neural functioning of the PSNS (parasympathetic nervous system). The PSNS is the most commonly used part of the autonomic nervous system (ANS), and is often known as the "rest and digest" portion of the ANS [37,38]. The PSNS is characterized by its use of acetylcholine as the main neurotransmitter for cellular communication. Tissues associated with the PSNS are characterized as having many acetylcholine receptors [18,37,38]. The results of this study found no significant changes in the VAChT + nerve fibers. Therefore, BPA exposure in juvenile porcine models does not lead to an upregulation of the hepatic PSNS in a manner which can be detected with statistical significance. This does not mean that the PSNS is not upregulated at all. It may be upregulated, but not at a significantly detectable level. What may be of more interest is the fact that some of the neuronal peptides colocalized with VAChT did show significant upregulation.
VAChT has quite often been visualized by way of immunohistochemistry using porcine animal models. For example, the team of Gonkowski used VAChT to study the PSNS of the porcine ileum [38], while the team of Wojtkiewicz used VAChT to study the PSNS of the porcine esophagus [39]. The aforementioned articles used immunostaining techniques very similar to this study. This is relevant since the liver is the first major organ to come into contact with what is absorbed by the digestive system. These "gut-brain" peptides are an important field of study when looking at dietary environmental exposure [40]. Although the hepatic PSNS, through the visualization of VAChT, did not show significant increases, it is possible that the other half of the autonomic nervous system (the sympathetic nervous system) may be showing significant upregulation by itself or colocalized with neuronal "gut-brain" markers. In this study, there were neuronal markers that showed statistically significant increased upregulation.
In previous studies, markers such as CGRP, SP, GAL, PACAP, and CART have been used to observe nerve-fibers, quite often in the gastrointestinal system. CGRP has been used as a spinal afferent marker [41] and has a role in cerebrovascular regulation [42], while substance P has been used as a similar marker, but more extensively [43]. SP has a role in inflammatory diseases, nociception, and depression [44,45]. Galanin has been found to potentiate the effects of norepinephrine, is a neuromodulator affecting glucose production in the liver [46], and has been correlated with diabetes mellitus in children [47,48]. Unfortunately, the mechanisms are not well understood. PACAP has been linked with food intake, appetite control, glucose metabolism [49,50], and more recently with psychological and behavioral disorders such as post-traumatic stress disorder (PTSD), hyperactivity, memory impairment, and stress-related illnesses [51][52][53]. In a similar way to the early studies of PACAP, CART has been linked with food intake, appetite control, and the regulation of lipids in adipose tissue [54][55][56]. More recently, abnormal patterns of CART have been associated with diabetes mellitus [57]. The mechanisms are not fully understood, but appear to be highly complex with multiple gene involvement [55].
Of the nerve fibers tested, only VAChT colocalized with GAL showed significant upregulation after bisphenol exposure at currently accepted recommended safe exposure levels. Incorrect expression of GAL has been indicated in problems with energy metabolism in children, including diabetes mellitus [46][47][48]. Again, the mechanisms for these correlations are not well understood. The results above show elevated VAChT + /GAL + nerve fibers at recommended safe levels, when compared to that of control samples. Furthermore, it is a rather dramatic increase for a level that is considered to be safe. Moreover, at ten times the recommended safe-level, which is not out of the bounds of possibility due to the ubiquitous nature of bisphenol in our modern environment, the upregulation of GAL + /VAChT + was very much higher than that of the control samples. These increases in GAL + /VAChT + nerve fibers could be a contributing factor to early onset diabetes and obesity in children and young adults who are exposed to BPA if the porcine models are an accurate depiction of human development, regardless of whether the dosage is legally acceptable or not. However, further research is needed to validate the above hypothesis.
At ten times the legally accepted safe level of bisphenol, three colocalized neuronal markers showed significant upregulation. These three were the VAChT + /GAL + (previously discussed), VAChT + /CART + , and VAChT + /CGRP + nerve fibers. At an exposure of ten times higher than recommended safe levels, the VAChT + /CART + immunoreactive nerve fibers were nearly two times higher than that of the control samples. Since CART has been shown to control metabolism via the CNS, it has a key role in the proper functioning of appetite regulation [40,[54][55][56][57][58][59]. Therefore, increased CART markers within the PSNS could be a contributing factor to increased obesity in children and young adults. This could be a factor in the correlation between CART and diabetes mellitus [57] since the liver is responsible for the homeostasis of glucose levels, but further research would need to be performed to verify such a claim. Childhood obesity and BPA exposure has been correlated [60], and a cross-sectional study in Chinese school children correlated BPA exposure with increased body mass index (BMI) [61]. Both studies showed that there was a statistically significant correlation between urinary BPA concentrations and increased BMI as well as obesity in children and adolescents. At a bisphenol exposure of ten times higher than recommended safe levels, the upregulation of VAChT + /CGRP + nerve fibers was significantly higher than that of the control samples. CGRP is a potent vasodilator and has been linked with metabolic regulation [41,42]. Increased upregulation may contribute to childhood obesity and diabetes using the same neuromodulating mechanisms as those described in VAChT + /CART + nerve fiber signaling [40,[54][55][56][57][58][59]61]. The currently available mechanisms linking changes in these markers with childhood obesity and diabetes are described below.
The three neural peptides mentioned above (CART, CGRP, and GAL) have been correlated with childhood obesity and diabetes in several studies, previously cited. Although few mechanistic studies have been published yet, a recent study found that CART modulated mesolimbic dopamine systems and affected reward and reinforcing behaviors which were "linked to eating disorders, including obesity and anorexia" [62]. Furthermore, CART, CGRP, and GAL have been more recently described as gut-brain markers as well as being present in the central nervous system [63]. Other studies have shown these gut-brain markers to be linked with diabetes and obesity in children mainly through altered regulation of metabolic gene expression [64][65][66][67]. Unfortunately, detailed mechanisms are an area of future research and are not available at this time.
Although this study did not notice any statistically significant changes in SP or PACAP immunoreactive nerve fibers, both of those neuronal markers were found to increase. BPA exposure has been correlated with hyperactivity, anxiety, and other behavioral problems in children [68][69][70][71][72]. A recent study showed that increased neuronal expression of several dozen genes during the early post-natal period was correlated with altered levels of anxiety [73]. The mechanisms appear to be highly complex, however, and only correlation studies are currently available. Furthermore, a previous study correlated increased PACAP expression with post-traumatic stress disorder [51]. Therefore, it may be valid in future research to investigate a link between BPA exposure, neural upregulation, and psychological disorders in children. However, these markers were not statistically significant in this study, and no significant conclusions can be drawn at the current time.
The histopathological examination of the liver showed changes consistent with glycogen depletion at high BPA exposure levels. It is possible that the increased GAL, CART, and CGRP could be causing an altered metabolism, which is evident in decreased hepatic glycogen levels. This explanation could tie together the histopathological observations with the upregulation of these neurochemical peptides. This, taken together with the literature cited above, could become a stepping off point to investigate the mechanisms of how BPA is altering hepatic metabolism in developing organisms. On the other hand, the glycogen depletion could simply be another indicator of hepatic trauma with no neurochemical involvement. Further research should be performed to investigate the phenomenon.
The Animal Models Used in This Study
The present study was completed on fifteen immature sows of the Piétrain x Duroc breed at the age of 8 weeks and about 18-20 kg body weight. Pigs were kept under typical laboratory conditions adapted for this animal species. The experiment was performed in compliance with the instructions of the Local Ethical Committee for Experiments on Animals in Olsztyn (Poland) decision number (28/2013; 22.05.2013).
After a 3-day adaptive period, the pigs were randomly divided into three experimental groups: (1) control group-placebo (empty gelatin capsules for 28 days during feeding); (2) experimental group I (received BPA capsules at a dose acceptable under European legislation-0.05 mg (50 µg) /kg bw/day); (3) Experimental group II (received BPA capsules at a dose 10 times higher than the acceptable level-0.5 mg /kg bw/day). Every four days before the morning feeding, all animals were weighed in order to determine their body weight and calculate the proper dosage of BPA.
Tissue Collection, Fixation, and Immunolabeling
After 28 days of BPA administration, the animals were premedicated with Stressnil (Janssen, Belgium, 75 µL/kg of body weight, intramuscular). After about 30 min, the animals were euthanized using an overdose of sodium thiopental (Thiopental, Sandoz, Kundl-Rakúsko, Austria, intravenous). Tissues were collected from all sows. Sections of liver tissues were fixed in 4% buffered paraformaldehyde, rinsed in phosphate buffer for three days, and kept in 18% sucrose at 4 • C. After at least two weeks, the fragments of liver were frozen at −23 • C and cut into 10 µm-thick sections using a microtome (Microm, HM 525, Walldorf, Germany). The sections were subjected to a routine double-labeling immunofluorescence technique according to the method described previously by Gonkowski [38,40] and Wojtkiewicz [74,75]. A condensed description of the method is as follows: 45 min of drying; incubation with a blocking solution, which included 10% normal goat serum, 0.1% bovine serum albumin, 0.01% NaN 3 , Triton X−100, and thimerozal in phosphate buffered saline (PBS) for 1 h; overnight incubation with a mixture of two "primary" antibodies raised in different species and directed towards vesicular acetylcholine transporter (VAChT), and one of the aforementioned substances i.e., CART, substance P, CGRP, GAL, or PACAP; incubation (for 1 h) with species-specific antisera conjugated to Fluorescein (FITC) or biotin, which was visualized by a streptavidin-CY3 complex (the specification of intravenous primary and secondary antibodies used in the present study is shown in Table 2). Rinsing with PBS (3 × 10 min, pH 7.4) was performed between each of the stages. During the present investigation, the standard controls of the specificity of "primary" antibodies were performed. These included pre-absorption of the particular antisera with appropriate antigens, as well as "omission" and "replacement" tests that completely eliminated immunofluorescence signals.
The Histopathological Investigation
To evaluate the number of VAChT + intrahepatic nerves, the nerves were counted using a microscopic observation field (0.1 mm 2 ). Nerves immunoreactive to VAChT were counted in four sections of the liver per animal (in five randomly selected observation fields per section) and the obtained data were pooled and presented as a mean ± SEM. The method used to evaluate the neurochemical characteristics of VACHT + nerves consisted of determining what percentage of all such nerve fibers were simultaneously immunoreactive to each of the other substances included in the investigation. To this end, at least 300 VAChT-labeled nerves in each studied animal were examined for immunoreactivity to the other particular substance studied. VAChT-positive nerve fibers were considered as representing 100%. The evaluation of immunopositive nerve fibers and the counting of nerves were performed by two independent investigators. Double-labeled nerve fibers were visualized under an Olympus BX51 microscope equipped with epi-fluorescence and appropriate filter sets. The obtained results were pooled and presented as a mean ± SEM. To prevent double counting of the same nerves, the sections of liver evaluated during the present study were located at least 100 µm apart. Statistical analysis was carried out via Student's t test (Graphpad Prism v. 6.0; GraphPad Software Inc., San Diego, CA, USA). The differences were considered statistically significant at p ≤ 0.05.
The histopathological investigation of the porcine hepatic tissue was performed using the following procedure: tissue samples were fixed in buffered 10% formalin. Subsequently, they were dehydrated in graded ethanol and embedded paraffin. Four-micrometer (4 µm) thick sections were placed upon silanized slides, deparaffinized, rehydrated in graded ethanol, and then stained with hematoxylin and eosin.
Conclusions
Although the BPA exposed liver samples showed no changes in the hepatic lobular structure, they did show observable levels of vacuolar degeneration, sinusoidal dilatation, and vascular congestion. These are indicative of early hepatic injury, especially after exposure to toxic substances. Other similar studies have been performed in vivo on rodents, and they have also observed hepatic trauma after both high and low dose BPA exposure. This is the first study to our knowledge examining the effects of BPA on porcine liver, which is a closer approximation of human physiology than mice or rat. If these trends are extrapolated to humans, then children continually exposed to bisphenol compounds for several years during their childhood could be at a significantly higher risk of liver damage as well as altered metabolism. To the best of our knowledge, damage to hepatocytes has not been correlated with upregulation of the immunoreactive nerve fibers used here. From the literature, we cannot support an argument that altered patterns of innervation cause damage to hepatocytes. Therefore, it is our opinion that in this study, BPA most likely caused early signs of hepatocyte damage independently of altering neurochemical patterns. Furthermore, hepatic glycogen depletion was observed, but it is not clear whether this was due to the upregulation of nerve-fibers in this study or if it was a product of hepatic damage. Of course, future research of the mechanisms involved is highly recommended.
It is not unreasonable to assume that a developing child could be exposed to ten times the suggested safe limit of bisphenol A. This EDC can be found everywhere today and many parents are still not aware of the dangers of BPA exposure [1][2][3][4][5]. Therefore, it may be recommended to revise the suggested safe levels of BPA exposure downward, as well as increase public awareness of the potential dangers of BPA-especially with regards to children. Moreover, outside of the PSNS, bisphenol A may be causing undesirable effects in children and young adults.
Conflicts of Interest:
The authors declare no conflict of interest. | 7,215.6 | 2017-12-01T00:00:00.000 | [
"Biology"
] |
Stabilization of DC Microgrids Under Cyber Attacks-Optimal Design and Sensitivity Analysis
Due to increased efforts on digitizing the modern power electronic systems and microgrids, their operational reliability and stability are prone to the risk of cyber attacks. In this paper, we inspect the overlooked stability issues caused by cyber-attacks, and present an overall design insight for stabilization of microgrids under cyber attacks. Firstly, we shed light on the optimal design policy and sensitivity aspects of the solution for microgrids under cyber-attacks. These results are based on a describing function-based modeling method to map the stability region. Secondly, the sensitivity impact due to system parameter variations and stabilization gains on stability is theoretically investigated. In addition, the range of sensitivity of parameter variations with respect to cyber attacks are calculated. Based on different design requirements, optimal values are theoretically obtained and then tested on microgrids having different parameters in a simulation environment, which justifies the ruggedness of the proposed design approach. We provide a generalized philosophy, which can be easily extended to the overall design, stability and parameter sensitivity of cyber-physical energy systems.
I. INTRODUCTION
D ISTRIBUTED controllers have emerged as a reliable prospect for networked control of microgrids because of high reliability and scalability within a fairly economic communication infrastructure [1].Distributed controllers equip neighboring information exchange between local controllers to achieve a global control objective [2], which can be regarded as a good compromise between centralized and decentralized control.In DC microgrids, secondary controllers can achieve average voltage regulation, energy balancing and proportional load sharing by updating the voltage references for the primary controllers.Then, the droop control is used in primary controller to regulate the output voltage for each converter.
In distributed controllers, communication channel is essential for exchange of information, which makes them vulnerable to cyber attacks by third-party adversaries.Several reports of cyber-attacks on power grids, PV farms, data centers, electric vehicles [3], [4], [5], [6] are recorded.There are many kinds of cyber-attacks, including false data injection attacks (FDIA), denial of service (DoS) [7], replay attacks [8], etc.These attacks are capable of compromising the confidentiality, integrity, and availability of information in energy systems, which may result in disrupting the control objectives [9] and possibly shutdown, which mandates essential conduct.
Current research on cybersecurity primarily focus on the evaluation of cyber attack effect, detection and mitigation strategies have been well discussed.The detection problem can be summarized by identifying a change in sets of inferred candidate invariants.Detection theories for detecting FDIAs on the current sensors, communication networks in the control architecture, as well as sensors and communication channels have been developed in [10], [11].Although many work provide promising choices in improving the resiliency of power grids against cyber attacks from an ultimate perspective of grid outage and partial/full blackouts, its impact on destabilizing the system as an intermediate stage is completely ignored.Instilling instability can be another viable arrangement by the adversary, which challenges the traditional stability principles in power electronic systems.This can be caused either by triggering instability via cyber attacks either in the cyber/physical layer or both simultaneously.
In connection with this, [12], [13] reveal the stability issues caused by cyber disturbances, paying more attention on instability due to communication delays and cyber network topologies.Moreover, the steady-state analysis and stochastic small-signal stability related to cyber-physical dynamics of DC microgrid under cyber attacks are given in [7] and [14].In [15], the presence of unknown nonlinear constant power loads is determined and a distributed nonlinear adaptive observer is proposed to address the security and stability issues.However, these studies fail to quantify the impact of cyber attack on the system stability.Recently, the instability phenomena caused by stealth cyber attacks is introduced briefly in [16].Further in [17], an abstract modeling principle of the impact of cyber attacks on stability of microgrids is provided alongside a solution to address the instability issues.In our previous studies [18], [19], we demonstrate that our proposed eventdriven detection and mitigation strategy allows best reported resiliency of N−1, given that N−1 converters are attacked in a 1949-3053 c 2023 IEEE.Personal use is permitted, but republication/redistribution requires IEEE permission.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
system with N converters.In [17], it is revealed that the oscillations caused by cyber attacks will not only affect the reliability of operation, but will also forbid the operation and decision of the abovementioned event-driven cybersecurity strategies.This can be explained owing to the lack of a formidable design approach in the selection of control quantities h i and l i as well as their impact on the effectiveness of detection being unclear.In addition, the design of the pinning gain and coupling gain are not well addressed in presence of cyber attacks.
Carrying over our previous work on design of a stabilization method of DC microgrid under cyber attacks [17], the selection of an optimal stabilization gain is critical for the dynamic performance of the system.As a result, the optimal design of parameters of an attacked system albeit the uncertainty in the type and magnitude of cyber attacks with a primary focus on the system performance is still an open research question.This study is significant as all the stability and design principles are manifested based on physical disturbances, but is worthy of extension into disturbances from the cyber layer.
To fill this gap, this paper provides an optimal design framework for power electronic systems for the first time in the realm of power electronics and extends the modeling prophecies to decipher sensitivity analysis of different system parameters with respect to multi-valued cyber attacks.We expand on our modeling principles and cyber-physical stability analysis in [17] to provide a formal relationship of system response with respect to different values of cyber attacks.The said relationship is achieved using a stabilizing gain in [17].Considering DC microgrids as the test system in this paper, a describing function-based method is firstly applied to derive the stable region, wherein the effects of parameter variations and stabilization gains on stability are investigated.
A. System Description
Fig. 1 shows a single-line diagram of networked dc microgrid with N agents consisting of renewable energy sources and DC/DC buck converters, which are connected by transmission lines to each other.Apart from the physical connection, these agents are linked by communication network to exchange information.The communication network receives and delivers data among agents, providing information for each controller.Each DC/DC converter is managed by inner voltage and current controllers, as shown in Fig. 1.On top, the secondary controller, comprising of an average voltage regulator and current regulator, is used to ensure global voltage regulation and proportionate load sharing by imposing voltage offsets from each layer, respectively.
In Fig. 1, an undirected cyber graph is considered, where each node represents an agent, also denoted as x = {x 1 , x 2 , . . ., x N } and are linked by edges via an associated adjacency matrix, N×N , where the communication weight a ij (from node j to node i) is modeled using the specified law: a ij > 0, if (ψ i , ψ j ) ∈ E, where E is an edge connecting two nodes, with ψ i and ψ j being the local and neighboring node, respectively.It should be noted that if Fig. 1.Cyber-physical DC microgrid with N agents -a stabilization scheme proposed in [17] is equipped to mitigate unstable instances due to cyber attacks.
there is no cyber link between ψ i and ψ j , then a ij = 0. Any given agent at ψ i node share current and voltage information with neighbors N i = {j | (ψ j , ψ i ) ∈ E}.The matrix representing incoming information can be given as, D in = diag{d in i }, where d in i = j∈N i a ij .Similarly, the matrix representing outcoming information can be given as, D out = diag{d out i }, where d out i = i∈N j a ji .Assembling the sending and receiving end information into a single matrix, we obtain the Laplacian matrix L = [l ij ], where l ij are its elements designed using, L = D in −A G .
The objective of cooperative control is to regulate the global average voltage and realize load current sharing proportionally.In order to achieve this, a voltage reference is generated using two voltage correction terms, which are responsible for average voltage regulation and proportionate load sharing, respectively and can be given by: where, Vi is the estimated average voltage at i th agent; V dcref is the nominal voltage; δ i is the current mismatch error (in (4)) for i th agent between the local per-unit and neighbors' per-unit output current.The output from voltage observer and current regulator in Fig. 1 can be mathematically represented as: where, τ represents the communication delay between i th & j th agent and c is the coupling gain.Moreover, I dc i and I dc j , Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
I max dc i and I max dc j are the measured and maximum output currents for i th agent and j th agent, respectively.
As a result, the local reference voltage V * i for i th agent considering the two voltage correction terms in ( 1)-( 2) can be given by: For a well-connected cyber graph in a DC microgrid, according to the cooperative-based consensus algorithm, the global control objectives can be given by:
B. Solution for Instability in DC Microgrids Caused by Cyber Attacks [17]
For a well-planned set of balanced attacks injected into multiple sensors or links, (6) will still be satisfied.This aspect has already been theoretically validated in [17].The balanced attacks can be modeled by: where, u a , V denote the vector representation of the attacked control input and the average voltage, respectively.κ is a binary variable, which denotes the presence of cyber attack element by 1, or otherwise.Moreover, X a = [λ i ]∀i ∈ N, is a matrix with the false data λ i for i th agent.It is worth notifying that the system is not under attack, when X a = 0.More details about W matrix can be obtained from [17].Reference [20] provides a cooperative vulnerability factor C i to detect the attacked voltage sensors, which can be represented as: where, h i is a positive constant.As shown in Fig. 1, the detection criterion can be given by: The attacked voltage sensors can be distinguished by (9).It is worth notifying that with different values of attacks, C i is different, which means that a large value of attack indicates larger C i and vice-versa.As a result, C i can be regarded as an adaptive variable according to different value of attacks.In order to reduce the effects of smart attacks on the stability, an adaptive solution is presented, as shown in Fig. 1.
As it can be seen in Fig. 1, C i is introduced in the secondary controller and is used to modify the proportional coefficient in sublayer II, thereby changing the voltage correction term only during attacks.Hence, a novel adaptive gain mechanism is proposed in [17], which exploits the positive-definiteness of the cooperative vulnerability factor C i in (8) during attacks.As a result, when a stealthy group of cyber attack elements of any magnitude in ( 7) is injected into DC microgrid, the adaptive proportional gain of the current regulator damps out the unstable modes, given by: where, K a is a positive gain and K H 2 P in is the previously set value of the proportional gain in the current regulator.As a result, a feedforward input from ( 9) is introduced as an adaptive term to solve stability issues in microgrids arising from cyber attacks.
A. Stable Regions
Based on the cyber graph model, the converter model, the controller and the transmission line model, the small-signal model for the DC microgrid including the adaptive terms from ( 10) is expressed below: where, {H v PI , H i PI }, {H PIV , H PII } are transfer functions of the average voltage regulator, proportionate current sharing, inner voltage and current loop PI compensators for different agents in diagonal matrix form, respectively.On the other hand, G id and G vd represent the plant transfer function of inductors and capacitors for different agents in diagonal matrix form, respectively.
As it can be seen from Fig. 2, the overall model of the DC microgrid with the proposed stabilization method includes a non-linear part and a linear part.Henceforth, a describing function (DF) [21] based stability method is adopted to investigate the stability of the system.
Denoting the approximate transfer function of the nonlinear part as N A , the whole system can be roughly transformed into a linear system in the frequency domain with a variable gain amplifier N A , as shown in Fig. 3. Using (9), we can employ the sign function to represent a balanced set of zero sum attacks, which is given by: where, u a ∈ R N×1 denotes the input attack vectors.According to the definition, the DF of the sign function can be Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.calculated as: Moreover, according to the small signal diagram shown in Fig. 2 for a system of N = 6 agents, the transfer function of the linear part can be deduced and given by: (14) where, The stability region for the system can be given by: (15) where, G Im and G Re are the imaginary part and the real part of G in (14), respectively.
Using (15), the relationship between λ and K a for different voltage/current regulator characteristics, parameters for DC/DC converters and loads are investigated, with the stability regions shown in Fig. 4-5.Fig. 4 indicates that with smaller K H 1
P and larger K H 1 I
for voltage observer in the secondary layer, the considered system in Fig. 1 with the proposed stabilization method is more likely to be stable against the stealth attacks.While for the current regulator, the stable region of λ -K a with larger K H 2 P and smaller K H 2 I will be wider.Furthermore, it can be seen from Fig. 5(a) that the stabilization method can be applied for DC/DC buck converter and boost converter, while it will take larger λ to destabilize a buck converter than for a boost converter.Consequently, the stability region of λ-K a for buck converter is wider.Fig. 5(b) indicates that with the decrease of the load, DC microgrids are more vulnerable to instability due to stealth cyber-attack, requiring larger K a to make the system stable.Moreover, the stability regions related to λ and K a with the change of the global voltage reference is shown in Fig. 5(c).It can be seen that when the global voltage reference increases, the value of λ, which disturbs the system stability will decrease, indicating that the stability margin of the system operating with a larger global voltage reference is reduced.However, with the introduction of the stabilizing gain K a , the stability region will be widened.Moreover, the system trends to be stable with smaller output voltage, larger input voltage and larger line resistance.In conclusion, the stability of DC microgrid under stealth attacks are affected by different factors, which creates a multi-dimension design challenge.
B. Multi-Objective Design
According to the previous analysis, the selection of parameters is very important to ensure the whole performance of the microgrid.The purpose of this subsection is to shed light on the optimal design of the solution for microgrids under cyber-attacks.A sequential multi-objective design method is proposed here, in order to obtain an optimal stabilization gain in view of the desired steady-state and transient properties.Steady-state convergence given by voltage regulation, current sharing and transient properties given by settling time and overshoot, are the indices that need to be minimized through a design process, as shown in the flowchart in Fig. 6.The design framework is summarized below: Step 1: Determine the stability regions, as per (15).Then, define the stable range (α 1 , α 2 ) with different system parameters.
Step 2: Determine the optimal design of steady-state performance using (16) to minimize the voltage regulation and the current sharing error.Comparing g 1 with the steady Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.state design performance, an optimal range of steady-state performance (β 1 , β 2 ) ∈ (α 1 , α 2 ) can be obtained.
Step 3: Determine the optimal design for transient performance using (17) to minimize the overshoot and tune to the desired setting time.In (17), the resonant peak of the magnitude M r can represent the overshoot while the phase margin ϕ m can indicate the setting time.Comparing g 2 with the transient design performance, an optimal stabilization gain for the considered system can be obtained.
Since the unit and value of M r and ϕ m are totally different, it is necessary to make a normalization.In this paper, a Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.maximum resonant peak of the magnitude M max is introduced to normalize the overshoot while the setting time is normalized by introducing π .It is worth notifying that M max and π are deciphered based on the design requirements.Define the design requirements as D(δ v , δ i , t s , i p ), where δ v denotes the voltage regulation error, δ i denotes the current sharing error, t s describes the setting time and i p indicates the overshoot of current in DC microgrid.By constraining the design requirements D(δ v , δ i , t s , i p ) as (δ v ≤ 0.05 V, δ i ≤ 0.01 A, t s ≤ 0.3 s, i p ≤ 2 A), K a can be optimized by the sequential multi-objective design method.According to the flow chart of the proposed method, the optimal K a is found out to be 5.2.In order to analyze the steady state and transient performance with the variation of K a , time-domain and frequency-domain results are presented, as shown in Fig. 7 and Fig. 8.It can be seen that the voltage regulation and current sharing error is quite small, when K a is larger than 0.3.With the increase of K a , the overshoot decreases with the increase in setting time.The resonant peak and phase margin shares similar trends with that of overshoot and setting time, respectively when K a changes.It should be noted that the stabilization gain K a is optimized for DC microgrids in this paper, however the framework can be generalised for optimization of other system parameters.
A. Sensitivity Framework
A sensitivity analysis based on DF stability method is proposed to intuitively and quantitatively investigate the influence of the parameters in DC microgrid in Fig. 15 under cyber attacks.The DF-based stability method is described in [21], which is shown in Fig. 9(a).After that, the Nyquist plot of G(s) is manifested into the frequency domain plot, as shown in Fig. 9(b).In Fig. 9(a), if the setpoint -1/N A is not encircled by the contour of G(s), the system is stable otherwise it will be unstable or critically stable.The real part and the imaginary part of Curve 1 and Curve 2 shown in Fig. 9(a) can be equivalently manifested into Fig.9(b).Curve 1 encircling the -1/N A can be converted as an equivalent condition in Fig. 9(b): in the frequency range where the real part Re 1 is less than -1/N A , the imaginary part X crosses the frequency axis once, and the crossed frequency is noted as f 0 .While for Curve 2, since it does not encircle the -1/N A , the real part Re 2 is larger than -1/N A at the crossed frequency f 0 .Hence, the stability criteria for Fig. 9(b) is that the imaginary part does not cross the frequency axis in the frequency range where the real part is less than -1/N A , denoted as The sensitivity of the key transfer function G(s) to the system parameters α can be described as: The absolute value of the sensitivity of the linear part transfer function G(s) to any given parameter α represents how a change in that parameter affects the magnitude of G(s).If Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.the sign of sensitivity is positive, it means that as the parameter increases or decreases, the linear part of G(s) increases or decreases, and vice versa.The sensitivity calculation results can therefore be used to know which parameters of the system have a greater impact on the system stability, and to enhance the system stability by adjusting the corresponding parameter accordingly.
We illustrate the response of G(s) in the frequency domain with respect to a change in the parameter α in Fig. 10.The solid line in Fig. 10 indicates that for the current value, X(f 0 ) = 0, Re(f 0 ) <-1/N A , indicating that the system is unstable.From here, the system stability can be improved by adjusting the parameter accordingly.The ideal way is to increase the real part while its imaginary part decreases, which means that the frequency range of Re(f 0 ) <-1/N A is reduced with the frequency of X(f 0 ) = 0 moving towards the right, as shown by the dashed lines.The system amplitude margin increases as the intersection of the dashed lines and the real axis is shifted to the right.
A large absolute value of sensitivity indicates that the parameter has a large effect on the correlation function, so it is more efficient to preferentially adjust those parameters having a large absolute value of sensitivity.
B. Sensitivity Analysis
The sensitivity analysis for different parameters is shown in Fig. 11-14, where the solid lines represent the real part and the dashed lines represent the imaginary part.In Fig. 11, with the increase of K a , the real part is decreased, whereas the imaginary part is increased.When K a is larger than 0.2, there are no interactions between zero and the imaginary part, which indicates that the system operates in a stable manner.Conversely, when K a is smaller than 0.2, there are interactions between zero and imaginary part.Moreover, at the frequency range of the imaginary part, the real part is smaller than zero, indicating that the system operates in an unstable manner.
In Fig. 12, the sensitivity analysis for the proportional gain K H 2 P and integral gain K H 2 I in current regulator is presented.With the increase of K H 2 P , the imaginary part is increasing, and the frequency region of interactions between zero and the imaginary part is decreased, whereas the real part is larger than zero, indicating that the DC microgrid is stable.As for K H 2 I , the considered DC microgrid is unstable when K H 2 P is smaller than 30 because the real part is smaller than zero.Based on the stability boundaries, the system stability is hereby improved by either increasing K H 2 P or decreasing K H 2 I .However, the proportional gain and integral gain in the voltage regulator has the opposite stability trends with that of the current regulator, as shown in Fig. 13.Moreover, the sensitivity of load is shown in Fig. 14, where the real part and the imaginary part are increased with an increase in R load .Especially when the overall load R load is smaller than 50 , DC microgrid is prone to instability under cyber attacks due to the very small real part at the frequency region of interaction between the imaginary part and the zero.
Upon analyzing Fig. 11-14, the sensitivity of K a , K H 2 P and K H 2 I are larger than others which indicates that these parameters have a higher impact on the stability of the considered system than K H 1 P , K H 1 I and R load .According to the sensitivity analysis, it is more efficient to improve the system stability by increasing K a , K H 2 P as well as by decreasing K H 2 I .
V. RESULTS AND DISCUSSIONS
The simulated system is shown in Fig. 15 with the controller for each converter being presented in Fig. 1.We analyze the impact and sensitivity analysis of different system parameters on the stability of DC microgrid under cyber attack(s).Although our previous solution proposed in [17] can be used to eliminate the oscillations, it is equally crucial to formulate a design philosophy of an optimal stabilization gain K a , which can be accommodated into any system with considerable parameter variations.Simulations have been carried out to test the effectiveness of the multi-objective design of K a .Different cases with variation parameters are presented and the simulation results are concluded in Table I.To verify the optimal K a for different cases, both the simulation results using optimal K a and parameters closed to optimal K a are also shown in Fig. 16-19.
In Table I, for each case, the optimal K a is obtained as per the optimal design method in Fig. 7. Formal design specifications have been provided for each case.In Case I & II, constraining the design requirements D(δ v , δ i , t s , i p ) as (δ v ≤ 0.05 V, δ i ≤ 0.01 A, t s ≤ 0.3 s, i p ≤ 2 A), we obtain an optimal K a of 5.2 and 3.3 with different system parameters, respectively.It is worth notifying that the only difference between Case I & II is the value of K H 2 I and R load .Furthermore, in Case III & IV, upon changing the design requirements as (δ v ≤ 0.05 V, δ i ≤ 0.01 A, t s ≤ 0.35 s, i p ≤ 1 A), we obtain the optimal K a to be 6.5 and 4.5 with different system parameters, respectively.It is worth notifying that the differences between Case III & IV is that the former operates with a different output voltage reference, whereas the latter operates with a different input voltage.The corresponding measured steady-state and transient performance metrics are also shown in Table I.
We now validate the quantitative results of our proposed design framework to monitor the specifications for steady-state and transient performance in time-domain simulations.As it can be seen in Fig. 16, with the increase of K a , the setting time will rise and the overshoot is reduced.When K a = 5, K a = 5.2, K a = 5.4, the setting time is 0.285 s, 0.029 s and 0.315 s while the overshoot is 2.1 A, 1.95 A and 1.93 A, respectively.The design requirements are only satisfied with K a = 5.2, which validates the ruggedness of the proposed multiobjective optimal design method.Similarly in Case II, when the system parameters are changed, i.e., PI controller gains for voltage regulator and current regulator, the stabilization gain K a is optimized to meet the same design requirements, which is different from that of Case I.It can be seen in Fig. 17 that K a = 3.3 comes out as the optimal value for Case II, by which both the steady-state performance and the transient performance of the attacked DC microgrid holds good.
Similarly, we test a new design specification Based on the design requirements, we obtain an optimal stabilization gain K a of 6.5 and 4.5 for case III & IV, respectively.The choice of K a is validated through time-domain simulations carried out in Fig. 18 and 19, respectively.It can also be seen that even a small change of K a (within ± 5%) incurs a trade-off in its performance, where either the steady-state or transient performance metric is not met.
In conclusion, under different circumstances, the stabilization gain K a should be considered carefully to ensure good dynamic performance of the attacked system.By using the proposed design method, an optimal stabilization gain K a with minimum sensitivity and maximum robustness for stability under cyber attacks can be obtained.It should be further Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.noted that the proposed design method can be extended to any system with defined stability bounds.
VI. CONCLUSION
This paper proposes a novel design philosophy and sensitivity analysis by mapping the stability of DC microgrids under cyber attacks to the dependence of system parameters for different cyber attack values.Firstly, a describing function based stabilization method is designed using a cyber attack detection metric as an adaptive feedforward to enhance the damping under stealth cyber attacks.Then, the stability regions of the microgrid under cyber attacks are investigated.Considering them as inputs, an optimal design philosophy is proposed considering the steady-state stability and transient performance of microgrids for quantitative formulation of the stabilization gain for a given system.The sensitivity of the stability approach is carried out to analyze the parameter sensitivity with respect to system stability.Finally, different case studies are carried out to validate the optimal calculation of the stabilization gain for microgrids having varying design requirements.It turns out that the small stabilization coefficient will lead to faster transient performance but larger overshoot voltage while large stabilization coefficient will get the opposite results.Moreover, it also provides an empirical idea on the critical parameters from a cyber-physical perspective, which will affect the overall system stability.Based on this study, we argue that the proposed mechanism will broadcast new manifestations on stability and modeling of microgrids not just being limited to physical disturbances, but also needs more analysis from an uncertain input in the cyber layer.Moreover, the proposed design philosophy can also be applicable for system designers with different design requirements to model against the cyberphysical interactions and their impact on the operation microgrids.
Simulation Parameters
It is to be noted that the line parameter R ij is connected from the i th converter (each of 10 kW) to the j th converter.Moreover, the controller gains are identical for each converter.
Converter: L se i = 3 mH, C dc i = 250 μF, I dc min = 0 A, I dc max = 28 A, V dc min = 270 V, V dc max = 360 V.
Fig. 2 .
Fig. 2. Small-signal diagram of the attacked DC microgrid in Fig. 1 under stealth cyber attack -the non-linear part includes cyber attack modeled as an non-deterministic disturbance.
Fig. 4 .
Fig. 4. Stability region: Relationship between λ -K a with change of the voltage/current regulator characteristics: (a) voltage regulator proportional gain, (b) voltage regulator integral gain (c) current regulator proportional gain, (d) current regulator integral gain.
Fig. 6 .Fig. 7 .
Fig.6.Flow chart of the sequential multi-objective design method for DC microgrids considering FDI attacks at vulnerable points.
Fig. 8 .
Fig. 8. Analytical results of transient performance on the impact of K a on time-domain and frequency-domain metrics.
Fig. 10 .
Fig. 10.Frequency domain plot of G(s) with the change of system parameters -the stability margin increases with the increase of real-part and decrease of the imaginary part of the sensitivity function.
Fig. 11 .
Fig.11.Sensitivity analysis for G(s) (Fig.15) to the stabilization gain K athe solid lines represent the real part whereas the dashed lines represent the imaginary part.
Fig. 12 . 2 P
Fig. 12. Sensitivity analysis for (Fig. 15) to the PI controller gains across voltage observer: (a) K H 2 P , and (b) K H 2 I .
Fig. 15 .
Fig.15.Simulated system of a 6-bus networked cyber-physical DC microgrid with the converters (C#1-C#6) distributed via tie-lines between them -V n and I n represent the measured capacitor voltage and inductor current, respectively for agent n.
Fig. 16 .
Fig. 16.Time-domain waveforms of Case I with design requirement D (δ v ≤ 0.05 V, δ i ≤ 0.01 A, t s ≤ 0.3 s, i p ≤ 2 A): (a) K a = 5, (b) K a = 5.2, (c) K a = 5.4.As calculated in TableIfor Case I, only K a = 5.2 complies with the said requirements of the overshoot and settling time bounds.
Fig. 17 .
Fig. 17.Time-domain waveforms of Case II with design requirement D(δ v ≤ 0.05 V, δ i ≤ 0.01 A, t s ≤ 0.3 s, i p ≤ 2 A): (a) K a = 3.1, (b) K a = 3.3, (c) K a = 3.5.As calculated in TableIfor Case II, only K a = 3.3 complies with the said requirements of the overshoot and settling time bounds.
Fig. 18 .
Fig.18.Time-domain waveforms of Case III with design requirement D (δ v ≤ 0.05 V, δ i ≤ 0.01 A, t s ≤ 0.35 s, i p ≤ 1 A): (a) K a = 6.3,(b) K a = 6.5, (c) K a = 6.7.As calculated in TableIfor Case III, only K a = 3.3 complies with the said requirements of the overshoot and settling time bounds.
Fig. 19 .
Fig. 19.Time-domain waveforms of Case IV with design requirement D (δ v ≤ 0.05 V, δ i ≤ 0.01 A, t s ≤ 0.35 s, i p ≤ 1 A): (a) K a = 4.3, (b) K a = 4.5, (c) K a = 4.7.As calculated in TableIfor Case IV, only K a = 3.3 complies with the said requirements of the overshoot and settling time bounds. | 7,807.8 | 2024-01-01T00:00:00.000 | [
"Engineering",
"Computer Science"
] |
Composite Scaffolds Based on Silver Nanoparticles for Biomedical Applications
1Department of Orthopaedics, Traumatology, Urology and Imaging, Faculty of Medicine, “Victor Babeş” University of Medicine and Pharmacy Timişoara, P-ţa Eftimie Murgu, No. 2, 300041 Timis,oara, Romania 2Faculty of Applied Chemistry andMaterial Science, Politehnica University of Bucharest, 1-7 Polizu Street, 011061 Bucharest, Romania 3Collagen Department, Leather and Footwear Research Institute, 93 Ion Minulescu, 031215 Bucharest, Romania 4Department of Technology of Materials and Devices in Dental Medicine, “Victor Babeş” University of Medicine and Pharmacy Timişoara, P-ţa Eftimie Murgu, No. 2, 300041 Timis,oara, Romania
Introduction
Silver nanoparticles are of increasing interest for scientists due to their very good biological properties and limited side effects.Used since 1000 BC, silver proved its biocidal activity for a wide number of bacteria and recently it was also known to be active in the treatment of cancer [1].As a consequence of silver multifunctionality (antiseptic [2], antitumoral [3,4], and IR-sensitizing agent [5]) the number of published papers dealing with silver nanoparticles increases exponentially yearly, at present over 10 000 papers [6] being indexed on SCOPUS database.The distribution of the published papers, per year, can be visualized in Figure 1.
In the case of bone cancer, many times surgical resection is necessary.In order to treat bone cancer the multifunctional COLL/HA-Fe 3 O 4 composite materials were proposed.The composite support assures a faster healing of the bone defect while magnetite can assure the necessary hyperthermia to induce tumoral cells death.It is also important to mention that magnetite can be activated, any time, by applying a proper, external electromagnetic field [36].
The current paper presents the synthesis and characterisation of new antiseptic materials based on silver nanoparticles embedded in collagen, hydroxyapatite, or collagen/ hydroxyapatite composite material.Silver nanoparticles were synthesised by two different methods: chemical reduction and plasma sputtering.The obtained materials are intended to be used as bone grafts.
Materials and Methods
Type I fibrillar collagen (C) gel having about 300000 Da, concentration of 1.6% (w/w), and pH 7.4 was extracted from calf hide as previously described [20,25].
Antiseptic collagen sponge was obtained by chemical reduction of Ag + in the presence of glucose and by plasma sputtering of Ag nanoparticles onto the collagen sponge.In both cases collagen sponge was obtained by cross-linking of the collagen gel with glutaraldehyde.For cross-linking 0.5% glutaraldehyde, reported to dry collagen, was used.
The reduction of Ag + occurs in the presence of glucose which undergoes an oxidation process as presented in the following reaction: Antiseptic HA powder was also obtained by the same two methods starting from HA powder obtained by coprecipitation from Ca(OH) 2 and NaH 2 PO 4 [23].
The antiseptic composite materials were obtained by a similar way as antiseptic collagen sponge but starting from mineralized collagen gel and COLL/HA composite sponges, respectively.
The COLL/HA composite material was synthesised as we described in our previously published papers [25,37].Briefly, the collagen gel (when plasma sputtering method is used) or silver containing collagen gel (when chemical method is used) was neutralized with Ca(OH) 2 24 h and then the proper amount of NaH 2 PO 4 was added and let for other 24 h to interact.During these steps which lead to the HA nucleation on the collagen, the pH was set at 9. The final steps consist in cross-linking followed by freeze-drying.
Plasma sputtering of silver nanoparticles was realised using a BAL-TEC SCD005 Sputter Coater with nitrogen plasma and the deposition current was 59 mA while the deposition time was set at 60 s.
The obtained materials were investigated by X-ray diffraction, IR spectroscopy, scanning electron microscopy, transmission electron microscopy, and antimicrobial activity against Escherichia coli.
X-ray diffraction analysis was performed using a Shimadzu XRD 6000 diffractometer at room temperature.In all the cases, Cu K radiation from a Cu X-ray tube was used.The samples were scanned in the Bragg angle, 2 range of 10-70.
For IR spectroscopy (Shimadzu 8400 FTIR Spectrometer) measurements, the spectra were recorded in the wavenumber range of 400-4000 cm −1 , with a resolution of 2 cm −1 .
SEM analyses were performed on a HITACHI S2600N electron microscope on samples covered with silver layer.
The transmission electron images were obtained on finely powdered samples using a Tecnai G 2 F30 S-TWIN high resolution transmission electron microscope (HRTEM) equipped with STEM-HAADF detector, EDX, and EELS.The microscope was operated in transmission mode at 300 kV while TEM point resolution was 2 Å and line resolution was 1 Å.
The antibacterial activity was evaluated in triplicate against Escherichia coli.Escherichia coli (K 12-MG1655) were cultured in a tube containing Luria-Bertani (LB) medium [38] at 37 ∘ C (LB medium composition: peptone, 10 g/L; yeast extract 5 g/L, NaCl 5 g/L).Sterile samples were incubated for 18 hours in test tubes containing 5 mL culture of Escherichia coli.Culture was obtained from a volume of 100 mL sterile culture medium.The sterile medium was inoculated with 1 mL of Escherichia coli (1%).Once obtained 5 mL of culture was placed over the samples.Optical density was determined after 18 hours of incubation.Incubation was performed in the incubator Laboshake Gerhardt.The bacterial growth was determined by measuring optical density for the four samples and control (Escherichia coli culture without sample) at 600 nm using UV-VIS spectrophotometer (Jenway Spectrophotometer).
The antibacterial activities were determined by calculating the inhibition of growth using [39] where is the inhibition of growth, %, 18 is the blankcompensated optical density at 600 nm (OD 600 = 3.36 of the positive control of the organism at 18 h), 0 is the blankcompensated OD 600 of the positive control of the organism at 0 h (OD 600 = 0.049), 18 is the negative control-compensated OD 600 of the organism in the presence of test sample at 18 h, and 0 is the negative control-compensated OD 600 of the organism in the presence of test sample at 0 h.
Results and Discussion
The antiseptic materials were characterized by appropriate methods.
3.1.X-Ray Diffraction.X-ray diffraction pattern was used to prove the formation of the AgNPs regardless of the synthesis method as we presented in Figure 2. Silver was identified based on the ASTM file number 0040783.Sodium nitrate was identified as a secondary crystalline phase, its presence being explained based on the collagen extraction technology.
Infrared Spectroscopy.
The three FTIR spectra reveal the absorption bands of the components except the AgNPs which appear far below the lower limit of wavelength of the spectrophotometer as Figure 3 showed.The main absorption band of HA appears as follows, a triple degenerate band associated with the O-P-O band at 560, 600, and 630 cm −1 ; a triple degenerate band at 1030, 1090, and 1110 cm −1 ; and a band associated with a symmetric stretch of P-O band at 960 cm −1 , while the main absorption bands of collagen appear at 1628 (amide I), 1540 (amide II), 1236 (amide III), 2854 (CH 2 asymmetric stretching), 2926 (CH 2 symmetric stretching), and 2957 (CH 3 symmetric stretching).The wide band from 3000 to 3600 cm −1 corresponds to the associated hydroxyl groups from collagen, hydroxyapatite, and water.
Scanning Electron Microscopy.
The silver particles cannot be identified by SEM images because of their low content and nanosize into the collagen composites (Figure 4).At 2000 and 3,500x magnification, the COLL/HA-Ag sample presents agglomerations which can be easily assigned to the inorganic, hydroxyapatite phase [24].This observation is also supported by the comparison with the COLL/Ag sample (Figures 4(a )-4(c )) where no agglomerations can be identified.Silver visualization will be possible at higher magnification using TEM or HRTEM.That is why only in the case of COLL/HA-Ag composite material agglomerates can be visualised on the collagenic matrices, these agglomerates being clearly identified on the collagenic matrix at a magnification of 2000x while in the case of COLL/Ag material no agglomerations can be identified at this magnification.
Scanning electron microscopy was also used for the characterization of HA-Ag nanopowder (Figure 5).Based on the micrographs, it can be seen that nanometric particles were obtained.The size and shape are difficult to determine based on the SEM images and consequently TEM will be further used to evaluate the size and to determine the shape of these nanoparticles.
Transmission Electron Microscopy
. TEM analysis was performed on pure silver nanoparticles obtained by plasma sputtering (Figure 6), COLL/Ag sample obtained by plasma sputtering (Figure 7), and HA-Ag nanopowder obtained by HA precipitation and chemical reduction of Ag + (Figure 8).In the case of pure silver nanoparticles obtained by plasma sputtering nanoAg agglomerates can be identified.From the point of view of particle size distribution very small particles with 1-2 nm as well as oversized particles with about 10-20 nm diameter can be visualized.The characteristic silver bands can be identified in SAED as well as silver oxide which means that during the deposition silver is partially oxidized to silver oxide.
In the case of COLL/Ag antiseptic sample, due to the collagen harsh matrix the silver is more uniformly deposited, the particles having generally 2-4 nm diameter.
Analyzing Figure 7, it can be seen that practically the particles are independent which means that collagen matrix acts as a dispersing agent and does not allow the silver nanoparticles to form agglomerates.
In the case of HA-Ag sample both HA and Ag can be identified based on their different contrast or based on their interplanar distances.At low magnification a severe agglomeration of the silver nanoparticles (darker nanoparticles) is noticed while, at high resolution characteristic planes of HA and Ag demonstrate their presence.Comparing with the COLL/Ag sample, the HA-Ag is less homogeneous because, in the bulk nanopowder, it is possible to identify silver-rich areas (containing silver agglomerates) but also silver-free areas (pure HA).Based on TEM image, silver as well as HA can be considered monodisperse, silver having spherical form and a maximum diameter of less than 20 nm.
Antimicrobial Studies.
As found in the literature data, the antimicrobial activity is dependent on concentration, silver size, and shape [40].Because only for the HA-Ag sample different compositions were obtained, the antimicrobial studies will be presented only for HA/Ag samples obtained by plasma sputtering and containing 10, 100, and 1000 ppm silver nanoparticles.The bacteriological experiments performed in vitro demonstrated the effectiveness of these samples in inhibiting the growth of Escherichia coli (Figure 9), even at low silver content.
It can be concluded that even at low content of silver nanoparticles (10 ppm), the HA-Ag sample inhibits the growth of E. coli (43%) while increasing content of silver induces a higher level of antimicrobial activity (51% for 100 ppm and 77% for 1000 ppm of nanoAg, resp.).
Based on the presented results these materials are intended to be further tested for the following applications, as presented in Table 1.
Conclusions
Three types of antiseptic, multifunctional materials were obtained, each having different potential medical applications.COLL/nanoAg is potential material for skin repair and can be used especially for the injuries caused by burns or cancer.HA/nanoAg and COLL/HA-nanoAg are potential bone grafts antiseptic materials but can be also used in different kinds of bone cancer, where surgical resection is necessary.Besides the material, in the cases of infections or tumours the silver-rich face of the materials has to be in contact with these tissues.When only antiseptic activity is required both symmetric (homogenous) and asymmetric materials can be used.In the cases of skin injuries it is recommended to use asymmetric COLL/Ag scaffolds and the silver-rich face does not have to be in contact with the skin, having only protective role for potential infections.
Figure 1 :
Figure 1: The evolution of the number of papers dealing with "silver nanoparticles."
Figure 7 :
Figure 7: TEM image of the antiseptic COLL/Ag matrix.
Table 1 :
Potential applications of the synthesized samples. | 2,709 | 2015-01-01T00:00:00.000 | [
"Materials Science"
] |
Synchronization of Fractional Delayed Memristive Neural Networks with Jump Mismatches via Event-Based Hybrid Impulsive Controller
: This study investigates the asymptotic synchronization in fractional memristive neural networks of the Riemann–Liouville type, considering mixed time delays and jump mismatches. Addressing the challenges associated with discrepancies in the circuit switching speed and the accuracy of the memristor, this paper introduces an enhanced model that effectively navigates these complexities. We propose two novel event-based hybrid impulsive controllers, each characterized by unique triggering conditions. Utilizing advanced techniques in inequality and hybrid impulsive control, we establish the conditions necessary for achieving synchronization through innovative Lyapunov functions. Importantly, the developed controllers are theoretically optimized to minimize control costs, an essential consideration for their practical deployment. Finally, the effectiveness of our proposed approach is demonstrated through two illustrative simulation examples.
Introduction
Compared to continuous control techniques such as feedback [1] and adaptive control [2], impulsive control technology represents an efficient discrete control method, only modifying the system state instantaneously under specific conditions [3].Consequently, impulsive control can save communication bandwidth and energy consumption.It has found extensive applications in time-varying delay systems [4], chaotic systems [5], and neural networks [6].On the other hand, the event-triggered mechanism, as a control strategy that updates control information based on the system state, can effectively conserve communication resources, reduce energy consumption, and boasts high robustness and adaptability.It has been applied in fields such as neural networks [7], singular systems [8], affine systems [9], PDE systems [10], and multiagent networks [11].However, isolated impulsive control can lead to frequent energy expenditures [12], and event-triggered control might result in communication congestion when implemented in multi-node neural networks [11].Hence, many researchers have integrated the advantages of these two control strategies, proposing event-based impulsive control strategies and achieving significant results in the domain of neural networks [13][14][15][16][17].
The memristor, first proposed by Chua in 1971 [18] and physically realized by HP Laboratories in 2008 [19], is acknowledged as the fourth fundamental circuit element.Its compact size, low energy consumption and intrinsic memory function, and ability to emulate brain synapses accurately, make it an ideal basis for constructing artificial neural networks that closely mimic biological brain functions [20].In leveraging these strengths, a category of neural networks based on memristors, referred to as MNNs, has emerged [21].Fractional-order differential operators, in comparison to integer-order ones, offer a more precise depiction of physical processes due to their non-local and memory properties, enhancing the adaptability of system processes [22].The integration of traditional MNNs with fractional-order operators, resulting in fractional memristive neural networks (FMNNs) [23], has seen widespread application in image encryption [24], audio encryption [25], and secure communication [26].Moreover, due to active device and amplifier switching speed limitations, neuron interactions often introduce time-varying delays, including discrete delays [27], distributed delays [28], and leakage delays [29].To our knowledge, studies on fractional memristive neural networks that simultaneously consider these three types of time-varying delays have just commenced, limiting their practical engineering applications-a gap that this study aimed to bridge.
Synchronization in FMNNs, a key aspect of neural network dynamics, has attracted extensive academic interest [30,31].Song and colleagues [32] crafted an adaptive continuous controller to robustly synchronize FMNNs, utilizing the continuous frequency distributed equivalent model as an analytical tool.Incorporating the reaction-diffusion phenomenon into FMNNs, Wu and associates [28] introduced both the pinning continuous feedback controller and the pinning continuous adaptive controller to ensure the asymptotic synchronization of FMNNs.Drawing upon the continuous hybrid adaptive controller, Kao et al. [29] delved into the Mittag-Leffler synchronization of FMNNs, specifically considering leakage delay.In the real-world context, driven-response FMNNs invariably suffer from imperfectly matched connection weights, termed jump mismatches [27,33,34].Addressing this, Ding et al. [27] and Zhang et al. [34] explored lag projective synchronization, employing sliding-mode control and linear feedback control, respectively.Further, Zhang et al. [33] devised a feedback controller to elucidate the quasi-synchronization conundrum.Despite their successes, these methods demand substantial communication resources, necessitating continuous control data transmission, which limits their practical applicability for FMNNs synchronization.This underscores the need for an event-based impulsive control approach, aiming for efficient control with minimized costs.
In this investigation, we present a novel event-based hybrid impulsive controller, specifically tailored to synchronize Riemann-Liouville-type FMNNs faced with mixed delays and jump mismatches.Our key advancements can be distilled into the following highlights:
•
With comprehensive consideration of discrete, distributed, and leakage delays, combined with jump mismatches, we augment the relevance of FMNNs to practical systems in industry.
•
With the aim of achieving control objectives for a controlled network at a lower control cost, we unveil two innovative event-based hybrid impulsive controllers, incorporating both static and dynamic event-triggering mechanisms.
•
Leveraging novel Lyapunov functions, we establish a duo of sufficient criteria, theoretically ensuring asymptotic synchronization in the aforestated FMNNs.
This research navigates the complexities of integrating mixed time delays and jump mismatches, enhancing model practicality and significantly challenging controller design.Furthermore, the inherent discontinuity of the memristor and the versatility of fractional-order operators make devising suitable trigger functions for our event-based hybrid impulsive controller particularly challenging, which is a crucial step to maintaining control effectiveness and avoiding Zeno behavior.
The structure of this paper unfolds as follows.In Section 2, we provide a detailed mathematical model of the aforementioned FMNNs.Section 3 lays out the foundational concepts and preliminaries essential for validating our proposed theories.In Section 4, we introduce the two proposed controllers along with their associated conditions, ensuring asymptotic synchronization, while circumventing the potential for Zeno behavior.Section 5 presents two illustrative simulation examples.Finally, Section 6 summarizes the essence and findings of this research.
Notations: The set of real numbers is denoted by R = (−∞, +∞), and the set of positive real numbers is R + = (0, +∞).An n-dimensional Euclidean space is represented by R n .Additionally, N is the set of integers, while N + is the set of positive integers.The well-known Dirac and Gamma functions are denoted by δ(•) and Γ(•), respectively.
Remark 1.
Memristive neural networks (MNNs) inherently face time delays due to circuit limitations, which can compromise their performance.Previous research [27][28][29]35] has tended to address discrete, distributed, or leakage delays either singly or in pairs, limiting holistic comprehension and application.Our work expands the conventional FMNN model to include these mixed delays, significantly improving its applicability and accuracy in real-world scenarios.
Main Results
In this section, we will explore the asymptotic synchronization problem of the FMNNs and describe the corresponding response system for (1) as follows: where ν i (t) is represented as a neuron state, and ψ i (t) is the novel controller to be designed.And κ * ij (•), ξ * ij (•), and ρ * ij (•) are described as follows: where switching jumps satisfy V j ∈ R + .Just like (2), the initial criteria for FMNNs (6) are where φ i (s) is bounded and continuous on [−τ max , 0].
Remark 2. The FMNNs, as outlined by Equations ( 1) and ( 6), are state-dependent differential systems where the connection weights are determined by the states of the neurons.Given that disturbances, whether internal or external, can lead to variations in connection weights between driven and response systems, addressing jump mismatches becomes essential.
denote the synchronization error.Therefore, according to (1) and ( 6), we know that the synchronization error system is The innovative event-based impulsive controller ψ i (t) is designed as follows: where k ∈ N represents the kth impulsive instant.The feedback control gains are p 1i ∈ R + and p 2i ∈ R, respectively.The impulsive moment sequence {t k } is a monotonically increasing series and satisfies t k → ∞ as k → +∞.For the purpose of subsequent proofs, this paper supposes that the neuron's state is right-continuous in an impulsive instant, i.e., it satisfies the conditions . Instead of assuming the impulsive strength as the constant, we consider it the function α ik ζ(t) satisfying Assumption 2.
Remark 3. The controller introduced herein was designed to efficiently achieve the control objective, using minimal resources and exhibiting resilience to unforeseen perturbations.To this end, a static event trigger strategy is detailed in Section 4.1, which is later refined to a dynamic strategy in Section 4.2 for heightened adaptability.
According to the controller ( 9), (8) could be translated as The specific control process is depicted in Figure 1.The value of the error FMNNs (ζ(t)) is obtained by calculating the difference between the states of the neurons in the response FMNNs (ν(t)) and the driven FMNNs (µ(t)) at the current instant.The signal receiver in the controller collects the value of the error system neurons and decides whether to update the value of the signal exporter based on the trigger condition.The response FMNNs update the state of their own neurons according to the output signals given by the controller (ψ(t)) in order to facilitate asymptotic synchronization with the driven FMNNs.
Assumption 2. The impulsive strength function α ik ζ(t) satisfies
where α k ij ∈ (0, +∞), ϱ ∈ N + , and k ∈ N. Remark 4. Within numerous impulsive control frameworks, the impulsive strength is often assumed to be constant, expressed as , where r ik is a constant.It is evident that Assumption 2 is satisfied when α k ii = r ik and α k ij = 0 for i ̸ = j.Consequently, the controller formulated in this study offers a more encompassing and versatile approach.
Static Event Trigger Strategy
Let the measurement error function be Then, the trigger function is defined as follows: where ι, ς ∈ R, where others, .Thus, the static event trigger condition is Theorem 1.With the assistance of the proposed controller (9) with static trigger condition (13), asymptotic synchronization is achieved in FMNNs ( 1) and ( 6) if Assumptions 1 and 2 and the following inequalities hold: Proof.Pick an appropriate Lyapunov function: where When t ̸ = t k , according to Lemmas 5 and 6, the derivative of According to Lemmas 2 and 3, one obtains Combining ( 16)-( 19) with (15), one could obtain At the same time, one could obtain From ( 20) to (23) and the measurement error function (11), we could obtain Moreover, the following inequalities hold according to the measurement error function (11) and ω(t) ≤ 0: Putting ( 25) into (24), one obtains , according to Assumption 2 and Theorem 1, one obtains The proof is completed.
Remark 5. Our research diverges from the existing literature [27][28][29]32,34,35] by implementing an event-based hybrid impulsive controller, as opposed to continuous or partially discrete controllers.This innovative strategy significantly reduces the need for continuous control information transmission, thereby decreasing energy and bandwidth consumption.
Definition 2 ([37]
).When ∃h ∈ R + s.t.inf k∈N {t k − t k−1 } > h, the system is said to evade Zeno behavior under the effect of the proposed controller.
Theorem 2. The FMNNs ( 6) could evade Zeno behavior with the effect of controller ( 9) under static trigger function ( 13) when Theorem 1 is satisfied.
Proof.Based on Theorem 1, we could obtain that According to the Riemann-Liouville fractional definition (Definition 1) and relating property (Property 1), one could obtain the following inequality: According to (26), one could obtain Obviously, the inequality always holds: According to trigger condition (13), one obtains Thus, the lower bound of where Based on Definition 2, the proof is completed.
Dynamic Event Trigger Strategy
To further enhance the flexibility of the controller, we defined the auxiliary dynamic function (28), which translates the static trigger condition ( 13) into a dynamic one: with the initial conditions ϖ(0) > 0. Thus, we define the dynamic trigger function as where ζ max (t) = max{ζ i (t)}, and p 1min = min{p 1i }.Thus, the dynamic trigger condition is Theorem 3. The controller with dynamic trigger condition (30) will help FMNNs (1) and FMNNs ( 6) achieve asymptotic synchronization if Theorem 1 holds.
Proof.We construct the new Lyapunov function V(t) = V(t) + ϖ(t).According to in- equality (24), its derivative is Owing to the trigger function υ(t) ≤ 0 and the measurement error function (11), the following inequality is obtained: Putting ( 32) into (28), one could obtain π(t) ≥ −(1 with initial condition π(0) ≥ 0, then the following inequality holds: Based on the comparison principle, the following inequality holds: Putting ( 33) into (31), the inequality V(t) < 0 holds.When t = t k , one could obtain the following inequality: The proof is completed.
Remark 6.The controller is activated by a static event trigger condition, given by Equation ( 13), when ω(t) exceeds zero.This suggests that the difference between the error system value ζ i (t k−1 ) at the last triggering instant and ζ i (t) at the current time exceeds a fixed constant (ιΞ min ζ min (t k−1 ) + ςΘ min )/(p1max + ιΞmax).To enhance adaptability and reduce trigger occurrences, we incorporate an auxiliary dynamic function ϖ(t) to adjust the triggering criterion.
Proof.When t ∈ [t k−1 , t k ), one obtains the following inequality based on the dynamic trigger function υ(t) ≤ 0, t ∈ [t k−1 , t k ): Owing to (27), the lower bound of where The proof is completed.
Remark 7. It can be observed that the control design in this paper includes many fixed parameters, such as Θ, Ξ, and so on.However, in the practical application of networks, excessive parameter designs often increase the engineering complexity.Therefore, reducing the total number of parameters in such controllers will be a problem worthy of careful consideration.
Numerical Example
This section presents two examples to illustrate the effectiveness of the proposed controller.
Example 1.Initially, we examine the static event trigger strategy within three-neuron FMNNs with mixed delays.The model can be represented as follows: H j µ j (s) ds, (35) with the parameters set as q = 0.8 and η 1 = η 2 = η 3 = 1.The leakage, discrete, and distributed delays are τ 1 (t) = e t 1+e t , τ 2 (t) = 0.6τ 1 (t), and τ 3 (t) = 0.2τ 1 (t), respectively.Therefore, τ 1 = 1, τ 2 = 0.6, and τ 3 = 0.2 and h 1 = 0.25, h 2 = 0.15, and h 3 = 0.05.The activation functions were chosen as F j (µ i (t)) = tanh µ j (t) , G j µ i (t − τ 2 (t)) = sin µ j (t − τ 2 (t)) , and H j (µ j t) = 0.3 sin µ j (t) , which implies that F j = G j = 1 and H j = 0. ).In the driven system for system (35), we define that the jump threshold V j = 3.The initial conditions are D q−1 R ν i (s) = (−0.6,0.6, 1.2), s ∈ [−τ max , 0]. Figure 2 shows the neurons' trajectory plots of the driven and response FMNNs, as well as the error FMNNs, without the effect of the controller.The neurons' trajectories of the driven-response FMNNs do not overlap in Figure 2a, and the ones in the error FMNNs exhibit sustained oscillations in Figure 2b, which indicate the absence of asymptotic synchronization between the driven-response systems without control intervention.In the following, the choice of appropriate controller parameters will enable the systems to achieve asymptotic synchronization. (a) -0.5 others.
And we chose ι = 0.8 and ς = 0.6.The impulsive strengths are which satisfy Theorem 1.Thus, one obtains that As per Theorem 1, the driven system (35) and its response system will asymptotically synchronize under the effect of controller ψ i (t). Figure 3 illustrates the neurons' trajectory plots of the drivenresponse FMNNs, as well as the error FMNNs, with the action of controller (9) utilizing the static trigger strategy.From Figure 3a, it can be observed that after t ≈ 0.7, the trajectories of the response FMNNs and the driven FMNNs coincide, indicating that they have achieved asymptotic synchronization.Moreover, in Figure 3b, the error FMNNs also stabilize at the same moment, further demonstrating the effectiveness of the controller.Figure 4 illustrates the time intervals between adjacent trigger instants of the designed controller, denoted as t k − t k−1 .It can be observed that the time intervals between adjacent trigger instants are always greater than 0, demonstrating that this controller can avoid Zeno behavior based on Definition 2. Example 2. In terms of the dynamic event trigger strategy, the driven and response FMNNs with mixed delays and jump mismatches are the same as in Example 1.And the parameters used for controller (9) are p 1i and p 2i in Example 1.The initial value of the auxiliary dynamic function is ϖ(0) = 0.08.As shown in Figure 5, the driven-response system achieves asymptotic synchronization at t ≈ 1.4.And Zeno behavior could be removed, which could be proven in Figure 6.
And the value of the auxiliary dynamic function is always greater than 0 in Figure 7, which coincides with Theorem 3. In addition, compared to the time intervals in Figure 4, it could be observed that the controller's trigger frequency in Figure 6 can be greatly decreased by inserting an auxiliary dynamic function, but at the cost of a longer period to achieve progressive synchronization owing to the more "relaxed" trigger condition.However, this conclusion is based solely on empirical evidence from simulation experiments.The theoretical rigor of this phenomenon remains to be established, which is a question we need to address in our future work.
Conclusions
The present study introduced a novel mathematical model for FMNNs that incorporates mixed time delays and jump mismatches.Subsequently, we designed two innovative hybrid impulsive controllers based on static or dynamic event-triggering mechanisms.In leveraging inequality techniques and impulsive analysis, synchronization criteria for the investigated systems weare derived by constructing novel Lyapunov functions.Theoretically, the design of these controllers effectively overcomes the substantial control cost challenges identified in prior research, providing crucial insights for real-world applications. | 4,151 | 2024-05-18T00:00:00.000 | [
"Computer Science",
"Engineering",
"Mathematics"
] |
ENHANCED RGB-D MAPPING METHOD FOR DETAILED 3 D MODELING OF LARGE INDOOR ENVIRONMENTS
RGB-D sensors are novel sensing systems that capture RGB images along with pixel-wise depth information. Although they are widely used in various applications, RGB-D sensors have significant drawbacks with respect to 3D dense mapping of indoor environments. First, they only allow a measurement range with a limited distance (e.g., within 3 m) and a limited field of view. Second, the error of the depth measurement increases with increasing distance to the sensor. In this paper, we propose an enhanced RGB-D mapping method for detailed 3D modeling of large indoor environments by combining RGB image-based modeling and depth-based modeling. The scale ambiguity problem during the pose estimation with RGB image sequences can be resolved by integrating the information from the depth and visual information provided by the proposed system. A robust rigid-transformation recovery method is developed to register the RGB image-based and depth-based 3D models together. The proposed method is examined with two datasets collected in indoor environments for which the experimental results demonstrate the feasibility and robustness of the proposed method.
INTRODUCTION
Detailed 3D modeling of indoor environments is an important technology for many applications, such as indoor mapping, indoor positioning and navigation, and semantic mapping (Henry et al., 2014).Traditionally, there are two main approaches to indoor 3D modeling, terrestrial laser scanning (TLS) and close-range photogrammetry.With TLS technology, the obtained 3D point clouds contain detailed structure information and are well suited for frame-to-frame alignment.However, TLS lacks valuable visual information that is contained in color images.Although color images are easily captured with off-the-shelf digital cameras and the rich visual information can be used for loop closure detection (Konolige and Agrawal, 2008;Nisté r, 2004), it is hard to obtain enough points for dense modeling through regular photogrammetric techniques, especially in dark environments or poorly textured areas (Henry et al., 2010;Kerl et al., 2013;Triggs et al., 2000).
Recently, the advent of RGB-D sensors such as the Kinect and Structure Sensor has led to great progress in dense mapping and simultaneous localization and mapping (SLAM) (Dryanovski et al., 2013;Hu et al., 2012;Whelan et al., 2013Whelan et al., , 2015)).The remarkable advantages of these systems are their high mobility and low cost.However, RGB-D sensors have some significant drawbacks with respect to dense 3D mapping.They only allow a measurement range with a limited distance * Corresponding author: Shengjun Tang and a limited field of view.They may cause tracking loss due to the lack of spatial structure needed to constrain ICP (iterative closest point) alignments (Henry et al., 2014).In particular, as the random error of the measurement depth increases with increasing distance to the sensor, only the data acquired within a 1-3 m distance to the sensor can be used for mapping applications (Khoshelham and Elberink, 2012).The RGB-D sensors capture RGB images along with per-pixel depth images, which enables the estimation of the camera poses and the scene geometry with an image-based algorithm, such as SLAM or structure-from-motion (SFM).Although the 3D scenes recovered from the RGB image sequences have a larger and longer range than the 3D model from the depth sensor, the motion between frames can only be recovered up to a scale factor, and the error of the motion can accumulate over time during frame-to-frame estimation (Kerl et al., 2013;Wu et al., 2014).The RGB image-based and depth-based methods for 3D modeling have their own advantages and disadvantages, but a more fundamental solution is desired to enhance the ability of the RGB-D sensors for indoor mapping (Steinbrucker and Kerl, 2013).
We introduce an enhanced RGB-D mapping approach for detailed 3D modeling of large-range indoor environments by combining the RGB image sequences with the depth information.The 3D models produced from the RGB images can be used as a supplement to the 3D model produced by the depth sensor.A robust automatic registration method is proposed to register the 3D scene produced by the RGB image sequences and the model from the depth sensor together.This paper is organized as follows.In Section 2, we briefly review related approaches.In Section 3.1, we describe the calibration methodology for both the RGB camera and infrared (IR) camera.In the Section 3.2, we give a general description of the device components and working mechanism of the RGB-D system.The procedure involved in our enhanced RGB-D mapping approach is also briefly introduced.Section 3.3 presents the relative pose estimation method from color image sequences.Section 3.4 describes the robust registration method to recover the rigid transformation relationship between the camera pose from SFM and from the ICP depth alignment algorithm.Section 4 presents the expanded results obtained with the enhanced mapping method, and we close with our conclusions in Section 5.
LITERATURE REVIEW
Due to the limitations in the measurement distance and accuracy of the RGB-D sensors, most of the research work in the past concentrated on alignment methods for depth frames to produce a 3D scene.Newcombe et al. (2011) proposed the KinectFusion method, which incrementally registers RGB-D frames.As it also accumulates drift during the mapping procedure, the KinectFusion is applied in small workspace mapping (Newcombe et al., 2011).Henry et al. (2012) proposed a method to incorporate visual information into the ICP algorithm for image registration, called RGB-ICP.It is fascinating to see that the RGB-ICP method can improve the alignment accuracy to a certain extent.However, the final models in their two experiments were still broken and lacked abundant details in unmeasured spaces.The authors suggested that it would be favorable to apply a visualization technique such as PMVS (patch-based multi-view stereo) to enrich the indoor model (Henry et al., 2012).Endres et al. (2014) accomplished similar work.They used RANSAC (random sample consensus) to estimate the transformations between associated key points and then generate a volumetric 3D map of the environment (Endres et al., 2014).They mainly concentrated on SLAM instead of scene modeling.Stuckler and Behnke (2012) presented an approach for scene modeling and pose tracking using RGB-D cameras.Only two experiments in a small range were conducted to evaluate the performance of the registration (Stuckler and Behnke, 2012).Although the improvement of depth alignment can enlarge the modeling range of the sensor significantly, the absolute distance limitation may cause trouble when modeling a large-scale indoor scene with a high arched roof such as in airport terminals or churches.Khoshelham and Elberink (2012) presented an experimental analysis of the geometric quality of depth data acquired by the Kinect sensor (a typical RGB-D system), and the results of their experiments showed that only the data obtained within a 1-3 m distance to the sensor can be used for mapping applications.The depth resolution also decreases quadratically with increasing distance from the sensor.Meanwhile, the field of view of the sensor may also cause "details lost" such that these lost details may cause trouble that it is hardly found through all of the spaces when modeling a large-scale indoor environment.Instead, the corresponding color image sequences may provide extra information for the unmeasured areas.The image-based modeling approaches can create 3D models from a collection of input images (Grzeszczuk 2002;Pollefeys et al., 2004;Snavely et al., 2006).In this paper, we used the SFM method to recover camera parameters and sparse 3D scene geometry (Hartley and Zisserman, 2003).PMVS2 was involved for dense 3D modeling (Furukawa and Ponce, 2010).Because the SFM procedure can only recover the motion between frames up to a scale factor, a precise global scale recovery method is required.
We introduce a robust registration method by combining color image sequences with depth information.The global scale of the pose from SFM can be recovered, and rigid transformation between the models from the two sources can be obtained for their automatic registration.The major contributions of this research are 1) the developed method can extend the modeling range of the RGB-D sensors and enrich the scene details by integrating depth information and image information; and 2) a robust registration method is developed to recover the scale and the rigid transformation between the camera pose from SFM and from depth alignment with the ICP algorithm.
Overview of the Enhanced RGB-D Mapping System
The RGB-D sensor system used in this research contains two sensors, an RGB camera and an IR sensor.The IR sensor is combined with an IR camera and an IR projector.This sensor system is highly mobile and can be attached to an iPad, iPhone, or other mobile instruments.It can capture 640x480 registered color images and depth images at 30 frames per second.Figure 1 shows its hardware structure.The lower panels of Figure 1 show an example frame observed with the RGB-D sensor.The white part in the depth image indicates that no depth information is measured due to the distance limitation or surface material.The proposed enhanced RGB-D mapping approach can be divided into three stages: the calibration stage, the image-based 3D modeling stage, and the rigid transformation recovery stage, as illustrated in Figure 2. First, an internal calibration method for both the RGB camera and the IR camera is conducted to obtain the intrinsic parameters of the cameras.Second, the SFM method is used for camera pose generation.Third, to register the 3D models from color image sequences to the models from depth information, a robust registration method is proposed by establishing the geometric relationship between them.An accurate global scale and rigid transformation can be obtained, which are used for absolute camera trajectory recovery.Finally, the absolute camera poses are used for dense 3D modeling with a PMVS tool, and the produced models are well matched with the 3D model from the depth sensor.The proposed method is examined using actual indoor datasets.The experimental results demonstrate the feasibility and effectiveness of the proposed method.
Camera Calibration
The main concept of camera calibration is based on the pinhole camera model, which illustrates the relationship between the image point and the corresponding ground point as a function of camera internal and external parameters.
The difference between the RGB camera and the depth camera is in the method of data collection.The RGB camera collects RGB images all the time.However, the data collected by the depth sensor depends on the status of the IR projector.When the IR projector switches on, the IR camera will collect the depth data for the scene, but if the IR projector is switched off, the IR camera will capture an ordinary image like the RGB image but on the IR band.The depth images on the IR band are used for the calibration progress.On the basis of the corresponding images, we apply the commonly used Bouguet (2011) method to calibrate the RGB camera and depth camera.
Finally, the focal length ( ℎ , ℎ ) and the coordinate of the principal point ( ℎ , ℎ ) of the IR camera are obtained.The internal parameters of the RGB camera are also calculated including the focal length ( , ) and the coordinate of the principal point ( , ).These are all used in the robust registration process detailed in Section 3.4.
Relative Motion Estimation
Relative pose estimation by computing consistent feature matches across multiple images is a classic problem.Numerous algorithms have been proposed to solve this issue (Chiuso et al., 2000;Hartley and Zisserman, 2003;Snavely et al., 2006Snavely et al., , 2008;;Hu et al., 2015).Normally, two steps would be involved in the relative motion estimation: key-point detection and matching.
In our work, we add an advance outlier rejection method to eliminate the false matches using the depth information and the pose derived from the ICP algorithm as a priori information.
We summarize the steps in the motion estimation algorithm as follows.
Key-Point Detection and Matching:
The SIFT detector (Lowe, 2004) is used for image feature detection.Typically, thousands of SIFT key points can be detected from each color image from an RGB-D sensor with 640*480 pixels.Based on the local descriptor of each key point, we use the approximate nearest neighbors package proposed by (Arya et al., 1998) for feature matching.
Camera Pose Estimation:
We then robustly estimate a fundamental matrix between frames Fn-1 and Fn, and Fn and Fn+1, using the five-point algorithm (Nisté r, 2004) and RANSAC (Fischler and Bolles, 1981).Some outliers are removed with respect to the recovered fundamental matrix.It should be noted that not all of the RGB images need to be processed.Key frames are selected automatically based on the number of features tracked.Then, the rotation R and translation T are recovered by matrix factorization.This minimization problem is solved with the Levenberg-Marquardt nonlinear optimization (Nocedal and Wright, 2006), and then R and T are further refined.
Robust Registration of Depth-based and Image-based Models
Due to the nature of the RGB image-based method used for 3D modeling, we obtain the transformation relationship Tn,n+1 between the image pair {n, n+1} through relative motion estimation because the motion between frames can only be recovered up to a scale factor.The RGB image and the depth image are registered automatically by the sensor system itself, which facilitates the scaling and transformation of the relative model using the global distance from the depth images.The key step at this stage is to recover a global trajectory for the RGB image sequences by incorporating depth frames.First, the depth-based camera model is introduced below.Two kinds of coordinate systems, the camera coordinate system and the sensor coordinate system, are used.Then, scale and rigid transformation recovery are detailed.
Camera Model for Depth Images:
The RGB-D camera uses the ICP algorithm for depth alignment.A relative camera pose for each frame can be obtained.By knowing the focal length ℎ , ℎ of the camera and the center of the depth image ( ℎ , ℎ ), we can compute the object coordinates Xc, Yc, Zc, in the camera coordinate system as follows: = ℎ The rigid body transformation that relates points ̃~[ 1 ] in the sensor coordinate system of the referenced frame to points ̃~[ 1] in the camera coordinates of the current frame can be written as where R is the rotation matrix from current frame Fn to the referenced frame, t is the translation matrix from current frame Fn to the referenced frame, and X, Y, Z are the real object coordinates in the 3D scene.
Figure 3 shows the relationship between the camera and sensor coordinate systems.
Fn Fn+1
P(X,Y,Z) Sensor coordinate system Camera coordinate system Figure 3.The relationship between the camera and sensor coordinate systems
Scale Recovery
Based on the feature matches on the visual RGB images, the object coordinates for each tie point can be obtained by space intersection using the image orientation parameters.In this work, we select the registered frame that possesses the most corresponding points between the RGB frame and the depth frame as a control.As shown in Figure 4, for each feature match located on the RGB image, the image coordinates can be obtained and the corresponding depth value can be extracted from the registered depth image.Those points with no depth value are discarded.The object coordinates of each point can be calculated from Equation (1).former is obtained from the space intersection of the visual images, and the latter from the depth images.Then, the relative scale S can be determined from the distance ratio between the points pairs of the two points sets Pm and Pn as follows: For robustness, a large number of scale ratios for point pairs is calculated at random, and three scale sets can be obtained.In our experiment, over 8000 scale values are calculated for this relative scale estimation.The Pau ta Norm and RANSAC methods are used for outlier rejection as in Equation ( 4), where Si is the scale value in one of the scale sets, is the median value of the scale set, and is the root-mean-square error of the scale set.
Pau ta Norm is conducted iteratively until no outliers exist.Then, the proper scale is determined by the mean value of the remaining scales.The point sets from the space intersection of the visual images are scaled to a new points set Ps as follows: where Sx, Sy, Sz are the scale factors in the three directions, and XT, YT, ZT are the object coordinates of the points set from triangulation.
Rigid Transformation Recovery:
After scale recovery, it is necessary to find the optimal rotation and translation between the two sets of corresponding 3D points so that they are aligned.We compute the rigid transformation matrix using Besl's method (Besl and McKay, 1992).The solution can be used for a dataset of any size as long as there are at least three corresponding points.A least square solution is used to minimize the following error: In particular, a RANSAC iteration is used for outlier rejection.An initial transformation matrix is calculated with all of the point pairs.The initial transformation is applied on the points set Ps, after which a new transformed points set PST can be obtained, and the distance of each points pair in PST and Pn can be calculated as in Equation ( 7).[
Absolute Camera Trajectory Recovery:
As we use a pinhole camera model to describe the relationship from 2D to 3D for the RGB camera, a scene view is formed by projecting 3D points into the image plane using a perspective transformation as follows: where (u, v) are image coordinates.( , ) are the focal lengths of the RGB image expressed in pixel units.(cxrgb, cyrgb) is the principal point that is usually at the image center.(Rr, tr) indicate the relative camera pose.It is convenient to combine equations ( 8) and ( 9) into one matrix equation as follows: According to equation ( 10), the absolute camera trajectory Ra, Ta can be written as follows: Finally, the absolute camera trajectory can be used for dense modeling with the PMVS tool, and the produced 3D dense model can be matched with the 3D model obtained from the structure sensor.
Datasets
In this section, field tests are carried out to validate the feasibility and effectiveness of the proposed enhanced RGB-D mapping method.Two sets of data are collected using the structure sensor attached to an iPad Air.The camera calibration results are shown in Table 1.
Experimental Results and Analysis
It should be noted that some color deviation may exist in the RGB images collected by the RGB-D sensor due to inaccurate perception of color in the indoor environment with the ever-changing light.Therefore, only the images without color deviation were used for pose estimation.
For the first experiment, all 244 RGB images were used for dense modeling due to the uniform source of light.For geometric registration, 266 feature points with valid depth information detected from the first RGB image were filtered out, and 1437 homonymous points within the view range were used as check points.They were extracted from the feature-matching results.The performance of the geometric registration was examined in object space.Table 2 lists the statistics of the discrepancies between the transformed point set and the point set from the depth image, including the Threshold, number of iterations, check points, and the RMSE in three directions.According to Table 2, the Threshold value was set at 0.1 due to the smooth surface of the meeting table.
As Table 2 shows, the registration accuracy was examined for each iteration.During the first iteration, all of the feature matches were used to recover the rigid transformation matrix.As expected, it generated the worst results because no outliers were rejected.The accuracy in the following two iterations generally remained unchanged.However, the accuracy in the Y and Z directions was significantly improved in the last iteration, in which the discrepancies were reduced from meter-level to centimeter-level in both the Y and Z directions.The models from the two sources were merged using the derived scale matrix and rigid transformation matrix.Figure 6 Table 2 shows the accuracy of the registration.In the first iteration, all 432 feature points were used for transformation derivation.As there were some false matches, the obtained registration accuracy was about 1 m in the three directions.The outliers were rejected in the second iteration using the RANSAC method, and the discrepancy was reduced to 0.3, 0.4, and 0.8 in the X, Y, and Z directions, respectively.The last iteration achieved centimeter-level registration accuracy in all three directions.Figure 7 shows the scene from the image sequences, that from the sensor system, and the registered scene.As shown in Figure 7(a), the scene from the image sequences can cover only a part of the measured corridor because only some of the images were used in the SFM procedure.
SUMMARY AND CONCLUSIONS
The key issues when using RGB-D sensors to produce 3D models are the limited measurement distance and the field of view.We have presented an enhanced RGB-D mapping scheme by combining RGB image sequences with depth information.This scheme aims to combine the model produced by the image sequences with the close detailed model to permit further and more detailed indoor modeling.The globle scale of the motion between RGB frames can be recovered by integrating the depth information and visual information provided by the system.Based on the robust registration method, the scaled camera motion is automatically transformed to the sensor-used coordinates system.Further experiments undertaken in the indoor environment to validate the feasibility and robustness of the proposed method show that it can automatically achieve accurate geometric registration between two models from different architectures.The loss of details with the sensor model can be well repaired by fusion with the model from the image sequences.Accordingly, the enhanced RGB-D mapping system can extend the measurement distance of the structure sensor system.
The next step in this research will to be improve the depth alignment process by using the visual features in the image.
Although the structure sensor can detect a range up to 9.0 meters, the sensor manufacturer limits the distance to a maximum of 3 meters.One reason for this probably relates to the accuracy of ICP alignment.The registered far-range model obtained from the RGB image may be able to provide a better constraint for depth registration.
Figure 2 .
Figure 1.(Top) The hardware scheme of the RGB-D sensor, (bottom left) the acquired depth image, and (bottom right) the acquired RGB image
Figure 4 .
Figure 4. (Left) Feature matches from an RGB image.(Right) Feature matches on the corresponding depth image Two corresponding point sets Pm and Pn can be obtained.The
For
the first dataset, a sample registered frame with the RGB image (left) and depth image (right) is shown in Figure 5(a).The white part in the depth image indicates that no depth value is measured due to the distance limitation or the type of surface material.This dataset contains 244 registered frames collected in a big meeting room.Because of the lack of shape structure, the IR view range is only set at 4.98*2.16*1.37 m to ensure uninterrupted tracking.The second dataset was collected along a corridor.The whole length of the trajectory was about 26.5 m.It contains 305 registered frames.The two images in Figure 5(b) show the RGB frame (left) and depth frame (right).
Figure 5 .
Figure 5. (a) Sample images of the first dataset in a meeting room.(b) Sample images of the second dataset along a corridor (a) shows the model from the image sequences, which was produced from the 244 RGB images.In consideration of the tracking lost, the volume of the model was set to 4.98*2.16*1.37 m.The sensor system only selected a part of the depth information to model the scene.Figure6(b) shows the model from the sensor.As expected, the image-based modeling approach achieved a larger measuring range.Registering of the latter to the former significantly enriched the details of the 3D scene
Figure 6 .
Figure 6.Generated 3D models from the first dataset.(a) RGB image-based 3D model, (b) depth-based 3D model, and (c) registered 3D modelIn the second experiment, due to the color deviation of some images, only 172 RGB frames with fairly accurate colors were used for dense 3D modeling.This involved 432 feature matches for geometric registration.Because of the distinguishing shape features, the Threshold value was set at 0.03.During the rigid transformation recovery process, the outliers were eliminated by comparing the registration accuracy with the threshold.Table2shows the accuracy of the registration.In the first iteration, all 432 feature points were used for transformation derivation.As there were some false matches, the obtained registration accuracy was about 1 m in the three directions.The outliers were rejected in the second iteration using the RANSAC method, and the discrepancy was reduced to 0.3, 0.4, and 0.8 in the X, Y, and Z directions, respectively.The last iteration achieved centimeter-level registration accuracy in all three directions.Figure7shows the scene from the image sequences, that from the sensor system, and the registered scene.As shown in Figure7(a), the scene from the image sequences can cover only a part of the measured corridor because only some of the images were used in the SFM procedure.Figure 7(b) shows the obtained corridor model from the depth image.Although all of the depth information was merged together for model generation, significant details were lost, especially on the ceiling and the floor.The main reason for this may be the limited field of view of the IR sensor.The registered model is shown in Figure 7(c).The two models were matched well with the aid of the scale and transformation parameters.More importantly, the model obtained from the RGB images can be a good supplement to the model obtained from the sensor system.The structure information relating to the ceiling and the floor is enhanced by combining these two models.
Figure 7(b) shows the obtained corridor model from the depth image.Although all of the depth information was merged together for model generation, significant details were lost, especially on the ceiling and the floor.The main reason for this may be the limited field of view of the IR sensor.The registered model is shown in Figure7(c).The two models were matched well with the aid of the scale and transformation parameters.More importantly, the model obtained from the RGB images can be a good supplement to the model obtained from the sensor system.The structure information relating to the ceiling and the floor is enhanced by combining these two models.
Figure 7 .
Figure 7. Generated 3D models from the second dataset.(a) RGB image-based 3D model, (b) depth-based 3D model, and (c) registered 3D model − ) ̃~[ 1 ] in the world coordinate system to the points set ̃~[ 1 ] derived from the color images.
A criterion is set up to robustly filter out the outliers whenever the distance of points pair Dis is over Threshold (in our experiment, Threshold varied with the dataset used).Besl's method is conducted iteratively until no outliers exist.Then, the proper rigid transformation matrix R1, t1 between Ps and Pn is recovered.The following equation relates the points set
Table 1 .
Calibration results of IR camera and RGB camera
Table 2 .
Statistics of discrepancies in object space | 6,174 | 2016-06-02T00:00:00.000 | [
"Engineering",
"Computer Science",
"Environmental Science"
] |
A Novel Polyvinylpyrrolidone-Stabilized Illite Microparticle with Enhanced Antioxidant and Antibacterial Effect
Illite is a clay mineral that shows antioxidant and antibacterial activities because of the abundance of important clay elements in its structure. However, illite has low bioactivity due to its low solubility and electron-donating ability in aqueous solutions. Therefore, we aimed to develop polyvinylpyrrolidone (PVP)-stabilized illite microparticles (P-lite MPs) via polymer adsorption on illite surfaces. An increasing amount of PVP was used to coat a fixed amount of illite to prepare P-lite MPs of different hydrodynamic diameters in the range of 4–9 μm. These sizes were maintained for 2 weeks during storage in a biological buffer without any noticeable changes. The stabilization of illite microparticles using a hydrophilic PVP polymer improved their aqueous dispersity and free radical-scavenging activity. Since the large surface area of microparticles provides several sites for interactions, the smallest P-lite MP exhibited the highest antioxidant and antibacterial activities. More importantly, the MPs showed effective free radical-scavenging activity in vitro without any cytotoxicity. Therefore, P-lite MPs with improved bioavailability may represent a suitable bioactive material for various industrial and biomedical applications.
Introduction
Clay minerals are natural aluminosilicates widely deposited on the earth's surface [1]. They support plant growth as a major component of soils and are traditionally used in pottery, absorbents, and paints [2,3]. Furthermore, they are used in a wide range of applications, including cosmetics, biocides, and pharmaceuticals, because of their characteristic structures and chemical compositions [4,5]. They have been used for treating gastrointestinal and topical diseases since ancient times [6]. The exact mechanism underlying their therapeutic effects remains unknown; however, several studies have evaluated the important factors that affect the anti-inflammatory and antimicrobial activities of clay minerals, including metal element composition, toxin adsorption, oxidation state, pH, and surface properties [7,8]. Thus, the application of clay minerals has attracted attention in the biomedical field for protection against infection and inflammation.
Clay minerals can be classified into five types: kaolinite, illite, chlorite, smectite, and vermiculite [9][10][11]. In particular, illite is known for its bioactivity, large reserves, and potential economic benefits. However, it has low bioavailability in aqueous solutions. Clay minerals exhibit different swelling properties in the presence of water. Smectite has a high cation-exchange capacity and expansion capability, whereas illite is a non-expanding clay [12] because the interlayer cations in illites prevent the entry of water molecules into their structures [13]. Since the antibacterial activity of clay minerals depends on their hydration and release of soluble metal ions, the flocculation of clay minerals has been resolved via polymer adsorption [14,15].
Preparation of P-Lite MPs
For preparing P-lite MPs, PVP was first dissolved at 25 • C in 5 mL of DI water into different concentrations (50, 100, and 200 mg/mL). The PVP solutions were mixed with 50 mg of illite and allowed to react for 15 h at 4 • C using a rotatory shaker. After the reaction, the excess PVP was removed using an Amicon Ultra-15 centrifugal filter (molecular weight cutoff 100 kDa; Merck Millipore, Billerica, MA, USA). The solutions of PVP-coated MPs were then lyophilized to a powder state for 3 d and stored at −20 • C before use. They were denoted as P-lite1, P-lite2, and P-lite3 based on the weight ratio of illite to PVP (1:5, 1:10, and 1:20). Bare illite MPs were prepared without PVP using the same method as mentioned above.
Characterization of P-Lite MPs
The developed illite and P-lite MPs were characterized using several techniques [22,23]. The hydrodynamic diameters and size distribution graphs were obtained using a Zetasizer (ELSZ; Otsuka, Osaka, Japan). The MP morphology associated with each amount of PVP coating was observed via SEM (JSM-6701F; JEOL, Tokyo, Japan). The interactions between illite and PVP were determined via FTIR (FT/IR-460 plus; Jasco, Tokyo, Japan) and XPS (VG Multilab 2000; Thermo Fisher Scientific, Waltham, MA, USA).
Stability of P-Lite MPs
The illite and P-lite MPs were freeze-dried for ease of storage until use. The MPs were dispersed again in PBS to confirm that their properties were maintained after lyophilization without the use of any cryoprotectant. The hydrodynamic diameter of the MPs was measured using a Zetasizer. Further, the long-term stability of the MPs was monitored for 2 weeks in PBS at 37 • C. The MP solutions were incubated at 37 • C, and their sizes were measured every week using a Zetasizer.
In Situ Antioxidant Activity of P-Lite MPs
The protective effect of antioxidant samples against the degradation of deoxyribose by hydroxyl radicals was evaluated [24]. An aqueous mixture of EDTA (0.1 mL, 0.1 mM), FeCl 3 (0.1 mL, 0.1 mM), H 2 O 2 (0.1 mL, 1 mM), potassium phosphate buffer (0.5 mL, 20 mM), and ascorbic acid (0.1 mL, 0.1 mM) was prepared to produce hydroxyl radicals. 2-Deoxy-Dribose (0.1 mL, 3.75 mM) was added to the solution. Subsequently, 1 mL of illite and P-lite MPs (10 mg/mL) was added to the reaction mixtures. The reaction was allowed to occur for 1 h in a 37 • C incubator and terminated by adding 1 mL of TBA (1% w/v in 50 mM NaOH) and 1 mL of TCA (2% w/v in DI water). Degraded deoxyribose produced a pink chromogen upon heating the mixture at 85 • C for 20 min after the reaction. A microplate reader was used to measure the absorbance of the sample solutions at a wavelength of 515 nm. The antioxidant activity of the illite and P-lite MPs was calculated using this Equation (1) [25]: A control was prepared using DI water as a substitute for the sample solution, and a blank was prepared without H 2 O 2 and the sample solution.
The antioxidant activity of the illite and P-lite1 MPs was further compared by monitoring the H 2 O 2 reduction after the MP treatment [26]. The 2 mM H 2 O 2 solution was prepared in a 50 mM phosphate buffer. Then, a 0.6 mL H 2 O 2 (2 mM), 0.4 mL phosphate buffer (50 mM), and a 0.1 mL MP solution (5, 10, and 20 mg/mL) were sequentially added and mixed for 10 min using a rotatory shaker. The absorbance of the reaction mixtures was measured at a wavelength of 230 nm to determine the inhibition of H 2 O 2 .
In addition, the DPPH radical-scavenging activity of the illite and P-lite1 MPs was analyzed to determine their antioxidant potential [27]. First, 2 mg DPPH was dissolved in 10 mL methanol. A solution of equal volumes of DPPH and MP (50 mg/mL) was mixed in a 96-well plate and kept at room temperature in the dark for 30 min. The negative control was prepared by adding DI water to the DPPH solution. A decrease in the DPPH level was determined by measuring the absorbance of the mixtures at a wavelength of 515 nm, indicating the antioxidant activity of the MPs.
Antibacterial Activity of P-Lite MPs
The antibacterial activity of the P-lite MPs was quantitatively evaluated against S. aureus ATCC 6538 using a colony-counting method [28]. The bacteria were cultured in Luria-Bertani (LB) agar plates (BD Difco, Sparks, MD, USA) containing 1.5% agar at 37 • C. A single colony was inoculated into the LB broth and cultured overnight at 37 • C before use. This culture was suspended in fresh LB broth until the optical density (OD 600 ) reached 0.1. The P-lite MPs (0.5 mg/mL) were subsequently added to each culture for evaluating bacterial growth inhibition during 24 h of incubation. DI water was used as a negative control. The suspensions were diluted to a factor of 10 6 after incubation, and 100 µL of each test suspension was spread over an agar plate using glass beads. The number of colonies that appeared after overnight incubation was counted to determine the viability of S. aureus.
In Vitro Cytotoxicity and Antioxidant Activity of P-Lite MPs
The biocompatibility of P-lite1 was analyzed using NIH 3T3 fibroblasts. The cells were seeded in a 96-well plate at a density of 10,000 cells/well. They were incubated up to approximately 80% confluency in a humidified atmosphere of 5% CO 2 at 37 • C. The P-lite1 (0.01-1.0 mg/mL) was then treated for 24 h. The control group was treated with cell media instead of a sample solution. After incubation, Cell Counting Kit-8 (CCK-8) solution (Dojindo Laboratories, Kumamoto, Japan) was used to analyze the cell viability. It produced an orange-colored formazan from viable cells that exhibit absorbance at a wavelength of 450 nm. The cell viability after the MP treatment was calculated using this Equation (2): In addition, the in vitro antioxidant activity of P-lite1 was assessed by reducing the in vitro ROS level induced by the oxidative stress agent, H 2 O 2 . NIH 3T3 (10,000 cells/well) in a 96-well plate was stimulated by 100 µL H 2 O 2 (5 µM) and subsequently treated by 100 µL P-lite1 (0-100 µg/mL) for ROS scavenging during a 4 h incubation. Each 200 µL cell media were treated in control groups to determine the natural ROS level of the cells without the MP treatment. Then, the intracellular fluorescent dye, H2DCFDA (10 µM), was used to treat the cells after washing several times with PBS. Dichlorofluorescein was produced in response to in vitro ROS during a 1 h incubation in the dark, and its fluorescence (Ex/Em = 485/535 nm) was measured using a microplate reader. The ROS level% was calculated based on the fluorescence intensity of the control and sample groups.
Statistical Analysis
Every experiment was repeated in triplicate, and the resulting data were averaged to be expressed as the mean ± standard deviation. Student's t-test was used to compare statistically significant differences between any two experimental groups. The differences were considered to be statistically significant if p < 0.05, highly significant if p < 0.01, very highly significant if p < 0.001, or not statically significant if p > 0.05. Next, symbols were allocated to indicate statistical significance, namely # for p > 0.05, * for p < 0.05, ** for p < 0.01, and *** for p < 0.001.
Preparation and Characterization of P-Lite MPs
Illite MPs were successfully prepared in an aqueous solution via metal intercalation between PVP and illite to enhance the antioxidant and antibacterial activities of illite ( Figure 1). Based on the weight ratio of illite to PVP, a large amount of PVP was coated on the surface of the illite. Similarly, Stuart et al. found that the adsorption of PVP increased with an increasing polymer dosage [29]. Consequently, the hydrodynamic diameters of the P-lite MPs increased from 4.4 ± 0.3 µm to 6.7 ± 0.4 µm and 9.2 ± 0.5 µm with an increase in the amount of PVP, whereas that of bare illite was 2.9 ± 0.1 µm (Figure 2a). The size distributions of the MPs indicated that these sizes were fairly uniform ( Figure 2b). Two-dimensional sheets of illite and P-lite MPs were observed via SEM ( Figure 3). Bare illite possessed the typical layered structure of clay minerals observed previously [30]. The SEM images of the P-lite MPs showed that the clay flakes increased in size and contained relatively smoother surfaces after polymer coating.
lite MPs increased from 4.4 ± 0.3 μm to 6.7 ± 0.4 μm and 9.2 ± 0.5 μm with an increase in the amount of PVP, whereas that of bare illite was 2.9 ± 0.1 μm (Figure 2a). The size distributions of the MPs indicated that these sizes were fairly uniform ( Figure 2b). Two-dimensional sheets of illite and P-lite MPs were observed via SEM ( Figure 3). Bare illite possessed the typical layered structure of clay minerals observed previously [30]. The SEM images of the P-lite MPs showed that the clay flakes increased in size and contained relatively smoother surfaces after polymer coating. lite MPs increased from 4.4 ± 0.3 μm to 6.7 ± 0.4 μm and 9.2 ± 0.5 μm with an increase in the amount of PVP, whereas that of bare illite was 2.9 ± 0.1 μm (Figure 2a). The size distributions of the MPs indicated that these sizes were fairly uniform (Figure 2b). Two-dimensional sheets of illite and P-lite MPs were observed via SEM (Figure 3). Bare illite possessed the typical layered structure of clay minerals observed previously [30]. The SEM images of the P-lite MPs showed that the clay flakes increased in size and contained relatively smoother surfaces after polymer coating. lite MPs increased from 4.4 ± 0.3 μm to 6.7 ± 0.4 μm and 9.2 ± 0.5 μm with an increase in the amount of PVP, whereas that of bare illite was 2.9 ± 0.1 μm (Figure 2a). The size distributions of the MPs indicated that these sizes were fairly uniform (Figure 2b). Two-dimensional sheets of illite and P-lite MPs were observed via SEM (Figure 3). Bare illite possessed the typical layered structure of clay minerals observed previously [30]. The SEM images of the P-lite MPs showed that the clay flakes increased in size and contained relatively smoother surfaces after polymer coating. FT-IR and XPS were performed to analyze the chemical interactions between the illite and PVP in P-lite MPs. The characteristic peaks of PVP were observed in the FTIR spectra, as previously reported [31]. The peaks at 2952 cm −1 , 1667 cm −1 , and 1280 cm −1 were attributed to the C-H stretching, C=O stretching, and C-N stretching vibrations of PVP, respectively (Figure 4a) [32]. The FTIR spectra of illite showed Si-O stretching and Al-O-H bending peaks at 973 cm −1 and 898 cm −1 , respectively [33]. In addition, the bands in the range of 824 cm −1 and 534 cm −1 were attributed to the Si-O stretching and bending modes in illite. After performing polymer coating, these illite-based peaks were absent in the spectra of the P-lite MPs, indicating that PVP was coated on the surface of the illite MPs. Further, the slight red-shift of the C=O stretching bands to 1659 cm −1 possibly indicates the formation of hydrogen bonds between the C=O of PVP and the silanols in illite [34,35]. The chemical compositions of PVP, illite, and P-lite MPs were analyzed using XPS (Figure 4b).
The elements O1s, N1s, C1s, Si2s, and Al2s were present at 530, 400, 284, 103, and 75 eV in their XPS spectra, respectively [36]. The illite was found to comprise its typical elements, including O, Si, and Al. The organic components of PVP, namely C, N, and O, were found in the XPS spectra of the P-lite MPs, indicating that the PVP was coated on the surface of the illite. The Si2S region of the illite was red-shifted to 102 eV after PVP coating. This peak was assigned to Si-O-C bonds, which determine the chemical interaction between PVP and illite, referred to as metal intercalation [37]. A similar phenomenon was observed in the Al2s region of the P-lite MPs. Taken together, these findings indicate that the metal intercalation of PVP into illite was successful.
Stability of P-Lite MPs
Lyophilization is performed to dry the MPs in a solution to facilitate transportation and storage until use. This process may exert considerable stress on the MPs, causing an increase in their size and aggregation. Thus, lyophilization stability is often achieved by using lyoprotectants, such as sucrose and trehalose [38]. In this study, the freeze-dried MPs were readily dispersed in a biological buffer without using any lyoprotectant. The stability of the illite and P-lite MPs was analyzed by monitoring the changes in their hydrodynamic diameters after lyophilization and after two weeks of storage in PBS ( Figure 5). Their hydrodynamic diameters were maintained before and after freeze-drying (Figure 5a). The diameters of P-lite1, P-lite2, and P-lite3 MP were 2.9 ± 0.1 µm, 5.3 ± 0.4 µm, and 8.2 ± 0.6 µm before lyophilization. They barely changed after lyophilization (3.0 ± 0.3 µm, 5.1 ± 0.1 µm, and 8.5 ± 0.2 µm, respectively). However, the diameter of bare illite changed after lyophilization from 3.8 ± 0.2 µm to 2.5 ± 0.4 µm with a statistical difference (p < 0.05), which indicates that P-lite MPs can be lyophilized for long-term storage prior to their future applications. The illite and P-lite1 MPs were stable during two weeks of storage in a biological buffer without any change in their hydrodynamic diameters (Figure 5b). Their diameters after stability analysis were 3.5 ± 0.1 µm and 2.8 ± 0.1 µm. The P-lite1 MPs were suspended for a relatively longer period in the biological buffer than the bare illite MPs because the hydrophilic PVP provides steric and electrostatic stability due to its amide and methylene groups [39]. In contrast, the hydrodynamic diameters of the P-lite2 and P-lite3 MPs decreased, respectively, to 3.4 ± 0.1 µm and 5.5 ± 0.3 µm after two weeks of storage in the buffer. The PVP might have desorbed from the surface of the illite due to its weak interaction.
Antioxidant Activity of P-Lite MPs
The free radical-scavenging activity of illite and P-lite MPs was measured to evaluate their antioxidant activity ( Figure 6). Bare illite is a poor antioxidant material and was found to scavenge only 3.2 ± 0.7% of the hydroxyl radicals (Figure 6a). Notably, the P-lite MPs exhibited high radical-scavenging activity (p < 0.001). Considering that PVP does not show any antioxidant activity, the radical-scavenging activity of the P-lite MPs may have increased because the PVP coating on the illite surface enhances the interaction of MPs with hydroxyl radicals in an aqueous solution [40]. In addition, the radical-scavenging activity of the relatively small P-lite MPs may be high because of their larger surface area compared to large MPs for facilitating interaction with radicals. This is supported by our results showing that the P-lite1 MP exhibited the highest hydroxyl radical-scavenging activity of 81.7 ± 0.4%. The antioxidant activities of P-lite2 and P-lite3 MPs were 70.4 ± 0.3% and 51.2 ± 1.9%.
The free radical-scavenging activity of illite and P-lite MPs was measured to evaluate their antioxidant activity ( Figure 6). Bare illite is a poor antioxidant material and was found to scavenge only 3.2 ± 0.7% of the hydroxyl radicals (Figure 6a). Notably, the P-lite MPs exhibited high radical-scavenging activity (p < 0.001). Considering that PVP does not show any antioxidant activity, the radical-scavenging activity of the P-lite MPs may have increased because the PVP coating on the illite surface enhances the interaction of MPs with hydroxyl radicals in an aqueous solution [40]. In addition, the radical-scavenging activity of the relatively small P-lite MPs may be high because of their larger surface area compared to large MPs for facilitating interaction with radicals. This is supported by our results showing that the P-lite1 MP exhibited the highest hydroxyl radical-scavenging activity of 81.7 ± 0.4%. The antioxidant activities of P-lite2 and P-lite3 MPs were 70.4 ± 0.3% and 51.2 ± 1.9%. The P-lite1 MP was also effective in inhibiting H2O2 (Figure 6b). Its antioxidant activity increased dose-dependently from 5.8 ± 2.8% and 17.4 ± 6.9% to 62.5 ± 3.0%, while the illite could barely scavenge H2O2 (6.4 ± 5.4% at 20 mg/mL). Similarly, the DPPH radicalscavenging activity of illite alone was very low (Figure 6c). However, that of P-lite1 MP was enhanced to 29.8 ± 1.7% with a statistically significant difference (p < 0.001). This result correlates with Jeong et al., who found that illite shows low DPPH radical-scavenging activity because of its low cationic-exchange capacity [41]. However, the P-lite1 MP exhibited antioxidant activity three times higher than illite alone, suggesting that PVP coating on illite surfaces offers more chances to interact with radicals for their reduction. Therefore, an illite to PVP weight ratio of 1:5 may considerably increase the radical-scavenging activity of illite.
Antibacterial Activity of P-Lite MPs
Illite has been previously reported to show antibacterial activity; however, it did not inhibit S. aureus growth in our study due to its poor solubility in aqueous solutions [42]. The P-lite MPs inhibited the growth of S. aureus to a great extent compared to that obtained using the control (Figure 7). The viability of S. aureus decreased to 32% after treatment with the P-lite1 MPs. Notably, the increase in the amount of PVP coating on the illite from P-lite1 to P-lite3 decreased the antimicrobial activity, indicating that the relatively The P-lite1 MP was also effective in inhibiting H 2 O 2 (Figure 6b). Its antioxidant activity increased dose-dependently from 5.8 ± 2.8% and 17.4 ± 6.9% to 62.5 ± 3.0%, while the illite could barely scavenge H 2 O 2 (6.4 ± 5.4% at 20 mg/mL). Similarly, the DPPH radical-scavenging activity of illite alone was very low (Figure 6c). However, that of P-lite1 MP was enhanced to 29.8 ± 1.7% with a statistically significant difference (p < 0.001). This result correlates with Jeong et al., who found that illite shows low DPPH radicalscavenging activity because of its low cationic-exchange capacity [41]. However, the P-lite1 MP exhibited antioxidant activity three times higher than illite alone, suggesting that PVP coating on illite surfaces offers more chances to interact with radicals for their reduction. Therefore, an illite to PVP weight ratio of 1:5 may considerably increase the radical-scavenging activity of illite.
Antibacterial Activity of P-Lite MPs
Illite has been previously reported to show antibacterial activity; however, it did not inhibit S. aureus growth in our study due to its poor solubility in aqueous solutions [42]. The P-lite MPs inhibited the growth of S. aureus to a great extent compared to that obtained using the control (Figure 7). The viability of S. aureus decreased to 32% after treatment with the P-lite1 MPs. Notably, the increase in the amount of PVP coating on the illite from P-lite1 to P-lite3 decreased the antimicrobial activity, indicating that the relatively small P-lite MPs could show high antibacterial activity against S. aureus. This is inconsistent with the result of D. Bhatia et al., who determined a good antibacterial activity of PVP against S. aureus [43]. The decrease in antibacterial activity with an increase in PVP coating may be attributed to a decrease in the interaction and bioavailability of bactericidal metal elements in bacteria with an increase in PVP coating, similar to the results of the hydroxyl radical-scavenging activity assays [44], indicating the synergistic antibacterial activity of P-lite MPs. Therefore, an illite to PVP weight ratio of 1:5 may considerably inhibit S. aureus growth via illite MP treatment.
PVP against S. aureus [43]. The decrease in antibacterial activity with an increase in PVP coating may be attributed to a decrease in the interaction and bioavailability of bactericidal metal elements in bacteria with an increase in PVP coating, similar to the results of the hydroxyl radical-scavenging activity assays [44], indicating the synergistic antibacterial activity of P-lite MPs. Therefore, an illite to PVP weight ratio of 1:5 may considerably inhibit S. aureus growth via illite MP treatment.
In Vitro Cytotoxicity and Antioxidant Activity of P-Lite MPs
The cytotoxicity of the P-lite1 MP was analyzed by monitoring the change in cell viability after MP treatment in NIH 3T3 fibroblast cells (Figure 8a). It was found that more than 95% of cells survived after treatment with 0-1 mg/mL P-lite1 MPs (100.0 ± 3.7%, 101.3 ± 5.9%, 101.0 ± 7.4%, 101.8 ± 3.5%, and 102.3 ± 2.0%, respectively). Notably, the highest concentration of P-lite1 MPs, 1 mg/mL, did not show any cytotoxic effect, exhibiting cell viability of 102.3 ± 2.0%. This result correlates with that of Seong et al., who determined the biocompatibility of illite and illite-polyethylene composite [45]. Further, PVP is one of the safe materials for biomedical use approved by the U.S. Food and Drug Administration, which implies that the P-lite1 MP possesses an in vitro biocompatibility for its biomedical application [46].
In Vitro Cytotoxicity and Antioxidant Activity of P-Lite MPs
The cytotoxicity of the P-lite1 MP was analyzed by monitoring the change in cell viability after MP treatment in NIH 3T3 fibroblast cells (Figure 8a). It was found that more than 95% of cells survived after treatment with 0-1 mg/mL P-lite1 MPs (100.0 ± 3.7%, 101.3 ± 5.9%, 101.0 ± 7.4%, 101.8 ± 3.5%, and 102.3 ± 2.0%, respectively). Notably, the highest concentration of P-lite1 MPs, 1 mg/mL, did not show any cytotoxic effect, exhibiting cell viability of 102.3 ± 2.0%. This result correlates with that of Seong et al., who determined the biocompatibility of illite and illite-polyethylene composite [45]. Further, PVP is one of the safe materials for biomedical use approved by the U.S. Food and Drug Administration, which implies that the P-lite1 MP possesses an in vitro biocompatibility for its biomedical application [46]. PVP against S. aureus [43]. The decrease in antibacterial activity with an increase in PVP coating may be attributed to a decrease in the interaction and bioavailability of bactericidal metal elements in bacteria with an increase in PVP coating, similar to the results of the hydroxyl radical-scavenging activity assays [44], indicating the synergistic antibacterial activity of P-lite MPs. Therefore, an illite to PVP weight ratio of 1:5 may considerably inhibit S. aureus growth via illite MP treatment.
In Vitro Cytotoxicity and Antioxidant Activity of P-Lite MPs
The cytotoxicity of the P-lite1 MP was analyzed by monitoring the change in cell viability after MP treatment in NIH 3T3 fibroblast cells (Figure 8a). It was found that more than 95% of cells survived after treatment with 0-1 mg/mL P-lite1 MPs (100.0 ± 3.7%, 101.3 ± 5.9%, 101.0 ± 7.4%, 101.8 ± 3.5%, and 102.3 ± 2.0%, respectively). Notably, the highest concentration of P-lite1 MPs, 1 mg/mL, did not show any cytotoxic effect, exhibiting cell viability of 102.3 ± 2.0%. This result correlates with that of Seong et al., who determined the biocompatibility of illite and illite-polyethylene composite [45]. Further, PVP is one of the safe materials for biomedical use approved by the U.S. Food and Drug Administration, which implies that the P-lite1 MP possesses an in vitro biocompatibility for its biomedical application [46]. The antioxidant potential of P-lite1 MPs in various biomedical fields was determined in vitro using NIH 3T3 fibroblasts (Figure 8b). The cells with and without H 2 O 2 treatment exhibited the highest and lowest ROS levels, respectively. H 2 O 2 -induced ROS accumulation was resisted by the P-lite1 MP. Accordingly, the ROS level decreased after an increasing amount of the P-lite1 MP was treated. Notably, the P-lite1 MP at 100 µg/mL was able to scavenge 55% of the ROS (p < 0.05). The mechanism underlying the ROS regulation of clay and polymer composite still requires further investigation. However, several studies have demonstrated the effect of clay minerals and derived composites related to in vitro oxidative stress [47]. While there remains an unmet need to counteract toxic ROS, P-lite1 MPs are a potent antioxidant material with a strong potential for future use.
Conclusions
Illite was stabilized by coating the surface of PVP to enhance its bioavailability and antioxidant and antibacterial activities. An increasing amount of PVP was coated on a fixed amount of illite, resulting in a size increase of the P-lite MPs. The illite plates were observed to have a typical layered structure before and after PVP coating. Further, it was determined that PVP was chemically bound on the surface of illite based on FTIR and XPS analyses. The developed P-lite MPs maintained their hydrodynamic diameters after lyophilization and after 2 weeks of storage in a biological buffer at 37 • C, indicating good stability after coating with PVP. Notably, the P-lite MPs possessed high antioxidant and antibacterial activities after coating PVP on the surface of illite. In addition, the MPs showed effective free radical-scavenging activity in vitro without any cytotoxicity. Therefore, P-lite MPs may be used as antioxidants and bactericides in biomedical applications. | 6,437.2 | 2021-12-01T00:00:00.000 | [
"Materials Science",
"Chemistry"
] |
Isotopic fractionation of zirconium during magmatic differentiation and the stable isotope composition of the silicate Earth
Abstract High-precision double-spike Zr stable isotope measurements (expressed as δ94/90ZrIPGP-Zr, the permil deviation of the 94Zr/90Zr ratio from the IPGP-Zr standard) are presented for a range of ocean island basalts (OIB) and mid-ocean ridge basalts (MORB) to examine mass-dependent isotopic variations of zirconium in Earth. Ocean island basalt samples, spanning a range of radiogenic isotopic flavours (HIMU, EM) show a limited range in δ94/90ZrIPGP-Zr (0.046 ± 0.037‰; 2sd, n = 13). Similarly, MORB samples with chondrite-normalized La/Sm of >0.7 show a limited range in δ94/90ZrIPGP-Zr (0.053 ± 0.040‰; 2sd, n = 8). In contrast, basaltic lavas from mantle sources that have undergone significant melt depletion, such as depleted normal MORB (N-MORB) show resolvable variations in δ94/90ZrIPGP-Zr, from −0.045 ± 0.018 to 0.074 ± 0.023‰. Highly evolved igneous differentiates (>65 wt% SiO2) from Hekla volcano in Iceland are isotopically heavier than less evolved igneous rocks, up to 0.53‰. These results suggest that both mantle melt depletion and extreme magmatic differentiation leads to resolvable mass-dependent Zr isotope fractionation. We find that this isotopic fractionation is most likely driven by incorporation of light isotopes of Zr within the 8-fold coordinated sites of zircons, driving residual melts, with a lower coordination chemistry, towards heavier values. Using a Rayleigh fractionation model, we suggest a αzircon-melt of 0.9995 based on the whole rock δ94/90ZrIPGP-Zr values of the samples from Hekla volcano (Iceland). Zirconium isotopic fractionation during melt-depletion of the mantle is less well-constrained, but may result from incongruent melting and incorporation of isotopically light Zr in the 8-fold coordinated M2 site of orthopyroxene. Based on these observations lavas originating from the effect of melt extraction from a depleted mantle source (N-MORB) or that underwent zircon saturation (SiO2 > 65 wt%) are removed from the dataset to give an estimate of the primitive mantle Zr isotope composition of 0.048 ± 0.032‰; 2sd, n = 48. These data show that major controls on Zr fractionation in the Earth result from partial melt extraction in the mantle and by zircon fractionation in differentiated melts. Conversely, fertile mantle is homogenous with respect to Zr isotopes. Zirconium mass-dependent fractionation effects can therefore be used to trace large-scale mantle melt depletion events and the effects of felsic crust formation.
INTRODUCTION
Over the past twenty years the field of non-traditional stable isotope geochemistry has proliferated different isotope systems developed and applied to various geo-and cosmo-chemical problems (see reviews by Johnson et al., 2004;Teng et al., 2017). The stable isotopes of the highfield strength elements (HFSE; Zr, Hf, Ti) have received relatively little attention to date, however, with only Ti being explored in terms of natural mass-dependent stable isotope variations (e.g. Millet et al., 2016;Greber et al., 2017;Deng et al., 2018Deng et al., , 2019. The HFSE are of particular interest for understanding processes such as melt genesis because they behave incompatibly during partial mantle melting events (Woodhead et al., 1993;Johnson, 1998), and, as a consequence, are highly enriched in crustal rocks (for Zr $ 200 ppm; Rudnick and Gao, 2003) relative to the mantle (for Zr $ 4 ppm; McDonough and Sun, 1995). Furthermore the HFSE, including Zr, are relatively insoluble in sub-critical aqueous fluids and are highly refractory, meaning that they are resistant to later modification or resetting by metamorphism or alteration (Brenan et al., 1994). As such, Zr can serve as a high-fidelity tracer of mantle depletion events and the genesis of ancient igneous rock and crust (Condie, 2005).
Zirconium isotope geochemistry has seen limited exploration in terms of mass-dependent variations. Almost all studies have been limited to exploring nucleosynthetic anomalies (e.g. Akram et al., 2015;Akram and Schö nbächler, 2016). The only mass-dependent study of Zr within natural samples was limited to a series of geological standard reference materials (SRM), spanning bulk major element compositions between basalt and granite ([SiO 2 ] = 49.9 wt% to 69.9 wt%) (Inglis et al., 2018). It was found that d 94/90 Zr IPGP-Zr , which represents the deviation of the 94 Zr /90 Zr ratio from the IPGP-Zr standard in parts per thousand, increases with increasing SiO 2 content from 0.044 ± 0.044‰ to 0.186 ± 0.035‰, demonstrating not only that resolvable Zr stable isotope variations exist in nature, but also that Zr isotopes can potentially serve as sensitive tracers of magmatic differentiation. If this is the case then it is anticipated that Zr stable isotopes can be used to tracer ancient magmatic differentiation and provide insight into the emergence and evolution of differentiated crustal lithologies throughout Earth history.
To examine the suitability of Zr stable isotopes as a tracer of magmatic processes and to estimate the Zr isotope composition of the terrestrial mantle, new high-precision mass-dependent Zr isotope data are presented for a range of mid-ocean ridge (MORB) and ocean island (OIB) basalts, along with two well-characterised magmatic differ-entiation suites from Kilauea Iki lava lake, Hawaii, and Hekla volcano, Iceland.
Ocean island basalts (OIB)
To examine possible isotopic heterogeneities that may be preserved within the mantle sampled by OIB, fourteen whole rock OIB lavas were analysed. These OIB were selected from different intraplate volcanic islands from the Atlantic and Pacific oceans and have been previously studied for major & trace element and isotope systematics. Samples were selected to give a range of different radiogenic isotope ''mantle flavours" such as EM-1, EM-2 and HIMU. Specifically, the OIB samples analysed here comprise: three samples from São Nicolou island of the Cape Verde archipelago (Millet et al., 2008;Mourão et al., 2012) (Hart and Jackson, 2014), two samples from El Hierro of the Canary Islands (EH15 and EH17) (Day et al., 2009(Day et al., , 2010, one sample from Tristan da Cunha (TDC -BM1962, 128[114]) (Baker et al., 1964) and one sample from Gough Island (ALR 40G) (le Roex, 1985).
Where available the literature major and trace element data for these samples are presented in Table 1 and Supporting Information Table 1. For a number of samples trace element data was not available. In this instance trace element abundance measurements were performed on the same sample aliquots used for Zr isotope measurements and are presented alongside the literature elemental data in Supporting Information Table 1. 2.1.3. Magmatic differentiation suites 2.1.3.1. Hekla volcano (Iceland). The Hekla volcano is an active volcanic fissure situated in the South Iceland Volcanic Zone. The volcano has been active since 1104 A.D. and has seen 18 historic eruptions, with the most recent occurring in 2000 A.D (Hö skuldsson et al., 2007). The volcano is one of the most active on Iceland and, unlike most others on the island, produces an array of lavas spanning a bulk compositional range between primitive basalt to evolved rhyolite ($45-72 wt% SiO 2 ) (Sigmarsson et al., 1992;Chekol et al., 2011). Differing models of magmatic evolution for Hekla have been proposed. Sigmarsson et al. (1992) suggested a multi-stage model whereby basaltic melt pools towards the bottom of a shallow crustal magma chamber undergoes fractional crystallisation and evolve along a line of liquid descent to basaltic andesite. This melt triggers melting of crustal lithologies to form a magma of dacitic composition, which in turn mixes with the basaltic andesite magma to form a melt of andesitic composition. This hybrid melt progresses along a line of liquid descent to generate the rhyolites. This model has been recently challenged based on coupled radiogenic isotope data and geophysical observations, that the differentiation of the basaltic parent melt to intermediate compositions of basaltic-andesites could be accounted for by simple closed system fractional crystallisation (Chekol et al., 2011). This model differs from that of Sigmarsson et al. (1992) in that it suggests that these early basic to intermediate melts were generated within a deep seated magma chamber, this in turn supplied magma to a series shallower, crustal melt lenses which underwent a process of assimilation fractional crystallisation (e.g. DePaolo, 1981). Despite these two differing models no fundamental difference exists with respect to the application of the Hekla suite to examine the magmatic behaviour of Zr isotopes owing to the nature of the potential crustal assimilant.
In recent years Hekla has been used as a natural laboratory to examine the mass-dependent stable isotope behaviour of several elements (Schuessler et al., 2009;Savage et al., 2011;Chen et al., 2013;Prytulak et al., 2017). The nine Hekla samples analysed here are taken from the study of Savage et al. (2011) and represent magmatic differentiates with SiO 2 contents spanning from 46.4 to 72.1 wt% and MgO contents of between 0.08-5.6 wt%.
2.1.3.2. Kīlauea Iki (Hawaii). The Kīlauea Iki lava lake formed during the 1959 eruption of the Kīlauea volcano, where large volumes of basaltic lava was erupted and ponded within the Kīlauea Iki pit crater and underwent relatively rapid cooling and differentiation as part of a closed system (Helz and Thornber, 1987). The resulting differentiation sequence comprises lower olivine cumulates to evolved andesitic melt segregation veins (Helz, 1987). As part of an extended campaign, the United States Geological Survey (USGS) conducted an extensive drilling program of the solidifying lava lake. This campaign resulted in the recovery of >1500 m of drill core, which sampled a range of lithologies between the most primitive to most evolved magmatic differentiates. These samples have been wellcharacterised in terms of petrography, major and trace element geochemistry (Helz, 1987;Helz et al., 1994;Helz and Taggart, 2012).
Much like Hekla, Kīlauea Iki has been used as a case study for examining the effect of magmatic differentiation on various stable isotope systems (Tomascak et al., 1999;Teng et al., 2007;Teng et al., 2008;Chen et al., 2013;Badullovich et al., 2017;Kato et al., 2017;Amsellem et al., 2018). The nine samples analysed as part of this study were originally characterised by Helz et al. (1994) and Helz and Taggart (2012), but have been analysed as part of the aforementioned stable isotope studies. They represent a range of different SiO 2 contents of between 46.7 and 57.1 wt% and MgO contents of 2.4 and 13.5 wt%.
Zirconium isotope measurements
Zirconium isotope measurements were performed using the method described in Inglis et al. (2018) that is summarised here. Depending on the Zr content of the samples, between 20 and 150 mg of whole-rock sample powder was weighed directly into clean Savillex PFA Teflon squared bodied 7 mL beakers, herein referred to as Teflon bombs, to obtain $1-2 lg of sample Zr. The sample powders were spiked prior to dissolution with a 91 Zr-96 Zr double spike at a Zr proportion of 43:57 spike to sample. Initial sample decomposition was achieved by the addition of concentrated HF (29 M) and HNO 3 (16 M) acids at a ratio of 1:2 and heating in high walled hotplate at 165°C for 5 days. This dissolution technique has been demonstrated to fully dissolve zircon grains and high silica rocks efficiently for Zr isotope measurements (Inglis et al., 2018). Following this initial decomposition, the samples were evaporated to dryness and residues were re-dissolved in 6 M HCl and 16 M HNO 3 to ensure complete dissolution of any fluoride phases that may have formed during the initial HF step. To ensure that the data obtained for the samples dissolved by this method were not biased by incomplete dissolution of refractory phases (i.e. zircon) repeat dissolution tests were made using high pressure-temperature steel digestion vessels (Parr bombs). For the samples digested in this manner, the sample powder was weighed into 3 ml Savillex hex beakers, spiked accordingly before concentrated HF and HNO 3 acids were added at a ratio of 1:2. These sample beakers were then placed inside the Teflon Ò interior chamber of the Parr bomb and $3 ml of 1:2 HF:HNO 3 were added to enable vapour exchange between the Teflon chamber and sample beakers when subjected to high P-T. The sealed Parr bombs were then placed inside an oven and heated Hart and Jackson (2014) at 220°C for 7 days, after which samples were refluxed in 6 M HCl and 16 M HNO 3 prior to column chemistry. The isolation of Zr from the sample matrix was achieved using a two-stage ion exchange chromatography. The first stage of this chemistry was performed on BioRad TM Poly-Prep columns filled with AG1-X8 (200-400 mesh) anion exchange resin. Samples were loaded onto the column and the matrix eluted in 4 M HF, while the fraction containing the sample Zr was recovered in 6 M HCl + 0.01 M HF. This sample fraction was then evaporated to dryness and re-dissolved in 12 M HNO 3 . For the second stage of the chemistry procedure the sample solutions were loaded onto BioRad TM PolyPrep columns packed with 1 mL of Eichrom DGA resin. The matrix was then eluted from the column, first in 12 M HNO 3 and then in 3 M HNO 3 . Finally, the Zr fraction was recovered from the column in 3 M HNO 3 + 0.2 M HF. The Zr fractions were evaporated to dryness before being brought back into solution in 0.5 M HNO 3 prior to mass spectrometry.
All Zr isotope measurements were performed on a Thermo Scientific Ò Neptune Plus multiple-collector inductively coupled plasma mass spectrometer (MC-ICPMS) housed at the Institut de Physique du Globe de Paris, France (IPGP). Samples were introduced to the instrument, which was run in low mass-resolution mode, via a quartz SIS spray-chamber and PFA 50 lL min À1 nebuliser at a running concentration of 200 ng mL À1 total Zr solution, which gave a total Zr beam intensity of $20 V. The intensity of all the isotopes of Zr were collected ( 90 Zr + , 91 Zr + , 92 Zr + , 94 Zr + and 96 Zr + ) alongside the ones of 88 Sr + and 95 Mo + -the latter in order to monitor for interferences of 94 Mo + and 96 Mo + on 94 Zr + and 96 Zr + , respectively. Between all samples, baseline corrections (on peak zeros) were performed in clean 0.5 M HNO 3 , the effects of which were also negligible. After each measurement a 15 min wash-out was performed with clean 0.5 M HNO 3 in order to return to background beam intensities. Because it is known that Zr is not particular stable in dilute HNO 3 tests were made to examine the effect of running samples in 0.5 M HNO 3 + 0.1 M HF. For these tests, all samples, standards, on peak zeros and wash solutions were prepared in 0.5 HNO 3 + 0.1 M HF and introduced into the instrument using a Savillex PFA cyclonic spray chamber and an inert sapphire injector. Instrument operating parameters are the same as when running in 0.5 M HNO 3 except washout times were reduced to 7 min. Several total procedural blanks were measured as part of this study. These were found to range between 100 and 200 pg total Zr, which is negligible when compared to the $<2 lg of sample Zr processed.
All of the Zr isotope data presented (given in Table 1) represent the average of four individual sample measurements, with the reported error being the twice standard deviation (2 sd) of these four measurements, except for the case of the standard reference material data discussed in 3.1, where individual measurements are used. Data was reduced via a series of double-spike inversion calculations using the double-spike data reduction tool IsoSpike (Creech and Paul, 2015). All data is reported in standard delta notation as d 94/90 Zr IPGP-Zr , which represents the 2.2.2. Trace element abundance measurements Trace element abundance measurements were performed for all twelve of the MORB samples and eight of the OIB samples. Roughly 50 mg of sample powder was weighed directly into clean Teflon bombs or round bottomed 7 mL Savillex Ò beakers, added to which was 1 mL 29 M HF and 2 mL 16 M HNO 3 . These were then heated in a high walled hotplate for four days at 130°C, before being evaporated to dryness, re-dissolved in 2 mL of 6 M HCl and refluxed at 130°C for a further three days; this final HCl reflux was to ensure that all fluoride phases formed by the addition of HF were fully brought into solution. Prior to analysis, samples were once again evaporated to dryness and brought back into solution in 0.5 M HNO 3 and diluted by a factor of 2000.
Trace element concentrations were measured using an Agilent 7900 ICP-QMS housed at the IPGP in low resolution mode. Sample introduction was achieved with a micro-nebulizer (MicroMist, 0.2 mL/min) through a Scott spray chamber. Masses between 23 (Na) and 75 (As) were measured using a collision-reaction interface with helium gas (5 mL/min) to remove polyatomic interferences. Scandium and indium internal standards were injected after inline mixing with the samples to correct for signal drift and matrix effects. A mix of certified standards was measured at concentrations spanning those of the samples to convert count measurements to concentrations in the solution. Uncertainties on sample concentrations are calculated using algebraic propagation of blank and sample counts uncertainties. Additionally, BHVO-2 was analyzed as an unknown. Comparison of the values obtained for this reference material with certified concentration data demonstrates an external reproducibility of between 5-10% for all elements given in Supporting Information Table 1. Fig. 1. Data for the standard reference materials basalt BHVO-2 and granite GA. Data points represent individual measurements of five separate repeat dissolutions for BHVO-2 and two repeat dissolutions for GA. The hollow symbols for both BHVO-2 and GA represents data presented in (Inglis et al., 2018), while the filled symbols are data generated as part of this study. For both samples, the grey solid line represents the mean of n and the shaded box represents the 2sd of n. Fig. 2. The Zr stable isotope composition (d 94/90 Zr IPGP-Zr ) of products of igneous differentiation from basaltic magmas (Kīlauea Iki and Hekla, OIB and MORB), and standard reference materials, analysed as part of this study. Each data point represents four measurements (n) of the same sample aliquot, with the error bar being the 2sd of n. The grey solid line surrounded by the grey box represents the primitive mantle value and the 2sd uncertainty, as discussed in the text.
Standard reference materials
As part of this study a series of external standard reference materials (SRM) were analysed in order to validate the accuracy of data collected in the campaign against previously published values for these SRM (i.e. Inglis et al., 2018). Two separate repeat dissolutions and ion exchange separations of basalt BHVO-2 were carried out, as well as a single dissolution of the granite GA. Additionally the rhyolite, RGM-1 was also analysed for the first time for Zr stable isotopes. The data for these standard reference materials is provided in Table 1.
The individual d 94/90 Zr IPGP-Zr values for repeat measurements of BHVO-2 and GA that have been analysed here and elsewhere (Inglis et al., 2018) are presented in Fig. 1
Zirconium isotope composition of MORB, OIB and igneous differentiates
The Zr isotope data for the MORB and OIB samples are given in Table 1 and presented alongside all other Zr isotope data from this study in Fig. 2
The Zr stable isotope composition of MORB and OIB
The MORB and OIB samples have been analysed to determine the Zr isotopic composition of mantle derived basaltic melts. Of the two sample types, the OIB show a restricted range of d 94/90 Zr IPGP-Zr values (mean d 94/90 Zr -IPGP-Zr = 0.046 ± 0.037‰; 2sd, n = 13) and all plot within analytical uncertainty of one another (Fig. 2), and of previous Zr isotope measurements of the Hawaiian basalt SRM BHVO-2 (0.044 ± 0.044‰; Inglis et al., 2018). It is apparent that these samples are isotopically homogenous, with no variation between geographical area or relationship with isotopic mantle flavour (e.g., HIMU, EM). Based on this observation, we suggest that the fertile mantle source regions sampled by OIB is uniform with respect to Zr stable isotope composition.
The MORB samples studied here have been grouped accordingly to their chondrite normalized La/Sm ratio (La/Sm N ) based on the classification of (Schilling, 1975;Schilling et al., 1983). By this scheme samples with La/ Sm N < 0.7 are termed normal or N-MORBs and are suggested to represent products of melting of the depleted MORB mantle (DMM). Samples with La/Sm N > 1.8 are termed enriched or E-MORBs, whilst samples with La/ Sm N ratios between the two end members are classed as transitional or T-MORB. This grouping assumes that both T-and E-MORBs represent increased melting of a more fertile, primitive mantle source.
The variation of d 94/90 Zr IPGP-Zr values seen within the MORB samples (-0.045 ± 0.018 to 0.074 ± 0.023‰ for d 94/90 Zr IPGP-Zr ) is resolvable outside of analytical uncertainty for many of the samples. The MORB samples ana- (Schilling et al., 1983). The error bars on individual isotope measurements represents the 2sd of n. The solid horizontal black line surrounded by the grey box represents the estimate of the primitive mantle (0.048 ± 0.032‰; 2sd, n = 48). lyzed as part of this work were selected to give a broad geographical distribution and thus representative of different classifications of MORB type (e.g. N-, T-and E-MORB; Schilling et al., 1983). The Zr isotopic composition of T-and E-MORB types are within analytical uncertainty of one another (see Fig. 3) and also plot within the range of values seen in OIB. In fact, the mean d 94/90 Zr -IPGP-Zr for T-and E-MORB types (0.053 ± 0.040‰; 2sd, n = 8) is indistinguishable within error of the OIB mean value (0.046 ± 0.037‰; 2sd; n = 13), consistent with the concept that these melts are likely tapping a mantle source region, which, much like the ones sampled by OIB, is isotopically homogenous with respect to Zr stable isotopes. The origin of incompatible trace element enrichments in MORB is debated; some argue that it is melting of a deeper, more fertile mantle region (i.e. plume source) that can account for such trace element enrichments within E-MORB (Schilling et al., 1983), while others have evoked recycling of oceanic crust and minor amounts of continental material (Hofmann and White, 1982). More recently it has been suggested that incorporation of metasomatically enriched sub-crustal lithosphere could be a viable mechanism for the formation of E-MORB (Workman et al., 2004). The new Zr isotope data for the E-and T-MORB samples presented here does not provide definite insight into the mechanism of E-MORB formation, but does imply melting of a more fertile mantle source given the uniform, unfractionated Zr isotope data displayed for these samples.
The Zr isotope values obtained for the N-MORB samples show a resolvable variation from the T-and E-MORB samples (Fig. 3). With the exception of one sample from the Mid Atlantic Ridge (RD87 DR18-102), the N-MORB samples are offset towards lighter values. These represent the lightest values for any basalts analyzed to date. To a first order, it would thus appear that the melting regime experienced during melting of depleted MORB mantle is responsible for producing an isotopically light melt, relative to T-, E-MORB, or OIB, or that the source of the N-MORB had been previously depleted in the heavier isotopes by continued melt extraction. It is well known that mantle melting and melt extraction processes can exert a strong effect on other stable isotope systems (e.g. Weyer and Ionov, 2007;Huang et al., 2017). However, the lack of Zr isotope measurements of depleted MORB mantle (DMM) samples (e.g. abyssal peridotites), precludes us from commenting exactly as to the origin of this isotopic variation within these samples. One possible scenario is that partial melting and extraction of the melt could preferential incorporate heavy Zr isotopes, progressively driving the source region of these N-MORBs towards lighter values. It is possible that this may result from incongruent mantle melting and citing of isotopically light Zr in an octahedral coordination within mantle orthopyroxene (i.e. Niu, 1997). There is a negative correlation between Zr isotopic composition and Zr/Sm in the N-MORB samples Fig. 4) indicating isotopically light Zr is coupled with high Zr/Sm in N-MORB samples. Orthopyroxene has similar partition coefficients (K D ) for both Zr (0.014-0.036) and Sm (0.016-0.039), with an average Zr/Sm fractionation factor of $0.9, and significant possible extremes (0.3-2.2) (Salters and Longhi, 1999). The correlation with Zr isotopes and Zr/Sm is plausibly consistent with increased influence of orthopyroxene melting in some of the isotopically light N-MORB samples. On the other hand, by investigating komatiites (25-40% partial melts of the mantle), Deng et al. (2018) has highlighted a progressive depletion of both heavy Ti isotopes and incompatible trace elements in the mantle during the late Archean and suggest that this signature is present within the mantle sources of modern MORB samples. The authors considered that such a depletion of heavy Ti isotopes in the depleted MORB mantle could not be solely attributed to partial melting of the mantle (i.e. mantle depletion by the extraction of mafic crust), and that a reworking of mafic crust and recycling of the melt residues into the mantle would be needed to account for the formation of the depleted MORB mantle. This is also a plausible mechanism for the correlation between Zr isotopes and Zr/Sm observed here (Fig. 4), since the melt residues from the crust would preferentially incorporate Sm over Zr (Foley et al., 2002) and light Zr isotopes.
Fractionation of Zr stable isotopes during igneous differentiation
A major objective of this study is to examine the effect of magmatic differentiation on Zr isotopes. This has been tested by studying two separate, cogenetic differentiation suites -Kīlauea Iki and Hekla. The Kīlauea Iki suite displays a restricted range in d 94/90 Zr IPGP-Zr values, with a mean of 0.044 ± 0.023‰; 2sd, n = 9, and displays no apparent covariation with indices of differentiation (Fig. 5). Indeed, the Zr isotope data for this suite are indistinguishable within uncertainty of the mean values for T-and E-MORBs, and also for OIB samples. We conclude from this that the melts produced at the Kīlauea Iki volcano are sampling a mantle source region that, like other OIB, is homogenous with respect to Zr isotopes and that basaltic magmatic differentiation in this setting leads to little or no Zr isotope fractionation. None of the phases formed during continued differentiation of the Kīlauea Iki magmas are responsible for fractionating Zr stable isotopes.
Different systematics are observed for the Hekla sample suite. These samples span a much greater compositional range, and represent a continuous differentiation suite. Consequently, they are ideally suited to examine the effect of more extreme degrees of magmatic differentiation. d 94/90 Zr IPGP-Zr values increases together with the SiO 2 content (Fig. 5) with a steep inflection of the d 94/90 Zr IPGP-Zr values at $65 wt% SiO 2 , whereby values diverge from the range seen in OIB, T-and E-MORB to significantly heavier values, up to 0.52‰, suggesting that there is a control on Zr isotopes during the dacitic stages of differentiation. To understand the mechanism for this isotopic fractionation it is important to consider the elemental behavior of Zr during differentiation. Typically, Zr behaves as an incompatible element during melting, and consequently is concentrated into the melt during continued fractional crystallization (i.e. Woodhead et al., 1993). This elemental behavior of Zr is evident within the Hekla sample suite and is shown on Fig. 5. It is apparent that during evolution between the primitive basaltic melt at >$45 wt% SiO 2 and more evolved dacitic melts at $65 wt% SiO 2 , elemental Zr is continually enriched in the melt. At SiO 2 contents >$65 wt% a steep decrease in [Zr] is observed, which is assumed to represent the precipitation of a Zr rich phase, most likely zircon, which is removed from the residual melt. Indeed, previous studies have suggested the zircon saturation was reached in the Hekla melts (Sigmarsson et al., 1992;Bindeman et al., 2012;Weber and Castro, 2017). Within the Hekla suite it is likely that Zr concentration ([Zr]) would increase linearly until the point of saturation is reached. Owing to the lack of samples spanning the compositional range of SiO 2 contents between 59.64 -68.31 wt %, within which the point of Zr saturation is likely to occur (Watson and Harrison, 1983), this has been estimated by plotting trendlines pre and post zircon saturation and using the intercept of these two lines to infer the point of Zr saturation (Fig. 4). Based on this, the point of Zr saturation within the Hekla melt is suggested to occur at $66.75 wt% SiO 2 . Given the density (q) of zircon ($4.5 g cm À3 ) relative to that of rhyolitic melts ($2.2 g cm À3 ; (Murase and McBirney, 1973)), it is plausible that after the appearance of zircon on the solidus a degree of crystal settling likely occurred, and the zircon was partitioned into the cumulate phase, thus removing it from the residual melt. Strikingly, there is a strong relationship between the behavior of elemental [Zr] and d 94/90 Zr IPGP-Zr , whereby the point of suggested zircon crystallisation is marked by an enrichment of the heavier isotopes of Zr within melts. Precipitation of zircon within the Hekla suite is the likely driver for the large isotopic fractionation seen within these samples.
Theory predicts that equilibrium stable isotope fractionation is largely controlled by the bonding environment of a given element, with the magnitude of the resulting isotopic fractionation being roughly proportional to the bond stiffness between the two equilibrated phases, with the heavier isotopes being concentrated where bond stiffness is greatest (e.g. Urey, 1947;Schauble, 2004). The bond stiffness in such a system can be controlled by a number of factors including oxidation state, the type of elements involved and coordination numbers. Indeed, the shortest and strongest (and thus stiffest) bonds are associated with lower coordination numbers, thus it is predicted that low coordination number lattices will be enriched in the heavier isotopes. The coordination of Zr in silicate melts has been studied by Farges et al. (1991), who suggested that generally Zr is found with 6-fold coordination in silicate melts, but an increase in 8-fold coordinated Zr accompanying Zr saturation is noted. Furthermore, Zr K edge X-ray absorption near edge structure measurements have confirmed the 8fold coordination of Zr ions within the lattice of zircons, relative to melts with lower coordinated Zr (Tobase et al., 2015). In this scenario the crystallisation of 8-fold coordinated Zr ions within zircon would incorporate the lighter Zr isotopes, whilst the residual melt is enriched in the heavier isotopes.
Building on this interpretation that zircon crystallisation is responsible for driving the isotopic fractionation seen within the most magmatically evolved rocks presented here, we have modelled the d 94/90 Zr IPGP-Zr evolution of a residual melt during the progressive fractional crystallisation of zircon. A Rayleigh distillation equation is used (Eq. (2)) to calculate the d 94/90 Zr IPGP-Zr of the residual melt decreasing concentration of Zr, which is assumed to reflect continued zircon crystallisation.
Where f represents the fraction of Zr remaining in the melt, a is the isotopic fractionation factor between the precipitating zircon and the melt, and d 94 Zr (initial) represents the starting d 94 Zr of the model. The model presented here is based on the data from the four Hekla samples that are suggested to represent post-zircon crystallization melts (see Fig. 5). These samples were selected because they represent a relatively simple melting and crystallisation regime from one parent melt. From these data the a zircon-melt has been derived empirically, given a distillation curve that best fits the measured data (Fig. 6). Based on this we suggest a a zircon-melt of 0.99950 best describes the results observed here.
An estimate of the Zr isotope budget of the primitive mantle
Despite the evidence for Zr isotope fractionation during igneous differentiation, isotopic fractionation is only apparent at the onset of Zr saturation in melts (>$65 wt% SiO 2 ; Fig. 5). In addition, is has been demonstrated that melt extraction processes occurring within the DMM could possibly impart a control on Zr isotope compositions, but the absence of peridotite data prohibit us from elucidating this process fully. Furthermore, owing to its incompatible nature, it is likely that during mantle melting Zr is strongly partitioned into the silicate melt, suggesting that partial melting should exert little effect on Zr isotope systematics. As such it is appropriate to use basaltic samples to give an estimate of the primitive mantle value for Zr isotopes. Considering the effect of igneous differentiation and MORB melt extraction we can use the mafic samples presented here and by Inglis et al. (2018) to place a constraint on the primitive mantle Zr isotope composition.
Despite covering a wide range of temporal and spatial settings, the data for the basaltic materials (OIB, T-and E-MORB, Kīlauea Iki and the Hekla samples containing <65 wt% SiO 2 ) are all isotopically undistinguishable from one another within analytical uncertainty, ultimately suggesting that the mantle sampled by these melts is isotopically homogenous with respect to Zr isotopes. Following the assumption that the d 94/90 Zr IPGP-Zr of the primitive mantle is estimated based on the average and 2sd of mafic samples, the primitive mantle composition can be estimated at 0.048 ± 0.032‰; 2sd, n = 43. The data used to calculate the primitive mantle value are given in Supporting Information Table 2 and the average and 2sd of these measurements is presented as the black solid line and grey box on Fig. 2. Since Zr is a purely lithophile element with an estimated concentration in the Earth's mantle that is chondritic (e.g. Fig. 6. A Rayleigh distillation model for the evolution of d 94/ 90 Zr IPGP-Zr during the progressive removal of Zr from the residual melt, which is taken to represent zircon crystallisation. Three different distillation curves are given for 3 different a zircon-melt . An empirically derived a zircon-melt of 0.99950 can best account for the Hekla data presented here (orange circles). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Palme and O'Neill, 2014) the isotopic composition of the Earth's mantle represents the isotopic composition of the bulk Earth and we can conclude that the best estimate of the d 94/90 Zr IPGP-Zr of the bulk Earth is equal to 0.048 ± 0.032‰.
CONCLUSIONS
A range of basaltic igneous rocks and differentiates been analysed in order to understand the Zr stable isotope composition of primitive mafic melts and to examine the effect of igneous differentiation on Zr isotopes. The OIB samples display a restricted range of d 94/90 Zr IPGP-Zr values, which are unresolved from previous measurements of basalts (Inglis et al., 2018), or from T-and E-MORB samples. Of the MORB samples, those with a (La/Sm) N ratio < 0.7 display a resolvable variation in Zr isotopes. Because these MORB samples are from melting of mantle source regions that have seen significant prior melt extraction, it is probable that these petrogenetic process exert a strong control on Zr isotopes. To further test this hypothesis the Zr isotopic composition of DMM samples (peridotites) would have to be analysed.
Two igneous differentiation suites have also been examined. It was found that samples from the Kīlauea Iki volcano, which span SiO 2 contents of between 46.7 and 57.1 wt%, showed no resolvable isotopic variation, and that the mean value obtained for these samples is indistinguishable within error from the mean value obtained from the OIB, T-and E-MORB samples. Unlike Kīlauea Iki the samples from Hekla volcano span a much greater range in SiO 2 contents (46.4-72.1 wt%), which correlates with d 94/90 Zr IPGP-Zr values for these samples. Linking the d 94/90 Zr IPGP-Zr values with Zr content of the samples, we conclude that the isotopic fraction seen within the Hekla samples occurs as a result of zircon crystallisation in the melt, whereby isotopically light Zr is incorporated into zircon and removed from the melt, driving this residue towards a heavier isotopic composition.
Based on these observations lavas originating from the effect of melt extraction from a depleted mantle source ((N-MORB) or that underwent zircon saturation (SiO 2 > 65 wt%) are removed from the dataset to give an estimate of the primitive mantle Zr isotope composition of 0.048 ± 0.032‰; 2sd, n = 48. These data show that major controls on Zr fractionation in the Earth result from incongruent melting of the depleted MORB mantle and by zircon fractionation in differentiated melts. Conversely, fertile mantle is homogenous with respect to Zr isotopes. Zirconium mass-dependent fractionation effects can therefore be used as tracers to examine large-scale mantle melt depletion events and the effects of felsic crust formation.
ACKNOWLEDGMENTS
We thank the ERC under the European Community's H2020 framework program/ERC grant agreement # 637503 (Pristine)) and for the UnivEarthS Labex program (no. ANR-10-LABX-0023 and ANR-11-IDEX-0005-02). Parts of this work were supported by IPGP multidisciplinary program PARI, and by Region île-de-France SESAME Grant (no. 12015908). Thibault Sontag and Pascale Louvat are thanked for assistance in the chemistry labs and with the MC-ICPMS facility at IPGP, while Pierre Burckel is thanked for his help with the ICP-MS measurements. Manuel Moreira is acknowledged for providing the MORB samples. This paper was greatly improved by insightful reviews from Fang Huang and two anonymous reviewers alongside careful editorial handling from associate editor Qing-Zhu Yin. | 8,743 | 2019-04-01T00:00:00.000 | [
"Geology"
] |
Violations of Löwenstein's rule in zeolites
We predict that in aluminosilicate zeolites, non-Löwenstein Al–O–Al sequences are favoured in the presence of protons and disfavoured when Na+ ions are the charge compensating species.
Introduction
The use of zeolite catalysts in petrochemistry entirely revolutionised the industry over half a century ago. Since then, zeolites have become the workhorses of petrochemical processing, and are used extensively throughout the petrochemical industry. 1 Now, at a time of fast depleting traditional fuel sources and increasing toxic gas emission, zeolite catalysts are at the forefront of the development of 'green' alternatives to longestablished petrochemical processes. 2 Green processes must operate at optimum efficiency 3 and for catalytic processes this requires the structural elucidation of existing catalytic materials. Unequivocally resolving a material's structure can expedite the identication of structure-activity relationships, which in turn, can accelerate the development of material specic design rules that are necessary for the rational design of new, more sustainable and efficient catalysts.
It is well understood that zeolite catalytic functionality originates from negatively charged tetrahedral units of AlO 4 distributed throughout the aluminosilicate framework, and their associated charge-compensating cations located in nearby pores. Yet, despite major recent advances in experimental techniques, 4 at present it is not possible to determine the absolute position of framework aluminium or accompanying counter-cations exactly. Furthermore, there are currently no established design rules that can be applied to infer framework aluminium's preferred and precise position. However, Löwenstein's rule 5 of "aluminium avoidance" is commonly assumed; this states that on forming the aluminosilicate zeolite framework there is a disinclination for tetrahedral units of alumina to exist adjacent to one another, forbidding formation of -Al-O-Allinkages, and restricting the minimum Si/Al ratio of any zeolite to unity.
Löwenstein's rule was conceptualised in 1954 and since then there have been few suggestions that violations of the rule are possible. [6][7][8][9][10][11][12][13] Indeed, the scientic literature reports that "aluminium avoidance" is observed in zeolites almost without exception. 5,14,15 Löwenstein's rule has hence become a fundamental law of zeolite science, and the possibility of non-Löwensteinian ordered zeolites is oen not considered. This is true of most theoretical studies where the omission of non-Löwensteinian frameworks is considered a simple way to reduce unnecessary computational expense by shrinking the number of potential congurations. [16][17][18][19][20][21][22][23] However, recent advances in supercomputing services and the development of increasingly efficient codes, mean it is now tractable to evaluate both Löwensteinian and non-Löwensteinian frameworks accurately through quantum mechanical approaches.
Characterisation techniques, such as X-ray diffraction, are currently unable to distinguish between framework silicon and catalytically important aluminium distributed throughout the zeolite, except in rare cases where there is strict ordering, such as in Goosecreekite. 24 On the other hand, atomistic modelling techniques can be used as a tool to provide insight into the most probable location of framework aluminium in real zeolites. Using framework crystallographic data for a particular zeolite, quantum mechanical methods can unambiguously resolve the most energetically favourable distribution of both Si and Al. However, there is a further complication. It is well documented that the framework aluminium distribution of a given zeolite is highly dependent on the synthesis details. 25 The Si/Al ratio of the initial synthesis gel, synthesis temperature, reaction times, counter-cation identity and kinetic factors may all cause differences in the nal structural chemistry, and hence catalytic activity of the resultant framework. Furthermore, Perea et al. and Schmidt et al. recently showed that for a zeolite sample at a given Si/Al ratio, aluminium is inhomogenously distributed throughout the framework, 4,26 supporting earlier work by von Ballmoos and Meier, that reported the presence of Al zoning in single crystals. 27 Commercial zeolites are typically synthesised using alkali metal cations as the charge compensating species, and facile ion-exchange techniques may be used post-synthesis to replace the metal cation with a proton, hence generating Brønsted acid O-H sites proximal to the location of aluminium. A key open question, which we partially address here, is whether the nature of the counter-cation affects the positioning of aluminium. However, the broader question is whether there is a clear thermodynamic incentive to form ordered or partially ordered frameworks and whether the position of aluminium can be predicted. Here, we present results obtained for the active small-pore zeolite catalyst SSZ-13, which displays a CHA-type framework topology. 28 The CHA framework ( Fig. 1) is made up of layers of hexagonally arranged double 6-ring (D6R) units connected by tilted 4-rings, giving rise to a characteristic 'cha' cavity accessible through an 8ring pore system. 28 Using periodic density functional theory (DFT) implemented in the program CP2K 29-31 we investigate all possible arrangements of framework aluminium, including non-Löwensteinian distributions, surveying the aluminium distribution of SSZ-13 at Si/Al ratios of 17, 11 and 8, in both Brønsted acidic H-SSZ-13 and the as-synthesised Na-SSZ-13. To our knowledge this is the only exhaustive study of zeolite framework aluminium distribution with different Si/Al ratios at this fully periodic quantum mechanical level of theory.
Results
A decisive variable in optimising catalytic activity is the Si/Al ratio as this dictates the density of charge compensating species, such as acidic sites. We compare three quite distinct Si/Al ratios to probe how the Si/Al ratio affects aluminium ordering.
High silica SSZ-13 Si/Al ¼ 17 A single hexagonal CHA unit cell contains 36 symmetry equivalent T-sites; in order to methodically explore all of the possible congurations of 2 Al per unit cell, corresponding to a Si/Al ratio of 17, a single aluminium atom, Al1, was substituted into an arbitrary T-site. Maintaining Al1's position, a second aluminium, Al2, was sequentially introduced into the remaining 35 T-sites. To maintain charge-neutrality, each individual aluminium substitution requires charge compensation by a cationic moiety. For H-SSZ-13, each cationic proton may reside at one of four oxygen sites at the apices of the alumina tetrahedra, yielding four potential topologically inequivalent Brønsted acid O-H sites per Al substitution, and hence a total of 560 unique combinations of 2 Al per unit cell. We used the periodic DFT method (at the PBE level) 32 to fully optimize each individual framework model to equilibrium density; the resulting data is shown in Fig. 2, where the relative energy per unit cell (U.C.) (with respect to the average total energy) is given as a function of framework aluminium separation.
Assuming Löwenstein's rule 5 is valid, and the principle of aluminium avoidance is adhered to, we would expect the highest energy SSZ-13 structures to be those containing aluminium atoms at separations equivalent to that of a "forbidden" -Al-O-Allinkage, and structures with larger aluminium separations to become increasingly more stable, in accordance with Dempsey's rule 33 (a less sophisticated rule which states, on the basis of electrostatics, that negatively charged alumina units are inclined to be positioned as far away from one another as possible).
As predicted from Löwenstein's rule, the highest energy congurations for both H-SSZ-13 and Na-SSZ-13 are those containing adjacent aluminium atoms, with a separation of approximately 3Å (Fig. 2). However, beyond this distance the relative energy landscapes for the two forms of the zeolite become dramatically different.
In accordance with Löwenstein's rule, and what has already been widely observed in sodium-containing zeolites, the Na-SSZ-13 global minimum (Fig. 3a) contains aluminium pairs as next-next-nearest neighbours (NNNN), 16 and there is a +44.3 kJ mol À1 per U.C. energy penalty for forming the most favourable non-Löwensteinian (NL) structure. Ignoring barriers, the penalty to form a NL structure is at least 10kT, where k is the Boltzmann constant (assuming a typical synthesis temperature of $450 K), which suggests -Al-O-Allinkages are very unfavourable in Na-SSZ-13. In the global minimum structure, the aluminium ions are separated by a distance of 6.18Å, and their associated Na + cations reside at the parameters of the 8-ring apertures of the 'cha' cavity. However, the H-SSZ-13 global minimum structure (Fig. 3c) is remarkably different, containing adjacent aluminium ions along the edge of the 6-ring at a separation of 3.28Å, violating Löwenstein's rule. In this structure the two associated protons, H1 and H2, are separated 4.36Å and arranged trans to one another; H1, which mediates the aluminium ions, is directed into the plane of the 6-ring, and H2, positioned at the connecting edge of the D6R, is oriented away from H1, and directed into the 8-ring window of the 'cha' cavity. The most stable Löwensteinian (L) structure ( Fig. 3d) contains aluminium ions as next-nearest neighbours (NNN), at a 'non-Dempsey' separation of 4.60Å, with both protons directed into different 8-ring windows of the 'cha' cavity. The energy penalty for forming the L structure rather than the NL structure is +14.2 kJ mol À1 per U.C., approximately one third of the energy difference between the global minimum NL/L structures for Na-SSZ-13. DE(NL global minimum À L global minimum ) for Na-SSZ-13 is +44.3 kJ mol À1 per U.C., whilst DE(NL global minimum À L global minimum ) for H-SSZ-13 is À14.2 kJ mol À1 per U.C., indicating a strong enthalpic incentive for Löwensteinian congurations when Na + is the charge compensating cation and a modest enthalpic incentive to adopt non-Löwensteinian linkages when the charge compensator is a proton. Free energy calculations that include the vibrational entropy contributions to the energy show that the relative stability of the L and NL H-SSZ-13 congurations is maintained beyond typical synthesis temperatures (see ESI †), demonstrating a clear thermodynamic preference for adopting non-Löwensteinian structures for the proton compensated structure, a result that clearly conicts with accepted wisdom. Furthermore, the NL H-SSZ-13 global minimum is not unique and seven other NL ordered frameworks (excluding the global minimum structure), all of which contain proton arrangements similar to those displayed in the NL global minimum structure (Fig. 3c), are more stable than the global minimum L H-SSZ-13 structure.
To test our unexpected H-SSZ-13 result we further investigated the lowest energy structures using the higher level hybrid functional PBE0, 34,35 and van der Waals corrected functionals, vDW-DF2 and PBE + D3. The relative energies calculated using these methods show good correlation with those calculated using the standard PBE functional, conrming the robustness of our predictions. The results for these calculations, presented as energy correlation plots, are included in the ESI † (S2 and S3).
Low silica SSZ-13 Si/Al < 17
Exploring SSZ-13 with lower Si/Al ratios becomes increasingly complicated with each introduction of additional aluminium. To avoid calculating the prohibitively large number of combinations of 3 Al per unit cell SSZ-13 (Si/Al ¼ 11), we employed a method of stepwise aluminium incorporation. In this approach, the NL and L ordered 2 Al per unit cell global minima according to the prior DFT ( Fig. 3c and d) were used as the initial structures. A single Al, Al3, was sequentially introduced into each of the remaining silica T-sites of both structures, and the appropriate counter-cation positioned at one of the four apical oxygen sites. For each NL and L initial global minimum structure, a total of 136 distinct framework arrangements were created for Na-SSZ-13 and H-SSZ-13, respectively (544 calculations in total).
Each structure was optimised and the NL and L H-SSZ-13 initial congurations gave the same 3 Al per unit cell global minimum structure. The structure, Fig. 4a, contains a chain of three oxygen linked aluminium atoms, [O-Al-O] 3 , with each charge-compensating proton located at a bridging oxygen and arranged trans to its neighbour(s). Once again, Na-SSZ-13 did not follow the same trend as H-SSZ-13, where each initial structure yielded different global minimum structures; the Löwensteinian structure favouring the third aluminium at the NNN position, 19 and the non-Löwensteinian structure favouring Al at the NNNN position. The corresponding gures for these structures can be found in the ESI (S6 †).
Using the H-SSZ-13 (Si/Al ¼ 11) global minimum as the new initial structure, we then proceeded to investigate 4 Al per unit cell, equivalent to a Si/Al ratio of 8. The global minimum structure, shown in Fig. 4b, contains a chain of four oxygen linked aluminium atoms arranged in a 4-ring, with protons arranged trans to one another. In the sodium form of this structure (S6 †), the fourth Al resides in the NNN position, again in accordance with Löwenstein's rule, and what has already been documented for similar zeolites. 19 All four sodium cations position themselves proximal to the aluminium ions, at the centre of both faces of the aluminium doped D6R unit and at the parameters of the proximal 8-rings. It appears that as the aluminium content of the zeolite is increased, the aluminium clusters into zones of concentrated -Al-O-Al-, this is contrary to the general belief that aluminium is reasonably well dispersed throughout the frameworks of real samples. 4,26 It should be noted that these results cannot imply whether the minimum Si/Al ratio is 1.
Other zeolite framework types
To ascertain whether our unexpected ndings manifest in other proton compensated zeolite frameworks, or are unique to CHA, we investigated a selection of framework-types by the same methods previously discussed. The selected frameworks, LTA, RHO and ABW, are shown in Fig. 5, and their corresponding densities are included in the ESI † (S7). 28 Each of the frameworks contain a single symmetry equivalent T-site, and exhibit contrasting densities and topologies to that of CHA. The least dense of the frameworks, LTA, has a highly controversial history regarding aluminium distribution at Si/Al ratios tending to 1, where previous work has suggested the existence of non-Löwensteinian (NL) linkages. 6,7 Investigation of each framework (2 Al per unit cell) using DFT revealed that all three framework types possess NL global minimum structures in their protonated forms, and that the protons adopt the same 'trans'-like orientation as seen for CHA. The data for each structure is shown in Fig. 6, and the corresponding global minimum framework structures for each framework type can be found in the ESI † (S8). The energy penalty for forming the L structure (DE(NL global minimum À L global minimum )) for high density H-ABW is +55.7 kJ mol À1 per U.C., +14.2 kJ mol À1 per U.C. for H-CHA, +9.2 kJ mol À1 per U.C. for H-RHO and +8.3 kJ mol À1 per U.C. for H-LTA, which correlates with their respective densities. These results suggest that NL linkages are more strongly preferred in denser zeolites, but even in LTA, which is one of the lowest density zeolites, the energy penalty for forming L structures is $2kT at typical synthesis temperatures ($450 K).
To discern whether the preference for NL ordering over L ordering can be extended to other ring systems we examined the protonated MOR framework. Due to the large number of symmetry inequivalent tetrahedral framework sites of the MOR framework, we augmented our approach to focus only on the thermodynamic stability of aluminium pairs as nearest neighbours compared to next-nearest neighbours for each of the four symmetry equivalent T-site present within the framework. Once again, the DFT data showed the NL ordering to be preferred over the 'traditional' Löwensteinian ordering. For these structures DE(NL global minimum À L global minimum ) ¼ À16.1 kJ mol À1 , this value is consistent with the trend observed between density and preference for the formation of Al-O-Al. Further information about these calculations, results and the NL MOR global minimum structure are included in the ESI † (S9).
Discussion
This work provides evidence for non-Löwensteinian ordering in protonated zeolite frameworks, where there is a thermodynamic preference for Al 3+ ions to exist adjacent to one another linked by a bridging hydroxyl moiety oriented 'trans' to its nearest neighbour proton. This prediction holds true across a range of different frameworks, and we have shown that in low silica frameworks there is a preference for the formation of discrete aluminium clusters. However, this is not the case for sodiumcontaining zeolites, where the global minimum structures are Löwensteinian ordered frameworks. In low silica sodium frameworks, next-nearest neighbour aluminium distribution is favoured, but next-next-nearest neighbour distributions are preferred with increasing aluminium content. Marked differences between the most thermodynamically stable aluminium distributions of protonated and sodium-containing zeolites have been discerned demonstrating the inuence of countercation identity on framework aluminium location. In addition, Dempsey's rule 36 is violated in the global minimum structures of all investigated frameworks. The literature contains several reports of violations of Dempsey's rule in zeolites, 16,19,37 and it has been established that non-covalent interactions, present between framework oxygen and extra-framework cations, may distort aluminium distributions away from true Dempsey ordering. 37 On close inspection, violations of Dempsey's rule in Na-SSZ-13 can be rationalised by simple electrostatics. As shown in the global minimum structure for 2 Al per unit cell (Fig. 3a), there is a preference for Na + cations to maximise their coordination with framework oxygen whilst minimising unfavourable cation-cation interactionsas illustrated by the collection of unusually high energy structures (with aluminium separations of 5.80-8.20Å) in Fig. 2a, all of which contain Na + cations at relatively unfavourable short separations, causing these structures to be destabilised compared with what would be expected from Dempsey's rule. The importance of Na + cations in determining the distribution of framework aluminium throughout a zeolite is also reected in the variation in the position of the third aluminium for the two Na-SSZ-13 structures with 3 Al per unit cell. In the Löwensteinian structure, the NNN Al position is favoured, and the associated Na + cations occupy two 8-rings and one 6-ring, with minimal repulsions between the counter-cations. However, the NNNN Al position is favoured for the non-Löwensteinian structure, in which the Na + cations occupy only one 8-ring, and the two 6-rings of the D6R. In this structure, a single 6-ring and 8-ring occupancy are lled by virtue of the initial non-Löwensteinian arrangement of the aluminium ions. NNN substitution would result in Na + occupancy of a six-ring that is already lled. Despite the NNNN position traditionally being thought of as more unfavourable, in the NL case, it is the only aluminium position which can satisfy the Na + coordination requirements whilst minimising unfavourable Na-Na interactions.
Rationalising the non-Dempsey aluminium distribution in sodium-containing frameworks is straightforward, whilst untangling the thermodynamic preference for NL ordering in protonated frameworks is more complex. As demonstrated by sodium-containing frameworks, non-covalent interactions play a signicant role in determining aluminium distribution, we hence speculated that hydrogen-bonding interactions could be the cause of the unanticipated stability of the NL ordering in protonated zeolite frameworks. Fujita et al. demonstrated that hydrogen bonding interactions cause aluminium atoms to reside in close proximity to one another in zeolite Beta. 37 The separation between framework oxygen and H1 and H2 in 2 Al per unit cell H-SSZ-13 indicates the existence of two hydrogen bonds (O-H/O < 2.5Å) per aluminium in both the global minimum structure and the lowest energy Löwensteinian structure. We hence examined the robustness of the order of stability predicted in this work by using other density functionals. A representative subset of structures were selected and re-optimised with the revPBE 38 and BLYP functionals, 39,40 which have been shown to underbind hydrogen bonding interactions in water and ice structures (whilst PBE overbinds). 41 The results (S1 †) show that decreasing the hydrogen bonding strength in this way has no qualitative effect on the results and little quantitative effect, indicating that whilst hydrogen bonding must play a part in stabilising the H-SSZ-13 structures, it is not the decisive factor that controls whether NL is favoured over L.
Next we considered the charge distributions in the structures. On comparison of the Bader charges for 2 Al per unit cell Na and H-SSZ-13 we found the charge on the Na + cation is +0.92, far greater than that of the proton in corresponding H-SSZ-13 NL structure, H + ¼ +0.66. Consequently, the charge on the framework oxygen atoms covalently bound to the protons is reduced in comparison to the corresponding oxygen atoms in the Na-SSZ-13 structure, O ¼ À1. 47 In the sodium loaded zeolites, the interaction between Na + and framework oxygen is primarily electrostatic and there is essentially complete charge transfer between Na + and framework oxygen, as reected by the computed Na + charge and so the difference in ionicity/charge between a framework oxygen coordinated to Na + and those not coordinated to Na + is rather small. In H-SSZ-13, the electrons are smeared across the covalent O-H bond and the effective charge on the bridging oxygen is reduced and the alumina units favour adopting next-nextnearest neighbour structures. The clustering or islanding of aluminium has been noted in silicon-aluminium phosphate zeolites 16 but not in aluminosilicate zeolites.
To check whether the qualitative result is sensitive to the extra-framework cation, we performed further calculations, substituting Na + and H + cations in the 2 Al per unit cell SSZ-13 model for intermediate sized Li + cations and optimising all congurations to equilibrium density. The DFT results are included in the ESI † (S4 and S5), and are remarkably similar to that of Na-SSZ-13, showing a thermodynamic preference for 'traditional' Löwensteinian ordering over non-Löwensteinian with a DE (NL global minimum À L global minimum ) ¼ +51.2 kJ mol À1 per U.C. However, for Li-SSZ-13, the global minimum structure shows marked differences in alkali cation position, with Li + ions capping the faces of individual D6R units, rather than located at the parameter of the 8-rings, as was the case for Na-SSZ-13 at this Si/Al ratio. Because Li + cations are considerably smaller than Na + cations, the Li + ions are able to get closer to the D6R due to their higher charge density.
SSZ-13 is typically synthesised from a sodium solution with a nitrogenous structure-directing agent, yielding Na-SSZ-13, which is subsequently ion-exchanged post synthesis to give the protonated, Brønsted acid active form of the zeolite catalyst, H-SSZ-13. 42 It is this form of the zeolite that is used to catalyse methanol-to-olen conversion, a proposed lucrative, nonpetroleum route for the production of short-chain organic compounds. At present, there is no viable way to synthesise H-SSZ-13 directly, most probably due to the role of counter-cations in directing the progress of zeolite formation during synthesis. As shown by our results, the location of framework aluminium is directly affected by counter-cation identity, and we can therefore assume that the distribution of aluminium in the global minimum Na-SSZ-13 framework is most representative of what would likely be seen in typical samples of SSZ-13, as it is this cation which determines the position of Al. However, our predictions suggest that a direct synthesis of H-SSZ-13 (H-CHA), H-LTA, H-RHO, H-ABW and H-MOR should favour NL aluminium ion ordering. Interestingly, high resolution mass spectrometry data concerning the incorporation of aluminium in prenucleating silicate species by Schaack et al., 43 indicates that Löwenstein's rule is not obeyed for all silicate species. The work provides evidence of 4-ring units containing -Al-O-Al-, but concludes that whilst these species may occur in solution, species that obey Löwenstein's rule are preferentially formed. Nevertheless, the observation of pre-nucleating building units with -Al-O-Allinkages hints that this motif may not be as elusive as is generally believed, and these sequences may be found in crystals.
Because direct synthesis of proton compensated zeolites has not yet been achieved, direct validation of NL ordered frameworks in protonated zeolites cannot be assessed immediately. However, with regard to the synthesis of H-zeolite frameworks, we propose that the formation of -Al-O-Almight be facilitated via two post-synthetic methods. The rst is to use water, which has been shown to facilitate the making and breaking of -Si-O-Si-and -Al-O-Si-. 44 Long-term steeping of H-SSZ-13 in water could be expected to lead to the redistribution of Al in the framework, yielding -Al-O-Alas the thermodynamically preferred arrangement. Potentially, very slightly acidic or basic water might enhance the rate of rearrangement without dealumination or desilication of the zeolite framework. A second potential approach is, in essence, reverse-dealumination; placing a zeolite crystal in a solution containing an excess of alumina units with the assumption that for high alumina zeolites, the aluminium content will rise, increasing the likelihood of alumina units situated adjacent to one another. Previously, this has been achieved in high-silica ZSM-5 via AlCl 3 vapour treatment, and in very low-silica zeolite Y using non-crystallisation inducing alkaline solutions (e.g. KOH) in the presence of large concentrations of extra-framework aluminium. 45,46 An intriguing question is whether the NL linkages that we have predicted are present in existing samples, and if so, what signatures could be used to unambiguously identify these -Al-O-Al-sequences. Recent atom tomography work 4,26 has vividly demonstrated that the distribution of aluminium in a typical ZSM-5 zeolite sample is very heterogeneous. At present there is no available method that can accurately distinguish framework aluminium from framework silicon withÅngström resolution. 4 A 2010 work by Shin et al. 8 concerning possible non-Löwensteinian structures observed in gallosilicates, discusses the possibility of using of 17 O magic angle spinning (MAS) NMR to detect non-Löwensteinian ordering, a method which has been successful in identifying -Al-O-Allinkages in aluminosilicate glasses. 47 We have examined the global minimum H-SSZ-13 structures (Si/Al ¼ 17) and predicted 29 Si, 27 Al solid-state, MAS NMR shis and vibrational frequencies, in an attempt to discern whether spectroscopic signatures exist that would be indicative of the presence of non-Löwensteinian ordering (see ESI †). However, at a Si/Al ratio of 17, typical for SSZ-13, the predicted 29 Si NMR data shows that there is a slight decrease in the negativity of the chemical shi values for -Al-O-Alcontaining frameworks. However, these shis are well within the anticipated range for a zeolite at this Si/Al ratio, and far too similar to the chemical shis of the surrounding Si atoms to be used practically as a characterisation method. Similarly, predicted vibrational frequencies indicate that characteristic stretches would not be detectable due to overlap of Al-O(H)-Al stretches with that of Si-O(H)-Si and Si-O(H)-Al, and -Al-O-Alstretches with Si-O-Al. This data is included and discussed in the ESI † (S10 and S11).
If the proposed post-synthetic techniques or alternative synthetic strategies are successful in realising zeolites with NL framework aluminium distributions, as predicted by this work, these materials would be potentially invaluable for the development of new zeolite catalysts. Despite the advantages of using zeolites in catalysis, for example, specicity and size exclusion properties, it is well documented that the catalytic efficiency of microporous materials is oen limited by restricted access to active sites. Introducing ordered, controllable meso-and macroporosity to the framework provides a solution to mass transport limited diffusion through the porous zeolite network. The introduction of hierarchy has also been shown not only enhance catalytic activity, but also stability in a range of zeolite frameworks. A variety of both bottom-up and top-down strategies have proved successful for hierarchically ordered zeolite synthesis. The post-synthetic introduction of mesoporosity by the extraction of framework atoms is a particularly popular method, and can be achieved by acid, base or steam treatment of the zeolite material. 48,49 One can imagine how techniques such as these could be used to dealuminate low-silica aluminium cluster-containing materials, similar to those predicted in this work. For example, removing all four alumina units in the 4 Al per unit cell H-SSZ-13 global minimum structure predicted by DFT would increase the 7 A, 8-ring aperture cavity system, with a void-space of approximately 10Å in diameter, to up to 17Å, approaching mesoporosity. Crucially, the calculations indicate that not only is aluminium clustered, but it is also located in predictable, ordered positions, which suggests that introduced porosity via selective dealumination could be controllable in H-zeolites.
The reaction mechanisms and deactivation pathways of real catalytic zeolite materials is relatively a poorly understood area of zeolite science, not withstanding remarkable recent advances. 50,51 In part this is due to a lack of molecular-level information concerning the location of framework alumina and associated counter-cations, which are thought to be integral to the catalytic reaction mechanism. Clustering of aluminium and the associated clustered acid sites, as predicted by the DFT results, is suggestive of new, potentially more reactive sites (due to the density of acid sites) and new reaction pathways which have not yet been considered. Perea et al. have shown that the Si/Al distribution can be inhomogeneously distributed throughout the zeolite framework, 4 furthermore, silicon islanding (formation of silicon rich regions that must also give rise to aluminium rich areas) has been shown to be present in SSZ-13's silicoaluminophosphate counterpart SAPO-34. 52 Hence, it is conceivable that aluminium cluster motifs, including non-Löwensteinian linkages already exist in real zeolite materials, and may impact reaction and deactivation pathways operating in current catalysts.
The realisation of zeolite materials with contradistinct aluminium distributions to those synthesised by traditional routes holds enormous potential for the future of zeolite catalysis. We hope this work stimulates experimental investigation into the direct or post-synthesis of non-Löwensteinian ordered zeolites and further characterisation of existing materials.
Methods
The majority of the periodic DFT calculations were performed using the CP2K code, 29-31 and additional benchmark calculations for energetics and solid-state NMR were performed using the CASTEP code. 53 Results were calculated using the PBE 32 functional, although further calculations using revPBE 38 and BLYP 39,40 were included to verify our initial 2 Al per unit cell SSZ-13 ndings. These calculations, and methods, are discussed in detail in the ESI, † along with a full description of the single-point energy PBE0 (ref. 34 and 35) calculations mentioned in our Results and Discussion. All framework structures were obtained in their all-silica form from the database of zeolite structures, 28 and permutations of 2, 3 and 4 Al per unit cell models created by the methodology discussed in the main body of the text. Individual models were fully geometry optimized to equilibrium density, with variable lattice parameters in CP2K as 1 : 1 : 1 cells using the high quality TZV2P basis set and an energy cutoff of 650 Ry. Only the ABW framework was optimized as a 2 : 2 : 2 supercell, due to its small unit cell size. We also tested a selection of larger 2 : 2 : 2 supercells for each of the frameworks, although we saw no meaningful change in the relative energies using the larger cells. Additional computational details are included in the ESI. †
Conflicts of interest
There are no conicts to declare. | 7,025.2 | 2016-12-13T00:00:00.000 | [
"Chemistry"
] |
Unaccusativity and the syntax of imperatives in East Circassian
This paper presents novel evidence for the syntactic distinction between unergative and unaccusative verbs in East Circassian (or Kabardian). The evidence concerns a particular strategy of forming imperatives – simultaneous causativization and reflexivization – which is only applicable to unaccusative predicates. I argue that this type of imperative involves the promotion of the internal argument to the a higher position through the use of the causative morpheme which has been grammaticalized to mark imperative mood. The observed patterns suggest that imperative mood, while generally associated with the CP-layer, must be sensitive to the structure of vP.
1. Introduction.This paper addresses the syntactic distinction between unergative and unaccusative verbs in East Circassian, a language that has not been previously observed to draw such a divide.The evidence for unaccusativity comes from an unlikely source -the morphology of imperative mood.In particular, unaccusative verbs may form a special type of imperative that is unavailable for unergative verbs.This imperative form involves the transitivization of the verb via a synthetic causative morpheme and reflexivization of the causee.An example of this imperative form can be seen in ( 1) 1 -I will refer to this form as the reflexive causative strategy of imperative formation throughout this paper.
(1) z-o-m@-Ke-g w @bẑ REFL.ABS-2SG.ERG-NEG-CAUS-be.angry'Don't be angry (lit.don't make yourself angry)' Importantly, despite both the causative and reflexive morphemes being highly productive in the language, this particular construction is only available in the imperative mood.I argue that the limitation of this form to unaccusative verbs is due to the selectional properties of the imperative head involved: (i) it selects VP as its complement and licenses an external argument specifier via ergative case assignment, but (ii) it does not introduce a new θ-role.This combination of properties necessitates the recycling of the internal argument of an unaccusative verb through reflexivization and restricts the use of this head to unaccusative predicates.The sensitivity of an imperative mood head to the internal structure of VP in East Circassian calls for locality between the imperative head and VP, thus challenging the longstanding assumption that imperative force is introduced in the periphery of CP.
East Circassian is uniformly ergative in both case assignment and verbal agreement, drawing no distinction between intransitive verbs with an agentive or patientive θ-role.Thus, both an unergative verb like dek .
w -a 3ABS-COM-go-PST 'The girl got married (lit.went with s.o.).' (3) ps@-r water-ABS Ø-ŝt-a 3ABS-freeze-PST 'The water froze.'Well-known diagnostics for unaccusativity such as resultative constructions have yet to be tested in the language2 , while other standard diagnostics such as auxiliary selection and impersonal passive constructions (Levin & Rappoport Hovav 1994) are not applicable in East Circassian.Thus, the imperative construction presented here is the only documented diagnostic for syntactic unaccusativity in the language.
The remainder of the paper is structured as follows.Section 2 presents the reflexive causative strategy of marking imperative mood and discusses its distribution.Section 3 accounts for the restrictions on the distribution of this construction, arguing that the selectional features of the imperative head involved limit its usage to unaccusative predicates.Section 4 discusses the implications of the presented data for our understanding of imperative syntax.Section 5 concludes.
2. The pattern.This section outlines the distributional properties of the reflexive causative imperative form.I show that the use of this form is restricted to intransitive predicates that entail affectedness on the part of their sole argument, i.e. a class of predicates that have been documented to behave as unaccusative verbs cross-linguistically (Arkadiev 2008).
MORPHOLOGY OF IMPERATIVE MOOD.
In East Circassian, imperative mood is characterized with a particular morphological profile: (i) the lack of overt TAM morphology; (ii) the omission of second person singular agreement morphology in the absence of negation; (iii) prefixal negation (as opposed to suffixal negation in the indicative mood) (Kumakhov 2006).Examples of imperative forms can be seen below.The imperative form of qj@w@ve-'stand' with a singular second person addressee (4a) is contrasted to the same verb in the indicative mood (4b): in the former case overt agreement with the subject is impossible, in the latter case it is obligatory.Subject agreement on the imperative form is overt if the subject is plural (4c), or in the presence of negation (5a).Note also that negation in the imperative mood is expressed via the prefix m@-(4c), as opposed to suffixal negation -q@m in the indicative mood (5b).
(4) a. sjaw@ž' 1SG.PP+after (*w@-)q-j@-w@ve (*2SG.ABS-)DIR-LOC-stand 'Stand behind me!' b. we you sjaw@ž' 1SG.PP+after *(w@-)q-j@-w@v-a 2SG.ABS-DIR-LOC-stand-PST 'You stood behind me.' c. sjaw@ž' 1SG.PP+after f@-q-j@-w@ve 2PL.ABS-DIR-LOC-stand 'You(pl) stand behind me!' (5) a. m@Per@se apple Ø-*(w@-)m@-š'x 3ABS-2SG.ERG-NEG-eat 'Don't eat the apple.' b. a-r DEM-ABS ŝ@-s-a LOC-sit-PST parj@ nothing Ø-j@-š'x-a-q@m 3ABS-3SG.ERG-eat-PST-NEG 'He sat and didn't eat anything.'2.2.REFLEXIVE CAUSATIVE STRATEGY.In addition to the unmarked imperative form described above, for a number of intransitive verbs the imperative mood may be expressed via the use of the causative morpheme Ke-.In this case the second person subject is promoted to the position of the ergative causer, while the causee is expressed as the absolutive direct object that is coindexed with the causer and thus marked with the reflexive morpheme z@-(6b).For the surveyed verbs, this form is never obligatory and exists alongside the regular unmarked imperative form.Examples of verbs that may form this type of imperative are g w @bẑ@-'be angry' and X w @ž'@-'get well (lit.become again)': in (6a) and (7a) we can see the regular unmarked imperative form; this is contrasted with (6b) and (7b), where a causative morpheme Keis added and the reflexive morpheme z@is used to mark the causee in the absolutive position.The unmarked form and the reflexive causative form are interpreted as synonymous by speakers and are deemed acceptable in identical contexts.
REFL.ABS-CAUS-become-RE
'Get better (lit.make yourself become again) soon!' Besides the addition of the causative and reflexive morphology, the morphosyntactic properties of this form are identical to the unmarked imperative: the same prefixal negation m@is used (6b), and second person singular subject agreement is dropped in non-negated forms (7b).
Notably, this strategy is not available for all intransitive predicates.For example, the unergative verbs g w e-'yell' and qefe-'dance' are incompatible with the reflexive causative imperative form (8a), (9a); only the unmarked imperative form may be used in this case (8b), (9b).
(10) z@-Ke-hez@r REFL.ABS-CAUS-ready 'Get ready (lit.make yourself ready)!' (Standard East Circassian;Kumakhov 2006:223) However, my data suggests that this form is not in fact restricted to stative predicates.The trademark property of dynamic predicates in East Circassian is prefixal present tense marking me-(word-initially) / o-(word-internally) (Kumakhov 2006:158); based on this criterion several of the predicates that may form the reflexive causative imperative are in fact classified as dynamic.For example, the verbs s@meŽe-'be sick' and qjex w ex w @-'fall' may form the reflexive causative imperative (11), ( 12) despite the fact that they both take the dynamic present tense prefix me-/o-(13)-( 14).
REFL.ABS-DIR-2SG.ERG-NEG-CAUS-fall
'Don't fall (lit.don't make yourself fall).' 3 The causative morpheme is expected to take the form Kahere and in the following example due to a regular phonological alternation: /e/ → /a/ in the penultimate syllable of a stem that ends in the sequence CeCe (see e.g.Kumakhov 2006:58-59;Bagov et al. 1970:32-33).This alternation within the causative morpheme Kecan be seen below: (1) haq w @ŝ@q w @-xe-r dishes-PL-ABS m@-thaŝ .@ž'-a-we NEG-wash-PST-ADV qe-v-m@-Ka-ne DIR-2PL.ERG-NEG-CAUS-stay 'Don't leave (lit.make stay) the dishes unwashed.' (13) zeč .'exerj@ all.PL.ABS Ø-me-s@maŽe 3ABS-DYN-be.sick'Everyone is sick.' ( 14) Ø-q-o-x w ex w 3ABS-DIR-DYN-fall 'S/he is falling.'Thus, the stative-dynamic distinction is not the relevant criterion for defining the distribution of the reflexive causative imperative.Rather, the generalization is that this form may only be used with unaccusative verbs.The distribution of the reflexive causative is summarized in (15): the left column lists the verbs for which this form is available; the right column lists verbs which may not form this type of imperative.
(15) REFLEXIVE CAUSATIVE: *REFLEXIVE CAUSATIVE: š'@ne-'to be afraid' ž'jej@-'sleep' X w @-'become' š'@s@-'sit' X w @ž'@-'get well' pseńe-'speak' K w @bẑ@-'be angry' g w e-'yell' pŝ .ent .e-'sweat' qefe-'dance' s@meŽe-'be sick' ŝt@-'freeze' qjeX w ex w @-'fall' X w ebeŝe-'overheat' As can be seen from the list of verbs presented in (15), the verbs that form the reflexive causative imperative all semantically entail affectedness of the individual they are predicated over, i.e. they can be classified as affective or patientive.In many languages this class of verbs forms a uniform morphosyntactic class in terms of e.g.subject case marking (Arkadiev 2008).In accordance with the widely assumed Unaccusative Hypothesis (first introduced by Perlmutter 1978), the sole argument of such verbs originates as an internal argument within VP (16); these verbs are generally classified as unaccusative.Unaccusative verbs are opposed to agentive, or unergative, verbs, which select for an external argument in a higher position -in Minimalist terms -in Spec,vP (17); see e.g.Harley (2011).Thus, the reflexive causative imperative is only possible for unaccusative verbs, i.e. verbs which take a sole internal argument.( 16) vP
DP
It is important to note that outside of this construction, both causative and reflexive morphology is productively used with all types of verbs.For example, in (18) we can see the causative morpheme Keused with the unergative verb ž'jej@ 'sleep', which, as we saw in (15), may not form the reflexive causative imperative.
'Give up (lit.shelter yourself from) sweets!' However, despite the widespread use of both causative and reflexive morphology, the two are not productively combinable as in the reflexive causative imperative form.In particular, the coindexation of the causer with the causee in a synthetic causative is not acceptable, even for the class of unaccusative verbs listed in (15).For example, while the verb g w @bẑ@-'be angry' may form the reflexive causative imperative (6b), this same form (with the causee and causer coindexed via reflexivization) cannot be used in the indicative mood (20a).Importantly, the use of the causative morpheme is perfectly acceptable in the absence of a binding relationship between the causer and causee, as can be seen in ( 20b), where the absolutive causee is referenced on the verb with regular third person morphology and is interpreted as non-coreferent with the causer.
CAUS-
g w @bẑ be.angry -a -PST 'S/he i angered him/her j/*i .'Thus, the reflexive causative construction, i.e. the use of the causative morpheme Keto introduce a causer that is coreferent with the causee, is only possible in the imperative mood.This leads us to conclude that the reflexive causative form is a strategy of marking imperative mood for unaccusative predicates.
To conclude this section, the reflexive causative form is acceptable (i) only in the imperative mood and (ii) only with unaccusative verbs.In the following section I propose an analysis that accounts for these two restrictions: the causative morpheme in this construction is in fact the spellout of the functional head responsible for imperative formation, and its distributional restrictions are a consequence of its selectional properties.
3. Unaccusative imperative: an analysis.I argue that the distributional restrictions of the reflexive causative imperative form are derived from the semantic and syntactic properties of the morpheme Ke-.In particular, the causative morpheme Kein this construction has grammaticalized to mark imperative mood and is thus stripped of its causative semantics; consequently, it does not involve the introduction of an agentive θ-role.On the other hand, this head has retained its causative syntax: it is a v 0 head that assigns ergative case to its specifier.The restriction to unaccusative verbs is a consequence of the fact that this head selects for VP, combined with the two properties listed above: the lack of agentive semantics and presence of external-argument licensing syntax.In particular, since Kedoes not introduce its own DP, it must assign case to the internal argument within VP.Unergative predicates are then incompatible with this head due to the lack of an internal argument.
3.1.-Ke IS AN IMPERATIVE HEAD.As we saw in section 2, the reflexive causative construction is only used in the imperative mood -outside of this context, the coindexation of the causer and causee of a causativized predicate via reflexivization is unacceptable.This raises two questions: (i) why is the causative reflexive construction unacceptable in non-imperative contexts, and (ii) why is this construction acceptable in the imperative mood?I propose the following answer: the coindexation of the causer and causee in a causative construction is anomalous due to the semantics of the causative head; in the reflexive causative construction, on the other hand, the causative prefix Keis not in fact functioning as a causative head, but has grammaticalized to mark imperative mood.
According to Pylkkänen (2008), the primary function of a causative functional projection Cause 0 is to introduce an additional event of causation.Since the causative morpheme in East Circassian always involves the introduction of an ergative causer, this head is bundled together with the external argument licensing Voice 0 /v 0 projection.Thus, in its causative use, the morpheme Kefulfills two functions: (i) the introduction of an event of causation and (ii) the introduction of an agentive θ-role relating to this event ( 21).
(21) CAUSATIVE Ke 1 -: Cause 0 + v 0 a.Cause 0 : introduces an event of causation b. v 0 : introduces an external θ-role for the causer Following Legate's (2008) analysis of ergative case as inherent, I assume that ergative case in East Circassian is assigned to the external argument by the head that introduces it, i.e. v 0 .This head is also the locus of φ-agreement with the ergative DP, which is in most cases exponed overtly on the predicate (see e.g. ( 20b)).In a causative construction, then, the syntactic job of the causative head Ke 1 -is to license the external argument via ergative case assignment and agree with this argument in φ-features (22).( 22) To summarize, the causative head Ke 1 -has three main functions: (i) the introduction of a causing event, (ii) the introduction of an agentive θ-role for the causer, and (iii) ergative case assignment and agreement in φ-features with its specifier.
The reflexive causative imperative form, unlike a regular causative construction, does not carry any clear causative semantics -speakers generally use these forms interchangeably with the unmarked imperative and cannot readily identify any difference in meaning.I propose that the reason for this lies in the fact that the marker Kein this construction has in fact been bleached of causative semantics, and has come to instead denote an imperative mood head (23). 423) IMPERATIVE Ke 2 -= IMP 0 (Imperative operator) While there are not many mentions of a grammaticalization path from causation to imperative mood, functional motivations for such a path have been noted.In particular, Gusev (2005) argues that imperative constructions are a type of causative construction -a performative one.Subsuming imperative mood under the class of causative constructions is motivated by the fact that the functional role of an imperative speech act is to "cause an event to be realized" (Gusev 2005:16).5 It is also worth noting that causative morphology is cross-linguistically often used to mark hortative (1 st person imperative) mood -a subtype of imperative mood (Xrakovskij 2001).
Semantically, then, this form has nothing in common with the homophonous causative head described in (21): it does not introduce a causing event, nor does it assign an agentive θ-role.The difference in distribution between this form and the regular causative head then stems out of this difference in semantics: in particular, the introduction of a causer that is coindexed with the causee is semantically anomalous in a causative construction.The source of this anomaly is not fully clear, although it is likely to stem out of the particular type of causation the causative head denotes. 6This ban on coreference between the external and internal argument (corresponding to the causer and causee respectively for the regular causative construction) is absent for the imperative Ke 2 -simply because this form does not carry the causative or agentive semantics of the regular causative head.
3.2.IMPERATIVE Ke-ASSIGNS ERGATIVE CASE.Note that, despite the lack of causative semantics, imperative Ke 2 -morphosyntactically resembles a regular causative head: it appears to increase the valency of the verb it attaches to by introducing an ergative external argument; the φ-features of this external argument are exponed on the predicate via regular ergative agreement.Thus, the unmarked imperative form of an intransitive verb like pŝ .ent .e-'sweat' licenses just a single internal argument (24a), while the reflexive causative counterpart licenses two arguments: the internal one and an external argument, which triggers 2 nd person singular agreement on the predicate (24b).'Don't get sweaty (lit.don't make yourself sweat).' An important property of this construction, however, is the coreference relation between the core internal argument and the external one that is licensed by the imperative Ke 2 -.Thus, while syntactically there are two DPs, both of which are assigned distinct case values (the internal argument -absolutive case, the external one -ergative case), semantically they refer to a single participant.Thus, while imperative Ke 2 -assigns ergative case, it does not introduce a new participant, but merely assigns it to the one that is already present in the structure.The reason for this unusual behavior is that, despite the shift in semantics, the imperative Ke 2 -is syntactically still v 0 , i.e. it has retained the syntactic properties of the regular causative head Ke 1 --in particular, the ability to assign ergative case to its specifier and agree with its specifier in φ-features.Thus, the imperative Ke 2 -is merged into the structure above the unaccusative VP and triggers the raising of the internal argument to its specifier position for ergative case assignment and φ-agreement (25).( 25) At first glance, such a divorce between inherent case assignment and θ-role licensing is problematic, given that inherent case is defined as "inherently associated with certain θ-positions" (Woolford 2006:112).However, despite lacking a semantic θ-role, the position that is assigned inherent ergative case by imperative Ke 2 -is nevertheless a "θ-position" in the sense that it is the specifier of v 0 -a functional head that is generally responsible for the θ-role of the external argument.
REFLEXIVIZATION AS REPAIR.
We have established that the reflexive causative imperative involves the use of an imperative head which is equivalent phonologically and syntactically to the causative head Ke 1 -, but is semantically distinct from it in that it does not introduce semantics of causation, but rather marks imperative mood.The last ingredient to the reflexive causative is deriving the reflexivization of the internal argument.Since the movement of the internal argument to Spec,vP is very local -within the boundaries of vP -the reflexivization of the lower copy can be seen as a repair of movement that is too local, which is a violation of the Anti-Locality Constraint (Grohmann 2003).This constraint states that a movement chain must be sufficiently long, in particular, a moved constituent must not land within the same syntactic domain as its lower copy.The relevant syntactic domains are roughly equivalent to phases -in Grohmann's (2003) terms they are called Prolific Domains.vP is such a domain: the internal argument in a reflexive causative construction is raised to a position within vP, giving rise to an Anti-Locality violation, which is then repaired via reflexivization.
INTERIM SUMMARY.
To summarize this section, the reflexive causative imperative is formed via the use of the imperative Ke 2 -, a functional head that has grammaticalized from the corresponding causative morpheme to mark imperative mood.This head has lost causative semantics and thus does not license an external θ-role.It has, however, retained the syntax of causative v 0 in that it enters and agreement relationship with and assigns ergative case to its specifier.In order to assign case, this head triggers the raising of the internal argument from within VP to its specifier.This brings about a violation of the Anti-Locality Constraint and thus gives rise to reflexivization of the lower copy.
This analysis explains the restriction of this construction to the imperative mood and the lack of causative semantics in this type of imperative, as well as presents a basis for the reflexivization pattern.The following section outlines how the analysis proposed in this section can account for the restriction of the reflexive causative strategy to unaccusative verbs.
3.5.DERIVING THE UNACCUSATIVE RESTRICTION.The imperative Ke 2 -is only compatible with unaccusative predicates, i.e. predicates with a sole internal argument, due to its selectional properties.In particular, this imperative head selects for VP.Combined with the case-assigning properties of this head, this ensures that the only type of predicate the imperative Ke 2 -may combine with is one with an internal argument within VP, but no external argument, i.e. an unaccusative predicate.Below I outline why the imperative Ke 2 -is incompatible with (1) unergative verbs and (2) transitive verbs.
* IMPERATIVE Ke 2 -+ UNERGATIVE VERBS:
The imperative Ke 2 -cannot combine with an unergative VP, because this type of constituent does not contain an internal argument.The lack of an internal argument in VP means that there is no DP within this projection to assign ergative case to, since the imperative -Ke 2 does not license a θ-role of its own -the constructed vP then lacks a core DP whatsoever.
We can see what the hypothetical structure of imperative Ke 2 -+ ž'jej@-'sleep' would look like in (26): there is no DP for imperative Ke 2 -to assign ergative case to or to agree withsuch a derivation would fail to converge.The imperative Ke 2 -is incompatible with transitive VP for the same reason why transitive verbs cannot generally be used in the absence of an external θ-role, either overtly expressed or existentially bound, as in passives. 7Given the decompositional approach to argument structure in Minimalism, where the external argument is introduced outside of VP, it is not fully clear how to structurally implement this constraint, but it is considerably more general than just a constraint on the combinatory properties of imperative Ke 2 -: transitive verbs may generally only be used in the presence of an external θ-role.A simple implementation of this constraint would be to simply specify the selectional properties of imperative Ke 2 -so that it only selects for a VP headed by an unaccusative predicate, i.e. one that is generally not combinable with an external argument.
To summarize, imperative Ke 2 -is a type of ergative-assigning v 0 which selects for a VP with an internal argument.This VP must be headed by a predicate that does not need to be combined with an external argument.These selectional restrictions ensure that the imperative Ke 2may only combine with unaccusative predicates.
4. Implications.The existence of an imperative head like Ke 2 -has long-reaching implications for the theory of imperative syntax generally.In particular, within accounts that assume that imperative mood is represented in the syntactic architecture, the projection responsible for this semantic component is expected to merge high in the clausal periphery (see e.g.Rivero & Terzi 1995;Rizzi 1997;Han 1998;Zeijlstra 2006).The reason for this lies in the standard assumptions about the semantics of imperative force: "As Op IMP [the imperative operator -KE] encodes the illocutionary force rather than the propositional content of the sentence, it cannot be located below other functional projections" (Zeijlstra 2006:415).What this means is that operators like propositional negation cannot take scope over imperative force, i.e. a negative imperative sentence like (27a) can only be rephrased as (27b), with negation taking lower scope than directive force (expressed here as 'I request/order that X'), but not as (27c), where negation takes scope over the directive force.The imperative head Ke 2 -, on the other hand, must select for an unaccusative VP and thus merge very low -significantly lower than NegP, where negation is assumed to be introduced (see e.g.Zanuttini 1997;Giannakidou 1998).Thus, the reflexive causative imperative construction provides a challenge for the syntax-semantics interface: a functional head must be merged low, but interpreted high.
This type of conflict at the syntax-semantics interface, however, is a well-attested one.Examples of such phenomena include Quantifier Raising8 : quantifiers are assumed to covertly raise (syntactically or at LF) in order to take scope over syntactically superior DPs and operators such as negation.Another domain where such a mismatch has been observed is comparative constructions: degree phrases have been argued to undergo covert extraposition in order to achieve the proper scope configuration (see e.g.Heim 2000).
This leads us to conclude, following Zanuttini et al. (2012); Portner (2016), that when it comes to imperative force, the mapping from syntax to semantics need not be a direct one, i.e. imperative force need not be interpreted in the position where it is syntactically introduced.The particular implementation of this remains undetermined: the imperative head may raise covertly to take wide scope, or perhaps illocutionary force is imposed on the utterance pragmatically, rather than through propositional semantics, as argued e.g. by Condoravdi & Lauer (2012).I leave the resolution of this question to further research.
Conclusion.
The reflexive causative strategy of forming imperatives in East Circassian is only available for unaccusative predicates.This strategy involves the use of an imperative head that has grammaticalized from the causative marker Ke-.In the process of grammaticalization, this head has shifted semantically from introducing a causing event and external θ-role to marking imperative mood.Syntactically, on the other hand, this imperative head has retained the caseassigning and agreement properties of the regular causative marker.This leads to an otherwise unacceptable coreference relation between the causer (ergative case-assigned DP) and causee (base position of the internal argument in VP).This imperative head is compatible only with unaccusative predicates due to the fact that (i) it selects for VP and (ii) this VP must contain a DP that is eligible for ergative case assignment.
This paper provides empirical support for the syntactic distinction between unergative and unaccusative verbs in East Circassian.Additionally, the sensitivity of an imperative mood marker to the internal structure of VP, namely the presence or absence of an internal argument, requires a low merge site for this imperative head, thus challenging the assumption that imperative force is introduced in the clausal periphery. | 5,990.6 | 2017-06-12T00:00:00.000 | [
"Linguistics"
] |
Extraterrestrial Metallic Iron in the Lacustrine, Epicontinental and Oceanic Sediments: A Review of Thermomagnetic and Microprobe Analyzes Data
Particles of metallic iron are often found in sedimentary rocks, but concentration is normally very low. Metallic iron in deep-water ocean sediments is usually considered to be of extraterrestrial origin [1-3]. However, many sediments contain iron particles related to volcanic activity, bacterial activity, and metamorphism etc. Therefore, it is important to find signs of metallic iron of extraterrestrial origin.
Introduction
Particles of metallic iron are often found in sedimentary rocks, but concentration is normally very low. Metallic iron in deep-water ocean sediments is usually considered to be of extraterrestrial origin [1][2][3]. However, many sediments contain iron particles related to volcanic activity, bacterial activity, and metamorphism etc. Therefore, it is important to find signs of metallic iron of extraterrestrial origin.
In recent years, we have studied the spreading and composition of metallic iron particles in the Pleistocene lacustrine sediments of the Darhad Basin, northern Mongolia, in the Upper Miocene sediments of Lake Baikal, in epicontinental sediments of Miocene, Oligocene, Eocene, Cretaceous, Late Jurassic, and Early Cambrian age in different regions of North Eurasia and in ocean sediments of the North-Western Atlantic [4][5][6][7][8][9][10]. This article represents a result of a review and generalization of thermomagnetic and microprobe analyzes data for mentioned above articles and regions.
Investigation Technique
Thermomagnetic analysis (TMA) was carried out in the Paleomagnetic Laboratory of the Geological Department of Kazan State University, using Curie express balance (D.M.Kuzina is measurement executor). It included measurement of the specific magnetization of samples in the magnetic field of 200-500 mT at room temperature (M 20 ) and its temperature dependence M(T) up to 800°C. The heating rate was 100°C/min. The obtained thermomagnetic curves were used to determine the Curie temperatures (T c ) of magnetic minerals in the samples. The accuracy of determination of Curie temperature is ~5-10°C. To evaluate the content of magnetic mineral in the sample, an M(T) curve was extrapolated from each Curie temperature to room temperature to determine the specific saturation magnetization of mineral with a given Curie temperature. The ratio of the obtained magnetization to the known saturation magnetization of the mineral is the content of this mineral in the sample [11]. The accuracy of this estimation of the mineral content is rather low, but this is not significant on the background of fluctuations in the contents of metallic iron within several orders of magnitude.
Microprobe analysis (MPA) was carried out in the Borok geophysical observatory, Institute of Physics of the Earth RAS (V.A.Tsel'movich is measurement executor), using a Tescan Vega II microprobe with an energy dispersive spectrometer. Operation conditions: accelerating voltage 20 kV, current 0.2 nA, beam diameter ~0.2 μm, and analyzed zone length 1-2 μm. The MPA measurements were made in polished sections, and magnetic fractions. The content of the metallic iron are very low in the sediments, so the magnetic fraction extracted and measured. The samples were ground and sonically dispersed, and their magnetic fraction was separated with a permanent magnet. The fraction was applied over a carbon double-sided adhesive tape and rolled with a glass rod to make the particle surface oriented parallel to the table surface.
TMA and MPA complement each other. In many cases, the magnetic minerals detected by TMA are not identified by MPA and vice versa. Since the TMA was conducted on a small piece of the rock while the MPA handled the magnetic fraction from another piece of the same sample. pure (Figures 4 and 5). Only a minor part of samples contains metallic iron with Ni, Cr and Si impurities, particles of FeCr alloy containing 10-15% Cr and particles of more complex composition, for example FeCrNi alloy containing Cr, 15-17%; Ni, 10-12%. There are also magnetite balls, apparently, of extraterrestrial origin ( Figure 5) [7].
For study, the sediments were sampled from the lower 500-600 m of the borehole BDP-98. They formed in Miocen age at the paleodelta of the Barguzin River and were characterized by a high rate of accumulation 7-13 cm/ kyr. The studied section is rather uniform by all magnetic parameters. Particles of metallic iron are identified by T c =710-770°C; they are extremely rare in the studied sediments and are chaotically distributed ( Figure 6). Such particles were reliably detected in only five samples. The content of iron is lower than 10 -3 % ( Figure 6).
The distribution of iron content is bimodal, with a distinct "zero" mode ( Figure 7). This regularity does not depend on the lithology of sediments and the redox conditions of their accumulation (e.g., the presence or absence of pyrite). Zero groups are absent and distribution is unimodal for terrestrial magnetite from the same rocks ( Figure 7). Scarcity of metallic iron in the Baikal sediments distinguishes them from continental (Eurasia) and oceanic (Atlantic) sediments of different
Results of TMA and MPA
According to TMA and MPA data in all studied samples there are unevenly distributed throughout sediments: 1) magnetite and cationdeficient magnetite (T c =575-650°C) is ubiquitous magnetic mineral, and main part of sample magnetization (M 20 ) (correlation coefficient is 0.94); 2) iron hydroxides, such as goethite (T c =80-150°C, which disappears on the second heating; its portion in M 20 is <5%); 3) most of the studied samples show magnetization growth at >500°C, expressed as a "pyrite" peak caused by the oxidation of Fe-sulfides (pyrite, pyrrhotite and hydrotrolite) to magnetite [12,13]. Relatively low correlation between the contents of magnetite and pyrite (its peak height) suggests the independent formation of these minerals. Magnetite is mainly a terrigenous mineral, which got into the sediments independently of their redox conditions, and pyrite is mainly an authigenic mineral formed in the sediments under reducing conditions. 4) Hematite (T c~6 75°C) is present in many samples but in a very low contents. 5) Metallic iron particles present everywhere in all deposits, but in very low contents. Further article analyzes the behavior of metallic iron in the sediments of different regions [6].
Metallic iron particles are extremely scarce in the studied sediments and are chaotically distributed (Fig. 1). Iron was reliably determined only in 26 samples. The content of iron is usually lower than 10 -3 %. Relatively high iron contents are observed in the depth ranges 64.73-68.73 and 83.20-87.07 m (Figure 1), the presence of iron and its content correlate neither with the height of the pyrite peak (correlation coefficient is 0.08) nor with the content of magnetite (correlation coefficient is -0.11, Figure 2), i.e., do not depend on the redox conditions in the sediments. A group of samples lacking iron particles (the so-called "zero" group) include 79% of the studied samples, if all unreliable data on the presence of native iron are used for the estimation, and 90%, if only the reliable data are taken into account ( Figure 3a). And zero group absent for terrestrial magnetite (Figure 3b). For detailed MPA investigation of metallic iron particles and other minerals, we chose nine samples.
According to the MPA data, all five studied samples contain particles of pure iron (Figures 8a-8e); seldom, Si impurity ( Figure 8b) and noticeable Cr impurity (Figures 8f-8k) occur. The iron is oxidized. We think that iron oxidation takes place when extraterrestrial particles pass through the Earth's atmosphere.
For study, the Pleistocene-upper Kimmeridge sediments were sampled from the DSDP boreholes 386, 387, 391A and 391C. Deposition was predominantly continuous; the rate of sedimentation varied from 0.2 to 4.7 cm/kyr. Particles of metallic iron are ubiquitously present in the studied sediments. Their concentrations are nonuniformly distributed (Hole 391A), and the highest are revealed in the lower Berriasian-lower Valanginian sediments (Hole 391C). Against a common background, locally increased concentrations of iron (up to 10 -2 %) are observed. The shape of the histogram with a clearly pronounced zero group is a specific feature reflecting extraterrestrial nature of the accumulation of iron particles. It is important to note that this specificity doesn't depend on either the lithological features of the sediments or the redox conditions of their accumulation (for example, it is insensitive to the presence or absence of pyrite).
According to the MPA data (Figures 11a-11g), all samples contain particles of pure iron; seldom, Si, S impurity and noticeable Ni, Cr impurity occur. The iron is not infrequently oxidized. The average content of the Ni admixture is almost identical in all the studied sections: 6% (Hole 386), 5.8% (Hole 387), 4.7% (Hole 391A), and 6.4% (Hole 391C). These values are close to the average and modal Ni content in the particles of metallic iron from the epicontinental sediments of Eurasia (see section below). The form of iron particles is typical for all sediments ( Figure 11).
The role of redeposition of iron particles is assessed from the correlation between the concentrations of metallic iron and terrestrial magnetite+titanomagnetite in the sediments. It is found that the effect of redeposition is not observed only in the sediments from Hole 386 (r=-0.105). In the other holes, the coefficient of correlation is 0.28 (387), 0.439 (391A), and 0.307 (391C), which indicates that redeposition of this particles is real. The effect of redeposition is best pronounced in the Miocene deposits of gravitational flows in Hole 391A (where r=0.439), which are marked by the lowest concentrations of iron particles ( Figure 9). Obviously, together with the other magnetic minerals, rare particles of iron (both of terrestrial and extraterrestrial origin) were occasionally carried to these carbonate oozes, which were redeposited from the Blake Plateau by geologically instantaneous gravitational flows. In contrast, the most intense jumps in concentration are revealed in the intervals where the correlation between iron particles and other magnetic minerals is absent (Hole 386).
The composition and distribution of particles of native iron in eight sections of the Cretaceous-Danian sediments in the Caucasus, Crimea and Kopet Dagh were studied using TMA. The studied sediments are abundant with particles of metallic iron. The latter are identified in 330 of 571 studied samples in concentrations ranging from ~10 -5 % to 0.05%, and their distribution is bimodal ( Figure 12). "Unzero" group is characterized by lognormal distribution with the mode in the interval 0.04-0.15 × 10 -3 %. Intervals enriched with the iron particles were revealed in sediments of Seravalian (12-13 Ma), Santonian (84-86 Ma), and Cenomanian (94-96) age and at the Maastrichtian/Danian boundary (64-66 Ma) ( Figure 13) [9].
The iron content increases from west to east. The Cretaceous deposits of the Crimea are very poor in iron; the most is ≤ 10 -4 %. The Upper Cretaceous carbonate deposits of the Caucasus contain more iron: not infrequently attains 0.5-10 × 10 -3 % (Figures 13 and 14). The highest iron contents are observed in the East, in the Kara-Kala section, where it attains 0.05% (Figure 13). The appearance and accumulation of iron does not depend on the redox conditions in sediments, which is shown by the lack of correlation of iron with the presence of cationdeficient magnetite (the high-oxidizing conditions), on the one hand, and "pyrite" (the reducing conditions), on the other hand, in the sediments. T c= 680-780°C. A peak of the elevated iron content with nearly constant nickel of 5% was found in all studied sections, i.e., this is a global effect. There is no correlation between the concentration of iron particles and the nickel content in them (r=-0.024).The global pattern of the distribution and composition of the iron particles clearly indicates that their origin is associated with interplanetary dust. At the same time, the particles of Fe-Ni alloy and pure nickel are very rare, and Cambrian sediments in lakes, seas and oceans, different lithology and redox conditions. The concentration of particles varies widely-from none to 0.05%, mostly between 10 -5 and 10 -3 % (Figures 1, 6, 9 and 13 and the sum of all data on Figure 14 [4][5][6][7][8]). It is logical to associate with interplanetary dust.
2) The bimodal distribution of iron particle concentrations with a necessarily present and clearly expressed "zero" group of the samples, in which iron particles are absent (not detected by TMA). This feature stems from the limited amount of cosmic dust deposited on the surface of the Earth. It is a known fact that 1 m 3 of interplanetary space contains about 100000 particles of interplanetary cosmic dust. Therefore, upon deposition of cosmic dust onto the Earth's surface, only one of ten cm 3 contains such a particle, while iron particles are much rarer. The zero group is related to the parts of the sediments that do not contain any iron particles of cosmic origin. This trend is identified in all the studied sedimentary sequences (Figures 3, 7, 10 and 12) and, thus, it is global. This bimodal distribution of particles absent for terrestrial minerals, for example, magnetite (Figures 3, 7, 10 their concentration does not correlate with the content of iron particles. Most likely, the particles of Fe-Ni alloy are mainly due to impact events.
Discussion on extraterrestrial nature of metallic iron particles in terrestrial sediments
Our studies revealed a number of quite simple statistical indications pointing to the extraterrestrial origin of metallic iron in the sediments: 1) Widespread (global) distribution of metallic iron particles in sediments in different regions and ages, from the Quaternary to significant role of redeposition of native iron. It is the same in terms of the appearance of correlation. 4) Division metallic iron particles composition into three distinct groups. Particles of iron in their content of nickel impurities form three groups ( Figure 15): 1) Pure nickel-free iron, such particles form a separate group, 2) A group of Ni-containing iron with a mode 4-6% Ni, these particles are the most common metal in the meteorites and interplanetary cosmic dust. 3) Rare particles Fe-Ni alloy with a nickel content of >20% and mode of 50%.
The average content of the Ni admixture is almost identical in all the studied sections of sediments from the oceanic sediments of the NW Atlantic (Figure 15a), epicontinental sediments of Eurasia (Figure 15b). The global character of Ni content distribution in metallic iron is also highlighted by the similar pattern of histograms for sediments (Figures 15a and 15b) and Ni content in the metallic part of the meteorites (Figure 15c). Hence, we may conclude that the particles of metallic pure and nickelous iron in the meteorites have a common origin: both are products of the disintegration of planetary material. 5) The predominant particle size less than 100 microns ( Figure 16) corresponds to extraterrestrial particles that are preserved passing through the Earth's atmosphere, whereas for the earth particles there is no upper size limit [14,15]. 6) A negative correlation between the concentrations of iron particles and the rate of sedimentation. Against the scatter of the data, it is clearly seen that the zero group tends to increase with an increase in the sedimentation rate ( Figure 17). In particular, the [5,9] (c) a metal part of the meteorites [5,9]. N-the number of definitions. scatter of the data is controlled by the degree of redeposition of iron particles and their probable terrestrial origin, i.e., the situations when these particles participate in the accumulation of the sediments just as the terrestrial particles. In our case, this is reflected by the coefficients of the linear correlation between the concentrations of iron particles and magnetite of 0.3-0.6 [9]. In contrast to the general trend, at the points that are related to the redeposition (the open circles in Figure 17), the dependence of the size of the zero group and the rate of sedimentation vanishes. In the case of terrestrial native iron, we should expect the distribution to follow the Poisson zero-mode distribution, which is supported by the single-mode distribution of the magnetite content having knowingly terrestrial origin in the same sediments [9,10]. The absence of a correlation between the concentrations of terrestrial magnetic minerals (e.g., magnetite) and the rate of sedimentation is clearly seen in Figure 18. The coefficient of linear correlation is 0.032.
Сonclusions
Firstly, the main methodical result noted: the use of TMA to 800°C in combination with MPA allow for faster and easily obtain a quantitative evaluation of the content and composition of metallic iron particles in the sediments. Today thermomagnetic analysis is the only simple method to quantify the presence and distribution in sediments the magnetic particles including iron of extraterrestrial origin with high Secondly, we note the main result-the justification of extraterrestrial origin metallic iron particles in terrestrial sediments. It is the system of evidences: 1) Widespread (global) distribution of particles, 2) Bimodal particle content distribution with the obligatory distinct zero mode; 3) Lack of correlation between particles concentrations of iron and earth minerals as magnetite; 4) Three independent groups of metallic iron are identified by the content of nickel impurities: pure iron, iron with an admixture of nickel (kamacite), and Fe-Ni alloy; 5) Iron particle size is limited to 100 µm; 6) An inverse relationship between the concentration of iron particles and sedimentation rate. The totality of these factors clearly indicates the extraterrestrial nature of metallic iron particles. | 3,970.4 | 2016-09-26T00:00:00.000 | [
"Geology",
"Environmental Science"
] |
How can constraint-induced movement therapy for stroke patients be incorporated into the design of a tangible interface? The case study of the ‘Biggest Hit’
Abstract Stroke causes significant damage to the brain and often results in severe weakness on one side of the body. Survivors are likely to compensate for the loss of function through an increased use of the less affected arm and the nonuse of the affected arm. In some cases, this can be overcome through constraint-induced movement therapy (CIMT) by restraining the less affected arm to require the use of the affected arm when performing tasks. We report on the research and design of an interactive radio that facilitates CIMT at home. The usability of the design was assessed by stroke therapists. Feedback indicates that the radio is successful in restraining the movement while encouraging repetitive movement of the affected arm, but does not deliver CIMT fully. We highlight the opportunity to focus on the ‘part-task learning’ and ‘initiation’ components of CIMT for the design of a tangible interface for stroke rehabilitation.
Introduction
The worldwide burden of stroke is increasing and is a topic of particular concern in New Zealand. In 2012/2013 approximately 70 000 New Zealanders were diagnosed with a stroke (Ministry of Health, 2013), and only 30% of these were subsequently able to be independent in activities of daily living (ADL) (Bonita, Broad, & Beaglehole, 1997). Rehabilitation that aims to recover lost motor function is generally limited to the 12 months immediately following the stroke and the benefits of rehabilitation during the chronic stage following rehabilitation are unclear (Aziz, Leonardi-Bee, Phillips, Gladman, Legg, & Walker, 2008). In New Zealand the trend is to promote early hospital discharge and provide rehabilitation in the community setting or home environment (Stroke Foundation of New Zealand & New Zealand Guidelines Group, 2011). In addition, because of the success of medical interventions, increasing numbers of stroke survivors are living longer, with limited access to continued rehabilitation during their chronic recovery stage. Therefore, there is a demand for effective self-directed therapeutic systems. Constraint-induced movement therapy (CIMT) has proven to deliver positive outcomes during the chronic stage of stroke recovery but it requires rehabilitation therapists to provide direct oversight (MacKenzie & Viana, 2016). Developments in the use of digital technologies can facilitate rehabilitation following stroke (Jordan, Sampson, Hijmans, King, & Hale, 2011) and these are able to be applied to the chronic stage of stroke recovery. Using everyday objects that stroke survivors enjoy and are motivated to engage with offers the potential to deliver a meaningful form of self-directed rehabilitation. This case study presents the process and outcomes of a 'research-through design' method using an interactive radio with specified and controllable functionality with the therapeutic goal of requiring the stroke survivor to use their affected arm when using the device.
Figure 1. During CIMT the patient is asked to wear a mitt or a cast on the unaffected side
Stroke is a form of brain injury caused by lack of blood flow or oxygen delivery to parts of the brain, causing irreversible injury. It affects 15 million people annually. A third of those people die, while a further third is left with a persistent disability (McKay & Mensah, 2004). The impact on an individual depends on the location within the brain and the severity of the stroke (Mallory, 2006) and can manifest in both physical and psychological symptoms. Due to discrete brain cell damage, stroke survivors can experience unilateral motor impairment in the form of hemiparesis, which is weakened muscles, or hemiplegia, which involves paralysis of muscles (DePiero, 2011a(DePiero, , 2011b. Stroke survivors are likely to compensate for the lost motor function with enhanced movement of their less affected side. This self-taught behaviour drives neuroplasticity changes in the brain opposite to where the stroke occurred (Adkins, Bury, & Jones, 2002). This learned suppression of movement limits possible recovery that could be gained through rehabilitation of the affected arm (Allred, Maldonado, Hsu And, & Jones, 2005;Taub, Uswatte, Mark, & Morris, 2006). Constraint-induced movement therapy (CIMT) originated from research on primates, which demonstrated that restricting the use of the less affected arm overcame learned nonuse of the affected arm. Further studies have also demonstrated that this also applies to humans. The concept of learned nonuse is that a portion of the functional deficits is due not to damaged cells within the brain but to the development of compensatory movement . Initiating use of the affected arm is required to overcome this learned suppression of movement. During rehabilitation, the participant is forced to wear a mitt or cast on the less affected hand (Figure 1) while carrying out repetitive tasks designed to initiate the use of the affected arm and hand (MacKenzie & Viana, 2016;. The intervention can deliver positive outcomes but has been criticised by therapists for being expensive and resource intensive in clinical practice (Viana & Teasell, 2012). The original protocol requires 6 hours of training for 10 consecutive working days, during which the restraint needs to be worn for 90% of waking hours. Stroke survivors criticise the need to wear the physical constraint and the long therapy hours and see those factors as a main reason for not participating in CIMT (Page, Levine, Sisto, Bond, & Johnston, 2002).
Aim
The aim of this research is to design a tangible interface using a radio and digital technology to facilitate self-directed CIMT for chronic stroke patients with an affected arm.
In the next section, we describe the development of an interactive radio that incorporates the principles of CIMT to restrain the less affected arm to force the use of the affected arm. The two core elements of intensive practise and restraint of the less affected arm are focused on to overcome the learned nonuse (Taub et al., 1994).
Based on the principles of CIMT the following criteria were used for the development of the tangible interface (Ullmer & Ishii, 2000).
• The object encourages the use of the affected body side.
• The object induces a repetitive movement.
Task specific training that is used in the rehabilitation process often employs everyday tasks and real objects; for example, using conventional cutlery to practise eating (Hubbard, Parsons, Neilson, & Carey, 2009). The interaction with the radio described in this paper focuses on re-educating the user to carry out one particular movement: reaching and grasping. This movement is essential in ADL and relearned during the rehabilitation process with therapists. Carrying out this movement requires a combination of gross and fine motor skills involving shoulder rotation, forearm flexion and extension, wrist tangential velocity, global hand rotation, as well as hand pronation, supination, adduction and abduction (Fan, He, & Tillery, 2006).
The functionality of a radio was chosen based on the motor activity log (MAL) , which is a structured interview used within CIMT to determine tasks of everyday living that the participant can focus on. The radio can play an essential part in peoples' lives but if the user experienced difficulties interacting with it, a malfunction would not cause any harmful effect.
Incorporating enhanced repetition of the movement that leads to neuroplasticity in the brain is achieved by limiting the time that the radio plays music. The radio turns on when the affected arm interacts with it and turns off after a pre-set time interval. The user is required to interact repeatedly with the radio order to keep it working.
Research through design
An iterative research through design process was used for to develop the tangible interface 'The Biggest Hit'. The term 'research through design' was introduced in Frayling's pamphlet (Frayling & Royal College of Art, 1993). The author differentiates between research into design, research by design and research through design, but does not clearly define the latter. Dorst and Dijkhuis (1995) distinguish between two design research streams: design as rational problem solving and design as a reflective process. This correlates with Burdick's (2003) description of design research. Designers create new information through the process of making and the cycle of prototyping, testing, analysing, and refining the work in progress (Burdick, 2003). Burdick emphasises the fact that critical reflection is an essential part of design research practice. Designers must be able to articulate their questions and conclusions (Burdick, 2003). Kroes (2002) argues that despite its process-oriented nature design methodology needs to address the nature of products that are designed. In the context of this paper Burdick's description of design research will be used, where the cycle of prototyping is connected to the reflective process about those design outcomes ( Figure 2).
Figure 2. Iterative design process
To address the complex design problem of incorporating a rehabilitation intervention in the design of a tangible interface, different prototypes based on a trial and error basis were developed to validate ideas and guide further development. The prototypes helped to develop knowledge and convince other stakeholders (Toeters, ten Bhömer, Bottenberg, Tomico, & Brinks, 2012). The final prototype was evaluated by stroke therapists with clinical expertise in CIMT to validate its usability and delivery of CIMT. Arduino, a rapid prototyping tool, was chosen. The hardware and software components offer a fast development and iteration process. To restrain movement, the Arduino Uno needs to recognise which arm is used to interact with the object. Near field communication (NFC) can offer this recognition in the form of an NFC board that is attached to the Arduino and NFC tags that the user can wear on the affected arm and hand ( Figure 4). When the NFC tag is in close proximity to the radio, the Arduino and NFC shield (Figure 3) within the radio recognise the tag. The radio just plays music when the affected arm is used to interact with the radio.
Results
In the following sections 5.1 -5.7 we will present the design results and critical reflection that led to the final development of the 'The Biggest Hit' in chapter 5.8. CIMT requires a focus on the use of the affected arm. Different design concepts were generated based on a framework of product influence (Tromp, Hekkert, & Verbeek, 2011) ( Figure 5) to direct the behaviour of the user. The different concepts incorporate CIMT components to encourage and in some cases even force the user to interact with one specific arm and hand. The framework distinguishes between the two dimensions 'salience-force' and 'visibility-invisibility', forming four different categories of influence: coercive, persuasive, seductive and decisive. Design with a coercive influence is strong and explicit in its influence and extrinsic motivation causes the behaviour change.
Influence of the design
CIMT is often described as 'forced-use paradigm' in the literature (Wolf, Lecraw, Barton, & Jann, 1989;Wolf, 2007); therefore, an apparent and strong design influence in the form of restriction of use was chosen for the current study. The radio can only be turned on when the affected side is used for the interaction with the object. The concept of this paper prototype is that it just plays music when the user makes it bounce. When the top component is touched ( Figure 6) the radio is supposed to move and play music. The bouncing movement that the radio displays is one similar to children's toys. It gives the user an immediate indication about the movement quality, for example whether too much force was applied. Two paper prototypes were developed in a first step to test the interaction.
Prototype 01
Findings: The iteration indicated that paper prototypes were unsuitable for testing the interaction. The prototypes fell over easily and were too big, with a size of approximately 350mm x 250mm x 150mm.
Conclusion: The next iterations should be made out of solid materials to perform the bouncing movement and should be smaller to be easily carried around and stored in the house. The concept of this iteration (Figure 7) is based on an ellipse to increase the bouncing movement. The user has the opportunity to touch the entire top part of the radio in order to turn it on and make it move.
Findings: Because of the ellipse form is the movement of the object not as steady as the bouncing movement of the children's toy that was referred to as a precedent. The radio started rotating around its own centre after being hit the first time. The prototype was printed using a table top UP 3D printer and ABS material, causing a lot of noise during movement. A sleeve in the form of 5mm felt was added to muffle the noise created by movement. Situating the NFC reader that restrains the functionality of the device in the top rather than the bottom component increased the connectivity of the device.
Conclusion: The form of the radio should be based on a complete circle to secure a smooth movement. The weight is required to be as low as possible to ensure a smooth movement and to prevent the object from falling over. The electronics need to be carried in the top component, which is the activation zone to start the radio.
Figure 8. Prototype 03 with a wooden top part and ceramic base
This iteration of the radio shows a slimmer design while the materials of the object relate more to objects that are used in the home environment: wood and ceramics.
Findings: The design shows stable movement due to the heavy weight at the top. The top component did not provide sufficient space to house the NFC board, Arduino Uno and radio board (130mm x 55mm x 20mm). During bouncing, the radio can potentially fall to the ground and the ceramic material would easily break.
Conclusion: The heavy weight of the base component provides a stable and smooth movement. The top component needs to be adjusted to house the electronics, requiring increased space inside the radio. For the fourth iteration (Figure 9), the top component was changed to accommodate all the required electronics. A tactile surface that is clearly visible on the top of the radio is designed to indicate and direct the user's interaction with the object.
Prototype 04
Findings: The fabric in the centre is not visible and the gap is too small, which potentially traps fingers. The top part of the radio should be changeable to allow people with somaesthetic deficits in their hands to choose a pattern that they can feel.
Conclusion: The pattern indicating where to interact with the object needs to be easily changeable. Due to the increased height of the object to accommodate all the electronics, the centre of gravity situated too high. The fifth iteration (Figure 10) of the radio demonstrates a changeable interaction area at the front with a round speaker at the back. The base contains additional weight.
Prototype 05
Findings: The movement is very stable due to the low centre of gravity. The top and bottom part are permanently glued together, limiting the ability to change the weight inside the radio. An external, additional radio board is needed because of the limited RAM of the Arduino.
Conclusion: Elements in and on the radio that can be changed by the user offer progression and challenge, which are beneficial to the rehabilitation process. There should be different textured areas available to the user and the user should be able to increase the weight. Figure 11. Prototype 06 with a wooden core For the sixth iteration (Figure 11), the radio was divided into two main sections situated around a wooden core. The interaction area is clearly visible through a colour change and its tactile qualities.
Prototype 06
Findings: The weight was too light and the radio always fell over after the first touch. The main concept was that the side elements could be detached from the core to offer the opportunity to adjust the internal weights. This was rather difficult to realise and the shells should be permanently attached to the core.
Conclusion: The top should contain all electronics while the base part provides the weight. The user should have the opportunity to progress in the training and so should have the opportunity to face new challenges. The ability to change the training intervals should be incorporated.
Figure 12. Bracelet with NFC tag
For the interaction with the final design prototype a NFC bracelet carries the NFC tag that unlocks the full functionality of the radio ( Figure 12). As stroke can affect the left or the right side, making a bracelet was an ideal option as it can be worn on either wrist. The appearance is similar to that of a watch to prevent stigmatising the user.
To start the radio, the user taps, touches, strokes, or hits the white interaction area at the top ( Figure 13). This area addresses the somaesthetic deficits in the hands and is detachable. Once the feeling in the hand starts to get better the area can be replaced with a textured area that is less noticeable.
To restrain movement, the NFC board inside the radio recognises when the NFC tag in the bracelet is close. Once the tag is recognised, the radio turns on and plays music for a pre-set training interval that varies between 30 seconds, 60 seconds and 90 seconds before shutting down again. The user is encouraged to interact with the radio again to turn it on. This repetitive movement elicits the neuroplasticity within the brain leading to motor recovery (Kleim & Jones, 2008). In order to progress in the rehabilitation, the user is able to increase the weight in the bottom component ( Figure 16).
Usability evaluation
The design prototypes were evaluated, in terms of usability and inclusion of rehabilitation effects, by one physiotherapist and two occupational therapists. A formative usability evaluation (Hartson, Andre, & Williges, 2001) during the design process helps to improve the design outcomes. This expert-based evaluation helps uncover usability problems the same way the user would (Hartson et al., 2001).
The therapists stated that interaction with the radio requires a movement that would be difficult for some stroke patients to carry out because of the wrist extension necessary to tap and make the object move. The fine motor skills for this type of movement require a high level of accuracy and small buttons at the rear of the radio would be difficult for stroke survivors to use. The therapists recommended to initially focus on gross movement and over time increase the difficulty and accuracy required for the interaction. This approach would be less frustrating for the user and be more feasible for self-directed use in the home environment. Starting with an initial easy movement and then progressing to more complex movements would decrease frustration.
One of the therapists appreciated the bouncing that the radio evokes as an additional form of feedback while another therapist mentioned that the movement enhances the risk of the object dropping to the floor. Lack of balance is a common symptom post stroke, affecting up to 83% (Tyson & Kent, 2006) of all stroke survivors. This lack of balance makes it difficult for the individual to pick up objects from the ground. They recommended attaching the radio to a surface to prevent it from falling to the ground.
The therapists assessed that the interaction radio is suitable to deliver self-directed rehabilitation for the intended target group. However, they did identify that focusing on other everyday objects, for example light switches or mobile phones, could be more beneficial because people interact with these more frequently on a day-to-day basis.
The base component contains weights that the participant can increase over time to keep the interaction challenging. One therapist identified that the weights in the bottom component should be decreased over time instead of increased. The decreased weight would require a higher level of accuracy to tap the radio and not make it fall over, and challenge the user more. This needs to be confirmed with further user testing by stroke patients.
The therapists mentioned that the interaction with the object will be mastered by the user at some stage. They recommended that once this stage is reached, the object should have a purpose and be able to be used in the home environment.
The design process
Stroke can produce a variety of symptoms and after getting feedback from the therapists it became clear that no one design solution fits this diverse user group. Observing a rehabilitation session was used as a starting point for the development of the radio, but despite gaining an understanding of how motor impairments of the arm and hand look it was sometimes quite challenging during the design process to decide which elements needed to be further iterated and changed.
CIMT within the design
The therapists emphasised that CIMT comprises more than a physical constraint and extensive repetitive task practise. They recommended focusing on the part-task learning within CIMT named 'shaping' for further development of the design prototype. Shaping breaks down the motor objective in small steps according to the participant's motor capability and is a behavioural technique to increase the amount and extent of use of the affected arm and hand. Each functional activity is addressed in a set of ten 30-second trials and is specifically outlined and defined in its components .
The therapists clarified that the intervention facilitates a behavioural change. The intervention contains different behaviour change techniques that enable the transfer of the relearned motor capabilities into ADL. Techniques that are used as part of the 'transfer package' within CIMT are, for example, a behaviour change contract that the stroke survivor and caregiver are asked to sign, or a home diary to document the use of the affected arm and hand .
Use of digital technology to facilitate the initiation of use
The technology used restrained the interaction to one specific side of the body but required the NFC tag to be in close proximity for rather a long time interval. The user had to interact rather slowly so the radio could recognise the tag on the bracelet. Further iterations should focus on a closer proximity of the tag to the radio in the form of an NFC ring so the radio recognises the tag faster.
Self-directed use
The therapists pointed out that the use of digital technology offers the opportunity to collect data about the time and intensity of use. Feedback is an essential part of the rehabilitation process that influences the engagement of the participant . Presenting data to the participants that shows progress over time can have a positive effect on long-term engagement.
Task
The radio was assessed as being suitable for the intended target group but a focus on tasks that are currently compensated with the use of assistive technology like reading, writing or household tasks (S⊘rensen, Lendal, Schultz-Larsen, & Uhrskov, 2003) might offer a greater potential to motivate the user to engage in the task.
Conclusion
The name CIMT suggests that the intervention mainly comprises of the constraining effect that the restrictive device has. Feedback from therapists who have experience in applying CIMT in clinical practice emphasised that the intervention evokes a behaviour change and that focusing on shaping and the initiation of use is more feasible to be included in a tangible interface, rather than concentrating on delivering the full intervention.
A further iteration of the radio that is being developed will take into account this feedback. Working with stroke patients for usability testing requires Human Disability and Ethic Committee approval (HDEC) which has been granted for the second stage of this research. | 5,455.8 | 2017-07-28T00:00:00.000 | [
"Medicine",
"Engineering"
] |
Gravitational wave echoes from interacting quark stars
We show that interacting quark stars (IQSs) composed of interacting quark matter (IQM), including the strong interaction effects such as perturbative QCD corrections and color superconductivity, can be compact enough to feature a photon sphere that is essential to the signature of gravitational wave echoes. We utilize an IQM equation of state unifying all interacting phases by a simple reparametrization and rescaling, through which we manage to maximally reduce the number of degrees of freedom into one dimensionless parameter $\bar{\lambda}$ that characterizes the relative size of strong interaction effects. It turns out that gravitational wave echoes are possible for IQSs with $\bar{\lambda}\gtrsim10$ at large center pressure. Rescaling the dimension back, we illustrate its implication on the dimensional parameter space of effective bag constant $B_{\rm eff}$ and the superconducting gap $\Delta$ with variations of the perturbative QCD parameter $a_4$ and the strange quark mass $m_s$. We calculate the rescaled GW echo frequencies $\bar{f}_\text{echo}$ associated with IQSs, from which we obtain a simple scaling relation for the minimal echo frequency $f_\text{echo}^{\rm min}\approx 5.76 {\sqrt{B_{\rm eff}/\text{(100 MeV)}^4}} \,\,\, \rm kHz$ at the large $\bar{\lambda}$ limit.
INTRODUCTION
The recent observations of gravitational wave (GW) signals from compact binary mergers by the LIGO and Virgo collaborations [1][2][3][4][5][6][7] have greatly moved our understanding of black holes and compact stars forward. The detected binary black hole merger events inspired many studies on black hole mimickers termed exotic compact objects (ECOs), whose defining feature is their large compactness: their radius is very close to that of a black hole with the same mass while lacking an event horizon. While some non-GW probes of ECOs have been studied [8], most studies are on the distinctive signatures from gravitational wave echoes in the postmerger signals [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28], in which a wave that falls inside the gravitational potential barrier travels to a reflecting boundary before returning to the barrier at the photon sphere after some time delay.
Considering the detected binary neutron star merger events, we want to explore the possibility of GW echoes also being signature of realistic compact stars. Generating GW echoes requires the star object to feature a photon sphere at R P = 3M , where M is the object's mass. For compact stars, the minimum radius should be above the Buchdahl's limit R B = 9/4M [29]. Therefore, GW echo signals are possible if R B < R < R P .
This compactness criterion excludes the realistic neutron stars [30,31]. This motivates the exploration of other more compact star objects such as quark stars composed of quark matter.
It was proposed by Bodmer [32], Witten [33] and Terazawa [34] that quark matter with comparable numbers of u, d, s quarks, termed strange quark matter (SQM), might be the ground state of baryonic matter at zero pressure and temperature. However, it was demonstrated in a recent study [35] that u, d quark matter (udQM) can be more stable than SQM and the ordinary nuclear matter at a sufficiently large baryon number beyond the periodic table. The SQM hypothesis and udQM hypothesis, as mentioned above, allow the possibility of bare quark stars, such as strange quark stars (SQSs) [36,37] that consist of SQM or up-down quark stars (udQSs) [38,39] that consist of udQM. In the context of recent LIGO-Virgo events, there are a lot of studies on the related astrophysical implications of SQSs [40][41][42][43][44][45] and udQSs [38,[46][47][48][49], many of which involve interacting quark matter (IQM) that includes the interquark effects induced by strong interaction, such as the perturbative QCD (pQCD) corrections [50][51][52] and the color superconductivity [53][54][55] In order to achieve a large compactness for stars to arXiv:2107.09654v2 [hep-ph] 5 Nov 2021 generate GW echoes, people commonly assumed ad-hoc exotic equations of state (EOS) [31,59,60] or special semiclassical treatment of gravity [61]. Here we demonstrate that the physically motivated interacting quark stars (IQSs) composed of IQM can have GW echo signatures within the classical Einstein gravity framework.
Referring to [48,57], we first rewrite the free energy Ω of the superconducting quark matter [56] in a general form with the pQCD correction included: where µ and µ e are the respective average quark and electron chemical potentials. The first term represents the unpaired free quark gas contribution. The second term with (1 − a 4 ) represents the pQCD contribution from one-gluon exchange for gluon interaction to O(α 2 s ) order. To phenomenologically account for higher-order contributions, we can vary a 4 from a 4 = 1, corresponding to a vanishing pQCD correction, to very small values where these corrections become large [51,57,58]. The term with m s accounts for the correction from the finite strange quark mass if applicable, while the term with the gap parameter ∆ represents the contribution from color superconductivity: The corresponding equation of state was derived in Ref. [48]: where Note that sgn(λ) represents the sign of λ. One can easily see that a larger λ leads to a stiffer EOS which results in a more compact stellar structure that is more likely to have GW echoes. Thus, for this study, we need to explore only positive λ space.
As shown in Ref. [48], one can further remove the B eff parameter by doing the following dimensionless rescaling: so that the EOS (2) reduces to the dimensionless form Asλ → 0, Eq. (6) or, equivalently, p = ρ − 2B eff , using Eq. (4). We see that strong interaction effects can reduce the surface mass density of a quark star from ρ 0 = 4B eff down to ρ 0 = 2B eff and increase the quark matter sound speed c 2 s = ∂p/∂ρ from 1/3 up to 1 (the light speed) maximally.
GW ECHOES FROM IQS
To study the stellar structure of IQSs, we first rescale the mass and radius into dimensionless form in geometric From Eq. (5), we see that the echo criterionλ 10 maps to the constraint on dimensional parameters The characteristic echo time is the light time from the star center to the photon sphere [10][11][12], where dΦ dr = − 1 ρ + p dp dr .
We can also do the dimensionless rescalinḡ such that Eq. (11) can also be calculated in a dimensionless approach. After obtaining the echo time, we directly get the GW echo frequency from the relation [10][11][12] and similarly, we can rescale it into the dimensionless formf echo via the relation In Fig. 3 where the coefficients c 1 ≈ 13.0361, c 2 ≈ 12.0661, c 3 ≈ 12.6916, and c 4 ≈ 10.3398 are the best-fit values, with an error only at the 0.1% level. The first termf min echo ≈ 2.3046 is the smallest echo frequency value achieved at theλ → ∞ limit, which maps to the largest compactness.
After rescaling back with Eq. (15), we obtain a relation between the minimal echo frequency for a given λ and the effective bag constant (17) Among all f low echo for differentλ, the minimal value is achieved at theλ → ∞ limit as f min echo = f low echo |λ →∞ ≈ 5.03 B eff 10 MeV/fm 3 kHz, (18) where B eff is in units of MeV/fm 3 , or, equivalently | 1,680 | 2021-07-20T00:00:00.000 | [
"Physics"
] |
Few-Shot Learning for Image-Based Nonintrusive Appliance Signal Recognition
In this article, we present the recognition of nonintrusive disaggregated appliance signals through a reduced dataset computer vision deep learning approach. Deep learning data requirements are costly in terms of acquisition time, storage memory requirements, computation time, and dynamic memory usage. We develop our recognition strategy on Siamese and prototypical reduced data few-shot classification algorithms. Siamese networks address the 1-shot recognition well. Appliance activation periods vary considerably, and this can result in imbalance in the number of appliance-specific generated signal images. Prototypical networks address the problem of data imbalance in training. By first carrying out a similarity test on the entire dataset, we establish the quality of our data before input into the deep learning algorithms. The results give acceptable performance and show the promise of few-shot learning in recognizing appliances in the nonintrusive load-monitoring scheme for very limited data samples.
Introduction
e nonintrusive load monitoring (NILM) [1][2][3][4] has achieved high automatic recognition of appliances' operational status, through the measurement of the complex signal from a single point on the mains supplying the building. Today, a number of issues attribute to the successful implementation of NILM appliance recognition systems.
ese issues include higher data acquisition throughput and more storage hardware, better simulation software, better imbedded implementation hardware, and the use of deep learning (DL) algorithms. Machine-learning (ML) algorithms premised on hand-engineered features achieve acceptable performance when the data count is relatively low. DL algorithms inherently achieve better feature extraction, and usually, the data count is very high. e performance of DL algorithms greatly outperforms that of the rest of hand-engineered algorithms. As a way of increasing the data count, data augmentation methods [5,6] normally complement data obtained from direct measurement. Data processing in MILM systems is either time series (TS) [2] or the image (IM) [7,8] equivalent of the appliance TS signals.
e IM data approach aims at availing more appliance features in a smaller space for improved but simpler identification through convolutional neural network (CNN) computer vision (CV). We can improve the feature base of the IM dataset to mimic a larger dataset by implementing multivariate IMs, information, and IM fusion inputs into the DL algorithms [9,10]. However, the cost of acquiring large amounts of data becomes high, mainly in terms of increased data acquisition time and increased storage memory requirements. Computation time and dynamic memory usage become higher during model execution in such situations. In addition, if used, data augmentation and fusion inherently add to the complexity of the IM preprocessing stages.
Few-shot learning (FSL) [11,12] allows the successful implementation of ML recognition algorithms on very limited input datasets. In FSL, ML algorithms mimic the ability of humans to identify an object in a different or new situation, based only on minimal or no prior interaction with that object [11]. e ability to learn-to-learn (also known as meta-learning (MEL)) from a previous situation makes it possible to achieve this type of recognition capability. run & Pratt [13] give a detailed description of the learn-to-learn process and the expected outcomes of a machine or algorithm that can learn-to-learn. MEL is achieved by using two algorithm approaches, namely, metric [11,[14][15][16] and gradient-descent [17,18] learning approaches.
In literature, usually to evaluate the effectiveness of FSL algorithms, we have a comparison to Baseline and Base-line++ models. e building of Baseline models is through a normal transfer learning classification approach. Baseline++ models are an improvement on the standard Baseline models [14,16,19].
e Bayesian, k-nearest neighbours (kNN), and the Siamese network [20,21] are successful early one-shot learning attempts to classify IMs.
e Bayesian method learns the relationship between inputs by using a probabilistic approach to relate the attributes of these inputs. In KNN (K � 1), the algorithm maps the feature space for two input IMs such that any new input IM outcome is determined by its nearest neighbour. e MEL approach can considerably enhance the performance of Bayesian, KNN, and Siamese classification networks.
ere has been successful application of FSL in areas such as robotics, natural language processing, acoustic signal processing, drug recovery, and CV [12]. However, there is scant documentation of FSL as specifically applied to NILM classification [20][21][22].
e difficulty in realizing one-shot classification has slowed its adoption in NILM systems [23]. Nonetheless, we show some FSL literature developments in NILM. e authors in Ref. [22] proposed the classification of a number of appliance signals using FSL. In Ref. [22], the authors make a comparison of the few-shot performance of the KNN, decision trees (DT), random forest (RF), and long short-term memory (LSTM) models. e models gave F1scores that varied from 0.898 to 0.930, which is an assessment of a model's accuracy on a given dataset. Moreover, the algorithms are not MEL and use power series (PS) appliance signal lengths determined by a sliding window to capture the minimum appliance activations. In Ref. [20], the authors proposed the Siamese neural network for classifying V/I trajectory images. Training of the Siamese networks is based on one-shot pairs of the same and different label V/I trajectory IMs. Similar appliances belonging to the training set form a cluster, with unrecognized appliances forming their own new cluster. e density-based clustering of appliances with noise (DBSCAN) technique provides improved clustering [20]. However, there is still need to improve on the classification performance of the system in [20], as some appliances are not recognized.
In this article, we propose the development of metricbased Siamese and prototypical FSL algorithms for the classification of the limited disaggregated appliance signal images in the NILM recognition. Contrary to the method in Ref. [22], we attack the FSL from a MEL CV perspective to improve the appliance signals' classification performance. We obtain a very limited in-house input dataset for the intended experiment from fourteen PS appliance operational status signals transformed into the signal IM equivalent form using Gramian angular summation fields (GASFs) [7,8]. e fourteen appliances considered in this article are made up of four light-emitting-diode (LED) mains lamps, two compact fluorescent (CFL) mains lamps, three modes of HP laptop operation, a refrigerator, a microwave oven, a desktop computer, a two-plate cooking stove, and a kettle. e contributions of this article are as follows: (i) e development of high NILM appliance classification Siamese and prototypical FSL algorithms based on CV. is results in a reduced dataset to as low as one appliance signal sample per class (oneshot) that effectively eliminates the negative voluminous data-related issues to NILM classification systems. (ii) To establish the level of closeness between data samples by carrying out a similarity test on the entire dataset. e similarity test value should be S TV ≥ 0.6. A lower similarity value would require data preprocessing. We arrive at a value of 0.6 by attempting to have data that are easily separable at first sight, leaving the extra-involved 0.4 separation to a betterdesigned metric-learning network structure.
We organized the remaining parts of the paper as follows. In Section 2, we present the similarity, loss functions, and meta-learning theory. Section 3 gives a presentation and detailed design of the proposed system. We also explain how the data are organized. In Section 4, we present and give a discussion of the experimental results. Section 5 gives a closure to the article through the conclusion.
Similarity Theory, Loss Functions, and Metalearning
2.1. Similarity eory. Standard ML method classifies objects by assigning a probability or class value to the object in relation to the known class labels. e ML algorithms sample a large number of labeled objects to be able to achieve a good classification. In contrast, the ML similarity approach assesses the level of similarity between two objects to show whether they belong to the same class.
Definition 1.
Two sets X and Y give a Cartesian product between them of X × Y � (x, y): A similarity measure S [24] is a function with nonnegative real values defined on the Cartesian product X × X: such that the following three properties are satisfied: 2 Computational Intelligence and Neuroscience e S is called a metric similarity measure [24]. e aim of metric similarity measure learning is to decrease the separation between the embedding points of similar inputs. To evaluate the similarity between objects, various similarity measures exist [25]. ese include the Euclidean distance, the Pearson's correlation for time series data, the Mahalanobis distance, which is a variation in the Euclidean distance with correlation, Dynamic Time Warping for time series comparison, cosine distance, Jaccard, and Tanimoto similarity measures [25]. For discrete systems, the similarity measures include the Jaccard index, Sorenesen coefficient, and the symmetric difference [24]. e most popular distance metric in ML is the Euclidean. e separation between the embedding of points of dissimilar inputs is to be increased. If x i ∈ R n is a number of points, then for similar points x i and x j to satisfy similarity [26], (2) e distance learning function in (2) is able to bring similar points together and dissimilar points apart in the embedding space: where A is an optimum matrix. For metric learning, A is semi-positive definite, A ≥ 0, and when A � I, we obtain the Euclidean distance [25,26].
Loss Functions.
e constructive loss function is well suited to metric learning. is function works on pairwise data samples and optimizes the training based on closeness or the absence of it between the samples. Let d W (x, y) � D W be the parameterized Euclidean distance between the outputs embedding of x i , x j as defined in (3). en, the contrastive loss function is where m > 0 is a margin. e margin is the radius encapsulating the embedding area, such that dissimilar samples will only contribute to the loss function if the metric distance is within the margin. Y is a binary indicator for the samples.
As an example for a pair of similar inputs, this value is 0 and, for two dissimilar inputs, it is 1 [27]. In other words, the first part of (3) deals with similar points, while the last part of the same equation deals with dissimilar points. e triplet loss (TL) [28] is another widely used metric loss function mainly in Siamese learning. In this particular case, we identify three input images (an Anchor (AC), a Positive (PO), and a Negative (NE)) each passed through one of three CNN shared weights parallel models (Siamese network) with the three embedding models concatenated.
e TL attempts to bring the embedding of the AC and PO closer, while it pushes further apart those of the AC and NE. e distance between the AC encoding (f(AC)) and the PO encoding (f(PO)) is e distance between the AC encoding (f(AC)) and the NE encoding (f(NE)) is e aim is to have d(AC, PO) ≤ d(AC, NE), that is, To avoid a trivial solution for (6) in which case the embedding would be equal, it is necessary to incorporate a hyperparameter margin ∝ as shown in the following equation: e margin makes sure that there is an appreciable separation between d(AC, PO) and d(AC, NE). e TL is
Meta-and Few-Shot Learning.
e meta-learning system works by training a large number of unrelated tasks. Each training task learns to classify images in a query set from the support set of that task (each task has its own support set and query set images. However, all tasks have the same classes and samples in the support set. e query set has the same number of samples across tasks. e images in each task are different). e test task that contains entries completely different from the training tasks would have learned a way of classifying the query test set from the support test set. e generation of a large number of training tasks (to optimize the training model) can only be achieved from datasets that have a large number of classes and relatively few samples per class. In few-shot learning, two popular datasets contain a very large class count to meet the requirements of training few-short models. e first is the Omniglot dataset comprising 50 alphabets with varying hand-written character (class) numbers each and having 20 samples per character for a total of 1623 characters (classes) [14,29]. e class count in the Omniglot dataset is high, but the samples per class are few. On the other hand, the Modified National Institute of Standards (MNIST) dataset used as a baseline for testing image ML algorithms has only 10 classes but many samples per class. e second is the miniImagenet dataset that uses 100 image classes divided into 80 training and 20 testing samples [14]. Each class in the miniImagenet has 600 samples. e authors in [23] used the few-shot method on the full Imagenet dataset for 1000 classes to achieve high accuracy, having just a few samples per class that varied from 1 to 3. Although these datasets provide a baseline for developing and testing successful few-shot algorithms, in this article, we have produced a more applicable in-house NILM dataset. As in Ref. [23], only in respect to the number of samples per class, our in-house NILM dataset is processed in three ways: (1) 14 (Way) × 3 (Shot), (2) 14 (Way) ×2 (Shot), and (3) 14 (Way) × 1 (Shot). We evaluate and test the performance of our system on these three data presentations; however, our ultimate goal is the 1 (Shot) model since this allows for the minimum possible data sample without considering the zero-shot scenario.
With N (Way) classes in the support set and each class having K (Shot) images for a total of N × K support set images, we aim to classify an image out of Q images in the query set. e classification problem is one-shot, three-shot, or five-shot when the value of K is one, three, or five, respectively. In few-shot learning, the dataset samples (K) are usually less than ten samples. A special case arises when K is zero (zero-shot learning (ZSL)). ZSL first learns a projection of labeled (train) data into a new feature space. It then places projections of unseen (test) data into the same feature space and evaluates the distance or similarity value between the train and test entries to establish their relationship [30,31]. Few-shot is an inductive transfer learning process where we optimize a new task based on previous knowledge about a different task with the same underlying structure. Metriclearning algorithms that include the MatchingNet [14], ProtoNet [15], and RelationNet [16] evaluate the distance or similarity function between images. By so doing, the algorithms can group images together that have smaller distance functions between them.
Siamese Network.
e Siamese network comprises single-input two-parallel-shared weight CNN networks that are both connected to the same distance function block that in-turn connects to a loss function block. e output of each CNN network before the distance function block is a vector space containing the features or embedding of each input. e similarity between the input embedding points is evaluated in the distance function block through the L2 norm (Euclidean distance) |x − y 2 |, L1 norm |x − y 1 | or cosine similarity cos(x, y). e loss function implements the contrastive or triplet loss-based model optimization during training. e Siamese network is most appropriate for oneshot learning [20,21].
Matching Network.
e matching network uses two different functions g θ and f θ to extract the embedding of the support and query sets, respectively. e cosine similarity function compares each support set image features (embedding) to the query set features, followed by softmax classification. Full context embedding (FCE) through LSTM networks allows the production of an embedding that is the resultant of all the support set image features. FCE improves the performance of the MatchingNet especially in complicated situations [14]. In (9), we show the relationship between the query test sample x, and query predicted label (y) from classification as [11,14] where k is number of support set samples, x i , y i represent the support set object-label pairs, S � (x i , y i ) k i�1 , and a is the attention mechanism. e attention mechanism a(., .) chooses the most significant attributes in evaluating the similarity in embedding points.
Prototypical Networks.
is is a less complex metriclearning algorithm that is capable of higher performance that matching networks. In this algorithm, we first find the prototype (c k ) mean class of every object in that class. Secondly, we realize the softmax classification of the test object (query) by establishing the Euclidean distance between the query and prototype embedding [15]. e calculation of the prototype point is as follows: where S k represents the k class support point, x i is feature point with label y i , and f ∅ is the embedding function having ∅ trainable parameters. e evaluation of the query where d is the Euclidean distance between the query and prototype class is as follows [15]: A bigger training class count than that for testing normally achieves better results, but maintains the class samples the same in both training and testing situations [11]. e training episode for the negative log-probability J ∅ � −logp ∅ (y � k|X) through SGD where k is the true class [15] is given in Algorithm 1.
Relation
Network. In this model, there is concatenation of the support set (f φ (x i )) and query set (f φ (x j )) feature maps produced by the same embedding function. e function that concatenates the feature maps is ). e concatenated result is processed in the relation module to output a similarity measure (relation score) between x i and x j of value 0 to 1. e number of relation scores depends on the number of classes in the support set. Equation (12) shows the expression for the relation score [16]: where ∁ is number of classes in support set, x i is support set objects, and x j is query set entry during model training.
Model-Agnostic Meta-Learning (MAML).
e MAML [18,32] is unique among meta-learning methods since it is implementable on any gradient-descent model. To address the meta-learning problem, if the MAML model successfully solves a previous task, then it should learn to deal with a new task in a faster way with improved performance. e MAML seeks to have a learnable parameter θ move close to the optimized θ * i parameter values of different tasks [18]. is θ becomes the initialization value, which is specific task finetuned. e θ trajectory involves the continuous optimization of the loss functions L i for the tasks [18]. We define a task as T i � p i (x), p i (y|x), L i that shows the distribution over the input p i (x), the distribution over the labels given the input p i (y|x), and the loss L i . e distribution of tasks is p(T). If f θ represents the classification model, then the training set loss is e gradient descent optimizes the loss as When the learning rate is α, the complete gradientdescent update is Training of the model to minimize L T i (f θ i ′ ) then follows in the meta-objective as % min Covering all the tasks, the stochastic gradient descent (SGD) updates the meta-optimization parameter θ as θ←θβ∇ θ where β is the meta step size [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].
Methodology
3.1. Proposed System. Based on literature review, compared to other metric networks, the matching network is more involved to realize [14] and normally achieves less performance. Due to this, we do not consider the matching network for application in this article. Due to its simplicity, it is possible to implement a relational metric-learning network. However, for now we only explore the prototypical network.
Appliance activation periods vary considerably, and this can result in imbalance in the number of appliance-specific generated signal images. ere is no effect on the performance of few-shot prototypical metric-learning networks by this data imbalance. In this article, we propose the application of prototypical networks. Prototypical networks only produce a prototype (average) value embedding point of the samples in each class during training. A comparison is made of the average prototypes with a test embedding point through the Euclidean distance metric. We first carry out a similarity test on the entire dataset to establish the level of similarity between the data samples. e application stage of the prototypical network will require a similarity test value of at least 0.6 to increase the accuracy of our few-shot learning model.
We give the flowchart of the proposed system in Figure 1. Our proposed system allows for quick determination of the suitability of disaggregated appliance data for metric learning before the actual few-shot learning. By so doing, we are able to preprocess the data before conversion into acceptable TensorFlow file formats, which can result in improved model training. We assign an acceptable data similarity value in the overall data similarity search.
In the proposed train and test few-shot metric model block exploded in Figure 2, we seek to address the recognition of limited appliances signals by employing a model (Model metric ) based on testing the similarity or dissimilarity between a known appliance signal image in the support set (D support ) and an unknown disaggregated appliance signal image in the query set (D query ). A conventional image-based deep learning neural model would require training by a very large sample count in (D support ). e proposed system includes a training dataset (D train ) to train the Model metric . Training of the model is through a larger base set split into a specific number of different tasks ( T i , i ∈ h for1 ≤ i ≤ h), for h tasks to optimize the loss function. e Model metric is the prototypical network. A 1 shot Siamese model can also be realized. e training allows for the realization of a model Computational Intelligence and Neuroscience 5 that learns to learn to place the embedding of similar classes together in the test task.
Dataset Preparation.
e dataset is made up of fourteen appliance categories or classes placed in an ALL_IMAGES main directory on the computer. ese appliances include four light-emitting-diode (LED) mains lamps (LED1-1 (5W), LED1-2(5W), LED2-1 (5W), and LED3-1 (5.5W)), two compact fluorescent (CFL) mains lamps (CFL1-1(12W), CFL2-1(14W)), three modes of HP laptop operation (lap-top_boot, laptop_ms_word, laptop_video), a refrigerator (fridge), a microwave oven (microwave), a desktop computer (desktop), a two-plate cooking stove (stove), and a kettle (K). A sample of our raw few-shot train support dataset is shown in Figure 3 and is comprised of GASF IMs initially in RGB format and shape 400 × 400 × 3. In Figure 3, we have shown only two samples out of ten samples per class. Using a PA1000 Tektronix [34] power analyzer in a laboratory setup, we measure the operational TS signals over the complete activation of the appliance. We then transform the appliance's activation signals to IM equivalent by using GASF. Figure 4 shows the images used in the test support and never seen before by the few-shot model. Figures 3 and 4, the sample images have different features and this property is used to successfully train and test the few-shot meta-learning model. It is important at this point to note that for the similarity test model, the samples in Figures 4 and 5 are considered one dataset, which is then split using the sklearn train_test_split. Converting the RGB images to grayscale and reducing image size helps to decrease the complexity of developed algorithms, speed up the process, and use less computation resources. e use of both the omniglot and miniImagenet datasets for evaluating developed FSL algorithms is widespread. We observe that typical file formats in FSL algorithms include the NumPy array (.npy), tar.gz (.tgz), or just straight image file folder. However, the IMs in these FSL algorithms are normally converted to grayscale (L) and resized to 28 × 28. e .npy grayscale images have an initial shape of 28 × 28. To take advantage of existing few-shot coding in literature, we prepare our custom dataset more or less in the same manner as for the omniglot and niniImagenet datasets. TFRecords files present data in binary record sequences. TFRecords is the recommended TensorFlow data format. We do not evaluate our final models on TFRecords as the conversion of various data formats to TFRecords requires different coding approaches. However, we do experiment with TFRecord files. For each appliance, we are able to capture at least ten activation signals, which results in ten signal IM samples per appliance class. e total number of resized IMs per one measurement exercise is 140. When we take the NumPy route, the produced IM NumPy array is reshaped to [number of classes, samples per class, IM width, IM height, channels] to give shape (14,10,28,28,1). We then split this into train, test, and validation data. We follow the directory structure of the omniglot dataset to achieve the NumPy and reshape above. e execution of the create-miniimagenet.py converts the image miniimagenet folder into train.npy and test.npy. On the other hand. the helper.py script converts the omniglot dataset to .npy.
As clearly seen in
We then run a custom-developed script to convert our ALL_IMAGE folder into train.py and test.py. In some instances, we performed the data split by producing train, test, and validation CSV files that contain the IM file name and label. e labeled IMs in this case are stored in their own separate folder.
Training Procedure.
Due to the extensive coding required for the FSL algorithms, we had to experiment with code examples from numerous GitHub repositories and from keras.io code examples [35,36]. We implemented the code in both python and keras in IPython and Jupyter platforms, respectively. In training some code, we used the Google Colaboratory (Google Colab.) notebooks platform in which we could easily install such packages as PyTorch. Google Colab also allowed us to use the graphics processing unit (GPU) facility not available on our HP 650 Notebook to speed up training. However, in these codes, we modified the utilities (utils) data handling part to accommodate our inhouse datasets. We also modified or added code for specific data results' visualization and experimented with various hyper-parameters. In some instances, we experimented with different number of convolutional layers. We also experimented with different epochs, episodes, and different number of support and query set classes and shots. However, our target system was the 1-shot model.
We trained the similarity test model in colab, with data loaded into My Drive in Google Drive. e RGB images of size 400 × 400 are resized to 28 × 28. Training is performed with a train-to-test split ratio 0.75 : 0.25 and batch size of one. e train shape is (105 × 28 × 28 × 3), and test shape is (35 × 28 × 28 × 3). High numbers of batch size did not improve system performance, probably due to our limited training samples. e embedding model is a three-layer VGG 2D convolutional network with filter sizes 32, 64, and 128 from the input and kernel size of 3. During training, we Computational Intelligence and Neuroscience experimented with various hyper-parameters and we would get slightly different classification results. However, for best classification results, we settled for the Adam optimizer with a learning rate of 1e − 3 as in [35], and we used the sparsecategorical-cross-entropy loss function.
To train the Siamese network, we create two directories each with four grayscale images of dimension 400 × 400 × 1. e directories are the 2_plate_stove and CFL1-1(12W) appliance classes. After preprocessing, the new data shape is 16,2,1,200,200, where 32 is the total sample size, 16 for 2 pairs input into the Siamese network. e 1, 200, 200 represents the new dimensions of the images in pgm format. As in Ref. [37], the base model consists of two 2D convolutional layers followed by flatten operation and two dense layers. e first 2D CNN layer had 6 filters each of size 3, ReLU activation, followed by max. Pooling (2, 2) and dropout 0.25. e second 2D CNN layer had 12 filters each of size 3, ReLU activation, followed by max. Pooling (2, 2) and dropout 0.25. e first dense layer is 128 units with dropout 0.1, and the last layer has 50 units with reLu activation. We used the contrastive loss and RMS optimizer. In addition, we developed a Siamese model based on the triplet loss function with a margin (alpha) of 0.2, 98 train grayscale samples and 42 grayscale test samples. We experimented with different image formats that proved to be difficult to implement in the coding of [37].
In the prototypical recognition system, the data were based on the RGB IMs of size 400 × 400. ese IMs from a total IM count of 140 are reshaped to 28 × 28 × 3. Two approaches were then used to format the input data into the prototypical network. e first approach involved the internal model augmentation through rotation at different angles to obtain a final train set shape of (400, 28, 28, 3) and a test shape of (160, 28, 28, 3). e second approach took the 140 IM samples and reshaped to train set shape (10, 10, 28, 28, 3) and test set shape (4, 10, 28, 28, 3), where 4 represents the test classes and 10 the number of samples per class for the test set. e second approach implementable on CPU because of the low memory requirements provided the results captured in this article. It was necessary to combine the different modules available in GitHub to come up with a TensorFlow prototypical network [38], which was also executed in colab under GPU. e codes are executed with the SGD optimizer and a learning rate of 0.1. e recognition efficiency generally increases as the number of episodes increases. In the first approach, the highest accuracy was at 30000 episodes for a frame size of 1000. However, in the second CPU approach, the maximum episode count was 600 episodes.
Similarity Search.
In Figure 5, we see the appliance recognition results based on similarity.
To evaluate the suitability of our dataset for metric learning, we use the code in [35]. In this similarity test algorithm, we infer images of the same class as being similar, while those between classes are not. A requirement in model training is the pairing of images in the same class for the similarity test. One image is the AC and the other the PO [35]. ere are 38 test samples out of the 140 total appliance (6) samples in the test set assigned to each class. e 2_plate_stove and cfl1-1 attained one hundred per cent recognition. e refrigerator and microwave oven also attained high levels of recognition. However, their relative high powers especially with the inclusion of the refrigerator switching spike some activations are almost similar between the two. e system also had difficulty in recognizing between the different operating modes of the laptop. However, the system was able to cluster all sample points as laptop among laptop_boot, laptop_video and laptop_ms_word, which in itself represents the success of the similarity test. With improved network and data, the similarity test system has potential for attaining high classification and hence passes the test criteria of 0.6. We give the similarity loss plot in Section 4.4
Siamese Network 1 Shot Learning.
In Siamese network training, we have two authentic (similar) images to which we assign an authentic label of 1 to the pair. For a pair of images between classes, we assign a not-authentic label of zero (0). During training, the input into the Siamese network is either the pair of authentic images or a pair of not-authentic images. e trained model provides the set coordinate of the embedding of each similar pair per class. In our case, we obtain the Siamese 1 shot experimental results on both the contrastive and triplet loss functions. When the contrastive loss function trained Siamese network is tested against the compact fluorescent lamp (CFL2-1(14W)), it returns a true target value of 1 as given in the part sample code: In triplet loss Siamese model, the train set shape is (98, 28, 28, 1) and the test shape is (42,28,28,1). On the other hand, a part test code for the triplet loss is In [15]: btch_size � 9 epchs � 200 steps_per_epch � int(x_train.shape[0]/btch_size) We give both the contrastive and triplet loss plots in Section 4.4. Figure 6 shows the results of the test imbedding in the triplet loss model. From Figure 6, there is a tendency for clustering of the embedding in any class. ese results here show that there is a need to increase the train dataset or redesign the model for deeper DL. ese results are in synchronization with the results shown in Figure 5 where the model tries with effort to obtain the classification of different appliance signals that are almost the same.
Prototypical Network.
e prototypical model achieves high accuracy early in the training and converges well. e train loss and accuracy plots are given in Section 4.4. To test the model, we specify different values of number of samples or shots in the support set (Ns), the different number of classes in the support set or ways (Nc), and the number of samples in the query set (Nq) whose class value is unknown. Table 1 shows the relation between test support and query set sample entries per given appliance class number. Table 1 gives all the few-shot learning test results collected for the prototypical network. In Tables 2, we show the summary of 2-way k-shot accuracy results for the prototypical network. In Table 2, the 2-way 7 shot gives the highest performance at 97.83% average test accuracy. Our data have four (4) test classes and ten (10) training classes. Hence, in the test and support class, the number of samples is either 4way k-shot, 3-way k-shot, 2-way k-shot, or 1-way k-shot. Likewise, the training test set can vary from 10-way k-shot to 1-k-shot. e 1-way k-shot is a theoretical postulation, since in reality, we cannot have a model that trains to detect one class in our case. However, a multiple sample within one class is feasible. e limited classes in our experiment will result in slight model overfit of 100% train accuracy to 97.83%. e 2-way 1-shot system gives a reasonable average test accuracy of 91.343%. e results in Tables 1 and 2 are based on a 5-way k-shot training set. A 10-way k-shot training set did not produce satisfactory results. Comparing the performance of the prototypical network with the metric similarity search at the beginning, we see an agreement between the two systems. Table 2 also shows the average accuracies of the 3-way k-shot and 4-way k-shot FSL test models.
In Tables 2, we see that the test accuracy goes up as the k-shot value goes up in the support set. e number of classes is the same in the test support and query sets. e four test cases belong to the refrigerator, kettle, LED2-1(5W), and CFL2-1(14W) mains lamps.
We now make a comparison of the results of this article to published results that use the same datasets. In Table 3, we show training dataset (TRDS), training classes (TRCL), training query set (TRQS), training accuracy (TRACC), test dataset (TEDS), testing classes (TECL), and the testing accuracy (TEACC).
From Table 3, we can clearly see that with a very limited training dataset, our model achieves a higher training accuracy and higher test accuracy than from publications that use the same data in different model architectures. Reference [39] is IM classification based on the capsule network, while Reference [40] is classification based on the ConvNet VGG image classifier. From the similarity metric test results at the beginning, we see that we have a number of classes whose embedding is very close to each other. We need to investigate how we can improve further the accuracy of our model by considering such issues as hybrid MEL systems [41,42].
ere is need to consider the visualization of the embedding including the actual class objects and labels from the query set. Figure 7 gives the training loss plots for the models developed in this article. e plots show the attempt by the models to reach convergence trough stable training. Due to the limited training data points, the models tend to overfit; however, they do produce acceptable performance.
Conclusion
In this article, we investigate the application of few-shot learning in the form of a Siamese and prototypical network for the classification of disaggregated appliance signal images. By first carrying out a similarity test on the entire image dataset, we see that there are some appliances whose embedding is extremely close to each other. We observe a clear separation of embedding in other instances. We infer this information from the given confusion matrix. Nonetheless, the results show that we can achieve acceptable recognition of appliance signals using the Siamese and prototypical fewshot learning network. Two major challenges have been encountered in this study. e first is the inadequate number of available training classes so that the models could provide improved generalization. e second challenge is the closeness of some of the appliance signals to each other resulting in impaired discrimination between appliances. Program execution on normal CPU was extremely slow, or the system would just crash. Fortunately, we were able to make use of the GPU facility on Google Colab platform.
In future, we investigate the application of the MAML algorithm and the possible application of hybrid metric and gradient-descent few-shot learning methods for improved recognition performance. We will also consider increasing the training data classes and examples. Of particular interest is the improvement of the N-way 1-shot recognition setup.
Data Availability e data used in this study are derived from public domain resources.
Conflicts of Interest
e corresponding author states that there are no conflicts of interest. | 8,846.6 | 2022-08-23T00:00:00.000 | [
"Computer Science"
] |
A novel Q-learning algorithm based on improved whale optimization algorithm for path planning
Q-learning is a classical reinforcement learning algorithm and one of the most important methods of mobile robot path planning without a prior environmental model. Nevertheless, Q-learning is too simple when initializing Q-table and wastes too much time in the exploration process, causing a slow convergence speed. This paper proposes a new Q-learning algorithm called the Paired Whale Optimization Q-learning Algorithm (PWOQLA) which includes four improvements. Firstly, to accelerate the convergence speed of Q-learning, a whale optimization algorithm is used to initialize the values of a Q-table. Before the exploration process, a Q-table which contains previous experience is learned to improve algorithm efficiency. Secondly, to improve the local exploitation capability of the whale optimization algorithm, a paired whale optimization algorithm is proposed in combination with a pairing strategy to speed up the search for prey. Thirdly, to improve the exploration efficiency of Q-learning and reduce the number of useless explorations, a new selective exploration strategy is introduced which considers the relationship between current position and target position. Fourthly, in order to balance the exploration and exploitation capabilities of Q-learning so that it focuses on exploration in the early stage and on exploitation in the later stage, a nonlinear function is designed which changes the value of ε in ε-greedy Q-learning dynamically based on the number of iterations. Comparing the performance of PWOQLA with other path planning algorithms, experimental results demonstrate that PWOQLA achieves a higher level of accuracy and a faster convergence speed than existing counterparts in mobile robot path planning. The code will be released at https://github.com/wanghanyu0526/improveQL.git.
Introduction
With technological developments and increasing demand, the scope for mobile robots is becoming more extensive, including applications in machine automation and in fields such as construction, the military, and agriculture [1]. The path planning ability of a mobile robot strategies, Shi et al. [25] used Q-learning for adaptive servo gains adjustment, and proposed a fuzzy-based method for tuning the learning rate in order to improve Q-learning performance. Li et al. [26] proposed a novel off-strategy interleaved Q-learning algorithm by introducing behavior control strategy. As regards Q-table improvements, Wang and de Silva [27] proposed a new distributed Q-learning algorithm, which updates a Q-table with local rewards to reduce Q-learning spaces. Song et al. [28] applied a dynamic wave expansion neural network to specified initializations of Q-values in a Q-table, which improved the convergence efficiency of Qlearning. Konar et al. [29] reduced the number of repeated updates of a Q-table by assuming the distance from the current state to the next state and the target, thereby reducing the time complexity of the algorithm.
However, Q-learning with the above improvements still needs to calculate all possible action-states, and therefore it still has the disadvantage of slow convergence speed. To solve this problem, metaheuristic optimization algorithms have been applied to improve the initialization phase of Q-learning. This provides a better initial state for Q-learning, and reduces the amount of time required for calculation and subsequent convergence.
A number of metaheuristic optimization algorithms have been proposed. Kennedy and Eberhart [30] proposed Particle Swarm Optimization, which originates from the predatory behavior of birds and seeks an optimal solution through collaboration and information sharing between individuals in the population. Passino [31] proposed Bacterial Foraging Optimization, which is a bionic random search algorithm that imitates the behavior of E. coli swallowing food in the human intestine. Rashedi et al. [32] proposed the Gravitational Search Algorithm, which uses the gravitational force between particles in the population to guide the movement of each particle to find the optimal solution. Yang [33] proposed the Bat Algorithm, which is a heuristic algorithm simulating bats in nature. The Bat Algorithm is mainly focused on searching for prey and avoids obstacles by simulating ultrasound to find the global optimal solution. Mirjalili [34] proposed Moth-Flame Optimization, a swarm intelligence optimization algorithm inspired by natural laws to simulate the spiral flight path of moths based on their navigational mechanism during flight. Mirjalili et al. [35] proposed the Gray Wolf Optimizer, which is an optimized search method based on the social hierarchy of gray wolves and inspired by their predatory activities. Inspired by the precise navigation of birds over long-distance aerial paths, Zamani et al. [36] proposed a novel differential evolution algorithm named the Quantum-based Avian Navigation Optimizer Algorithm (QANA). Mohammad et al. [37] proposed an efficient binary version of the QANA named BQANA to solve the feature selection problem of high-dimensional medical datasets. To solve engineering optimization challenges, Zamani et al. [38] proposed the Starling Murmuration Optimizer, which is based on the behavior of starlings during their stunning murmurations. Mirjalili and Lewis [39] proposed the Whale Optimization Algorithm (WOA) to simulate the spiral hunting behavior of humpback whales.
WOA has the advantages of a relatively simple concept, does not require gradient information, and is easy to implement. Therefore, in this paper WOA is selected to optimize the initial Q-table. However, similar to other population-based heuristic algorithms, WOA still has the problem of slow convergence speed and low convergence accuracy. Mafarjaa et al. [40] combined WOA with Simulated Annealing (SA), and implemented feature selection by embedding SA into WOA. Mafarjaa et al. [41] used WOA with an improved stochastic process or WOA with crossover and mutation operators in feature selection. Kaveh and Ghazaan [42] improved the original formula of WOA to enhance the convergence speed and increase the level of accuracy of the original algorithm. Combining WOA with a local search strategy, Abdel-Basset et al. [43] proposed the Hybrid Whale Algorithm to solve the problem of shop scheduling. To balance the capabilities of exploration and exploitation in WOA, Kaur and Arora [44] introduced chaos theory into WOA and proposed the Chaotic Whale Optimization Algorithm to improve and enhance the performance of the original WOA. Mohammad et al. [45] proposed an Enhanced Whale Optimization Algorithm (E-WOA) using a pooling mechanism and three improved search strategies named migrating, preferential selecting, and enriched encircling prey. E-WOA was applied to medical datasets to verify the effectiveness of the algorithm, especially to detect coronavirus disease in 2019. Mohammad et al. [46] proposed an efficient hybrid algorithm that combined WOA with an improved Month-Flame Optimization algorithm to solve the optimal power flow problem in power systems.
However, path planning methods for mobile robots using ε-greedy Q-learning still have three defects. First, Q-learning initializes a Q-table to zero at the time of initialization, increasing the time to calculate and update the Q-table, and subsequently resulting in a slow convergence process. Second, the strategy of ε-greedy Q-learning selects the next state in the exploration process too randomly, which means too much time is wasted in the exploration process. Third, because the value of ε is fixed, ε-greedy Q-learning path planning cannot switch processes flexibly between exploration and exploitation under any circumstances.
In order to solve the above problems, this paper proposes a new path planning algorithm named the Paired Whale Optimization Q-learning Algorithm (PWOQLA), which is based on an improved WOA and an improved ε-greedy Q-learning. Firstly, in order to correct the shortcoming of slow convergence caused by Q-learning initialization, WOA, as a metaheuristic optimization algorithm, is chosen for Q-table initialization instead of simply setting the values of a Q-table to zero. In this way, a Q-table that contains previous experience is learned before the exploration process. Thus, in the subsequent Q-learning path planning, the calculation time is reduced and a path with fewer steps and smoother corners is obtained.
Secondly, based on the pairing behavior of whales, a Paired Whale Optimization Algorithm (PWOA) is proposed to accelerate the convergence speed of WOA. The main innovation of PWOA is to pair each whale when initializing the population. When one paired whale finds a prey position, the position of the other paired whale is updated to the same prey position. The result of this improvement is to accelerate the speed of the whale population approaching a local optimal solution. Compared with the original WOA, PWOA further improves the convergence speed of Q-learning when initializing the Q-table.
Thirdly, to improve the convergence efficiency of ε-greedy Q-learning, which uses a random exploration strategy, a novel selective exploration strategy (SES) is proposed based on the relationship between current agent position and target position. During each exploration, the agent judges the relationship between those two positions. Based on the judgment of the relationship, the agent will selectively explore two directions that are closer to the target position, instead of exploring four directions at random. SES reduces the number of useless explorations to achieve the purpose of accelerating the convergence speed of ε-greedy Q-learning.
Fourthly, in order to switch flexibly between exploration process and exploitation process, we propose a nonlinear function that changes the value of ε in ε-greedy Q-learning dynamically based on the number of iterations. In other words, the exploitation probability of εgreedy Q-learning gradually increases as the number of iterations increases, whereas the exploration probability of the surrounding environment decreases. Therefore, by changing the value of ε dynamically, exploration and exploitation can be switched flexibly.
Finally, combining the above improvements to Q-learning and WOA, the result is the proposed PWOQLA. In PWOQLA, PWOA is applied to the Q-table initialization phase of the improved Q-learning. Compared with the original Q-learning algorithm, PWOQLA is more accurate and more efficient at robot path planning, and experimental results show that the proposed algorithm has a greater level of accuracy and faster convergence compared to several path planning algorithms with similar functions.
The rest of this paper is structured as follows. The second section introduces ε-greedy Qlearning and WOA. The third section introduces the working principles and steps of PWOQLA. The fourth section compares PWOQLA with similar algorithms and discusses the experimental results. The fifth section draws the conclusions.
Q-learning
Q-learning [17] is a model-less algorithm that is one of the main reinforcement learning algorithms. In the Markov environment, Q-learning has the ability to learn and provides an intelligent system to select the best action using experienced action sequences. Q-learning learns through the Q-value function. In the Q-value function, the state transition probability and the next status decide the current state and the selected action, and the agent receives an instant return after the selected action. The strategy of Q-learning is to find maximum rewards way into the future. Q-learning is called model-less because it compares the expected values of actions without an environmental model, and this is the advantage of Q-learning.
In Q-learning, each Q (s, a) has a corresponding Q-value. In the subsequent learning process, the next action is selected according to Q (s, a). The sum of the rewards obtained from executing a certain strategy and performing the current action is defined as the Q-value. The optimal Q-value is defined as the sum of the rewards acquired by executing related actions and executed according to the optimal strategy, which is defined as follows: In Eq (1), s t is the current state; a t is the action performed in state s t ; r t+1 is the reinforcement signal received after s t is executed and is also called the reward; s t+1 is the next state; γ is a discount factor (0 � γ < 1); and α is a learning coefficient (0 < α < 1). Each agent learning process can be considered as starting from a random state and adopting an ε-greedy strategy or Boltzmann distribution strategy to select the next actions. The εgreedy strategy is used in decision making. For example, when ε is initialized to 0.9, it means that there is a 90% probability that the agent will choose a behavior according to the optimal value of the Q-table, and a 10% probability of choosing a random selection. To allow the agent to search for all possible actions and update each Q (s, a) for each action, the random selection strategy is adopted. The agent observes the new state after executing the selected action. The Q (s, a) of the previous state and action is then updated in response to the maximum Q-value and the return of the new state. Based on the new state, the agent will continue to choose actions until it reaches the end state.
Whale Optimization Algorithm
The Whale Optimization Algorithm (WOA) is a heuristic optimization algorithm proposed by Mirjalili Seyedali [39]. The algorithm proceeds as follows. In the search space for the optimization problem, each humpback whale is a candidate solution, called a search whale. A set of search agent whales is used to find the global optimum of an optimization problem in WOA. For a given problem, the search process starts from a random solution when initializing and then updates candidate solutions according to optimization rules until the final criterion is met. In fact, WOA simulates the behavior of humpback whales looking for and attacking prey.
Encircling prey. The humpback whale recognizes the location of its prey and surrounds the prey. Because the prey position of the optimal solution is a priori unknown, the target prey position is presumed to be the current optimal solution, and other search whales update their positions through the "target prey". The mathematical model of prey behavior is as follows: In the above, X ! ðtÞ is the current position vector; G ! ðtÞ is the current optimal solution position vector; D ! is the distance between the search whale and the target prey; t is the current number of iterations; and A ! and C ! are coefficient vectors.
If there is a better optimal solution position vector, G ! ðtÞ should be updated in the current iteration. The formulae for calculating A ! and C ! are as follows: In the above, r ! a , and r ! c are random vectors in the range [0, 1], and a ! decreases linearly from 2 to 0 during the iteration.
Bubble-net strategy
Humpback whales move around their prey in a spiral path and simultaneously spit out bubbles to create traps. This is known as the bubble-net strategy for hunting prey. In the WOA model, the contraction and surround mechanism is achieved by reducing a ! in Eq (4). The fluctuation range of A ! decreases with decreases in a ! . According to Eq (4), A ! is a random value in the interval [−a, a]. Setting A ! to be a random value in the interval [−1, 1], the position of the search whale will move randomly to any position between the current optimal solution position and the previous position. The new position of the search whale is calculated as follows: In the above, D ! 0 means the best solution obtained so far, which represents the distance from the whale to the prey; l is a random number in the range [−1, 1]; and b is the constant of the logarithmic spiral shape and can be set to different values according to specific application scenarios. The humpback whale swims along a spiral path toward its prey. To update the whale's predatory position, the mathematical model of the whale's spiral path is as follows: ( In Eq (8), the variable p is a random number between 0 and 1. Searching for prey. As well as using the bubble-net strategy in the exploitation process, humpback whales also need to search for prey randomly in the exploration process. The mathematical model of searching for prey is as follows: In the above, X rand ��! ðtÞ is the position vector of a search whale randomly selected from the population.
In order to ensure exploration and convergence, when j A ! j � 1, the randomly selected search whale becomes the key point when other whales update the position. In other cases (j A ! j < 1), the current optimal solution position plays a pivotal role in updating other search whales.
Methods
The Paired-Whale Optimization Q-learning Algorithm (PWOQLA) is a path planning algorithm that uses an improved WOA to initialize the Q-value of an improved ε-greedy Q-learning. The aim of PWOQLA is to overcome the disadvantage of slow convergence in the original ε-greedy Q-learning. The first part of this section introduces the Whale Optimization Q-learning Algorithm (WOQLA), which combines the algorithms of the original Q-learning and original WOA. The second part introduces the process of improving WOA, and the third part introduces the process of improving ε-greedy Q-learning. The final part introduces the application of PWOQLA in path planning.
Whale Optimization Q-learning Algorithm
The Whale Optimization Q-learning Algorithm (WOQLA) is an algorithm for mobile robot path planning that combines the original WOA with Q-learning initialization. To overcome the shortcomings of Q-learning, such as slow convergence caused by initialization, WOQLA optimizes the initialization of the Q-table instead of simply setting the Q-values to zero.
In the initialization phase, WOQLA generates a number (n) of whale populations in a 20 × 20 grid space and uses the Q-value calculation in Eq (1) to calculate the fitness value of each whale. The position with the highest Q-value represents the best whale position. The WOA is then used to optimize the Q-value of each whale in the whale population. When the maximum number of iterations is reached, the initialization of the Q-table by WOA ends. The original ε-greedy Q-learning is then used for path planning according to the newly obtained Q-table. Based on the newly initialized Q-table, the Q-value calculation formula is used in the iterative update of the Q-table. After the iteration is completed, the final Q-table is obtained. From this Q-table, we can find the path with the largest Q-value, which represents the best path. In this way, the Q-table containing previous experience is learned through WOA before the Q-learning algorithm searches, which helps to reduce the subsequent calculation time and accelerates the speed of Q-learning convergence.
Paired-Whale Optimization Algorithm
WOA has the problems of slow convergence and low levels of accuracy. Inspired by research on humpback whales and the observation that they perform activities mostly in pairs [47][48][49][50], this paper proposes the Paired-Whale Optimization Algorithm (PWOA) based on the pairing behavior of humpback whales. Pairing behavior helps paired whale individuals to find food faster with the help of their peers, which accelerates the convergence speed of the original WOA. The main improvement of PWOA compared with the original is that the algorithm finds a mate for each whale when initializing the whale population, so that each whale has another whale paired with it. The pairing strategy is pairwise pairing in the order of randomly generated whale individuals. The original WOA is then executed. At each iteration, the fitness value of each whale is calculated. When whale G is found to be in the best position, the algorithm compares the fitness value of whale G with the fitness value of the pair of whale G. If the fitness value of whale G is large, the position of the paired whale is updated to the position of whale G. If the fitness value of whale G is small, the position of whale G is updated to the position of the paired whale. In this way, in each cycle, each pair of whales chooses the better position of the two to find their prey at the same time, then conducts their own exploration or exploitation process respectively. The current number of iterations in PWOA is t PW . The result is that the convergence speed of the final algorithm is accelerated. Such improvements accelerate the speed of the whale population approaching the local optimal solution, and also accelerate the convergence of the final algorithm. The pseudo-code of the PWOA algorithm is shown in Algorithm 1, and a flowchart is shown in
Improved Q-learning
In order to simplify a real-world application scenario, a 20 × 20 grid space is used to model the real environment. We assume that each grid position corresponds to a corresponding coordinate in real space. The value of each grid is mapped to the Q-table of ε-greedy Q-learning. When the reward is −1, the grid is an obstacle. When the reward is +1, the grid is free space. When the reward is 100, the grid is the target position. As shown in Fig 2, an agent has four random actions at position s t : action 1 goes up; action 2 goes right; action 3 goes down; and action 4 goes left.
In order to improve ε-greedy Q-learning, firstly, this paper proposes a novel selective exploration strategy (SES) based on the target position, with the aim of improving the convergence efficiency of the original ε-greedy Q-learning and to reduce the number of useless explorations. During each exploration, the agent first judges the relationship between the current agent position s t (x t ,y t ) and the target agent position s g (x g ,y g ). The agent will then explore two If x t �x g and y t <y g , then a =rand (1,2); if x t <x g and y t �y g , then a = rand (2,3). If x t >x g and y t �y g , then a = rand (3,4); if x t �x g and y t >y g , then a = rand (1,4). Secondly, in order to switch flexibly between exploration and exploitation process, the ε value in ε-greedy Q-learning is changed dynamically. The equation for calculating the value of ε is as follows: In Eq (11), u is the value of ε at the beginning of the iteration, and v is the incremental range of ε. The sum of u and v is set to 1, and u and v are temporarily set to 0.6 and 0.4 respectively. The variables a and b are the coefficient parameters of the dynamic curve, and their values are determined by the number of iterations. The variable t is the current number of iterations. The change curve of ε is shown in Fig 3. It can be deduced from Eq (11) that the changing trend of ε is decreasing. Therefore, as the number of iterations increases, the development probability of ε-greedy Q-learning is
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gradually increased, and the probability of exploring the surrounding environment is reduced. Consequently, the early stage attends to exploration capability whereas the later stage attends to exploitation capability.
To summarize these two improvements, firstly, we reduce the number of useless explorations by referring to the relationship between the target and the current position through the SES strategy; and secondly, the proportion of exploration and exploitation in different periods is planned reasonably with the ε curve. These two improvements help to reduce the amount of calculation in the algorithm and save computing resources.
Paired-Whale Optimization Q-learning Algorithm
The Paired-Whale Optimization Q-learning Algorithm (PWOQLA) is a path planning algorithm that uses PWOA to initialize the Q-table in improved Q-learning, instead of simply initializing the Q-table to zero. During initialization, a number of whale populations (n) is generated and matched in a 20 × 20 grid space. The Q-value calculation in Eq (1) is used to calculate the fitness value of each whale. The position with the highest Q-value represents the best whale position. PWOA is then used to optimize the Q-value of the whale population. After the number of iterations reaches the maximum, Q-table initialization is completed. Subsequent path planning is performed using the improved ε-greedy Q-learning based on the newly obtained Q-table. The current number of iterations in PWOQLA is t PWQ , and the final result represents the best path. The pseudo-code of PWOQLA is shown in Algorithm 2, and a flowchart of the algorithm is shown in
Experiment
In this section, we simulate the effect of PWOQLA in mobile robot path planning in a grid environment with 20 × 20 obstacles. The original Q-learning, Improved Decentralized Qlearning (IDQ) [51], A � algorithm [52], and WOQLA are compared with PWOQLA to verify the effectiveness of PWOQLA in path planning. The A � algorithm is one of the basic algorithms for path planning. IDQ is one of the classical algorithms for improving Q-learning and is often used as a comparison algorithm.
Experimental environment and parameters
The experiment is performed in a 20 × 20 grid. The number of simulations is set to 30 as this number of simulation samples represents the general sample-generation quantity that is sufficient to measure the performance of the algorithm [30,33,39]. The side length of each grid is a standard unit, and there is no fixed definition here. As shown in Fig 2, a mobile robot has four motion directions: action 1 moves forward, action 2 moves right, action 3 moves backward, and action 4 moves left. The reward and punishment rules are the same in Q-learning, IDQ, WOQLA, and PWOQLA. If the mobile robot encounters an obstacle, the penalty Qvalue is reduced by 1; if the mobile robot moves to free space, the reward Q-value is increased by 1; and if the mobile robot moves to find the target position, the reward Q-value is increased to 100. Finally, a 400 × 4 Q-table containing all the information on 400 positions and 4 actions at each position is established.
In Q-learning, α is the learning coefficient, and reflects the degree to which the previous Qvalue is retained. Following the work of Khriji et al. [53], α is set to 0.2 in this study. The variable γ is the discount factor, which represents how the agent treats future rewards when it receives the current reward. In this study, γ is set to 0.8 [53]. The number of iterations t in Qlearning is set to 500. In WOA, r ! a , r ! c are random vectors in the range [0, 1], and a decreases linearly from 2 to 0 during the iteration. The parameter b is a constant defining the logarithmic spiral shape, which is set to 1 in this study [54]; and l is a random number in the range [−1, 1]. The variable p is a random number between 0 and 1. The population number n of WOA is set to 30, and the number of iterations t PW and t PWQ are both set to 500. The parameter settings are shown in Table 1.
The experiment was conducted on an Intel (R) Core (TM) i7-7500U CPU @ 2.70 GHz platform. The graphics card was an Intel (R) HD Graphics 620, and the simulation software was MATLAB R2020a.
Experimental results and analysis of PWOA
By solving 8 classic benchmark functions used in the optimization problem, the efficiency of the PWOA is compared with the original WOA. In this experiment, the population size is 30 for both WOA and PWOA, and the maximum iteration is set to 500. The benchmark functions used in the experiment include three types: unimodal (F1, F2, F3); multimodal (F4, F5, F6); and fixed-dimension multimodal (F7, F8) [55]. Table 2 summarizes the details of the benchmark functions in these experiments, including the cost function, the number of design variables V_no, the range of optimization variables, and the optimal value f min .
The algorithms WOA and PWOA are run 30 times each for every benchmark function, starting with different populations randomly generated. Table 3, which include the average and standard deviation of the test cases. Table 3 shows that in F1, F2, F3, F4, F6, F7 and F8, both WOA and PWOA have reached the target optimal value, but the average value and standard deviation of the optimal fitness obtained by PWOA are both superior to WOA. This demonstrates that PWOA has greater convergence accuracy and algorithm stability compared with WOA. In F5, however, the standard deviation of the optimal fitness of PWOA is higher than that of WOA, indicating that the stability of PWOA is slightly worse. On the other hand, both WOA and PWOA eventually converge to the optimal value, and the average value of the optimal fitness of PWOA is better, which also reflects the advantages of PWOA. It can be seen from Fig 5 that in F3, F5, F7 and F8, when the difference between WOA and PWOA in the final convergence accuracy is not large, PWOA finds the optimal solution in the case of fewer iterations, indicating that PWOA has an excellent convergence speed compared to the original WOA. In F1, F2, F4 and F6, when the number of iterations is the same, the convergence accuracy of PWOA is higher than that of the original WOA.
Because the improved strategy of PWOA is to pair agents in the population in advance, the paired agents can share the information found in each iteration and help each other to move towards a better agent position. This strategy is equivalent to one agent exploring the search space twice in one iteration, which is more efficient. With the same parameters, PWOA is naturally superior to the original WOA. In general, PWOA improves the exploitation capability
Experimental results and analysis of PWOQLA
In this experiment, the performance of PWOQLA is compared with that of the original Qlearning, IDQ, A � algorithm, and WOQLA. We compare the averages and standard deviations of the running time, the number of path steps, and the number of rotation angles during 30 simulations, and analyze features, advantages, and disadvantages. The running time simply and directly reflects the efficiency of the algorithm: the shorter the time, the smaller the complexity of the algorithm, and the higher the efficiency. Because it is a square grid with the same distance between each node, the comparison of the number of path steps is equivalent to a comparison of the path length. Finding the shortest path is one of the ultimate goals of the path planning algorithm. Finally, the number of rotation angles is calculated to obtain the steering situation of the mobile robot under actual conditions. If the number of rotation angles is small, it means that the path is smoother, and that the mobile robot traveling along the path does not need frequent changes of direction, which means that the path planning algorithm is naturally more efficient. Figs 6-15 show the best paths obtained respectively by the A � algorithm, Q-learning, IDQ, WOQLA and PWOQLA in 6 experiments composed of different types of grid maps. In these figures, the blue dot represents the starting point, the red dot represents the destination, the grey squares represent the obstacles, the white squares represent free space, and the green line represents the final path. Table 4 shows a comparison of the time to calculate the target position in the maps. Table 5 compares the number of path steps, and Table 6 compares the number of rotation angles.
It can be seen from Table 4 that although the calculation time of the A � algorithm is shortest, the cost function f(n) of the A � algorithm only considers the target position and does not consider the obstacles in the map. This leads to the A � algorithm having the largest average and the largest standard deviation of the number of rotation angles, as can be seen from Table 6, which shows that the path smoothness of the A � algorithm is the worst. Table 4 also shows that, for the original Q-learning, when the number of obstacles increases, the calculation time gradually decreases. This is because the number of obstacles increases while the exploration space decreases, which saves time. In contrast, for IDQ, the calculation time gradually increases. This is because a greater number of local optimal solutions may be generated with the increase in the number of obstacles, which wastes time in this case. The calculation time for WOQLA and PWOQLA also increases with additional obstacles. When there are more obstacles in the map, the calculation time increases because early initialization may entrap Q-learning in a local optimal solution. When there are fewer obstacles in the map, the possibility of being trapped in a local optimal solution is reduced.
In general, PWOQLA achieves the shortest operation time among the algorithms except for the A � algorithm, followed by WOQLA and the original Q-learning, while IDQ has the longest operation time. According to Table 5, the average step values of the original Q-learning and IDQ are slightly higher than the other algorithms, while the average step value of PWOQLA is the shortest. These results show that in a disordered and irregular obstacle map, PWOQLA has the greatest path planning efficiency because it first optimizes the initialization of the Q-table, which simplifies the subsequent search strategy and accelerates the convergence speed. Experiment 2: Lattice obstacles. Experiment 2 sets out to verify the path planning ability of PWOQLA on a regular lattice map. Fig 11 shows a diagram of the optimal path result. Table 7 shows a comparison of the time to find the target position, the path step length, and the number of rotation angles for each algorithm in the experiment. Lattice obstacles test mainly the smoothness of the planning path. It can be seen from Fig 11 and Table 7 that the path planned by PWOQLA is the smoothest, with the shortest computational time and step value. Compared with the A � algorithm, the average number of rotation angles for PWOQLA is an improvement of 31.6%. Compared with the original Q-learning, the average number of rotation angles for PWOQLA is an improvement of 31.0%. The standard deviation in the number of rotation angles is also the smallest for PWOQLA, indicating that the path of PWOQLA is more stable and always finds the target with fewer rotations. Experiment 3: Strip obstacles. Experiment 3 studies the path planning of each algorithm when the initial position and target position are separated by multiple long-strip obstacles and the target cannot be reached directly. Fig 12 shows a diagram of the optimal path result. Table 8 shows the experimental results for each algorithm. Because the terrain is too complex, and the path to the destination needs to pass no less than 3 obstacles, the original Q-learning has the longest calculation time. The calculation time for PWOQLA is still the shortest. The average number of path rotation angles for IDQ, WOQLA and PWOQLA are all less than the original Q-learning, indicating that these algorithms have improved the smoothness of the optimized path. Their standard deviations in the number of rotation angles has also been reduced, indicating that the path is more stable.
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Experiment 4: Horizontal obstacles. Experiment 4 sets out to test the ability of these algorithms to pass through straight and narrow paths. From Table 9, it can be seen that the A � algorithm, Q-learning and IDQ cannot find the best path via the shortest route in each simulation, whereas WOQLA and PWOQLA perform well in this respect. Although WOQLA and PWOQLA have no advantage in computing time, the number of rotation angles has been significantly reduced. Compared with the original Q-learning, the number of rotation angles for WOQLA is reduced by 25.6% and the number for PWOQLA is reduced by 32.4%. Additionally, Fig 13 shows that WOQLA and PWOQLA take smoother paths and fewer turns to reach the destination. If the algorithm is applied to the path planning of mobile robots, these algorithms will reduce the time for the mobile robot to rotate and change direction, and save resources.
Experiment 5: Room type obstacles. Experiment 5 is a simulation of finding the target position in a room and testing the path planning ability of the algorithms when there are room-type obstacles. It can be seen from Fig 14 that the path found by PWOQLA is the best visible to the naked eye. Table 10 indicates that, except for the A � algorithm, PWOQLA has the shortest average operation time and is the most suitable for this scenario, while each algorithm can find the path with stability and the least number of steps every time. Experiment 6: Concave obstacles. The aim of Experiment 6 is to simulate finding the target position in a narrow concave tunnel. Combining Fig 15 and Table 11, it can be seen that
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the average number of rotation angles of the original Q-learning, IDQ, WOQLA and PWOQLA are almost the same, while the standard deviations are not much different, indicating that these algorithms are suited to this kind of scene. However, compared to other scenarios, the best path with the least number of steps cannot be found every time. In the Experiment 6 scenario, the A � algorithm and the original Q-learning will take detours to find the target position during some simulations, whereas IDQ, WOQLA and PWOQLA are more stable, being able to find the path with the least number of steps more often.
Wilcoxon rank-sum test. The Wilcoxon rank-sum test is a nonparametric hypothesis test, which is used to infer whether there is a difference between the distribution positions of two populations. It reflects the correlation of the experimental results of each algorithm in 30 independent runs. In this test, a p-value with a 95% significance level was computed, which means that when the test value is less than 0.05, it indicates that there is a significant difference between the experimental data of different algorithms. And the corresponding results for computational time, path steps and number of rotation angles are reported in Table 12.
According to Table 12, it can be seen that under different experimental map environments, compared with other path planning algorithms, data distribution on computational time is significantly different in PWOQLA, which indicates that PWOQLA has significantly improved the path planning time, proving its superiority. There is no significant difference between some data of path steps and number of rotation angles. First, due to the limitation of data
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types, and second, because other algorithms are excellent enough in the performance of these two test indicators, so the results in Table 12 are obtained.
Discussion
In general, except for the A � algorithm, PWOQLA has the best performance in these experiments, which is shown in the shortest calculation time and the smoothest path. The reason why PWOQLA has the best performance is that it uses PWOA to improve the initialization
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larger number of steps and a larger number of rotation angles. Considering the actual requirements for mobile robot path planning, PWOQLA is obviously better. In Experiment 4, the calculation time of PWOQLA is longest in five simulations. The reason why PWOQLA does not perform well in Experiment 4 is that the exploitation ability of PWOQLA has not been improved. When the obstacle area is relatively large and concentrated, the disadvantages of PWOQLA are more obvious. PWOQLA focuses more on improving the exploration strategy, mainly improving the calculation time of the algorithm. In Experiment 3, however, the path planned by PWOQLA is the smoothest, and both the average and the standard deviation of the
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rotation angles are the smallest. This shows that the pre-treatment during PWOQLA initialization compensates for the exploitation ability to a certain extent, enhancing an understanding of the map, and helping PWOQLA to find the optimal path. Comparing PWOQLA performances in all of these experiments, Experiment 6 is especially notable. In navigating concave obstacles, PWOQLA takes the shortest time in five simulations to find the target, with an average of only 0.85s and a standard deviation of 0.05s, which is the shortest too. The results of Experiment 6 show that PWOQLA performs best in computational time, indicating that it is the most suitable for the path planning of mobile robots in concave obstacle maps similar to this experiment, such as maps with many curves or narrow tunnels. In Experiment 4 on the other hand, PWOQLA takes the longest time compared with other PWOQLA performances, with an average computational time of 0.96s. This shows that PWOQLA is not the best performer when obstacles are regular and repeated. Thus, the exploitation capability of PWOQLA should be further improved.
Although the exploitation capability of PWOQLA is insufficient, the experimental results show that PWOQLA still meets the requirements of speeding up path planning time and finding the best path with fewer rotation angles. Moreover, PWOQLA overcomes the disadvantage of slower convergence in the original Q-learning.
Conclusions
The convergence speed Q-learning is slow because is too simple when initializing the Q-table and wastes too much time in the exploration process. To solve these problems, we propose PWOQLA. Firstly, the WOQLA proposal solves the problem of slow convergence speed caused by the simple initialization of the Q-table. Through this innovation, in which the
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original WOA is used to initialize the values of the Q-table, a Q-table containing previous experience is obtained before the exploration process. Thus, the convergence speed of ε-greedy Q-learning is accelerated. Secondly, the PWOA proposal speeds up the speed of the whale population approaching the local optimal solution, solving the shortcoming of slow convergence in the original WOA. Thus, the efficiency of Q-learning initialization in WOQLA can be improved by replacing WOA with PWOA. Thirdly, the SES proposal, which utilizes the position relationship between the current agent and the target, reduces the useless exploration of ε-greedy Q-learning and further improves the convergence speed. Fourthly, the proposal of a dynamically changing nonlinear function for ε overcomes the shortcoming that exploration and exploitation cannot be switched flexibly in the original ε-greedy Q-learning. Experimental results show that PWOQLA has greater accuracy and faster convergence speed compared with algorithms with similar functions.
Although PWOQLA balances exploration and exploitation capability in a static environment, the exploitation capability of PWOQLA is insufficient in a dynamic environment. Thus, PWOQLA could be combined with other algorithms that have strong exploitation capabilities when applied to path planning in dynamic or extreme environments. The method of determining the ε dynamic curve parameters in PWOQLA can also be further improved. In future work, we will apply PWOQLA to mobile robot path planning in dynamic or extreme environments and test its performance. | 9,746.8 | 2022-12-27T00:00:00.000 | [
"Computer Science"
] |
Molecular dynamics simulation analysis of Focal Adhesive Kinase (FAK) docked with solanesol as an anti-cancer agent
Focal adhesion kinase (FAK) plays a primary role in regulating the activity of many signaling molecules. Increased FAK expression has been associated in a series of cellular processes like cell migration and survival. FAK inhibition by an anti cancer agent is critical. Therefore, it is of interest to identify, modify, design, improve and develop molecules to inhibit FAK. Solanesol is known to have inhibitory activity towards FAK. However, the molecular principles of its binding with FAK is unknown. Solanesol is a highly flexible ligand (25 rotatable bonds). Hence, ligand-protein docking was completed using AutoDock with a modified contact based scoring function. The FAK-solanesol complex model was further energy minimized and simulated in GROMOS96 (53a6) force field followed by post simulation analysis such as Root mean square deviation (RMSD), root mean square fluctuations (RMSF) and solvent accessible surface area (SASA) calculations to explain solanesol-FAK binding.
Background:
Cancer has affected more than 15 million people across the globe and it is expected to affect 25 million people in the next 20 years [1]. Cancer is regarded as the fastest progressing noncommunicable disease with frequent appearance of numerous new forms every year, which are often resistant [2]. Even though massive hard work have been put by researchers, healthcare professionals, etc. in discovering, developing, and utilizing chemotherapeutic approaches for managing neoplasm, but still it continues to be a serious issue across the world at present. The identification of several unexplored classes of cell-cycle regulators and apoptotic stimuli were the emerging strategy in anti-cancer drug discovery. At present, a number of inhibitors have been discovered which modulates cellular resistance, hormonal milieu, angiogenesis, cellular migration, cell proliferation, and DNA targets [3]. The inhibition of angiogenesis (preventing new blood vessels formation) has been representing as an impressive strategic approach in managing cancer and which in turn prevention of metastasis.
Angiogenesis is the process in which new blood vessels originate from the existing blood vessel system [4]. Innumerable proangiogenic factors such as focal adhesion kinase (FAK), TGF-b, vascular endothelial growth factor (VEGF), angiogenin, fibroblast growth factor (FGF), and many other factors, also known as "angiogenic switch" promote constitution of new vessels [5]. In the case of tumors, these factors get over-expressed, that eventually enhances tumor growth and metastasis [6]. From last few years, various researches have revealed successful restriction of tumor proliferation by preventing accessibility of nutrient supply to the highly metabolizing cell like cancer [7]. The inhibition of these pro-angiogenic factors like FAK will lead to a halt in tumor progression.
Focal adhesion kinase (FAK) is a cytoplasmic tyrosine kinase (PTK2) that plays a primary role in growth factor mediated signaling and mediates significant role in cell migration, proliferation, and angiogenesis [8]. Several vascular growth promoting factors like insulin-like growth factor (IGF)-I, vascular endothelial growth factor (VEGF), and basic fibroblast growth factor (bFGF) activates FAK [9]. FAK have also been identified recently to be the prime factor in retinal angiogenesis [10]. Any mutation or alterations in the expression of FAK results in the generation of tumors promote metastasis and endorse vascular growth [11]. FAK has been associated with several forms of cancers like breast, colon, ovarian, prostate, head and neck, thyroid, oral, stomach, cervical, liver, sarcoma, melanoma, and glioblastoma [12]. It has been reported that blockade of FAK often results in reduction of metastasis and mobility in case of breast cancer [13].
Natural products have a huge reputation as promising anticancer agents and in the modern era, naturally derived products are frequently accepted in therapy among the masses [14]. A lot of dietary isoprenoid-based compounds have come into limelight owing to their chemopreventive and antiproliferative properties [15]. Some less known isoprenoid derivatives are now finding applications in mainstay chemotherapy [16]. Solanesol is believed to be among one of the most eligible candidates to demonstrate anti-cancer activity. Commercially, solanesol gets extracted from the tobacco plant, the richest source. As evidenced and rejuvenating the fact from several famous English literature that "Mother Nature inculcates all miraculous remedies in it", our search for an unexplored class ended in tobacco. In one-half, the American Cancer Society (ACS) sticks to the fact that tobacco is the leading cause of cancer. On the other hand, solanesol, the chemopreventive, anti-angiogenic and anti-tumor principle is obtained from the same plant, tobacco, which is quite mysterious and highlights the immense beauty of nature.
Solanesol is a non-cyclic polyisoprenoid alcohol (composed of nine isoprenoid unit) present mainly in solanaceous crops like tobacco, tomato, potato, eggplant, and pepper plants [17]. Solanesol appears as a waxy white solid at room temperature, it is optically inactive, non-polar in nature and exhibit solubility in like-wise non-polar solvents soluble The present research involves establishing of solanesol as a focal adhesion kinase (FAK) inhibitor by applications of computational in silico methods. Though, solanesol used as a bioactive agent in industries for decades, due to its highly flexible nature, there is no successful in silico protein binding and simulation data available online till date. We also proposed a method of binding of the highly flexible compound to protein targets using an enhanced contact based scoring method. This method scores the residues rather than the conformations. The higher scored residues were then used for more "focused" docking on those residue regions.
Methodology: Protein selection and preparation:
The crystallographic co-ordinates for Focal adhesion kinase (PDB ID: 4Q9S) [25] were retrieved from the Protein Data Bank (PDB). Prior to docking, protein structures were prepared by removing water molecules using UCSF Chimera software [26]. Following which, bond orders were assigned, and hydrogen atoms were added to the crystal structures.
Ligand preparation:
Solanesol exist in both cis and trans states, for this experiment we considered only trans is found in natural sources [27]. The structure of Solanesol was obtained from PubChem compound (CID 5477212). Gaussian 09 program was used to obtain the optimum geometry of the structures using the density function theory at the B3LYP/6-31G (d,p) level [28].
Molecular docking:
All the molecular docking studies of Solanesol to FAK were performed using Autodock 4.2 [29]. Autodock uses a semiempirical free energy force field to evaluate binding conformations of ligand while docking. The AutoDockTools was used for preparing protein and ligand parameters files. For ligands; the hydrogens, compute Gasteiger charges, and nonpolar H atom were added which ensuring the total charge corresponds to the tautomeric state followed; and, at last torsion tree root and rotatable bonds were chosen. For macromolecules; hydrogens, compute Gasteiger charges, and merge non-polar H were added which was followed by Stouten atomic salvation parameters assignment; and at last flexible residues PDBQT in addition to the rigid PDBQT file were created. A RMSD value inferior or close to 2A ° was considered as a successful docking [30].
Binding site analysis:
Solanesol is a 45-carbon chain with 26 rotatable bonds. As it is extremely flexible it is hard to determine the bind mode of it with the protein. The commonly used protocol for determination of binding pocket is "Blind docking", which was initially developed for to determining peptide docking with protein [31]. In this method the constrained ligand (or peptide) is docked with the whole protein surface. The place where it forms a cluster with higher energy determines the binding site. Then these sites were used for "refined docking" where the lowest binding modes for each of these places (in case if there are more than one) where determined by molecular mechanics and molecular dynamics studies. For calculating the possible area of interaction or binding site of a highly flexible ligand we enhanced blind docking using Ligand Contact Based Scoring function for Residues (LCBSR). This is an atomic contact/clash based scoring method, in which the residues are scored based on the higher favorable interactions and probability of formation of a hydrogen bond. As it doesn't depend on the clustering or solely on binding energy, it statistically enhances the probability of finding the possible binding site.
It can be represented as, The "Contact" here is defined as the instance when the difference between the distance of two atoms and the sum of their van der Waal radii is 0.4 A or more or, in other words, the distance is greater than the sum of van der Waal radii (Eq. 1) of two atoms. Whereas "Clash" is defined as the condition where the van der Waal radii of two atoms unfavourably overlaps each other and the distance is lower than the sum of radii (Eq. 2) of the two atoms.
This can be represented as: Where, ΣrVDW(i,j) is the sum of van der Waal radii of interacting atoms of ligand (i) and residue (j) and Dij is the distance between interacting atoms of ligand (i) and residue (j). A Higher value of LCBSR of any residue implies the residue may be a part of the binding pocket for the ligand and, if it is capable, it may also form a hydrogen bond with the ligand. Lesser score implies a lower interaction or high chances of unfavorable clashes or low chances of forming a hydrogen bond. Considering all the conformers may lead to false positives, thus conformers were separated in three criteria: (1) binding energy less than -2.0 kcal/mol; (2) binding energy less than -3.0 kcal/mol; and binding energy less than -4.0 kcal/mol. Provided -4.0 is roughly half the average of the binding energy (Average B.E = -7.10 kcal/mol) of all the three experiments, ensuring only conformations with low B.E were considered. The resultant values from each of these three were added to corresponding residues. This way the residues interacting more with the conformations of better binding energy will have a better score. For getting a statistically significant result, all the scores of the residues from all the three experiments were added to get the final score of each residue. Only those residues, which appeared in more than 2 experiments, were considered.
Refined docking:
Binding site for Solanesol was considered using residues with a higher LCBSR score. This binding site was then used for refined docking using Autodock. The experiment was done twice with (1) relaxed parameters, GA maximum energy evaluations 2.5 × 106, for 200 GA runs (2) exhaustive parameters, GA maximum energy evaluations 3.5 × 107, for 200 GA runs. method was used, with a coulomb cutoff of 1.2 nm, Fourier spacing of 0.16 nm and an interpolation of order 4. Energy minimization of the system was carried out using steepest descent algorithm with a tolerance value of 1000 kJ mol -1 nm -1 . After energy minimization, NVT and NPT equilibrations were done on the system until it reached the room temperature and water density. Production MD was performed for 20 ns time duration for both the simulations.
Molecular dynamics trajectories analysis:
The root mean square deviation (RMSD) and root mean square fluctuations (RMSF) of FAK backbone were calculated using "g_rms" and "g_rmsf" utility commands, respectively. A spherical probe of radius 1.4 Å across the protein surface was used for calculating solvent-accessible surface area (SASA) by "g_sasa" tool of Gromacs. Hydrogen bonds between Solanesol and FAK were calculated using "g_hbond" tool with proton donor and acceptor distance ≤ 3.5 Å and the angle between acceptor-donor-hydrogen ≤ 30.0 degrees.
Binding free energy calculations:
The molecular mechanics Poisson-Boltzmann surface area (MMPBSA) [38] approach was to estimate the binding free energy of protein-ligand interaction. For this purpose, "g_mmpbsa" [39] tool was used. The tool calculates the molecular mechanics potential energy and the free energy of solvation and excludes the entropy calculations. MM-PBSA calculations were performed using 1000 snapshots taken from last 5 ns of trajectories of the complex system. The MM-PBSA based binding affinity (ΔΔG) was calculated using the g_mmpbsa provided script.
ΔΔGBE=ΔGComplex-(ΔGReceptor + ΔGLigand) ΔEMM, ΔGSol and TΔS represent the molecular mechanics component in the gas phase, stabilization energy due to salvation, and a vibrational entropy term, respectively. ΔEMM is the summation of ΔEint, ΔEcol, and ΔEvdw, which are the internal, coulomb, and van der Waals interaction terms, respectively. ΔGsol is the salvation energy and it is divided into an electrostatic salvation free energy (GPB) and a non-polar salvation free energy (GSA).
Result and Discussion: Docking analysis Blinding docking and LBCSR Score:
Solanesol shows very small cluster with insignificant binding affinity towards FAK when docked "blindly" (Table 1). Though, the structure shows quite high binding affinity towards the kinase but the conformations with higher binding energy fails to form any significant cluster.
From all the generated conformations of Solanesol, which were having binding energy lower than -4.0 kcal/mol, all the favorable and unfavorable overlaps of the atoms were calculated using "FindClash" tool of UCSF Chimera. Chimera tool, "FindHbond" was also used to find the hydrogen bonds between the ligand and residue atoms. The default values were kept for all the calculation in Chimera.
An in-house python script was used to calculate the number of "Clashes", "Contacts" and "Hbonds" between all the conformations and residues as well as individual scores. The scores from all the three experiments were added to give a final score for each residue (Table 2).
Based on the LBCSR score calculated for all three experiments, the scores for all the residues were plotted as graph (Figure 3) as well as plotted as false color on the 3D structure of the protein (Figure 2). From the LBCSR score it can be inferred that the ligand shows a high affinity towards the region with Asp564, Asn551, Arg550, Leu553 and Ile428, respectively.
Refined docking:
All the residues with more than LBCSR score was considered for the active site prediction. A total of 77 residues were found to be above and incidentally which also forms the ATP binding site and the catalytic loop (546-551) and formed between the N and C lobe.
The centre of geometry (coordinates = 10.8, 1.0, 15.0) of these 77 residues was considered for the centre of the binding pocket of Solanesol. A grid of size 60 × 62 × 68 was considered to exactly fit all the 77 residues. Autodock4.2 was again used for docking of Solanesol with FAK with this grid setting for two more times, first time with default setting for 200 conformations and later docked with exhaustive setting for the same number of conformations. All 400 conformations were rescored using DSX online server with CSD settings ( Table 3).
Analysis of Final Docked structure:
The hydroxyl end of Solanesol binds to the binding site of ATP and interacts with Ile428, Val436, Ala452, Lys454 and Leu501 (Figure 4). These residues that forms the binding pocket for ATP, forms Alkyl-Pi hydrophobic interactions with the double bonds of the ligand. Where the isobutyl end of the ligand gets attached to the Catalytic loop and αC helix. The ligand interacts with Phe542, Arg545, Arg550 (Catalytic loop) and Phe478 (αC helix terminal) with Alkyl and Sigma-Pi interactions. Pro585, Ile586 near the ATP active site also forms similar hydrophobic interactions with the ligand. Oxygen of Solanesol forms a very conventional H-bond with OE1 of Gln438, which is very near to G-Loop and ATP binding site.
These 12 hydrophobic interactions of 11 residues with Solanesol stabilize the ligand at the middle of N and C lobe of FAK. As the ligand share interacting residues with both the side it may be act as a better inhibitor for FAK. This structure was used for molecular dynamics studies.
Analysis of Molecular Dynamics:
For the measuring the stability, the RMS deviation in the backbone of the Solanesol bound FAK and only FAK been measured and plotted in accordance to time ( Figure 5). After an initial instability, the backbone changes its shapes linearly with a linear slope increase in RMSD between 4.5ns to 7.7ns after again a short destabilization the system vaguely equilibrates from 9.4ns to 14.2ns. It takes the system almost 15ns to equilibrate, after which the system maintains it position and shape.
Comparison of the RMSD of both the trajectories from the minimized structures shows, Solanesol bound FAK backbone show more stability than that of independent FAK backbone. RMSF (Root mean Square Fluctuation) of Solanesol bond FAK exhibits less fluctuation at the places where Solanesol is bond ( Figure 6).
Total solvent accessible surface area (SASA) was checked by g_sas tool of Gromacs for analyzing the change in surface area with respect to time. It show a quite negative correlation with the RMSD suggesting the better binding of the ligand leads to a lower surface area of the protein thus closing the active site for any further contact. It remains stable for the wider part of 6ns -18ns range after which the backbone gets stabilized and may also affect the surface area.
MM-PBSA Calculation:
Binding site residues for Solanesol were selected by taking 3.5A radius from Solanesol. Molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) was calculated for the last 5 ns with 20 ps steps for the binding site residues versus Solanesol using g_mmpbsa tool. Per residue analysis of the result was done and plotted using the script provided. This analysis suggests that, Ile428, Gly431, Val436, Val484, Met499, Cys502 and Leu553 interacts most favorably with the ligand (Figure 7). Interestingly these all residues are part of ATP binding pocket of FAK. Gly431 is a part of the G-loop, which helps in the phosphorylation of the protein, also interacts favorably along with Leu584, which is part of the activation loop. A very low ΔΔG, of -113.85 kJ/Mol (Table 4), proves solanesol have a very high binding affinity towards the FAK structure. The change in binding energy with time was also plotted (Figure 8). It shows that the ligand gets stabilized with a very high binding affinity after 17 ns of simulation.
Conclusion:
We report the binding of Solanesol with FAK using a GROMOS96 (53a6) force-field simulated docked model of Solanesol-FAK complex. The binding of solanesol at the ATP binding site to inhibit the phosphorylation of FAK is explained. Data help to understand binding of flexible compounds with FAK for potential inhibition. | 4,177.6 | 2017-09-30T00:00:00.000 | [
"Chemistry",
"Medicine"
] |
Ascorbate sensitizes human osteosarcoma cells to the cytostatic effects of cisplatin
Abstract Osteosarcoma (OS) is the most common malignant bone tumor and a leading cause of cancer‐related deaths in children and adolescents. Current standard treatments for OS are a combination of preoperative chemotherapy, surgical resection, and adjuvant chemotherapy. Cisplatin is used as the standard chemotherapeutic for OS treatment, but it induces various adverse effects, limiting its clinical application. Improving treatment efficacy without increasing the cisplatin dosage is desirable. In the present study, we assessed the combined effect of ascorbate on cisplatin treatment using cultured human OS cells. Co‐treatment with ascorbate induced greater suppression of OS cell but not nonmalignant cell proliferation. The chemosensitizing effect of ascorbate on cisplatin treatment was tightly linked to ROS production. Altered cellular redox state due to increased ROS production modified glycolysis and mitochondrial function in OS cells. In addition, OS cell sphere formation was markedly decreased, suggesting that ascorbate increased the treatment efficacy of cisplatin against stem‐like cells in the cancer cell population. We also found that enhanced MYC signaling, ribosomal biogenesis, glycolysis, and mitochondrial respiration are key signatures in OS cells with cisplatin resistance. Furthermore, cisplatin resistance was reversed by ascorbate. Taken together, our findings provide a rationale for combining cisplatin with ascorbate in therapeutic strategies against OS.
| INTRODUC TI ON
Osteosarcoma (OS) is the most common primary malignant bone tumor and affects adolescents and children. 1 In addition, OS is the most frequent cause of cancer-related deaths in children and adolescents. 2 The current standard treatment for OS is a combination of chemotherapy and surgical resection. 3 The overall survival for patients with localized OS is approximately 65%-70%. 4 In recent decades, improved chemotherapy regimens have contributed to treatment outcomes, 5 but more than 30% of patients have recurrence and metastasis. 6 The response to preoperative chemotherapy is an important predictive factor for the prognosis of OS. 7 Thus, several attempts have been made to improve the treatment efficacy of poor responders using modified chemotherapy protocols, but a unified strategy has not been agreed upon. 5 The use of high-dose chemotherapeutic drugs for primary chemotherapy could be a solution, but systemic toxicity 8 and a risk of secondary cancer are concerns. 9,10 Thus, there is a pressing need to develop new strategies or modify current chemotherapy regimens to treat OS patients refractory to chemotherapy.
Cisplatin is one of the most widely used platinum-based anticancer drugs for treating a variety of solid tumors, including OS. 11 Cisplatin interacts with various cellular components, including chromosomal DNA, proteins, small peptides, lipids, and RNA, [12][13][14][15] resulting in suppression of tumor cell proliferation via multiple pathways. 15 In addition, cisplatin treatment induces oxidative stress, which contributes to its cytotoxic effects. 16,17 The adverse effects of cisplatin place limits on its clinical application. 18,19 Thus, the development of strategies to improve cisplatin treatment efficacy without increasing dose is important.
The anticancer effects of ascorbate (vitamin C) were proposed in the 1950s, 20,21 but contradictory results were reported in subsequent studies. 22 When administered intravenously at high doses, ascorbate has exhibited clinical and preclinical potential in cancer treatment, especially in synergy with other chemotherapeutic agents. 23,24 Additional studies have shown that ascorbate has an antitumor effect in a number of cancer models, including pancreatic, ovarian, and breast. [25][26][27][28][29] Several molecular mechanisms have been proposed for the cytotoxic effects of ascorbate, including increased pro-oxidant damage by generation of reactive oxygen species (ROS), but little is known about the effect of ascorbate on the cisplatin response in human OS. Normally, ROS are produced mainly by intracellular aerobic respiration and metabolism, consequently influencing cell and tissue homeostasis. An altered redox balance due to increasing ROS, however, is known to have pathophysiological effects, including oxidative damage of surrounding lipids, proteins, and DNA. It is thus important to better understand the effects of combined cisplatin and ascorbate treatment on the oxidative stress response in OS, including consequential effects on mitochondrial function and metabolic shift.
In the present study, we show that ascorbate enhances the antitumor effect of cisplatin via increased ROS production, and that the treatment of OS cells with cisplatin and ascorbate alters glycolysis and mitochondrial function. In addition, the co-treatment of OS cells with cisplatin and ascorbate reduces sphere formation, suggesting a chemosensitizing activity of ascorbate on cancer cells that retain cancer stem cell (CSC) properties. Briefly, 1 × 10 6 U2OS cells were cultured on three 10-cm dishes in the presence or absence of cisplatin. The cisplatin concentration was increased from 1 to 30 μmol/L over 6 months. The medium was changed every other day with occasional passage to maintain appropriate cellular confluency. Cisplatin resistance was confirmed by a cell proliferation assay.
Significance Statement
Chemoresistance is a major cause of cancer mortality.
We show that co-treatment with cisplatin and ascorbate induces higher ROS production and metabolic shift in osteosarcoma (OS) cells, leading to strong suppression of cell proliferation. In addition, acquired cisplatin resistance in OS cells is reversed by co-treatment with ascorbate, rationalizing a combination of cisplatin and ascorbate for OS treatment. and 10 μmol/L), or cisplatin plus ascorbate. Ninety-six hours after treatment, 10 µL of WST-8 (2-(2-methoxy-4-nitrophenyl)-3-(4nitrophenyl)-5-(2,4-disulfophenyl)-2H-tetrazolium) was added to each well and incubated for 2 hours at 37°C, after which the absorbance at 450 nm was measured immediately on a microplate reader (iMark; Bio-Rad). The background readings were subtracted from each original reading. The cell viability assay was performed in triplicate and repeated at least three times. The IC 50 was calculated from the curves constructed by plotting cellular viability vs drug concentration. A drug combination effect between cisplatin and ascorbate was evaluated by Combination Index. 31 ROS measurements were performed in triplicate and the entire experiment was repeated at least three times.
| Sphere formation assay
For the sphere formation assay, U2OS cells were resuspended in 0.33% agar gel and plated onto the top of a 0.66% agar gel layer in a 6-well plate. McCoy's 5A medium containing cisplatin, ascorbate, or cisplatin plus ascorbate was added to cover the agar gel layers. Ninety-six hours later, the medium containing the regents was removed and changed to normal McCoy's 5A medium. The medium was changed every other day and the number of spheres The raw reads were trimmed and quality-filtered using Trim Galore! (ver. 0.4.4), Trimmomatic (ver. 0.36), 32 and cutadapt (ver. 1.16) software. Clean reads were aligned using STAR (ver. 2.6.1a), 33 the count matrix generated using the featureCounts tool (ver. 1.6.1), 34 and differential expression analysis performed using DESeq (ver. 1.30.0) 35 with standard settings.
Genes with |log 2 FC| ≥ 2 and a P-value < .05 were subjected to Gene Ontology analysis using clusterProfiler (ver. 3.6.0). 36 We compared the gene expression levels from parental and cisplatin-resistant U2OS cells and picked the genes with significant expression in gene set enrichment analysis (GSEA). 37 The RNA sequence data have been deposited in the DDBJ database (accession number: DRA009407).
| Statistical analysis
Differences between groups were analyzed by an unpaired twotailed Student's t test. Multiple groups were analyzed by one-way analysis of variance. Results are presented as the mean ± standard deviation. P < .05 was considered significant.
| Ascorbate enhances the cytotoxicity of cisplatin in human OS cells
To assess the effect of ascorbate on cisplatin-induced cytotoxicity, we measured cellular viability after 96 hours of continuous cisplatin, ascorbate, or cisplatin plus ascorbate treatment. Cisplatin treatment decreased the viability of U2OS cells in a dose-dependent manner with an IC 50 of 15.5 μmol/L ( Figure 1A). In contrast, ascorbate treatment alone did not significantly affect the viability of U2OS cells at doses between 0.001 and 10 μmol/L. At 100 μmol/L, ascorbate treatment markedly reduced cellular viability ( Figure 1B). We next tested the chemosensitizing effect of ascorbate (1-30 μmol/L) on cisplatin. Although ascorbate treatment alone did not affect cellular viability at these doses, it enhanced the cytotoxic effect of cisplatin ( Figure 1C). The IC 50
| Synergistic ROS induction and DNA damage upon combined treatment with cisplatin and ascorbate
To gain insight into the potential mechanisms underlying the chemosensitizing effect of ascorbate on cisplatin treatment, we measured ROS production by DHE-based flow cytometry. U2OS cells were continuously exposed to cisplatin or cisplatin plus ascorbate at the indicated doses for 96 hours and intracellular ROS levels were measured. Cisplatin treatment increased intracellular ROS levels in a dosedependent manner (Figure 2A). In addition, ROS levels significantly increased in the cells treated with cisplatin plus ascorbate compared to cisplatin treatment alone. To evaluate the kinetics of intracellular ROS production in response to treatment with cisplatin and ascorbate, we measured ROS levels after 24-, 48-, and 96-hour exposure. Although ascorbate treatment alone did not increase intracellular ROS levels, the combined treatment results in an increase after 24 hours exposure, with further increase over time ( Figure 2B). Hence, cisplatin and ascorbate together enhance intracellular ROS production in U2OS cells. Figure 2C,D). Less than 10% of cisplatin has been reported to bind DNA, 38 but it is possible that the increase in γH2AX foci is due to this direct effect, enhanced by ascorbate. Thus, to confirm that ROS production significantly contributes to the observed DNA damage, we examined the effects of a ROS scavenger, NAC, on γH2AX foci formation. The addition of NAC markedly suppressed γH2AX foci formation ( Figure 2D). We can conclude, therefore, that cisplatin-induced ROS production leads to an increase in DNA damage, and that this effect is exacerbated upon addition of ascorbate.
| Enhanced mitochondrial respiration altered the metabolism of U2OS cells
An altered cellular redox state due to increased ROS can shift the balance of metabolic processes in the cell. In particular, ROS can
| Cisplatin and ascorbate treatment influences gene expression in the glycolytic and pentose phosphate pathways
Since combined treatment with cisplatin and ascorbate increases basal glycolysis, we sought to confirm and explain this increase by examining the expression of several genes involved in glucose metabolism. Firstly, we examined the levels of mRNA for HK2, the first enzyme in the glycolytic pathway, which phosphorylates glucose to produce glucose-6-phosphate. Cisplatin treatment increases HK2 mRNA levels ( Figure 4). Subsequently, we examined MCT4 (required for extracellular excretion of lactic acid produced by glycolysis), LDHA (converts pyruvate to lactic acid in the glycolytic pathway), and G6PD. G6PD is the first enzyme in the PPP, a pathway which provides NADPH for the synthesis of fatty acids, steroids, and ribose (for nucleotide and nucleic acid formation) and for maintaining reduced glutathione (an antioxidant). MCT4 and G6PD were upregulated in U2OS cells treated by cisplatin, and the expression levels were further F I G U R E 2 Ascorbate enhances ROS production in osteosarcoma cells. A, ROS levels in U2OS cells treated with cisplatin (0-100 µmol/L) and ascorbate (10 µmol/L) for 96 h as measured by flow cytometry. Intracellular ROS levels were determined by measuring the mean fluorescence intensity (MFI) of DHE-positive cells. MFI in the treated cells was expressed relative to MFI of the untreated cells (set at 1). B, ROS levels in U2OS cells measured by flow cytometry, 24, 48, and 96 h after treatment with cisplatin (0-30 µmol/L) and ascorbate (10 µmol/L). MFI in the treated cells was expressed relative to MFI of the untreated cells (set at 1). C, U2OS cells were treated with cisplatin (10 µmol/L) and/or ascorbate (10 µmol/L) in the presence or absence of ROS scavenger NAC (2 mmol/L), 96 h after treatment and the number of γH2AX dots was counted. D, Immunostaining of γH2AX (green) and DAPI (blue). The data represent the mean ± SD of triplicate samples from three independent experiments. *P < .05; **P < .01 LDHA was upregulated in U2OS cells treated with cisplatin but not significantly enhanced by the combined treatment ( Figure 4).
Since increased ROS are known to affect metabolic pathways, we examined whether the enhanced gene expression observed here on treatment with cisplatin (and/or combined cisplatin and ascorbate) is linked directly to ROS production. RNA levels for the genes were, therefore, assessed in the presence of NAC, a ROS scavenger. NAC treatment significantly suppressed the induction of HK2, MCT4, LDHA, and G6PD ( Figure 4). These data further support our findings that cisplatin and ascorbate synergistically modify mitochondrial function and glycolytic metabolism in U2OS cells, and that this is achieved, at least in part, by increased ROS production.
| Combined treatment with cisplatin and ascorbate suppresses U2OS sphere formation
A small subset of stem-like cells present in tumors, known as CSCs, are proposed to be responsible for cancer initiation, and tumor recurrence, metastasis, and chemoresistance. 39 Here, the sphere formation assay was used to identify a cell population with CSC properties in OS. 40 The assay is based on the ability of CSCs to form a three-dimensional sphere when grown in a gel matrix. To test whether combined treatment with cisplatin and ascorbate affects the sphere formation capacity of U2OS cells, the cells enclosed in agar gel were treated with cisplatin, ascorbate, or cisplatin plus ascorbate for 96 hours. The medium was changed to complete normal medium, and the culture continued for 21 days. Cisplatin plus ascorbate treatment significantly reduced the number and the average size of spheres, compared to untreated control and cisplatin or ascorbate treatment alone, or to untreated control ( Figure 5A-C).
These findings suggest that cisplatin-induced cytotoxicity is enhanced in the cells with sphere-forming ability (CSCs) in the presence of ascorbate.
| Ascorbate increases the chemosensitivity of cisplatin-resistant U2OS cells
Acquired chemoresistance of cancer cells is both a huge concern and a limiting factor for chemotherapy programs. Our next objective, therefore, was to establish whether ascorbate treatment restores the cisplatin sensitivity of cisplatin-resistant cells. We first estab- Figure 6D).
| D ISCUSS I ON
Chemoresistance is a major cause of cancer mortality. The response to preoperative chemotherapy is a particularly important predictive factor for the prognosis of OS patients. 7 Although the mechanisms underlying chemoresistance are complex and may vary among cancers, increasing evidence supports that heterogeneity is a driving force for chemoresistance in general, 44 and that the existing cell populations with chemoresistance can confer intrinsic resistance to chemotherapy. Supporting this view, cisplatin-resistant OS cells possess stem-like properties, 45 a small population of such CSCs having been recognized as drivers for tumor resistance and recurrence in a wide range of cancers.
In the present study, cisplatin treatment induced robust induction of γH2AX, which correlated with raised intracellular ROS levels. genes. 73 The signaling pathways activated or inactivated in cisplatin-resistant cells are not fully understood, but a link between cisplatin and ribosome biogenesis has been observed in multiple cancer cell lines. 74 For example, ribosomal protein L36 contributes to establishing cisplatin resistance in human cancer cells. 75 Expression levels of ribosomal protein L37 affect cell cycle arrest and DNA damage response after cisplatin exposure. 76 These reports, together with our data, indicate an intimate mechanistic link between cisplatin resistance and the ribosomal stress response.
Although further studies are necessary, our RNA sequence data suggest that the modification of ribosome biogenesis is dominant in cisplatin resistance in U2OS cells, which is at least partly due to MYC activation. In support of our findings, neuroblastoma with N-Myc overexpression become resistant to cisplatin 77 and cisplatin exposure activates c-Myc in head and neck squamous carcinoma. 78 In summary, the current study has identified a convergence of phenotypic and detailed metabolic transitions during shortand long-term cisplatin treatment. We propose that combined treatment with cisplatin and ascorbate efficiently suppresses the proliferation and sphere formation of human OS cells via ROS production and a significant metabolic shift. Importantly, the effects of a combination of cisplatin and ascorbate extend to sphere formation and, therefore, the stem-like cells in OS, which are often drug-resistant. Effective suppression of CSC growth, in addition to other tumor cells, could improve early treatment and survival in OS patients. In addition, potential therapeutic targets to circumvent cisplatin resistance have been identified by RNA sequencing analysis, which provides a potential platform for testing novel combinatorial therapies. We anticipate that these approaches will provide new therapeutic options for managing OS patients in the future.
ACK N OWLED G M ENTS
We thank Shinji Kurashimo, Shoei Sakata, and the members of the
CO N FLI C T O F I NTE R E S T
The authors declare that there is no conflict of interest.
DATA AVA I L A B I L I T Y S TAT E M E N T
The RNA sequence data have been deposited in the DDBJ database (accession number: DRA009407). | 3,847.2 | 2020-07-29T00:00:00.000 | [
"Medicine",
"Chemistry"
] |
Lyapunov inequalities for Partial Differential Equations at radial higher eigenvalues
This paper is devoted to the study of $L_{p}$ Lyapunov-type inequalities ($ \ 1 \leq p \leq +\infty$) for linear partial differential equations at radial higher eigenvalues. More precisely, we treat the case of Neumann boundary conditions on balls in $\real^{N}$. It is proved that the relation between the quantities $p$ and $N/2$ plays a crucial role to obtain nontrivial and optimal Lyapunov inequalities. By using appropriate minimizing sequences and a detailed analysis about the number and distribution of zeros of radial nontrivial solutions, we show significant qualitative differences according to the studied case is subcritical, supercritical or critical.
Introduction
Let us consider the linear problem The well known L 1 Lyapunov inequality states that if a ∈ Λ, then L 0 a + (x) dx > 4/L. Moreover, the constant 4/L is optimal since 4 L = inf a∈Λ a + L 1 (0,L) and this infimum is not attained (see [1], [7] and [8]). This result is as a particular case of the so called L p Lyapunov inequalities, 1 ≤ p ≤ ∞. In fact, if for each p with 1 ≤ p ≤ ∞, we define the quantity then β 1 = 4 L and for each p with 1 ≤ p ≤ ∞, it is possible to obtain an explicit expression for β p as a function of p and L ( [1], [10]).
Let us observe that the real number zero is the first eigenvalue of the eigenvalue problem Since zero is the first eigenvalue of (1.5), it is coherent to affirm that β p is the L p Lyapunov constant for the Neumann problem at the first eigenvalue. On the other hand, the set of eigenvalues of (1.5) is given by ρ k = k 2 π 2 /L 2 , k ∈ N ∪ {0} and if for each k ∈ N ∪ {0}, we consider the set (1.10) Λ k = {a ∈ L 1 (0, L) : ρ k ≺ a and (1.1) has nontrivial solutions } then for each p with 1 ≤ p ≤ ∞, we can define the constant An explicit value for β 1,k has been obtained by the authors in [3]. The case p = ∞ is trivial (β ∞,k = ρ k+1 − ρ k ) and, to the best of our knowledge, an explicit value of β p,k as a function of p, k and L is not known when 1 < p < ∞. Nevertheless, since β 1,k > 0, we trivially deduce β p,k > 0, for each p with 1 ≤ p ≤ ∞.
With regard to Partial Differential Equations, the linear problem has been studied in [2], where Ω ⊂ R N (N ≥ 2) is a bounded and regular domain, ∂ ∂n is the outer normal derivative on ∂Ω and the function a : Ω → R belongs to the set Γ defined as (1.13) Obviously, the quantity (1.14) is well defined and it is a nonnegative real number. A remarkable novelty (see [2]) with respect to the ordinary case is that γ 1 = 0 for each N ≥ 2. Moreover, if N = 2, then γ p > 0, ∀ p ∈ (1, ∞] and if N ≥ 3, then γ p > 0 if and only if p ≥ N/2. In contrast to the ordinary case, it seems difficult to obtain an explicit expressions for γ p , as a function of p, Ω and N, at least for general domains. As in the ordinary case, the real number zero is the first eigenvalue of the eigenvalue problem (1.15) ∆u(x) + ρu(x) = 0, x ∈ Ω ∂u ∂n (x) = 0 x ∈ ∂Ω so that it is natural to say that the constant γ p defined in (1.14) is the L p Lyapunov constant at the first eigenvalue for the Neumann problem (1.12).
To our knowledge, there are no significant results concerning to L p Lyapunov inequalities for PDE at higher eigenvalues and this is the main subject of this paper where we provide some new qualitative results which extend to higher eigenvalues those obtained in [2] for the case of the first eigenvalue. We carry out a complete qualitative study of the question pointing out the important role played by the dimension of the problem.
Since in the case of ODE our proof are mainly based on an exact knowledge about the number and distribution of the zeros of the corresponding solutions ( [3]), in the PDE case we are able to study L p Lyapunov inequalities if Ω is a ball and for radial higher eigenvalues. It is not restrictive to assume that Ω = B R N (0; 1) ≡ B 1 , the open ball in R N of center zero and radius one.
In Section 2 we describe the problem in a precise way and we present the main results of this paper. In Section 3 we study the subcritical case, i.e. 1 ≤ p < N 2 , if N ≥ 3, and p = 1 if N = 2. To prove the results in this section we will construct some explicit and appropriate sequences of problems like (1.12) where Dirichlet type problems play an essential role. In this subcritical case we prove that the optimal Lyapunov constants are trivial, i.e., zero.
In Section 4, we treat with the supercritical case: p > N 2 , if N ≥ 2. By using some previous results of Section 2, about the number and distribution of the zeros of nontrivial and radial solutions, together with some compact Sobolev inclusions, we use a reasoning by contradiction to prove that the optimal Lyapunov constants are strictly positive and they are attained. In Section 5 we consider the critical case, i.e. p = N 2 , if N ≥ 3. Because in this case the Sobolev inclusions are continuous but no compact, we demonstrate that the optimal Lyapunov constants are strictly positive but we do not know if they are attained or not.
Finally, we study the case of Neumann boundary conditions but similar results can be obtained in the case of Dirichlet type problems.
main results
From now on, Ω = B 1 , the open ball in R N of center zero and radius one. It is very well known ( [4]) that the operator −∆ exhibits an infinite increasing sequence of radial Neumann eigenvalues 0 = µ 0 < µ 1 < . . . < µ k < . . . with µ k → +∞, all of them simple and with associated eigenfunctions Moreover, each eigenfunction ϕ k has exactly k simple zeros r k < r k−1 < ... < r 1 in the interval (0, 1). For each integer k ≥ 0 and number p, 1 ≤ p ≤ ∞, we can define the set a is a radial function, µ k ≺ a and (1.12) has radial and nontrivial solutions } if N ≥ 3 and a is a radial function, µ k ≺ a and (1.12) has radial and nontrivial solutions} if N = 2.
We also define the quantity The main result of this paper is the following.
The following statements hold: (2) If N ≥ 2 and N 2 < p ≤ ∞ then γ p,k is attained. A key ingredient to prove this theorem is the following proposition on the number and distribution of zeros of nontrivial radial solutions of (1.12) when a ∈ Γ k .
Proposition 2.2.
Let Ω = B 1 , k ≥ 0, a ∈ Γ k and u any nontrivial radial solution of (1.12). Then u has, at least, k + 1 zeros in (0, 1). Moreover, if k ≥ 1 and we denote by x k < x k−1 < ... < x 1 the last k zeros of u, we have that where r i denotes de zeros of the eigenfunction ϕ k of (2.1).
For the proof of this proposition we will need the following lemma. Some of the results of this lemma can be proved in a different way, by using the version of the Sturm Comparison Lemma proved in [4], Lemma 4.1, for the p-laplacian operator (see also [7]). Other results are new.
Proof. To prove i), multiplying (1.12) by ϕ k and integrating by parts in B r k (the ball centered in the origin of radius r k ), we obtain On the other hand, multiplying (2.1) by u and integrating by parts in B r k , we have Subtracting these equalities yields where ω N denotes de measure of the N -dimensional unit sphere. Assume, by contradiction, that u does not vanish in (0, r k ]. We can suppose, without loss of generality, that u > 0 in this interval. We can also assume that ϕ k > 0 in (0, r k ). Since r k is a simple zero of ϕ k , we have ϕ ′ k (r k ) < 0 and since a ≥ µ k in (0, r k ) we obtain a contradiction.
Finally, if r k is the only zero of u in (0, r k ], equation 2.3 yields To deduce ii), we proceed similarly to the proof of part i), restituting B r k by A(r i+1 , r i ) (the annulus centered in the origin of radii r i+1 and r i ) and obtaining and ii) follows easily by arguments on the sign of these quantities, as in the proof of part i).
To obtain iii), a similar analysis to that in the previous cases shows that and the lemma follows easily as previously.
Proof of Proposition 2.2. Let k = 0. If we suppose that u has no zeros in (0, 1] and we integrate the equation −∆u = a u in B 1 , we obtain B 1 a u = 0, a contradiction. Hence, for the rest of the proof we will consider k ≥ 1. Let 1 ≤ i ≤ k. By the previous lemma u vanishes in the i disjoint intervals [r i , r i−1 ),...,[r 2 , r 1 ),[r 1 , 1). Therefore u has, at least, i zeros in the interval Finally, let us prove that u has, at least, k + 1 zeros. From the previous part, taking i = k, u has at least k zeros in the interval [r k , 1], one in each of the k disjoint intervals [r k , r k−1 ),...,[r 2 , r 1 ),[r 1 , 1). Suppose, by contradiction, that these are the only zeros of u. Then u does not vanish in (0, r k ) and applying part i) of Lemma 2.3 we obtain u(r k ) = 0 and a ≡ µ k in (0, r k ]. Applying now part ii) of this lemma, we deduce u(r k−1 ) = 0 and a ≡ µ k in [r k , r k−1 ]. Repeating this argument and using part iii) of the previous lemma we conclude u(r i ) = 0, for all 1 ≤ i ≤ k and a ≡ µ k in (0,1], which contradicts a ∈ Γ k .
For the proof of Theorem 2.1, we will distinguish three cases: the subcritical case (1 ≤ p <
The subcritical case
In this section, we study the subcritical case, i.e. 1 ≤ p < N 2 , if N ≥ 3, and p = 1 if N = 2. In all those cases we will prove that γ p,k = 0.
The next lemma is related to the continuous domain dependence of the eigenvalues of the Dirichlet Laplacian. In fact, the result is valid under much more general hypothesis (see [6]). Here we show a very simple proof for this special case.
where λ 1 (A(ε, R)) and λ 1 (B R ) denotes, respectively, the first eigenvalues of the Laplacian operator with Dirichlet boundary conditions of the annulus A(ε, R) and the ball B R .
Proof. For N ≥ 3 and ε ∈ (0, R/2) define the following radial function u ε ∈ H 1 0 (A(ε, R)): where φ 1 denotes the first eigenfunction with Dirichlet boundary conditions of the ball B R . It is easy to check that lim ε→0 A(ε,2ε) In the same way it is obtained lim ε→0 A(ε,2ε) u 2 ε = 0. In addition, from the variational characterization of the first eigenvalue it follows that λ 1 (A(ε, R)) ≤ On the other hand, using that the first Dirichlet eigenvalue λ 1 (Ω) is strictly decreasing with respect to the the domain Ω, it follows that λ 1 (A(ε, R)) > λ 1 (B R ). Thus and the lemma follows for N ≥ 3.
Proof. If k = 0, this lemma follows from [2, Lem. 3.1]. In this lemma a family of bounded, positive and radial solutions were used. Hence, for the rest of the proof we will consider k ≥ 1.
To prove this lemma we will construct an explicit family a ε ∈ Γ k such that lim ε→0 a ε − µ k L p (B 1 ) = 0. To this end, for every ε ∈ (0, r k ), define u ε : B 1 → R as the radial function where φ 1 (A(ε, r k )) and φ 1 (B ε ) denotes, respectively, the first eigenfunctions with Dirichlet boundary conditions of the annulus A(ε, r k ) and the ball B ε . Moreover these eigenfunctions are chosen such that u ε ∈ C 1 (B 1 ). Then, it is easy to check that u ε is a solution of (1.12), being a ε ∈ L ∞ (B 1 ) the radial function where λ 1 (A(ε, r k )) and λ 1 (B ε ) denotes, respectively, the first eigenvalues with Dirichlet boundary conditions of de annulus A(ε, r k ) and the ball B ε . Since the first Dirichlet eigenvalue λ 1 (Ω) is strictly decreasing with respect to the the domain Ω, it follows that which gives a ε ∈ Γ k . (The equality λ 1 (B r k ) = µ k follows from the fact that ϕ k is a positive solution of −∆ϕ = µ k ϕ in B r k which vanishes on ∂B r k ). Let us estimate the L p -norm of a ε − µ k : Taking into account that λ 1 (B ε ) = λ 1 (B 1 )/ε 2 , λ 1 (B r k ) = µ k , using N > 2p, and applying Lemma 3.1, we conclude and the proof is complete. Proof. If k = 0, this lemma follows from [2,Lem. 3.2]. In this lemma a family of bounded, positive and radial solutions were used. Hence, for the rest of the proof we will consider k ≥ 1.
Similarly to the proof of the previous lemma, we will construct some explicit sequences in Γ k . In this case, this construction will be slightly more complicated. First, for every α ∈ (0, 1), define v α , A α : B 1 → R as the radial functions: where r = |x|. It is easily seen that v α ∈ C 1 (B 1 ), A α ∈ L ∞ (B 1 ), and Now, for every α ∈ (0, 1) and ε ∈ (0, r k ), define u α,ε : B 1 → R as the radial function: where the eigenfunctions ϕ k and φ 1 (A(ε, r k )) are chosen such that u α,ε ∈ C 1 (B 1 ). An easy computation shows that u α,ε is a solution of (1.12), being a α,ε ∈ L ∞ (B 1 ) the radial function Again, using that the first Dirichlet eigenvalue λ 1 (Ω) is strictly decreasing with respect to the the domain Ω, it follows that We see at once that m α > 0 for every α ∈ (0, 1). Hence, if we fix α and choose ε ∈ (0, 1) such that m α /ε 2 ≥ µ k , it is deduced that a α,ε ∈ Γ k . Let us estimate the L 1 -norm of a α,ε − µ k : Doing the change of variables x = εy in the first integral and applying Lemma 3.1 in the second one, it is obtained, for fixed α ∈ (0, 1): Thus, from the definition of γ 1,k we have A α (y)dy , ∀α ∈ (0, 1). Now we will take limit when α tends to 0 in this last expression. For this purpose we first deduce easily from the definition of A α that A α (r) ≤ 16α(1− r 2 )/(− log r) ≤ 32α if r ∈ (α, 1) and A α (r) ≤ 16α + 2/α 2 /(− log α) if r ∈ (0, α). It follows that which gives lim α→0 B 1 A α (y)dy = 0 and the lemma follows from (3.12).
The supercritical case
In this section, we study the supercritical case, i.e. p > N 2 , if N ≥ 2. In all those cases we will prove that γ p,k is strictly positive and that it is attained. We begin by studying the case p = ∞.
Next we concentrate on the case N 2 < p < ∞. For every a ∈ L p (B 1 ) satisfying a L p (B 1 ) ≤ M and every u ∈ H 1 (B 1 ) radial nontrivial solution of −∆u = a u in B 1 we have i) z > ε for every zero z of u. ii) |z 2 − z 1 | > ε for every different zeros z 1 , z 2 of u.
Proof. Let z ∈ (0, 1] be a zero of u. Hence, multiplying the equation −∆u = a u by u, integrating by parts in the ball B z and applying Hölder inequality, we obtain .
From the above it follows that
.
From the change w(x) = v(z x), it is easily deduced that where we have used the compact embedding which is the critical Sobolev exponent). Thus, taking ε 1 > 0 such that M < ε 1 N p −2 α(N, p), we conclude part i) of the lemma with ε = ε 1 .
For the second part of the lemma, consider two zeros 0 < z 1 < z 2 < 1 of u. Taking into account that z 1 ≥ ε 1 and arguing in the same manner of part i), we obtain .
On the other hand, from the one dimensional change of variable w(x) = v(z 1 + (z 2 − z 1 )x), it is immediate that It follows that M ≥ ω C p , we conclude part ii) of the lemma with ε = ε 2 . Obviously, taking ε = min{ε 1 , ε 2 }, the lemma is proved. Proof. Take a sequence {a n } ⊂ Γ k such that a n − µ k L p (B 1 ) → γ p,k . Take {u n } ⊂ H 1 (B 1 ) such that u n is a radial solution of (1.12), for a = a n , with the normalization u n 2 H 1 (B 1 ) = B 1 |∇u n | 2 + u 2 n = 1. Therefore, we can suppose, up to a subsequence, that u n ⇀ u 0 in H 1 (B 1 ) and u n → u 0 in L 2p p−1 (B 1 ) (since p > N/2, then 2 < 2p p−1 < 2N N −2 , which is the critical Sobolev exponent). On the other hand, since {a n } is bounded in L p (B 1 ), and 1 ≤ N/2 < p < ∞, we can assume, up to a subsequence, that a n ⇀ a 0 in L p (B 1 ). Taking limits in the equation (1.12), for a = a n and u = u n , we obtain that u 0 is a solution of this equation for a = a 0 . Note that u n → u 0 in L 2p p−1 (B 1 ) and a n ⇀ a 0 in L p (B 1 ) yields lim B 1 |∇u n | 2 = lim B 1 a n u 2 n = B 1 a 0 u 2 0 = B 1 |∇u 0 | 2 and consequently u n → u 0 ≡ 0 in H 1 (B 1 ). Therefore, if a 0 ≡ µ k , then a 0 ∈ Γ k and a 0 − µ k p ≤ lim n→∞ a n − µ k p = γ p,k , and the lemma follows.
On the other hand, taking into account the continuous embedding H 1 rad (A(ε 0 , 1)) ⊂ C (A(ε 0 , 1)) and u n → ϕ k in H 1 0 (B 1 ), we can assert u n → ϕ k in C (A(ε 0 , 1)). Clearly min r∈(0,1]\A |ϕ k (r)| > 0. Then, for large n we see that min r∈(0,1]\A |u n (r)| > 0, which implies that u n does not vanish in (0, 1] \ A, for large n. Since u n has, at most, k zeros in A, we conclude that u n has, at most, k zeros in (0,1], for large n. This contradicts Proposition 2.2 and the lemma follows.
The critical case
In this section, we study the critical case, i.e. p = N 2 , if N ≥ 3. We will prove that γ p,k > 0. Proof. To obtain a contradiction, suppose that γ p,k = 0. Then we could find a sequence {a n } ⊂ Γ k such that a n → µ k in L N/2 (B 1 ). Similarly to the supercritical case, we can take {u n } ⊂ H 1 (B 1 ) such that u n is a radial solution of (1.12), for a = a n , with the normalization u n 2 H 1 (B 1 ) = 1. Again, we can suppose, up to a subsequence, that u n ⇀ u 0 in H 1 (B 1 ) and taking limits in the equation (1.12), for a = a n and u = u n , we obtain that u 0 is a solution of this equation for a = µ k .
We claim that u n → u 0 in H 1 (B 1 ) and consequently, u 0 = ϕ k , for some nontrivial eigenfunction ϕ k . For this purpose, we set lim B 1 |∇u n | 2 = lim B 1 a n u 2 n = lim B 1 (a n − µ k )u 2 n + lim where we have used a n → µ k in L N/2 (B 1 ) and u 2 n is bounded in L N/(N −2) (B 1 ) (since u n is bounded in H 1 (B 1 ) ⊂ L 2N/(N −2) (B 1 )). Thus, from standard arguments, we deduce that u n → u 0 = ϕ k in H 1 (B 1 ).
In the following, we will fix ε ∈ (0, r k ). Since a n → µ k in L N/2 (A(ε, 1)) and u n → u 0 = ϕ k in H 1 rad (A(ε, 1)) ⊂ C (A(ε, 1)), we can assert that a n u n → µ k ϕ k in L N/2 (A(ε, 1)) ⊂ L 1 (A(ε, 1)). Thus −∆u n → µ k ϕ k in L 1 (A(ε, 1)), which yields u n → ϕ k in C 1 (A(ε, 1)). It follows that, for large n, the number of zeros of u n is equal to the number of zeros of ϕ k in the annulus A(ε, 1), which is exactly k. Applying Proposition 2.2 we can assert that, for large n there exists a zero ε n ∈ (0, ε] of u n . Hence, multiplying the equation −∆u n = a n u n by u n , integrating by parts in the ball B εn and applying Hölder inequality, we deduce Bε n |∇u n | 2 = Bε n a n u 2 n ≤ a n L N/2 (Bε n ) u n 2 L 2N/(N−2) (Bε n ) .
From the above it follows that a n L N/2 (Bε n ) ≥ ∇u .
Taking limits when n tends to ∞ in this expression we deduce Choosing ε > 0 sufficiently small we obtain a contradiction. | 5,871.6 | 2011-09-23T00:00:00.000 | [
"Mathematics"
] |
Surgical and Oncological Outcomes of Robotic Resection for Sigmoid and Rectal Cancer: Analysis of 109 Patients from A Single Center in China
Background: Robotic colorectal surgery has been increasingly performed in recent years. The safety and feasibility of its application has also been demonstrated worldwide. However, limited studies have presented clinical data for patients with colorectal cancer (CRC) receiving robotic surgery in China. The aim of this study is to present short-term clinical outcomes of robotic surgery and further conrm its safety and feasibility in Chinese CRC patients. Methods: The clinical data of 109 consecutive CRC patients whoreceived robotic surgery at Sun Yat-sen University Cancer Center between June 2016 and May 2019 were retrospectively reviewed. Patient characteristics,tumor traits, treatment details, complications, pathological details, and survival status were evaluated. Results: Among the 109 patients, 35 (32.1%) had sigmoid cancer, and 74 (67.9%) had rectal cancer. Thirty-seven (33.9%) patients underwent neoadjuvant chemoradiotherapy. Ten (9.2%) patients underwent sigmoidectomy, 38 (34.9%) underwent high anterior resection (HAR), 45 (41.3%) underwent low anterior resection (LAR), and 16 (14.7%) underwent abdominoperineal resection (APR). The median surgical procedure time was 270 min (range 120 - 465 min). Pathologically complete resection was achieved in all patients. There was no postoperative mortality. Complications occurred in 11 (10.1%) patients, including 3 (2.8%) anastomotic leakage, 1 (0.9%) anastomotic bleeding, 1 (0.9%) pelvic hemorrhage, 4 (3.7%) intestinal obstruction, 2 (1.8%) chylous leakage, and 1 (0.9%) delayed wound union. At a median follow-up of 17 months (range 1–37 months), 1 (0.9%) patient developed local recurrence and 5 (4.6%) developed distant metastasis, with one death due to disease progression. Conclusions: Our results suggest that robotic surgery is technically feasible and safe for Chinese CRC patients, especially for rectal cancer patients who received neoadjuvant treatment. A robotic laparoscope with large magnication showed a clear surgical space for pelvic autonomic nerve preservation in cases of mesorectal edema. especially for patients with locally advanced rectal cancer after treatment with preoperative chemoradiotherapy. In our study, 37.6% patients presented with a BMI ≥ 24 kg/m 2 , and 55.4% patients with rectal cancer received neoadjuvant treatment. No conversion occurred with a median procedure time of 270 min, a median estimated blood loss of 50 ml and a median length of stay of 7 days. Only 11 patients (10.1%) experienced postoperative complications, which shows the remarkable surgical advantages of robotic surgery in patients with rectal cancer who received neoadjuvant treatment.
from the umbilicus to the anterior superior iliac spine, one third of the way from the anterior superior iliac spine. Robotic arm 2 (8 mm) was placed 3-4 cm below the xiphoid process. An assistant port was placed (12 mm) at the intersection of the vertical line through McBurney's point and the horizontal line through the camera port.
Total mesorectal excision (TME) and tumor-speci c mesorectal excision (TSME) were performed as previously described (Xu and Qin, 2016). The procedure of pelvic autonomic nerves preservation (PANP) was performed at the same time. The sigmoid mesocolon was cut along the right pararectal sulcus using the middle approach, and the inferior mesenteric artery was fully exposed. The inferior mesenteric artery was clamped and cut off approximately 1 cm from the root of the blood vessel in order to protect the superior hypogastric plexus. The "cavity effect" of electric heating equipment was quickly exposed, and Toldt's plane was subsequently entered.The white lamentous connective tissue in Toldt's space was cut sharply using an electric knife and kept in the neurosurgical plane of the white lamentous connective tissue at all times. We separated the posterior wall of the rectum closely behind the fascia propria of the rectum under direct vision in order to protect the inferior hypogastric nerve and the anterior sacral vessel. Similarly, sharp separation of the rectal lateral walls was performed near the outer edge of the rectal ligament and the inside edge of the pelvic plexus to protect the pelvic plexus. The anterior rectal space between the anterior and posterior Denonvilliers' fascia was separated to protect the branches of the pelvic plexus.
Follow-up
Patients were scheduled for subsequent visits every 3 months for 2 years then semiannually until 3 years after surgery. Physical examination, blood tests for carcinoembryonic antigen (CEA) and carbohydrate antigen 19 − 9 (CA19-9) levels, abdominal ultrasonography, and chest X-rays were performed every
Intraoperative Outcomes
The intraoperative outcomes are presented in Table 2. The median operative time for robotic surgery was 270 min, with a range of 120 min to 465 min. Median intraoperative transfusion volume for the total cohort was 2000 ml (range 1000-4500 ml). Median intraoperative urine volume for the cohort was 400 ml (range 100-2100 ml). Median estimated blood loss for the cohort was 50 ml (range 20-400 ml). Three patients had blood transfusion, including 2 patients in the APR group (12.5%) and 1 patient in the sigmoidectomy and HAR group (2.1%). None of the cases was converted to an open or laparoscopic procedure, and no intraoperative ureteral injury occurred. Twenty-two patients underwent preventive ileostomy, including 4 patients in the sigmoidectomy and
Survival Analysis
The median follow-up period for all patients was 17 months (range 1-37 months). One hundred and two patients (93.6%) in our study cohort were alive with no evidence of disease. One (0.9%) patient developed local recurrence, and 5 (4.6) patients developed distant metastasis. One patient died due to disease progression. The 2-year OS rate of all patients (n = 109) was 97.2% (Fig. 3A), and the 2-year DFS rate of nonmetastatic patients (n = 104) was 92.9% ( Figure. 3B). The 2-year DFS rate of patients in stages 0, I, II, and III were 100%, 95.5%, 90.5%, and 88.8%, respectively ( Figure. 3C).
Discussion
In this retrospective study, we investigated the surgical and oncological outcomes of robotic resection for sigmoid and rectal cancer in Chinese patients. Our data found that robotic surgery had a low conversion rate, low morbidity rate, and remarkable oncological outcomes, which con rms its safety and feasibility in Chinese patients with sigmoid and rectal cancer.
Rectal cancer resection is very di cult to perform using traditional laparotomy, but laparoscopic surgery has an advantage for rectal surgery under a clearer view despite the narrow and deep pelvic space. Several studies (Pai et al., 2015;Gomez Ruiz et al., 2016;Shiomi et al., 2014;Tang et al., 2017;Park et al., 2011) con rmed that laparoscopic surgery presented better short-term outcomes and comparable long-term outcomes compared to traditional laparotomy. The surgical advantages and comparable oncological outcomes of laparoscopic surgery were clearly demonstrated in patients with locally advanced rectal cancer after preoperative chemoradiotherapy in the COREAN trial (Jeong et al., 2014). Because of the features of robotic technology, robotic surgery is much more advantageous, especially for patients with locally advanced rectal cancer after treatment with preoperative chemoradiotherapy. In our study, 37.6% patients presented with a BMI ≥ 24 kg/m 2 , and 55.4% patients with rectal cancer received neoadjuvant treatment. No conversion occurred with a median procedure time of 270 min, a median estimated blood loss of 50 ml and a median length of stay of 7 days. Only 11 patients (10.1%) experienced postoperative complications, which shows the remarkable surgical advantages of robotic surgery in patients with rectal cancer who received neoadjuvant treatment.
As previously reported, the most commonly encountered complication was anastomotic leakage, and its average occurrence rate was 8.6% (range from 1.2-20.5%) (Trastulli et al., 2012;Cong et al., 2013) and 1.8 to 13.6% in robotic surgery (Kwak et al., 2011;Baik et al., 2009). Its occurrence affects the patient's quality of life, increases hospitalization costs, delays the implementation of adjuvant chemotherapy, and shortens the overall survival (Baik et al., 2009;Kulu et al., 2015). Eleven patients (10.1%) had postoperative complications, which included 3 patients who suffered anastomotic leakage. Due to the advantages of robotic surgery, such as 3D magni ed view, wristed instruments and stable camera platform, surgeons are able to maintain the su cient surgical dissection plane down to the pelvic oor, which minimizes damage to marginal vessels and allows performance of the rectal division and reconstruction e ciently and safely to shorten the procedure time.
More precise surgery also helps protect the autonomic nerves and reduce the occurrence of long-term postoperative complications, including defecation, urinary and sexual dysfunction (Shiomi et al., 2014). Jiang and coworkers (Wang et al., 2017)
described a signi cant increase in International Prostate
Symptom Score (IPSS) after surgery in the laparoscopic group, and more patients in the laparoscopic group (34.8%) perceived a severe damage in their overall level of sexual function following surgery than the patients in the robotic group (18.3%). Several studies (Kim et al., 2012;Luca et al., 2013) also claimed that robotic TME improved the preservation of urinary and sexual functions because the arms of the robotic device are stable and highly exible in the separation and exposure of tissues. With the high-resolution lens of the da Vinci surgical system to effectively recognize the nerve, the application of the PANP technique resulted in a signi cant reduction in the incidence of urinary dysfunction (4.6%) and sexual dysfunction (7.3%) in our study.
A positive circumferential margin or insu cient harvested lymph nodes leads to local recurrence (Marinatou et al., 2014). Although the relationship between su ciently harvested lymph nodes and local recurrence rate is controversial, the guidelines list the harvesting of < 12 lymph nodes as risk factor and noted that the performance of TME with clear surgical margins and adequate lymph node dissection were related to lower recurrence rate (Benson et al., 2018a;Benson et al., 2018b). In our study, the median positive total harvested lymph nodes was 0 (range 0-22), and the total harvested lymph nodes was 12 (range 1-51).The 2-year DFS of patients in stages 0, I, II, and III were 100%, 95.5%, 90.5%, and 88.8%, respectively, and the 2-year DFS of patients in stage III was slightly better than previous studies (65.2% − 82.8%) (Pai et al., 2015;Gomez Ruiz et al., 2016;Park et al., 2011). The high quality of the procedure (no positive resection distal margin and su cient harvested lymph nodes) and neoadjuvant treatment contributed to the remarkable oncological outcomes.
Several limitations should be acknowledged in the present study. First, this retrospective descriptive study included an uncontrolled, single-arm methodology and a limited number of patients from a single cohort. Although our study con rms the safety and feasibility of robotic surgery in Chinese CRC patients, the ndings must be validated in a prospective, multicenter clinical trial with a large population in the future. Second, the short follow-up duration was insu cient to evaluate 5-year survival outcomes, which may have led to a misestimation of the effect of robotic surgery on OS and DFS. Additionally, selective bias undeniably exists in our cohort.
Conclusion
Robotic surgery is technically feasible and safe for Chinese CRC patients, especially for rectal cancer patients receiving neoadjuvant treatment because a robotic laparoscope with large magni cation shows a clear surgical space for tumor resection in cases of mesorectal edema. Due to the advantages of robotic surgery, surgeons are able to perform the procedure e ciently and safely and help protect marginal vessels and the autonomic nerves, which reduces the occurrence of short-term and long-term postoperative complications and ensures clear surgical margins and adequate lymph node dissection.
Declarations
Ethics approval and consent to participate The present study was performed according to the ethical standards of the World Medical Association Declaration of Helsinki and was approved by the Institutional Review Board and Independent Ethics Committees of Sun Yat-sen University Cancer Center. The informed consent requirement was waived by the ethics committees based on the nature of this retrospective study, in which patient data were kept con dential.
Availability of data and material
The datasets used and analyzed during the current study are available from the corresponding author on reasonable request. The authenticity of this article has been validated by uploading the key raw data onto the Research Data Deposit public platform (www. researchdata.org.cn).
Competing interests
The authors declare that they have no competing interests. | 2,784.6 | 2021-01-22T00:00:00.000 | [
"Engineering",
"Medicine"
] |
The immanence and transcendence of God in Adamic incarnational Christology : An African ethical reflection for the public
This article argues that the transcendence and immanence of God amplified in Christ should influence African believers’ private and public ethics. It accomplishes this by engaging transcendence and immanence of God in the traditional African worldview. The African traditional worldview in many respects believes the transcendent God whose immanence is mediated by lesser spiritual intermediary powers. In responding to this view of God’s transcendence and immanence, we discuss the amplified transcendence and immanence of God in the Adamic incarnational Christological model. This model argues that in the incarnation, God’s transcendence and immanence is amplified by his assumption of our human mode of existence as the New Adam for our redemption. That is, even though God has always been transcendent and present within his creation before the incarnation, his immanence within humanity is amplified by God becoming man in and through Jesus Christ as the New Adam. The ascension of Jesus Christ does not diminish God’s presence within Christians. God continues to have his personal presence within believers through the dynamic presence of the Holy Spirit among them. The transcendence and immanence of God (amplified in Christ) therefore is brought to bear in the private and public ethics of Christians. In contrast to the limited immanence of human beings, God’s immanence is infinite. That is, there is nothing human beings can do which is outside of God’s reach and knowledge. It is from this perspective that African Christians are encouraged to live lives conscious of the infinite-immanent God, who sees both their private and public lives. The private and public life of believers should resemble God’s character and behaviour demonstrated by Jesus Christ, God incarnate, in his earthly ministry. Thus, the transcendence and immanence of God amplified in Christ influences African believers to live as the true ambassadors of Christ who exhibit exemplary ethical behaviour within the public sphere. The article reflects on the role of theological ethics in informing public ethics. As such it is theologically intradisciplinary but focusing on intertheological disciplines and their relationship to public space regarding ethics. It seeks to engage and influence public ethical behaviour in a context corruption and disregard of other human beings’ entitlements. Intradisciplinary and/or interdisciplinary implications: The article challenges the privatisation of Christianity to take a public role in order to influence the public. This approach contributes to shifting African Christians from being passive in the context of unethical behaviours to being active agents who influence the public. As such, it contributes to public, practical theology and public ethics.
Introduction
The transcendence and immanence of God are fundamental attributes of God that are closely linked together (Arseniev 1959:1).The former concept affirms God as the one who transcends space and time because he is the sole creator of everything (corporeal and incorporeal) (Horton 2011:253, cf. 253-258).The latter concept asserts God's ongoing presence within his creation while he remains distinct from it (creation) (Horton 2011).That is, God's immanence within his creation at all times and all places does not equate God with his creation as the pantheistic conception of God's presence posits (Grudem 1994:175;Horton 2011:40-41).In this way, the couplet understanding of the transcendent and immanent concepts of God affirm that God transcends both space and time as the sole originator of all things.However, his transcendence does not prohibit his direct presence within his creation (Grudem 1994:169-174).The transcendent and immanent concepts of God are part of the traditional African worldview of God, hence, it is important to understand the African view.This article argues that the transcendence and immanence of God amplified in Christ should influence African believers' private and public ethics.It accomplishes this by engaging transcendence and immanence of God in the traditional African worldview.The African traditional worldview in many respects believes the transcendent God whose immanence is mediated by lesser spiritual intermediary powers.In responding to this view of God's transcendence and immanence, we discuss the amplified transcendence and immanence of God in the Adamic incarnational Christological model.This model argues that in the incarnation, God's transcendence and immanence is amplified by his assumption of our human mode of existence as the New Adam for our redemption.That is, even though God has always been transcendent and present within his creation before the incarnation, his immanence within humanity is amplified by God becoming man in and through Jesus Christ as the New Adam.The ascension of Jesus Christ does not diminish God's presence within Christians.God continues to have his personal presence within believers through the dynamic presence of the Holy Spirit among them.The transcendence and immanence of God (amplified in Christ) therefore is brought to bear in the private and public ethics of Christians.In contrast to the limited immanence of human beings, God's immanence is infinite.That is, there is nothing human beings can do which is outside of God's reach and knowledge.It is from this perspective that African Christians are encouraged to live lives conscious of the infinite-immanent God, who sees both their private and public lives.The private and public life of believers should resemble God's character and behaviour demonstrated by Jesus Christ, God incarnate, in his earthly ministry.Thus, the transcendence and immanence of God amplified in Christ influences African believers to live as the true ambassadors of Christ who exhibit exemplary ethical behaviour within the public sphere.The article reflects on the role of theological ethics in informing public ethics.As such it is theologically intradisciplinary but focusing on intertheological disciplines and their relationship to public space regarding ethics.It seeks to engage and influence public ethical behaviour in a context corruption and disregard of other human beings' entitlements.
Intradisciplinary and/or interdisciplinary implications:
The article challenges the privatisation of Christianity to take a public role in order to influence the public.This approach contributes to shifting African Christians from being passive in the context of unethical behaviours to being active agents who influence the public.As such, it contributes to public, practical theology and public ethics.
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The African misconception of the divine: The transcendence and immanence of God
The traditional African concept of God's transcendence and immanence is inherent within the uniform beliefs of traditional African cultures in the interconnection between the spiritual and physical worlds (Dyrness 1990:44;Louw 2002:72;Lugira 2009:48;Mbiti 1989:74-85;Turaki 2006:34).That is, even though African scholars and theologians sometimes differ in their reference to African traditional worldview or views as a uniting concept, they concur that within the diverse beliefs of traditional African cultures, it is a common worldview thread of interconnection between the spiritual and physical worlds (Lugira 2009:48;Mbiti 1989:74-85;Turaki 2006:34).Mbiti (1989) encapsulates the interconnection between the physical and the spiritual worlds in his statement that the: spiritual universe is united with the physical, and that these two intermingle and dovetail into each other so much that it is not easy, or even necessary, at times to draw the distinction or separate them.(p.74) Firstly, in various African communities, the notion of the transcendence of God is rooted in the belief that the world is occupied with impersonal mystical power, which is present in every corporeal (animate) or incorporeal (inanimate) object or place (Turaki 2006:24).In Turaki's (2006) view: The potency, efficacy and durability of this power vary from object to object and from place to place.Some objects are inherently imputed more power than others, that is, they are assumed to be more naturally endowed with power than others are.(p.24) It is believed that this impersonal mystical power (associated with various kinds of natural objects such as plants, mountains, animals, etc.) can be taken and used by people through various mechanical means for either good or bad purposes in their communities (Turaki 2006:24).The evil users of this mystical power utilise it to injure other people within their societies and communities, while the good users use it to monitor or protect themselves against the evil users of this mystical power (Turaki 2006:24).Given this, in many traditional African communities, it is common to find people clothing or putting all kind of objects around their wrists, angles, waists, necks or arms as a means of protecting themselves from this impersonal mysterious power (Turaki 2006:24).In Turaki's (2006) words: Medicine men and women, diviners and seers use the impersonal power associated with natural objects, plants and animals for medicine, magic, charms and amulets.Some believe that the mysterious powers embedded in things or objects can be extracted for specific uses.Mysterious powers can also be transmitted through certain objects or by purely spiritual means.They can be sent to specific destinations to accomplish good or evil.They can also be contagious by contact with objects carrying or mediating such powers.(p.24) The impersonal powers can be used for both good and evil.The existence of wicked human beings and wicked spirit beings, who also have access to the mysterious powers, makes life full of uncertainties -rife with unpredictable wickedness and evil and dangerous to human beings.Thus, traditional Africans who believe in the impersonal powers feel that they are under the influence of those powers.
Secondly, various African cultures recognise that the spirit world is inhabited by many spirit beings (categorised as human and non-human spiritual powers) that are in a hierarchical relationship with one another (Lugira 2009:36-63;Mbiti 1989:77-80;Turaki 2006:54-66).Many scholars (cf.Agyarko 2010:52-54;Imasogie 1983:66;Lugira 2009:36;Mbiti 1989:15-77) agree that in the African concept of the spiritual world, God (Supreme Being) is the head of the hierarchy of these spiritual powers.This is because he is the sole creator of everything that exists, including the lesser spiritual entities.The lesser spiritual powers 'are thought to have been created by God.They are associated with him (God) and often stand for his activities or manifestations' in the world (Mbiti 1989:75).The fact that African people believe the Supreme Being to be the sole creator of all existing things implies that they perceive God as eternal, namely, the one who does not have a beginning or an end (Mbiti 1989:30-36).Lugira (2009:36) summarises the predominant African belief in the Supreme Being as the sole creator of everything.In this way '"most Africans" oral traditions have pointed to the existence of a power above which there is no other power, a Supreme Being, Creator, and Originator of the World' (Lugira 2009:36).Likewise, Mbiti (1970:45, cf. Turaki 1999:27) argues that 'our written sources indicate that practically all African peoples consider God as creator, making this the commonest attribute of the works or activities of God'.
Nevertheless, the problem emanating from the traditional African worldview is that God is not directly involved in everyday human activities, because he is transcendent and remote from the physical world (Lugira 2009:36-46;Turaki 2006:59-61).In saying this, we are aware that the transcendence of God in traditional African belief does not eliminate the concepts of God's omnipresence (his presence in all places and at all times), omniscience (his all-knowing) and omnipotence (his all-powerfulness) (Mbiti 1989:29-36).
That is why: African theologians and scholars speak about the transcendence of God, the Supreme Being, and claim that the space between God and human beings is filled with a hierarchy of gods, divinities and spirits who are sometimes called the intermediaries of God.(Turaki 2006:61) Firstly, this belief seems to come from African traditional stories, which state that the Supreme Being has prescribed various 'duties or responsibilities' to the lesser spiritual beings interacting with the physical world (Turaki 2006:56).
In this way, the Supreme Being is 'the ultimate peak of the pyramid, but he is too remote and inaccessible to play a role in [the] practical life' of Africans (Nurnberger 2007:75).Thus, many Africans believe that: most of the things humans need fall within the sphere of the authority of lesser spiritual beings, there is no need to go to God or bother him unless the lesser beings prove inadequate when it comes to providing powers, needs, purposes and security.(Turaki 2006:57) Hence, inherent within the African traditional worldview is ancestral veneration, which occupies a central place in traditional African religion (Triebel 2002:193, cf. Reed & Mtukwa 2010:148).The ancestors are those blood-related members of the family, clan or tribe, who have lived an outstanding life and who have supposedly thereby acquired supernatural powers after death, which enable them to function as both guardians and protectors of their living descendants (cf.Bediako 2004:23;Ligura 2009:48-50;Nyamiti 2006:3, 9;Oladosu 2012:160-161).The ancestors are viewed as being closer to living people than any other spiritual power, and they can either harm or bless their living descendants depending on the existing relationship between them (ancestors and the living people) (Oladosu 2012:161;Triebel 2002:187).This is why Triebel (2002) captures the centrality of ancestors in African traditional beliefs by concluding that: Because the ancestors cause misfortune on the one hand and because on the other hand only they can grant fortune, well-being, life, and a good living -that is, fullness of life -they alone are venerated.…Therefore this cult is really the central aspect, the center of African religion. (p. 193) However, the Africans' perception of God as a transcendent Supreme Being, who interacts with humankind through various spiritual intermediaries, seems to diminish the immanence of God in traditional African worldview.This is because even though Africans' understanding of the transcendence and immanence of God is not necessarily similar to a deistic view of God, the idea of a God who is indirectly present or involved within his creation is displayed in traditional African worldview.This (mis)conception could be taken to imply that God does not see things directly, because his presence is mediated by various spiritual intermediary powers.Possibly, this (mis)conception of God's transcendence and immanence could persist among Africans who then convert to Christianity.Some African Christians may not be conscious of the reality of God's transcendence and immanence in a way which influences their Christian public behaviour.Indeed, if one wishes African Christians to bring positive change in their African societies, 'a creative Christian engagement must answer' to this misconception of God's transcendence and immanence in traditional African worldview (Bediako 1995:99-100).Therefore, the following section will bring the perspective of the transcendence and immanence of God in the Adamic incarnational Christological framework as a step in informing some African Christians with a biblical view of God's transcendence and immanence.Following from this discussion is the following question: how can the immanence and transcendence of God amplified in Christ influence Christians' behaviour to mirror Christ and change society?
The transcendence and immanence of God in the Adamic incarnational Christological model
In response to the (mis)conception of the transcendence and immanence of God in traditional African worldview, it is important to acknowledge that Evangelical theology is grounded in the Christian doctrine of the Trinity (Nkansah-Obrempong 2010:294).The doctrine of Trinity affirms that God is one being yet three distinctive persons, namely Father, Son and Holy Spirit (cf.Jn 14:16-17 & Mt 28:19) (Torrance 1996(Torrance :15, 1995:131):131).The word 'persons' in reference to the triune God does not necessarily mean that there are three 'personalities in God' (Barth 1960:403).This aforementioned understanding would result in the notion of a God who is tritheistic in nature (Barth 1960:402-403).
In guarding ourselves against this potential challenge of tritheism, we argue that God is one incorporeal being (Jn 4:24), comprised of three distinctive persons without being separated or divided (Torrance 1995:110-145).We affirm the distinction between the Father, Son and Holy Spirit (but always in inseparable relationship with one another), which is determined by the indivisible oneness or unity in being (consubstantial) among the persons of the Godhead (Torrance 1996:169-202).The distinctive persons of the Godhead interpenetrate (perichoresis) each other, because the Father in John's (14:10) gospel is entirely in the Son and the Son is entirely in the Father (Calvin & McNeill 1960:143;Torrance 1996:169-202).Therefore: while the Lord Jesus Christ constitutes the pivotal centre of our knowledge of God, God's distinctive self-revelation as Holy Trinity, One Being, Three Persons, creates the overall framework within which all Christian theology is to be formulated.(Torrance 1996:2) It is important to note that all things were created by God the eternal Father, in and through his eternal Son; and that both the continual existence and sustenance of the entire creation is dependent on the transcendent, self-existing and infinite God (cf.Heb 1:3, Col 1:15-17 & Jn 1:3) (Barth 1966:56-58;Torrance 1981:135).In other words, Jesus Christ is the creator of all the invisible and visible things out of nothing; who lives and acts in 'lordly freedom' over his creation (Torrance 1981:4).His lordly freedom over creation as its creator, sustainer and saviour (cf.Heb 1:3) is evident in his amplified immanence within humankind in the incarnational mystery as he became flesh and dwelt among us (Jn 1:14).Here, the incarnation: is the new act of the eternal God whereby God himself becomes man without ceasing to be God, the Creator becomes creature without ceasing to be Creator, the transcendent becomes contingent without ceasing to be transcendent, the eternal becomes time without ceasing to be eternal.(Torrance 1996:214) Thus, in contrast to the traditional African worldview of God as the creator, whose immanence within humankind is mediated through multiple spiritual power, it is maintained that in and through Jesus Christ, God the originator of everything stepped down (from his eternal transcendent and infinite existence) into the space and time of human existence in order to save humanity.In other words, in the incarnation, God in Christ emptied himself of his honour and glory (Phlp 2:5-11) in order to have his personal presence among humanity, so that he could suffer for the sake of humanity's redemption.Therefore, the incarnation: constitutes the one actual source and the one controlling centre of the Christian doctrine of God, for he who became man in Jesus Christ in order to be our Saviour is identical in Being and Act with God the Father.(Torrance 1996:18) This is the one and only God who is omnipresent, omniscient and omnipotent.This implies that the transcendent and all powerful God sees all that humankind are doing, as well as knowing all that we are thinking because there is no part of his creation outside of his reach and presence.
Stated differently, the incarnation of God in Christ confronts the (mis)conception of God's transcendence and immanence in traditional African worldview with the fundamental reality that even though God is transcendent as the sole creator of everything, he is not too remote and inaccessible to play a role in the practical life of African people.This is because in Christ's incarnation, the transcendent God has once and for all moved into the bounds of space and time in order to have his personal presence among humankind as the New or Second Adam for the sake of humanity's redemption (Torrance 1992:126).This indicates that: although God transcends time and space, he enters both freely as through an open door that he has created.More than this, even enters must be understood analogically, since God is already present in every moment and permeates every place.(Horton 2011:256) That is, even prior to God's special immanence within his creation in and through Jesus Christ's incarnation, he (God) was both transcendent and immanent within his creation (Horton 2011:256;Zemek 1990:129-148).In Zemek's (1990:130) view, 'Psalm 113 provides a natural theological entrance into two corollary truths about God, His transcendence and His immanence'.Here, the Psalmist commands: [a]ll men to let the praise of God resound all the world over and motivates the appeal with the declaration that this incomparable God, transcending the heavens in glory, is the Sovereign of the world who controls the affairs of men below from his throne.(Zemek 1990:137-138) However, even though God has been always present within his creation (as its sustainer) before the incarnational mystery of Jesus Christ (cf.Ps 113), it is apparent that in Jesus Christ, God's special personal presence within humanity is amplified by his assumption of our human mode of existence as the New Adam (cf.Rm 5:12-21; 1 Cor 15:21-22) (Barth 1956:9-10;Torrance 2008:73).In this case, an understanding of the vicarious humanity of Christ as determined by the anhypostastic and enhypostastic principles is vital in deepening African believers' understanding of God's personal immanence within humankind as amplified in Christ (Barth 1958:49;Gunton 1992:47;Moltmann 1974:231;Torrance & Walker 2008:230).An anhypostatic union states that the human nature of Christ is without an independent centre of personhood, because it finds its centre or expression in the eternal person of the Son of God (enhypostastic union) (Torrance & Walker 2008:84, 229, 2009:lxxiii).Indeed, if the human nature of Christ does not have its own independent expression, and that this lies instead in eternal Word, this makes room for the reality that the Word, the Creator, assumed a common Adamic human nature, not merely a discrete one.
In other words, the couplet significance of anhypostasia and enhypostasia brings to the forefront the reality that in the incarnation, God in Christ was immanent within all humankind as the New Adam, because his human nature embraces all humankind, regardless of their tribal, national or genealogical categories (Bavinck 2006:306).Given this, 'the salvation of the world lies in the fact, that Transcendent God became Man, became near to me and like me, and that we are now "grafted" on Him' (Arseniev 1959:10).
The above understanding can be summarised as the Adamic incarnational Christological framework, which is substantiated by the view that salvation in Jesus Christ is the 'reversal of Adam's fall' (Dunn 1989:105;cf. Jewett 2013:80-82;Schreiner 1998:275).Scripture presents an Adamic Christology by drawing comparisons between Adam and Christ, either explicitly (cf.Rm 5:12-21; 1 Cor 15:21-22, 45-49) or implicitly (cf.Lk 3-4; Heb 2:5-18).In the comparisons between Adam and Christ, there is an ontological inclusivity of all mankind in their vicarious humanity.Here, Adam stands as the head of the fallen humanity, while Christ stands as the head of the redeemed humanity.Also, Adam is a type of Christ who is the real thing (the anti-type) which the type symbolises (cf.Rm 5:14) (Barth 1956:9-10, cf. Hultgren 2011:226).That is, even though there are continuities between Adam and Christ on the basis of the corporate solidarity of humankind in their vicarious humanity; the God-man, Jesus Christ transcends Adam in all respects as the one who 'undoes' Adam's sin and death for all humankind who believe in his saving person and work (Rm 5:12-21).Therefore, in the incarnational mystery, the transcendent God is personally immanent within humankind as the New Adam (Jesus Christ) for the sake of our redemption.That is to say: within this human-inhuman existence of Adam, Jesus Christ comes as the Son of God, the Son of man as Jesus calls himself, to live out a truly obedient and filial, that is a truly human life, in perfect and unbroken union with God the Father … In all of that Jesus Christ is the last Adam, the one who...brings to an end the bondage of Adam's sin, breaks its power and opens up a new and living way to God. (Torrance & Walker 2008:73) However, this does not mean that the Evangelical doctrine of the incarnation has never been contested in Christian history.Hick (1993) challenged the orthodox doctrine of incarnation.He challenged Barth (1956:346) as the representative voice of Evangelical theology in their claim of Christianity as the only true means of salvation, because of the uniqueness of the incarnation of Christ, the eternal Son of God (Barth 1956:346).
For this reason, Hick (1993:ix) de-constructed the Orthodox Christian doctrine of Christ's incarnation.In order to parallel Christianity with non-Christian religions, Hick (1993:ix) argues that the incarnation of the Divine Logos should be understood in a metaphorical sense.That is, 'Jesus embodied, the ideal of a human life lived in faithful response to God… and he accordingly embodied a love which is a human reflection of the divine love' (Hick 1987:21).In this way, Hick denies Jesus' claim (in Jn 10:30 & Jn 14:9) to be in one being with the Father (Hick 1995:53).He argues that these words were put in Jesus' mouth 60 or 70 years after Jesus' death by the Scriptural authors, who expressed their ideas which were developed during the expansion of the early Church (Hick 1995:53).However, Hick's serious weakness is his presumptuous claim to know Jesus better than the disciples, who knew him directly and were closer to him.
In conclusion, the traditional African worldview is continually confronted by the fact that God does not engage with humankind through various spiritual intermediaries.Instead, in his special-personal presence, God in the incarnation dwelt among us as the New Adam and saved us from sin and all its consequences so that we can live godly lives which brings honour and glory to him (cf. 1 Pt 2:9-12).This is the godly life which resembles God's behaviour and character amplified in his immanence in Christ.The underlying reality is that: Christ, through whom we return into favour with God, has been set forth before us as our example, whose pattern we ought to express in our life … we must take care that God's glory shines through us, and must not commit anything to defile ourselves with the filthiness of sin (1 Corinthians 3, 16, 6:19 & 2 Corinthians 6:16).(Calvin 1960:686-687) This is because the incarnation of the Son of God: was not the bringing into being of a created intermediary between God and man, but the incarnating of God in such a way that in Jesus Christ he is both God and man in the fullest and proper sense.(Torrance 1995:150) The paradoxical transcendence and immanence of God in our New Adam's ascension In Barth's (1956:23) view, 'the resurrection and the ascension (of Christ) is the main stay of everything' in the New Testament.However, the ascension of Christ confronts Christians with the paradoxical notion of the transcendence and immanence of God.This paradox is captured in Farrow's notion of the continuity and discontinuity between the present world and the world to come (Farrow 1999:46).In his book Ascension and Ecclesia, Farrow (1999:40&43) encapsulates this existing paradox of God's remoteness and nearness after Christ's ascension by delineating the existence of two histories in Scripture, namely, world history and covenant history.In the wider argument of his book, Farrow contends that through Jesus' ascension, world history and covenant history are now separated to our view, although world history is still ultimately determined by the covenant history.Concerning the covenant history, Torrance and Walker (2009:294) is in line with Farrow by the contention that the ascension of Christ 'is the ultimate end of creation and redemption revealed in the covenant of grace and fulfilled in Jesus Christ'.In other words, covenant history has 'already reached its goal' in Christ's ascension, and yet it is now out of our sight in heaven where Christ is seated at the right hand of God the Father (Farrow 1999:40).However, world history continues in this present era of Christianity, and believers are to continue to live in this world history without conforming to its observable sinful patterns (Farrow 1999:43).
Nevertheless, the ascension of Christ does not necessarily mean that God is distant from us because he has ascended into heaven where he is seated at the right hand of God the Father.Instead, as African believers continue to live in this interim period of Christianity, we affirm that God continues to have his complete presence or immanence within all Christians through the dynamic presence of the Holy Spirit in their lives.In arguing for God's real and ongoing presence within African believers through the dynamic presence of the Holy Spirit, we are closing a gap between the transcendence and immanence of God after Christ's ascension.That is, even though God in our New Adam (Jesus Christ) is absent from believers in the sense of his physical appearance, nonetheless, through the dynamic presence of the Holy Spirit, he continues to have real presence with them.In saying this, we have the same conviction as Torrance and Walker (2009) state that: It is through the Spirit that things infinitely disconnecteddisconnected by the 'distance' of the ascension -are nevertheless infinitely closely related.Through the Spirit, Christ is nearer to us than we are to ourselves, and we who live and dwell on earth are yet made to sit with Christ in heavenly places, partaking of the divine nature in him.(p.294) This is why Luke and John emphasise that the man Jesus Christ (our New Adam), the very God himself, is the one who gives the Spirit to those who are so deeply related to him as brothers (cf.Heb 2:5-18) and friends given to him by the Father (cf.Jn 10:29).In Luke, it is the ascended Jesus of Nazareth who sends the Spirit (Lk 24:36-49; Ac 1:2-4 & 2:4).In John, it is the resurrected man Jesus who breathes into his disciples his Spirit (Jn 20:22).The truth is that when Christians have Jesus by faith, they have full assurance and full security that they have the Holy Spirit.This is against certain neo-Pentecostal claims that the gift and possession of the Holy Spirit is to be doubted without further experiences.That is, we ought to agree with Torrance (1992) that in the early Church of the New Testament: when the crucified Jesus rose again from the dead and poured out his Spirit at Pentecost, the intrinsic significance of his person and all he had said and done broke forth in its self-evidencing power and seized hold of the church as the very Word or Logos of God.(p. 4) Given this, in view of the transcendence and immanence of God after Christ's ascension, one should maintain that the triune God does not plant African believers in eternal union and participation with himself (in the Son and through the Holy Spirit) and abandon them (Fee 1994:8;Murray 1998:141).Instead, the eternal Son of God came into our fallen world and adorned flesh as the New Adam in order to vicariously overcome the corruption that came through the first Adam and have a direct victory over evil.Victorious, he now indwells African Christians by the Spirit (cf. 1 Cor 6:19-20) and secures them in his inaugurated kingdom of righteousness as they await the kingdom's consummation (Fee 1994:8;Murray 1998:141).
Towards an ethical reflection of the transcendence and immanence of God for African Christians
Kandiah (2015:1) in Christian Today observed that the Church is growing slowest in Europe and North America and fastest in Africa.He reported that the growth of the African Church in particular is jaw-dropping.
In 1900 there were fewer than 9 million Christians in Africa.Now there are more than 541 million.In the last 15 years alone, the Church in Africa has seen a 51% increase, which works out on average at around 33 000 people either becoming Christians or being born into Christian families each day in Africa alone.
On the other hand, while the dawn of democracy across the African continent brought hope and promise to many people, this hope is increasingly being eroded by corruption, oppression and much unethical behaviour of public office bearers.Transparency International Perception Index (2014:9), an index that measures the perceived levels of public sector corruption worldwide (100 -being very clean and 0 -being highly corrupt) indicate that all African countries have a less than 50 points except Botswana with 63, and ranked 31 in the world.This is followed by Namibia and Rwanda with 49 points and ranked 55 in the world.Global average score is 43 whereas sub-Saharan Africa is 33.Worryingly, 92% of sub-Saharan African countries scored below 50 points.Nussbaum (2003:1) observed that African political leaders have betrayed their fundamental humanness.Macheka (2014:1) added his voice that African leaders have embraced corruption and departed from the cherished values and ideals aspired for post-colonial Africa.Masango (2002:707) echoed the same concerns as Macheka that the world views African leaders as plagued by corruption, dictatorship and many other bad governance practices.Jones (2015:6) describes the effects of corruption and unethical behaviour.He explained that corruption undermines democracy and good governance, it violates human rights, it distorts markets and it erodes quality of life.Corruption and unethical behaviour destroys people and abandons moral principles as well as norms of social justice.
Juxtaposing the above depressing African situation and the growth of Christianity prompts one to ask the question: why is there no positive relationship between growth of Christianity and resultant values with the level of corruption and unethical behaviour?Although this question is outside the scope of this discussion, it provides a pointing perspective to our discussion.Pugh (2004:1) commenting on the Christian Welsh revival (1904)(1905) and its leader, Evan Roberts, stated that it was abundantly clear that without the practical, courageous, and persistent application of the Christian ethic to every phase of human life, however trivial and ordinary, no person could even begin to call himself a Christian.One of the leading authorities on the Sociology of Religion, Rodney Stark (1996), in his book The Rise of Christianity, records a somewhat similar situation in a telling account of how Christianity grew in the first four centuries from an obscure, marginal Jesus movement to be a dominant religious movement deriving from its practices and ethos.This clearly illustrates the influence that Christianity and Christians should have in public life and behaviour in shaping society ethically, among other things.
However, the rampant corruption in African leadership has proved the African notion of Ubuntu to be a failure in acting as an instrument for unselfish leadership in Africa.
The African concept of Ubuntu denotes the essence of http://www.ve.org.zaOpen Access being human in African traditional terms (Tutu 1999:31-32).
In African traditional way, Ubuntu refers to 'generous, hospitable, friendly, caring and compassionate' people (Tutu 1999:31-32).However, the aforesaid corruption in African leadership fails to reflect the Ubuntu concept.The level of corruption in African leadership tends to connote African leaders and public office bearers as uncaring, unhospitable and uncompassionate.African leaders and public office bearers are benefitting illegally from money which is sometimes aimed to serve the poor and the marginalised within their various societies and communities.Now, is that hospitable, caring, friendly, compassionate and generous?
The answer to this question is an emphatic no!Maybe this is why Matolino and Kwindingwi (2013:200) and Eliastam (2015:2) indirectly indicate that the concept of Ubuntu can be manipulated to serve the interests of individuals, which complicates our understanding of the concept of Ubuntu.Given this, Magezi (2015:3) similarly sustains that 'Ubuntu is an outdated notion that does not change people's ethics to curb corruption and injustice'.The concept of Ubuntu has limited influence in African countries and societies because the qualities (such as hospitality, generosity, caring, etc.) associated with the concept are normally referred 'to people bound geographically and relationally' (Magezi 2015:3).In other words, the concept of Ubuntu is reminiscent of the inclusion and exclusion of other people depending on the coexisting relationships and the geographical locations.As a result, discrimination and corruption are ongoing challenges within various African nations and societies.Thus, Magezi (2015) sharply criticises the Ubuntu concept in his argument that: One other major concern raised against the current view of Ubuntu is its exclusiveness.Ubuntu's definition of community narrowly refers to people bound geographically and relationally.Ubuntu tends to exclude people who do not come from the same geographical area (ethnicity) or not filially related.(p. 3) Moreover, in taking the traditional African cultures seriously, Bujo (2001:xiv) has attempted to construct a moral tradition which is comprised of African traditional materials.The reason for this ethical construction is that Bujo views African traditional ethics as sharing some similarities with Christian ethics.He states that African ethics is communal in nature because it revolves around a relational structure which involves people (including the living, dead and the unborn children), the cosmos and God (Bujo 2001:1-6, 65).Bujo (2001) argues that: … hospitality, daily friendship, and dialogue with the members of other ethnic groups are vital laws from which no one is excepted.One who is not a member of my own group is ultimately also the 'property' of the other just as I myself am, and this means that I owe him respect and esteem.Thus, one is ultimately related to all human beings.(pp.5-6) Thus, in Bujo's view: Recognition of relatedness is important for proper appreciation of how Africans make moral judgments.African ethics ... is concerned with the significance of the community for the discernment and lying down of norms and for ethical conduct as a whole.This sense of relatedness goes beyond the concrete visible community to embrace the dead as well.(Ikechukwu 2008:591) It is within this (Bujo's) framework of interpersonal network that love, hospitality, friendships and dialogue take place beyond tribal and ethnic boundaries (Bujo 2001:5-6).However, Bujo's view that African communities comprise hospitality and friendship which they extend towards other African ethnic groups is contested from history (Ikechukwu 2008:595).History does not view African communities as receptive and hospitable of each other.In the past, Africa has witnessed ethnic conflicts among different ethnic groups (Ikechukwu 2008:595).In Ikechukwu (2008) understanding, these historical conflicts include: … the Nigerian pogrom of 1966, the Liberian/Sierra Leonean massacres, the Hutu/Tutsi genocides, and all, and all other such cases show, one common factor in all of them is the question of ethnic superiority and the unwillingness to confer equality on some people who are not of one's own family or stock.(p.595) In spite of the criticism facing Bujo's ethical dimensions, the fact that his Christian ethics resonates with the traditional African concept of communality, is noted and granted.However, the question is: what is the contribution of Bujo's ethical construction in the contemporary Africa, in which Christianity in Africa is reported as rapidly growing more than in any other continent, yet the practical lives of Africans are not changing (Kandiah 2015:1).Maybe this is why Magezi (2015:8, cf. Bowers 2009;Gifford 2008 are of the same opinion) in maintaining their view that African Christianity requires a fresh way that engages and challenges ongoing bad public practices and ills.Current African Christian thinking and reflection is deficient in addressing emerging challenges in the modern and technologically advanced Africa (Bowers 2009;Gifford 2008).
In view of the above, one can argue that the evident rate of corruption in African leadership reflects lack of accountability and little desire to act in public interest.Accountability is a challenge because people conduct themselves differently in their private and public spaces.This means that even though we can put human structures in place to influence people to act responsibly, the challenge remains that structures are always limited in bringing change and accountability among people in private and public spaces.Worse, structures do not address people's consciences.Therefore, this makes it imperative to fashion and construct theologies that arouse a sense of accountability and responsibility for individuals to conduct their various duties and obligations in a responsible, accountable and trustworthy manner in public or private spaces.
Now, the Christian worldview of the transcendence and immanence of God may arguably influence African believers to live as the true ambassadors of Christ in their private and public lives.This is because it challenges the traditional African concept of God, which views God's presence within his creation as mediated through various spiritual powers.
The Adamic incarnational Christological model presented in the transcendence and immanence of God in the Adamic incarnational Christological model heading argues that God had always been directly present within his creation before the incarnation; however, his presence within humanity is amplified by God's assumption of our human nature in and through Jesus Christ as the New Adam.That is, before and after the incarnation, God's immanence within his creation was not mediated by various spiritual powers inherent in the traditional African worldview.God has been always directly present within his creation as its creator and sustainer before he assumed our human mode of existence.
In saying this, we are moving towards the assertion that God's transcendence and immanence amplified in Christ should be brought to bear in the private and public behaviour of African Christians.This is because a correct understanding of these two interrelated attributes of God (the transcendence and immanence of God) can enable African Christians to be more cognisant of God's direct presence within his creation.
This above-mentioned Christian understanding of the transcendence and immanence of God has an important implication for the ethics of believers.The ethical implication arises from the fact that the transcendent and immanent God sees all that humankind are doing, as well as knowing all that we are thinking, because there is no part of his creation outside of his reach and knowledge (Jr 23:23-32).That is to say, God is omnipresent; therefore, he sees directly everything we do as part of his creation.In this way, the immanence of God amplified in Christ challenges Christians to live lives which correspond to their sanctified status in Christ because God sees us directly.Thus, people cannot have private and public behaviours such as stealing, committing adultery, gossiping and so on.For instance, even though one can embezzle state funds because he or she cannot be seen by other people, the immanence of God challenges them to be more conscious of the fact that God sees both their private and public life because there is nothing hidden from him.In saying this, we call African Christians not to live lives which are influenced by the fear and respect of other people as reverence of God.They should conduct themselves in a way worthy of their new life in Christ because they respect the infinite God who is directly present in every place and sees everything they do.To encapsulate this, although the presence of humanity is limited to a particular location in time, the opposite is true of God who has unlimited presence within his creation.This is why Psalm 139 calls our private and public ethics to be governed by the omnipresent God, who is all-knowing and all-seeing.In this Psalm, there is no place where King David could go where the omniscient and omnipresent God is not a permanent reality.
The notion of the transcendence and immanence of God corresponds with the actuality that God will hold all people accountable for their good and evil deeds they perform during their earthly lives.That is, when Christ appears to judge the living and the dead in his parousia, all people will be held accountable for the good and evil deeds they did (2 Cor 5:10) during their lifetime.The point that God will hold humankind accountable for their ethical behaviour during their lifetime qualifies the direct immanence of God within his creation.This is the God who sees everything we do in our private and public lives.Even though African Christians continue to live in this interim Christian period in which God is paradoxically transcendent and immanent in Christ's ascension, they should live exemplary lives (Rm 5:12, 12:2; 1 Pt 2:11b).They should practically live lives and conduct that correspond to their new status in Christ (Eph 6:16), the New Adam.The transformational aspect (Rm 12:2) of the minds of believers is purposed for their realization and discernment of God's will in all facets of their lives, so that they can live Christlike lives within their societies (Kruse 2012:465-466).
Likewise, in reconsidering Paul's juxtaposition of indicative and imperative (Rm 6:1-14) in light of Pauline Apocalypticism, Tsui (2013:313) calls Christians' behaviours and actions to be shaped by 'the apocalyptic vision of the new life in Christ, which the indicative conveys, captures believers into the reign of Christ characterized by freedom and serves as the locus whereby Paul articulates the imperative that subsequently guides believers' actions'.Here, Paul's command for the believers in Romans 6:12-13 is to correctly befit their new sanctified status in Christ (Tsui 2013:297-314).Hence, in applying Romans 12:1-2 and 6:1-14 to African Christians, one should be correct to advise Christians to develop functional Christ-like character in changing their societies.In commanding believers to change societies by their Christ-like behaviour and character, we remind Christians that God's empowering presence is with them through the Spirit.This is because: We are not left on our own as far as our relationship with God is concerned; neither are we left on our own to 'slug it out in the trenches', as it were, with regard to the Christian life.Life in the present is empowered by the God who dwells among us and in us.As the personal presence of God, the Spirit is not merely some 'force' or 'influence'.The living God is a God of power and by his Spirit the power of the living God is present with and for us.… The Spirit also empowers for endurance in the midst of adversity (Col.1:11, 2 Cor.12:9-10) and for everything else as we endure, awaiting the final glory, of which the Spirit is the guarantee.(Fee 1994:8) That is, through the dynamic presence of the Spirit in believers' lives, God enables African Christians to act as change agents to the rest of society.They should transform societies they live: [a] model of the kind of godly life the Father wants to see in every Christian.He who was God in the flesh was able to manifest the kind of holiness of character in his attitudes, behaviours, and interpersonal relationships that provided a concrete example of the moral image of God that he wanted to see restored in fallen man.Jesus became a demonstration of holiness with a human face, and by so doing became a model of life and character for everyone desiring to be remade in the image of the Holy One of the universe.(Coppedge 1980:93) The underlying reality is that by being partakers of God's ethical values in Christ, believers become the representatives or ambassadors of God in their daily lives (cf. 2 Cor 5:20) (Coppedge 1980:83;Nelson 2011:65;Wright 2010:246).
Christians are responsible for their performance and character, because they are representing the incarnated and ascended God, Jesus Christ.Thus, God's work of changing the world is not divorced from the agent work of believers (as the light of the world) as his partners to bring about that universal restoration, as Wright (2010:246) correctly observes: 'God's work of rescuing, restorative justice must happen in us in order that it can happen through us'.
Conclusion
This article argued that even though the self-existing and infinite God is transcendent, his transcendence does not eliminate his direct presence with his creation.Here, we challenged the traditional African worldview misconception of the transcendence and immanence of God.This is the misapprehension of God as a transcendent Supreme Being, who interacts with humankind through various spiritual intermediaries.By commencing from the Evangelical Trinitarian doctrine of God as one being yet three distinctive persons, we affirmed that in the incarnation, in and through Jesus Christ, God has his personal presence within us as our New Adam (cf.Rm 5:12-21 & 1 Cor 15).That is, even though the transcendent God has been always present within his creation since the beginning of creation as its creator and sustainer, his immanence within creation is amplified in the incarnational mystery, in which he became man for salvation of humanity.The ascension of Christ at the right hand of God does not undermine the continuity of God's personal presence within believers.Scripture assures Christians that there is an ongoing personal presence of God within them through the indwelling by the Holy Spirit.We further argued that the aspect of the transcendence and immanence of God amplified in Christ has huge implications for Christian ethics that should extend to society.The transcendent God who sees our entire private and public life is always present within his creation without being confined to a specific location as finite humankind is.This understanding should inform African Christians to live as the true ambassadors of God in their private and public ethics because the transcendent God sees and knows everything.In other words, God is not like finite human beings who are only present in a particular space in time.That is, there is nothing outside of God's reach and knowledge. | 10,987.2 | 2016-08-25T00:00:00.000 | [
"Philosophy"
] |
Critical Casimir effect in films for generic non-symmetry-breaking boundary conditions
Systems described by an O(n) symmetrical $\phi^4$ Hamiltonian are considered in a $d$-dimensional film geometry at their bulk critical points. A detailed renormalization-group (RG) study of the critical Casimir forces induced between the film's boundary planes by thermal fluctuations is presented for the case where the O(n) symmetry remains unbroken by the surfaces. The boundary planes are assumed to cause short-ranged disturbances of the interactions that can be modelled by standard surface contributions $\propto \bm{\phi}^2$ corresponding to subcritical or critical enhancement of the surface interactions. This translates into mesoscopic boundary conditions of the generic symmetry-preserving Robin type $\partial_n\bm{\phi}=\mathring{c}_j\bm{\phi}$. RG-improved perturbation theory and Abel-Plana techniques are used to compute the $L$-dependent part $f_{\mathrm{res}}$ of the reduced excess free energy per film area $A\to\infty $ to two-loop order. When $d<4$, it takes the scaling form $f_{\mathrm{res}}\approx D(c_1L^{\Phi/\nu},c_2L^{\Phi/\nu})/L^{d-1}$ as $L\to\infty$, where $c_i$ are scaling fields associated with the surface-enhancement variables $\mathring{c}_i$, while $\Phi$ is a standard surface crossover exponent. The scaling function $D(\mathsf{c}_1,\mathsf{c}_2)$ and its analogue $\mathcal{D}(\mathsf{c}_1,\mathsf{c}_2)$ for the Casimir force are determined via expansion in $\epsilon=4-d$ and extrapolated to $d=3$ dimensions. In the special case $\mathsf{c}_1=\mathsf{c}_2=0$, the expansion becomes fractional. Consistency with the known fractional expansions of D(0,0) and $\mathcal{D}(0,0)$ to order $\epsilon^{3/2}$ is achieved by appropriate reorganisation of RG-improved perturbation theory. For appropriate choices of $c_1$ and $c_2$, the Casimir forces can have either sign. Furthermore, crossovers from attraction to repulsion and vice versa may occur as $L$ increases.
Introduction
When media exhibiting low-energy fluctuations are confined by walls or interfaces, or macroscopic objects are immersed in them, their fluctuation spectrum changes [1,2,3]. This may induce long-range effective forces between such objects and boundaries. A much studied example of such fluctuation-induced forces are the Casimir forces between a pair of parallel and grounded metallic plates produced by their influence on the quantum vacuum fluctuations of the electromagnetic field [4]. These quantum electrodynamics (QED) Casimir forces are known to be very weak unless the separation of the bodies between which they act becomes very small. The latter condition is met in micro-electromechanical devices (MEMS). As has recently become clear, Casimir forces of this kind must be taken into account in the design of such systems. Since they tend to be attractive for simple geometries, they may impair the functioning of MEMS, causing stiction [5,6,7,8]. Owing to the interest in -and technological importance of -such small-scale systems, this insight has triggered considerable new activity in the study of QED Casimir forces. Crucial issues are the knowledge and control of their strength, sign, and geometry dependence [9].
Another example of fluctuation-induced forces that has attracted a great deal of attention recently are the so-called thermodynamic Casimir force caused by thermal fluctuations near critical points [2,10,11]. Predicted decades ago [12], they were verified experimentally first in an indirect way through the thinning of 4 He wetting layers near the lambda transition [13] and their effects on wetting films of binary liquid mixtures [14,15]. Subsequently they were measured directly in binary fluid mixtures near their critical points of demixing [16,17].
In this paper we shall be concerned with thermodynamic Casimir forces in systems with a film geometry bounded by two planar free surfaces at a finite distance L. We will consider systems that can be modelled by an n-component |φ| 4 Hamiltonian on sufficiently long length scales and study the Casimir forces directly at the bulk critical point. The internal O(n) symmetry (or Z 2 symmetry if n = 1) is presumed to be neither explicitly broken by surface contributions to the Hamiltonian nor spontaneously for all temperatures T ≥ T c,∞ , the bulk critical temperature. In other words, no ordered phase can occur for finite L when T ≥ T c,∞ . Choosing a generic kind of such non-symmetrybreaking conditions, we will investigate the critical Casimir forces and demonstrate two important features of them. First, they can have either sign, depending on properties of the two surfaces -an expected result since attractive and repulsive critical Casimir forces were found a long time ago for certain boundary conditions that ought to apply on long length scales [18,19,20]. Second, for appropriate surface properties, crossovers from attraction to repulsion of the Casimir forces and vice versa can occur as a function of film thickness L. A brief account of parts of our work was given in [21]. The purpose of the present paper is to provide details of the calculations and further results.
One motivation for our work is the obvious potential for cross-fertilisation between the fields of thermodynamic and QED Casimir effects. Since both types of effects share a number of characteristic features, mutual benefits may be expected. On the other hand, one must be aware of certain essential differences. Common to both types is that they exhibit universal properties and depend on gross properties of the fluctuating media and confining objects, as well as on their shapes and geometry. Two important differences are: (i) When studying QED Casimir forces, one frequently gets away with the analysis of effective Gaussian theories in which the coupling between the electromagnetic field and matter is accounted for by proper choices of boundary conditions. This usually holds even in the case of polarisable and magnetisable media where material properties also enter via dielectric and permeability functions. By contrast, adequate treatment of critical Casimir forces normally involve the study of non-Gaussian theories such as φ 4 theories or corresponding lattice models (e.g., Ising models) in bounded geometries.
(ii) In studies of QED Casimir forces such as Casimir's original work [4], the electromagnetic fields are taken to have zero averages. Hence the Casimir forces are entirely due to fluctuations -if there were no fluctuations, there would be no Casimir force. However, in the case of thermodynamic Casimir forces, the order-parameter densities φ(x) have nonzero averages in ordered phases, where the order may either result from spontaneous symmetry breaking or else be imposed by symmetry-breaking bulk or boundary fields. If the medium undergoes a phase transition from a disordered high-temperature to an ordered low-temperature phase, then the order-parameter profile φ(x) does not vanish in the latter. Such a nontrivial profile contributes to the size-dependent part of the free energy and hence, to the Casimir force. Consequently, a Casimir force will be obtained already at the level of Landau theory -i.e., in the absence of fluctuationswhenever it yields non-vanishing order-parameter profiles. Beyond Landau theory, the thermodynamic Casimir force will therefore consist of a part coming from a non-fluctuating background and a superimposed fluctuation-induced contribution.
The last statement applies in particular to confined binary fluid mixtures [17,22,23]. These are known to generically involve symmetry-breaking boundary fields. Therefore, the thermodynamic Casimir forces they yield will normally have contributions from non-fluctuating backgrounds on either side of the order-disorder transitions. Since even at the bulk critical temperature, φ(x) is not expected to vanish, this holds there as well.
It is well known that the boundary fields needed to describe binary fluid mixtures in contact with walls can have either sign, depending on which one of the two components gets preferentially adsorbed locally at the wall [10,12,22,23,24]. Furthermore, there is clear evidence based on theoretical and experimental work as well as on Monte Carlo simulations [10,14,15,16,25,26,27,28,29,30] that the critical Casimir force in binary fluid mixtures confined between two planar walls can be attractive or repulsive. Corresponding crossovers must occur and were investigated at the level of mean-field theory [31].
Casimir forces in binary fluid mixtures are particularly well suited for direct experimental measurements. However, from our above remarks it is clear that their analogy with QED Casimir forces is limited: owing to the generic presence of a nonvanishing order parameter profile at, above and below the critical temperature, only a part of them is fluctuation induced. Since we focus here on the case in which the symmetry φ → −φ remains unbroken at T c,∞ , we are dealing with critical Casimir forces that are entirely fluctuation induced and hence are more akin to QED Casimir forces, albeit due to thermal, rather than quantum, fluctuations.
The rest of this paper is organised as follows. In section 2.1 the model is specified and the boundary conditions are recapitulated. Next, the free propagator is determined in section 2.2 for general values of the surface interaction constants, its eigenfunction representation is given and the transcendental equations derived whose solutions yield its eigenvalues. In section 2.3, many-point cumulant functions are introduced, their renormalization recapitulated and their RG equations presented. These considerations are extended to the free energy and Casimir force in section 3. In the remainder of this section details of our approach are explained and our analytical results for the scaling functions of the L-dependent part of the free-energy density and the Casimir force are given. In section 3.5 it is shown how RG-improved perturbation theory can be reorganised to achieve consistency with the fractional series expansions in one encounters in the special case of two critically enhanced surface planes. Section 4 discusses our results, deals with the issue of how to extrapolate them to d = 3 dimensions and presents such extrapolation results for the scaling functions of the L-dependent part of the excess free-energy density and the Casimir force. Section 5 contains a brief summary and concluding remarks. Finally, there are 5 appendices describing various calculational details.
Model and boundary conditions
We consider a continuum model for a real-valued n-component order-parameter field We write the position vector as x = (x 1 , . . . , x d ) = (y, z), where y = (y 1 , . . . , y d−1 ) denotes the d − 1 Cartesian coordinates y j = x j along the slab and z = x d the remaining one across it. The thickness of the slab, L, is taken to be finite. We choose periodic boundary conditions along all y-directions so that the boundary ∂V of V consists of a pair of (d−1)-dimensional planes B 1 and B 2 at z = 0 and z = L. Assuming the absence of long-range interactions, we can choose the Hamiltonian to have the local form where L b and L j=1,2 are local bulk and surface densities depending on φ(x) and its derivatives.
In accordance with our considerations in the introduction we choose these densities to be O(n) symmetric. For the bulk density we make the standard choice where (∇φ) 2 is the usual short-hand for α (∇φ α ) 2 . It has recently been emphasised that lattice systems lacking cubic symmetry, such as systems involving monoclinic or triclinic lattices, lead to φ 4 bulk densities with a gradient-square term of the generalised form 1 2 g ij (∂ i φ) · ∂ j φ where ∂ i stands for the derivative ∂/∂x i and g ij is a non-diagonal, position-independent matrix [32]. We refrain from working with such generalised models because the matrix g ij is nothing but a constant metric [33]. The geometric effects it has can be absorbed by a proper choice of variables which of course enters the way lattice quantities are related to those of the standard bulk φ 4 model with action density (2.2). For details the reader might want to consult reference [33, p. 14-17].
The surface densities are given by The interaction constantsc 1 andc 2 of the two boundary planes are allowed to differ. They are known to reflect the weakening or enhancement of the local pair interactions at B 1 and B 2 , respectively [22,23]. In semi-infinite systems bounded by a plane B 1 , a threshold valuec sp of the enhancement variablec 1 exists such that a phase with longrange surface order appears (in sufficiently high dimensions) in a temperature regime above T c,∞ when the enhancement −δc 1 ≡c sp −c 1 is positive (is "supercritical"). The transitions that occur at T c,∞ in such semi-infinite systems are called ordinary, special and extraordinary, depending on whether the enhancement δc 1 is subcritical (δc 1 > 0), critical (δc 1 = 0) or supercritical (δc 1 < 0). Analogous statements hold for semi-infinite systems bounded by the plane B 2 with surface enhancementc 2 .
In order to rule out spontaneous symmetry breakdown at T = T c,∞ for large L, we require that both enhancement variables δc j ≡c j −c sp satisfy the condition δc j ≥ 0, i.e. are non-supercritical.
From the boundary contribution to the classical equation of motion we get the boundary conditions of Landau theory where ∂ n is the inner normal derivative on ∂V = B 1 ∪ B 2 . Beyond Landau theory these boundary conditions still hold in an operator sense (inside of averages) [22,23,34,35,36].
Free propagator
A quantity of central importance for the renormalization-group (RG) improved perturbation theory we are going to use below is the free propagator G L atτ = 0. It is given by the operator inverse G L = (− ) −1 subject to the boundary conditions (2.4), where = ∇ 2 is the Laplacian. Let |m be the complete set of eigenfunctions of the operator −∂ 2 z ≡ −∂ 2 /∂z 2 on the interval [0, L] satisfying the boundary conditions That is, we have and the eigenstates fulfil the orthogonality and completeness relations m|m = δ mm (2.8) and ∞ m=1 z|m m|z = δ(z − z ), (2.9) where the label m = 1, 2, . . . , ∞ enumerates the eigenvalues k 2 m by size, starting with the smallest one.
To exploit the translation invariance of the system along the direction parallel to the boundary planes B j , we Fourier transform with respect to the difference of y coordinates, writing where we have introduced the notation We thus arrive at the spectral representation (2.12) Since our assumption that both enhancement variablesc j are non-supercritical implies that the associated renormalized variables c j (whose definition will be recalled in the following section 2.3) are nonnegative, we shall need the eigenvalues k 2 m and eigenfunctions |m only forc j ≥ 0. In this case, there are infinitely many eigenvalues k 2 m for finite L, all of which are nonnegative and non-degenerate (see reference [37, Appendix A] and below). A zero eigenvalue k 2 1 = 0 occurs for arbitrary L ∈ (0, ∞) only whenc 1 =c 2 = 0.
Let us briefly summarise the relevant properties of the eigensystem {|m , k 2 m } we shall need in our subsequent analysis. On dimensional grounds the eigenfunctions must have the form z|m = L −1/2 υ m (z/L|c 1 L,c 2 L). (2.13) It is convenient to introduce the dimensionless variables ζ ≡ z/L, κ m ≡ Lk m , C j ≡c j L. (2.14) Setting L = 1 in equation (2.13) one concludes that the functions υ m can be written as The analogue of the boundary condition (2.5) implies that the phase shift ϑ m is given by We can choose it such that 0 ≤ ϑ m ≤ π/2, which leads to sin ϑ m = 1 The limiting values ϑ m = 0 and ϑ m = π/2 are obtained whenc 1 → 0 andc 1 → ∞, respectively.
Using these results along with equation (2.15), the normalisation constant λ m can be computed in a straightforward fashion. One obtains To determine the spectrum {κ 2 m }, we use the analogue of the boundary condition (2.6), (2.20) This yields the transcendental equation for κ m , with Equations (2.5)-(2.7) specify a regular Sturm-Liouville problem for which the following mathematical properties are known (see e.g. references [38], [39,Kap. IX], [40,Kap. IV.3] and [41, chapters 8, 9]): (i) The eigenvalues κ 2 m (C 1 , C 2 ) are real, nondegenerate, countable and accumulate only at ∞. (ii) They can be ordered such that κ 2 m < κ 2 m for m < m . There is a smallest eigenvalue κ 2 1 but no largest one, i.e. κ m → ∞ as m → ∞. (iii) The eigenfunctions υ m corresponding to different eigenvalues are orthogonal with respect to the standard L 2 scalar product in L 2 (0, 1). ‡ (iv) The normalised eigenfunctions are a complete orthonormal set (basis) in the Hilbert space L 2 (0, 1). (v) When C 1 and C 2 > 0, we can use the Robin boundary conditions (2.5) and (2.6) in conjunction with the fact that the eigenfunctions vanish only for Dirichlet boundary conditions at the boundary planes B j to conclude that υ(dυ/dζ)| ζ=1 ζ=0 = −C 2 υ 2 | ζ=1 − C 1 υ 2 | ζ=0 < 0. Fulfilment of this condition guarantees (by theorem 7 of reference [40, p. 234]) that κ 2 1 and hence all κ 2 m are strictly positive. The non-degeneracy of the eigenvalues κ 2 m can be verified explicitly by showing that the positive zeros κ m of R C 1 ,C 2 (κ) are simple. To this end, one can compute the derivative R C 1 ,C 2 (κ) ≡ ∂ κ R C 1 ,C 2 (κ) at κ = κ m and express the trigonometric functions cos κ m and sin κ m in terms of κ m , C 1 and C 2 using equations (2.21) and (2.17) along with the analogue of the latter implied by the boundary condition at ζ = z/L = 1. This gives , (2.23) which is nonzero for all C 1 ≥ 0, C 2 ≥ 0 and κ m > 0. [20]. However, for general values of the C j , the zeros κ 2 m of the transcendental equation (2.21) cannot be determined in closed analytical form. This is a familiar difficulty, which makes the evaluation of the single and double mode sums m one encounters in the calculation of one and two-loop Feynman graphs of the free energy a nontrivial problem. We shall turn to this issue in section 3. Note also that in some of the above formulae we have tacitly assumed that C 1 and C 2 are both positive. However, these equations remain valid, firstly, for all m when either one of the C j vanishes while the other remains positive, and secondly, for all m > 1 when C 1 = C 2 = 0, because the respective κ m then all approach positive values in the corresponding limits. Hence one can simply set C 1 or C 2 (or both) to zero in the respective equations. The case of m = 1 with C 1 , C 2 → 0 is special in that κ 1 → 0. It is an easy matter to check that the correct limiting eigenfunction υ(ζ|0, 0) = 1 results, independent of the order in which the limits C 1 → 0 and C 2 → 0 are taken.
Many-point cumulants, their renormalization and RG equations
We proceed by providing some of the necessary background on the renormalization of the theory defined above. § Let us begin by recalling the bulk and boundary counter-terms required to absorb the ultraviolet (UV) singularities of many-point cumulant functions. To this end we consider the (N +M 1 +M 2 )-point cumulant functions (2.25) involving N fields φ α j (x j ) located at points in the interior of V and M 1 +M 2 fields φ β k on the boundary planes B 1 and B 2 . As indicated, we take the first M 1 boundary points to lie on B 1 and the remaining ones on B 2 .
Equations (2.12)-(2.17) imply that the p transform of the free propagator for general nonnegative values ofc 1 andc 2 can be written aŝ . (2.26) Its explicit form is known [33,42]. It is given by the expression into which the right-hand side of equation (B5) of reference [33] turns upon replacement of itsκ ω by i.e. (2.28) Both expressions (2.26) and (2.28) are exceedingly difficult to work with. To understand the nature of the UV singularities of the theory, it is better to treat the boundary terms L j as interactions and work with the free propagator forc 1 =c 2 = 0. The latter is nothing but the free propagatorĜ NN is the free bulk propagator forτ = 0 in the pz-representation. As expounded in reference [22], the j = 0 contribution from the first term in square brackets in equation (2.29) is the origin of the familiar primitive bulk UV singularities. The j = 0 and j = −1 contributions from the second term in square brackets are singular at coinciding points on B 1 and B 2 , respectively. The additional UV singularities they produce can be absorbed by counter-terms with support on these boundary planes, i.e. the surface counter-terms required for the corresponding semi-infinite systems [22,35,36]. All other contributions in the square brackets do not diverge at coinciding points and hence do not give rise to additional UV singularities. The upshot is that the usual bulk reparametrizations of the surface enhancement variablesc j and the boundary operators φ B 1 (y) ≡ φ(z, 0) and φ B 2 (y) ≡ φ(z, L) suffice to absorb the UV singularities of the functions G (N ;M 1 ,M 2 ) .
Following reference [43], we choose the factor that is absorbed in the renormalized interaction constant as where = 4 − d and γ E is the Euler-Mascheroni constant. This choice ensures that the bulk renormalization factors Z φ , Z τ and Z u as well as the surface renormalization factors Z 1 and Z c , when determined by minimal subtraction of poles in , up to second order in u reduce to the two-loop results given in references [22], [34], [35], [36], [44] and used in Krech and Dietrich's work [19,20]. The quantityτ c,∞ is the critical bulk value ofτ . Further,c sp is the critical enhancement value associated with the special surface transition. In a theory whose UV singularities are regularised by means of a large-momentum cut-off Λ, these quantities diverge ∼ Λ 2 and ∼ Λ, respectively. In our calculations below we shall utilise dimensional regularisation. Note also that the surface renormalization factors Z 1 and Z c depend exclusively on u and but not on c j (nor on L) when fixed by the requirement that the UV poles in be minimally subtracted. In our calculations of the L-dependent part of the free energy at the bulk critical point and the critical Casimir force to be described in section 3 we shall need Z c merely to first order in u. We therefore quote the result for convenience. Upon introducing the renormalized cumulants we can now derive RG equations for these functions by varying µ at fixed bare parameters u,τ ,c 1 ,c 2 , and L. Let us define the exponent functions (where ∂ µ | 0 indicates a µ-derivative at fixed bare parametersů,τ ,c 1 ,c 2 , L) and the operator Then the RG equations can be written as They are completely analogous to those for the renormalized cumulants of the respective semi-infinite geometries (L = ∞ with either M 2 = 0 or M 1 = 0). We have given them here for general τ , even though we will restrict ourselves to the critical case τ = 0 in our calculations in section 3.
Definitions
We next turn to the free energy and the Casimir force. Introducing the partition function Z and the total free energy F via we define the reduced free-energy density per hyper-surface area A, This quantity can be decomposed as where f b and f s are the bulk free-energy density per d-dimensional volume LA → ∞ and the excess free-energy density per hyper-surface area A → ∞, both of which are defined by appropriate thermodynamic limits (see e.g. references [22] and [45]). The former depends only on the bulk interaction constants, the latter additionally on the boundary interaction constants. It is a sum of the reduced surface excess free-energy densities f s,j of the corresponding semi-infinite systems bounded by either B 1 or B 2 : The remaining term in the decomposition (3.3), the reduced residual free-energy density f res , contains the full L-dependence of f − Lf b . The effective ("Casimir") force per hyper-surface area to which it gives rise is where the ellipsis stands for all other (bulk and surface) variables on which it depends.
Renormalization of the residual free energy and Casimir force
Inspection of the perturbation series of the reduced free energy F/k B T reveals that the bulk reparametrizations (2.31) and surface reparametrizations (2.32) are not sufficient to absorb all UV singularities. This is because both the bulk free-energy density f b as well as the surface free-energy densities f s,j have additional primitive UV singularities [22]. To cure these, additive bulk and surface counter-terms are required. Since these counter-terms must merely absorb primitive UV singularities of f b and f s,j , respectively, they can be chosen independent of L. One convenient way to fix them is by subtracting from f b the Taylor expansion in δτ , and from f s,j that in δτ and δc j about nonvanishing reference values to the appropriate orders (see e.g. [ Hence this quantity satisfies a homogeneous RG equation, namely The latter can be solved in a standard fashion by means of characteristics. Let us define the running variablesū( ) andc j ( ) as solutions to the initial value problems Let u * be the infrared-stable zero of the beta function β u for d = 4 − < 4. We shall need its expansion below only to O( ). Solving the flow equations (3.9) forc j yields where Φ is the surface crossover exponent whose expansion is known to O( 2 ) [35,36]. Since we shall need the expansion of the RG eigenexponent y c to first order in , we recall the result In the large-length-scale limit → 0, the running variablesū andc j behave as respectively, where E * c (u) is a non-universal amplitude. We now set τ = 0, solve the RG equation (3.7), choose the flow parameter as µL = 1 and use the above limiting expressions forū andc j . This gives the asymptotic behaviour with The analogous scaling form of the reduced critical Casimir force per hyper-surface area follows by differentiation with respect to L. It reads To appreciate these results, recall that the large-L form of the residual free-energy density at the bulk critical point T = T c,∞ , for given asymptotic large-scale boundary conditions BC, is conventionally written as where ∆ BC is an L-independent universal, but BC dependent, number, called "Casimir amplitude". According to our result (3.15), a scaling function D appears for general values of c 1 and c 2 in place of the Casimir amplitude -that is, the Casimir amplitude becomes scale-dependent.
On the other hand, various Casimir amplitudes ∆ BC can be recovered from the knowledge of D(c 1 , c 2 ). Since we assumed both surface enhancement variables c j to be non-supercritical, and also ruled out the breaking of the O(n) symmetry via boundary terms, the case of Robin boundary conditions we consider includes the four cases The first two of these amplitudes, ∆ (O,O) and ∆ (O,sp) , are known to have expansions in integer powers of . The leading two terms of these series expansions were determined in reference [20]. The corresponding results can be written as and and By contrast, the Casimir amplitude ∆ (sp,sp) does not have a power-series expansion in . As shown in references [43] and [46], the presence of the k 1 = 0 mode leads to a breakdown of the expansion of ∆ (sp,sp) and produces additional half-integer powers j/2 with j = 3, 5, . . ., which are modulated by powers of ln when j ≥ 5. The expansion is known to order 3/2 ; it reads [43,46] The -expansion results for the scaling function D(c 1 , c 2 ) we are going to derive below must be consistent with the series expansions (3.21)-(3.25) and equation (3.20). This requirement provides nontrivial checks for these results.
Perturbation theory
We next turn to the loop expansion of the reduced free-energy density and its computation forτ = 0 to two-loop order. The zero-loop contribution f [0] vanishes in the disordered phase. The next two terms can be written as and for generalτ ≥ 0. Here we have introduced the functions For the parameter values for which they are needed in equation (3.29), a lengthy but straightforward calculation yields with the polynomials (3.32) The p-integrals in the above equations (3.28) and (3.29) can be handled in a standard way using dimensional regularisation. The main difficulty one then is faced with is the calculation of the resulting single and double sums over the not explicitly known eigenvalues κ 2 m . We have done this by means of complex integration, modifying the Abel-Plana techniques described in reference [37] for our purposes. ¶ The technical details are given in Appendix A-Appendix B. Here we just present our results.
As before, we use the notation Q [l] to specify the l-loop term of a quantity Q. We choose the additive constant in the free-energy density such that the dimensionally regularised bulk free-energy density f b vanishes forτ = 0. Hence Our results for the surface free-energy densities read and f [2] s,j (τ = 0,ů,c j ) = where we have introduced the familiar quantity In order to write the one-and two-loop residual free-energy densities in a compact fashion, it is helpful to define the functions (3.39) ¶ As we show in Appendix A.2, it can also be derived from the result (2.26) for the free propagator. and Z (d) In terms of these, our results can be written as and (3.42)
Renormalized residual free-energy density and scaling functions
The functions X (d,1) c 1 L,c 2 L have simple poles at d = 4, caused by the behaviour of the respective pre-factor of the integral in equation (3.38). These UV singularities imply that the two-loop term (3.42) is not regular at = 0. It has a simple pole originating from the terms proportional to X (d,1) . It is an easy matter to check that this pole gets cancelled by the contribution ∝ u/ one obtains from f [1] res (L; 0,c 1 ,c 2 ) upon expressing the bare variablesc j in terms of their renormalized analogues c j via equations (2.32) and (2.34). Substitution of the one-and two-loop terms (3.41) and (3.42) into equation (3.6) therefore yields indeed a UV-finite O(u) result for the renormalized residual free-energy density f res,R (L; 0, u, c 1 , c 2 , µ), namely and J (σ) .
(3.46)
To obtain the expansion of the scaling function D, we set u = u * . Using (3.47) one sees that the result is consistent with the predicted scaling form (3.14) and yields the expansion For the special values c j = 0 and ∞, the functions D 0 and D 1 can be analytically computed in a straightforward manner. One finds where a 1 (n) is the coefficient defined in equation (3.24). These results confirm the validity of the relations (3.20) to first order in . However, the present form (3.48) of our result does not yield the contribution ∼ 3/2 to D(0, 0) = ∆ (O,sp) /n. The reason is that we assumed that c 1 + c 2 > 0 so that the lowest eigenvalue k 2 there is a zero mode in the free propagator. As already mentioned, this causes a breakdown of the conventional RG-improved perturbation theory at T c,∞ [43,46,47]. In the following we will improve our results in such a manner that they fully comply with all of the small-expansions of Casimir amplitudes given in equations (3.21)-(3.25), including the fractional expansion (3.25) of ∆ (sp,sp) to O( 3/2 ).
3.5.
Modified RG-improved perturbation theory 3.5.1. Formulation and results It is known from references [43], [46] and [47] how one can cope with the mentioned zero-mode problem one encounters at τ = 0 when c 1 = c 2 = 0: one can reorganise RG-improved perturbation theory such that it becomes well-defined at τ = 0. This suggests an obvious strategy to ensure consistency with the small-expansions of ∆ (sp,sp) to 3/2 . We should reorganise RG-improved perturbation theory for general c 1 > 0 and c 2 > 0 in a way that reduces to the one used in previous work [43,46] for the case c 1 = c 2 = 0.
We now setτ = 0 and define an effective (d − 1)-dimensional field theory with Hamiltonian H eff [ϕ] by integrating out ψ: (3.55) To determine H eff [ϕ], we use perturbation theory. The contribution to the two-point vertex caused by the coupling between ϕ and ψ, to first order inů, originates from the graph . (3.57) It represents a local interaction corresponding to a shift δτ L ofτ . The Hamiltonian To obtain the free-energy density f (L; 0,ů,c 1 ,c 2 ) in the present modified perturbation scheme, we must add to f ψ (L; 0,ů,c 1 ,c 2 ) the contribution associated with the ϕ-field. We denote it as f ϕ and define it via ϕ (L; 0,ů,c 1 ,c 2 ) + f [2] ϕ (L; 0,ů,c 1 ,c 2 ) + . . . .
(3.61)
Here f [1] ϕ and f [2] ϕ are the one-and two-loop terms of a (d − 1)-dimensional φ 4 theory with quadratic and ϕ 4 interaction constants δτ L +k 2 1 andů∆ 1,1,1,1 /L, respectively. Their explicit expressions may be inferred from equation (4.28) of reference [43]. They read f [1] ϕ (L; 0,ů,c 1 , Building on the reorganisation of perturbation theory just described, we now wish to compute the residual free-energy density f res (L; 0,ů,c 1 ,c 2 ) and express it in terms of renormalized variables to obtain improved results for its scaling function D(c 1 , c 2 ) and that of the Casimir force. Clearly, from these results all Taylor expansions in reported in sections 3. [46] and [43] when c 1 = c 2 = τ = 0.
What makes this approach technically difficult to implement is that the eigenvalues k 2 m , whose behaviours for smallc 1 +c 2 we gave in equation (2.24), are not explicitly known for general values ofc 1 andc 2 . Hence we shall have to resort again to numerical means.
Let us start by taking a look at the effective two-point vertex whose one-loop approximation appears in the expressions (3.62) and (3.63) for f [1] ϕ and f [2] ϕ . Its renormalized counterpart is given by γ (2) . Thus its Fourier p-transform γ where c j denote the scaling variables defined in equation (3.16). Further, E * h is a non-universal amplitude whose representation as a trajectory integral can be found in equation (3.85c) of reference [22] but will not be needed in the remainder. Since this amplitude drops out of the Casimir force, we need not keep track of it and may therefore set it to 1 henceforth.
In Appendix C we determineγ R to one-loop order, show that it is UV finite and compute the scaling function Ω(c 1 , c 2 ) to O( ). The result is where κ 1 and λ 1 represent the eigenvalue κ 1 (c 1 , c 2 ) and the normalization factor λ 1 (c 1 , c 2 ), respectively. The extrapolation one obtains for Ω(c 1 , c 2 ; d = 3, n = 1) by evaluating the above O( ) result at = 1 is depicted in figure 2. Since the eigenvalues κ 1 (c 1 , c 2 ) are analytically known for all combinations of (c 1 , c 2 ) with c j = 0, ∞, j = 1, 2, the expansions of the corresponding limiting values of Ω can be determined exactly. The and Ω(c 1 , c 2 ) = c 1 + c 2 + O(c 2 1 , c 2 2 , c 1 c 1 ) + n + 2 n + 8 (3.70) The first term on the right-hand side reflects the small-c j behaviour κ 2 1 (c 1 , c 2 ) ≈ c 1 + c 2 implied by equation (2.24). The remaining terms originate from the expansion of the shift δτ to linear order, whose zeroth-order term is according to equation (14) of reference [46] (where it was denoted as δτ Just as in our calculation of γ R , the pole term gets cancelled by the counter-term provided by the contribution linear inc 1 +c 2 = µZ c (c 1 + c 2 ) to k 2 1 . If we substitute equation (3.71) into k 2 1 + δτ L along with equations (3.72) and (3.73), express the result in terms of renormalized variables and set u = u * , we recover the expansion of Ω(c 1 , c 2 ) to linear order in c j given on the right-hand-side of equation (3.70).
We now insert the scaling form (3.66) of the effective two-point vertex into the expressions (3.62) and (3.63) for f [1] ϕ and f [2] ϕ . Expressing the sum in terms of renormalized variables yields
(3.75)
Here the ellipsis stands for contributions that are O(u * , 2 ) as long as Ω(c 1 , c 2 ) = O( 0 ). This condition is fulfilled whenever c 1 + c 2 > 0. Depending on whether this is the case or not, the function D ϕ (c 1 , c 2 ) has an expansion in integer powers of , namely (1). The origin of these UV singularities is obvious. The free-energy density f ϕ of the effective (d − 1)dimensional theory at d = 3 involves UV singularities of the form Λ 2 and Ω ln Λ. The bulk and surface counter-terms included so far do not cure these; additional subtractions (of the kind needed for a super-renormalizable effective bulk theory in d − 1 = 2 dimensions, cf. [48]) would be needed. Evaluated at d = 3, the first term on the righthand side of equation (3.75) would then yield a contribution (Ω/8π)[1 − γ E − ln(Ω/4π)] to f ϕ,res,R and hence to D ϕ . Such logarithmic terms are encountered at d = 3 also in Gaussian film models; see e.g. reference [49].
Let us postpone any further discussion of the behaviour of D ϕ at d = 3 for the moment and first compute the free-energy contributions f [1] ψ and f [2] ψ . The former differs from f [1] through the lowest-mode contribution. This is given by equation (3.62) with the shift δτ L set to zero. Hence we have To determine the two-loop graph of f [2] ψ , we must subtract from the two-loop graph of f [2] and .
(3.82)
To visualise the result, we have plotted in figure 3 the difference between the O( ) expression (3.48) for D(c 1 , c 2 ) and its analogue (3.80) for D ψ (c 1 , c 2 ) one obtains in the scalar case n = 1 upon evaluation at = 1. This difference corresponds to the contribution from the lowest mode m = 1 to the series expansion of D(c 1 , c 2 ) to O( ). It vanishes as (c 1 , c 2 ) approaches the origin and reaches its minimum at the fixed point (c 1 , c 2 ) = (∞, ∞) corresponding to large-scale Dirichlet boundary conditions at both boundary layers B 1 and B 2 .
Combining equations (3.75) and (3.80), we can write the result of the modified RG-improved perturbation theory used in this subsection as (3.83) Figure 3. Contribution from the lowest mode m = 1 to the expansion of the scaling function D(c 1 , c 2 ) for n = 1, evaluated at = 1. This quantity is given by where D ϕ stands for the expression defined through the right-hand side of equation (3.75) in conjunction with equation (3.67), while D ψ represents the O( ) series expansion in equation (3.80) with the expansion coefficients given by equations (3.81) and (3.82), respectively. Note that the result must be utilised with care. It is not suitable for direct evaluation at d = 3 ( = 1). We defer a discussion of this and related issues to section 4.
3.5.2.
Consistency with fractional expansion for c 1 = c 2 = 0 and Ginzburg-Levanyuk criterion Our motivation for working out the modified RG-improved perturbation theory described in section 3.5 was the goal to achieve consistency of the theory for general nonnegative values of the enhancement variables c 1 and c 2 with the approach used in references [46] and [43] to study the zero-mode case c 1 = c 2 = 0 of critical surface enhancements. Since the former approach reduces to the latter when c 1 = c 2 , it is clear that consistency is ensured and the fractional expansion (3.25) must be recovered. To see this explicitly from the results of the previous subsection, recall that κ 1 vanishes as c 1 + c 2 → 0. Therefore, D ψ,0 (c 1 , c 2 ) and D ψ,1 (c 1 , c 2 ) approach the limiting values D 0 (0, 0) and D 1 (0, 0), respectively. Furthermore, the first term on the right-hand side of equation (3.75) yields the 3/2 term according to equation (3.77). That the modified RG-improved perturbation theory is controlled for small , irrespective of whether c 1 + c 2 is positive or zero, can also be seen from a criterion of the Ginzburg type [50,51]. Letγ (4) of the effective four-point vertex γ (4) (y 1 , . . . , y 4 ). The analogue of equation (3.66) tells us thatγ (4) (0, 0, 0) ∼ u * µ 2η L d−5+2η , where the proportionality factor is a function of the scaling variables c 1 and c 2 . Following a standard reasoning (used also by Sachdev in his study of finite-temperature crossovers near quantum critical points [48]), we can construct fromγ (2) Sinceγ (2) (0) is proportional to Ω(c 1 , c 2 ), this measure of the strength of the nonlinearities in H eff behaves for small as Hence the Ginzburg-Levanyuk-type criterion U 1 is satisfied when 1. once the non-universal amplitude E * c (u) has been fixed. As is borne out by figure 4, choices of (c 1 , c 2 ) exist for which these paths start in the region D < 0, enter the region of positive values as L increases and finally return back to the region D < 0. Hence one expects that crossovers of the Casimir force from attractive to repulsive and back to attractive behaviours should occur as a function of L.
Discussion of results and extrapolation to d = 3 dimensions
The result for the scaling function D n=1 (c 1 , c 2 ) of the Casimir force that follows from this extrapolation for D n=1 (c 1 , c 2 ) via equation (3.18) is displayed as a three-dimensional plot in figure 5 and as contour plot in figure 6.
To obtain these plots, we proceeded as follows. We substituted the extrapolated expression [D 0 + D 1 ] =1 for the scaling function D in equation (3.18). For the prefactor d − 1 + y c we used the value 2.718 corresponding to Hasenbusch's recent Monte Carlo estimate y c (n=1, d=3) 0.718(2) [52]. Let us note that some earlier Monte Carlo calculations led to significantly larger values for this exponent [53,54,55], but others and more recent ones [56,57,58,59] yielded similar numbers. Field-theory estimates based on the expansion to second order and the massive field-theory approach to two-loop order [60,61] gave y c (1, 3) 0.75 and y c (1, 3) 0.85, respectively. For a detailed list of Monte Carlo and field-theory estimates for y c (1, 3) the reader is referred to reference [52]. Choosing a somewhat larger value of y c (1, 3) such as the quoted field-theory estimates would lead to small quantitative, but no qualitative changes in figures 5 and 6.
The behaviour of the plotted function D is qualitatively similar to that of D. As is obvious from figures 5 and 6, the critical Casimir force does exhibit the anticipated crossovers from attraction to repulsion and back to attraction for appropriate choices of (c 1 , c 2 ). According to a theorem for systems satisfying reflection positivity [62], the Casimir force cannot become repulsive for equal enhancements c 1 = c 2 . This conforms with the fact that the Casimir force, by continuity, is attractive (i.e. D < 0) in the vicinity of the 11 diagonal. By choosing (c 1 , c 2 ) sufficiently away from the 11 diagonal, one can ensure that a double sign change of F occurs as L increases. A fascinating consequence is that for such choices of (c 1 , c 2 ), critical values L = L 0 (c 1 , c 2 ) of the film thickness exist for which the critical Casimir force vanishes.
In the extrapolations for D n=1 (c 1 , c 2 ) and D n=1 (c 1 , c 2 ) presented above, we tacitly assumed that c 1 + c 2 > 0. Knowing that the expansion breaks down when c 1 = c 2 = 0 (becoming fractional), we may expect to see indications of this breakdown in the behaviour of these extrapolations near the origin. This is indeed the case, though only very close to it. To demonstrate this, we depict in figure 7 This function [D 0 + D 1 ] n=1 (c, c) has an infinite slope at c = 0. Its asymptotic behavior near the origin can be determined analytically in a straightforward fashion. One finds (4.1) The in-set in figure 7 shows a comparison of [D 0 + D 1 ] n=1 (c, c) and its asymptotic form (4.1) for small c. The term ∝ c 1/2 in equation (4.1) results from that part of the two-loop contribution f [2] res whose mode summation m 1 ,m 2 is restricted to m 1 = 1 in either one of the two loops and to m 2 > 1 in the respective other. The easiest way to recover it is to expand D ϕ (c, c)| n=1 to O( ). The coefficient of the O( ) term is precisely the contribution ∝ √ c in equation (4.1). It is a consequence of the (spurious) infrared singularity one encounters in this expansion due to the m = 1 mode with κ 1 (c, c) → 0, and would imply an infrared singular derivative ∂ c of the function (4.1) at c = 0. This is a spurious infrared singularity since the system is not expected to exhibit critical behaviour at T − T c,∞ = c 1 = c 2 = 0 when L < ∞. The extrapolated scaling function [D 0 + D 1 ] n=1, =1 of the Casimir force behaves analogously near the origin, as should be clear from equation (3.18).
To illustrate that the spurious behaviour of [D 0 + D 1 ] n=1 (c, c) near the origin is due to the zero-mode contribution, we also display the function [D ψ,0 + D ψ,1 ] n=1 (c, c) in figure 7. The latter function is regular at c = 0 and has a finite positive slope there, since it does not involve the zero mode m 1 = 1. Its value at c = 0 agrees with that of The remaining brown curve in figure 7 represents an extrapolation based on equation (3.83), namely the function This means that we have discarded the two-loop contribution to D ϕ and replaced the pre-factor A d−1 /(d − 1) of the one-loop term by its value at d = 4. To understand the rationale for this approximation, one should note the following. If c 1 = c 2 = 0, then this term reduces precisely to the a 3/2 (n) 3/2 contribution to D(0, 0). If we expand, on the other hand, this choice of D ϕ to linear order in when c 1 + c 2 > 0 and substitute it into D ψ,0 + D ψ,1 + D ϕ , we recover the O( ) result D 0 + D 1 . Hence, in the limit c → 0, D app (c, c) approaches the value one obtains for ∆ (sp,sp) | n=1, =1 by evaluating the small-expansion (3.25) at = 1. Furthermore, its derivative ∂ c D app is finite at c = 0. Despite these appealing features, we refrain from showing a plot of this function for all c ∈ (0, ∞) because away from the origin this function deviates considerably from the O( ) extrapolation [D 0 + D 1 ] n=1 . The reason is that Ω(c 1 , c 2 ; = 1) becomes fairly large for large c 1 + c 2 (see figure 2) and the difference between (A 3 /3)Ω(c, c; ) and its extrapolated O( ) expansion (1+ ∂ )(A 3 /3)Ω(c, c; 0)| =1 is not small. Away from the origin, we therefore do not consider D app to be superior to the naïve extrapolation D 0 + D 1 .
As we mentioned earlier, the pre-factor A d−1 /(d − 1), has a UV pole at d = 3. Being guided by the aim to achieve consistency with the small-expansion for c 1 = c 2 = 0, we expanded it in and hence could replace it by its value at d = 4 at the order of our calculation. In an extrapolation based on equation (3.83) one might be tempted to use the value of the UV finite one-loop term of D ϕ one obtains in the manner described below equation (3.77) by subtracting the pole term [Ω(c 1 , c 2 , = 1)] (d−1)/2 and evaluating the difference at d = 3. However, such an approach would mix the RG approach based on the expansion we used for f ψ with elements of a fixed-dimension RG approach. The corresponding extrapolation would again lead to substantial differences from the O( ) extrapolation D 0 + D 1 for large values of c 1 + c 2 . We feel that such attempts to evaluate D ϕ directly at d = 3 should be based on a RG approach in fixed dimension d = 3. Such an approach is known to involve the study of the theory away from the bulk critical point [63,64]. Furthermore, the surface enhancement variables c 1 and c 2 provide two mass parameters in addition to the bulk correlation length one has to deal with. A corresponding massive RG approach in fixed dimension d = 3 based on references [60] and [61] -or combined with elements of the strategy followed in reference [65] -is technically very demanding and beyond the scope of the present work, albeit conceivable.
It is instructive to compare the extrapolated scaling function D n=1 of the critical Casimir force displayed in figures 5 and 6 with their exact analogues res (1; 0, c 1 , c 2 )/n (4.3) of the Gaussian theory in d = 3 and d = 4 dimension. Here, the one-loop term (3.41) must be substituted for f [1] res . A plot of these functions on the diagonal c 1 = c 2 ≡ c is shown in figure 8. As one sees, the extrapolation D n=1 (c, c) lies for most values of c below and above the Gaussian scaling functions (4.3) with d = 4 and d = 3, respectively. Having already discussed the spurious small-c behaviour of the extrapolation, let us add a comment about the limiting behaviour at large c. It has been known for long that deviations of the surface enhancement variables c j from their fixed point values c j = ∞ associated with the ordinary surface transition correspond to irrelevant surface scaling fields ("extrapolation lengths") whose RG eigenvalues are given by the momentum dimension −1 [66,22]. Taking into account the corrections to scaling ∝ L −1 implied by them is crucial for a proper analysis of Monte Carlo simulation results for Casimir forces [26,27,28,29,30]. Our small-results enable us to explicitly verify the presence of such corrections to scaling. In order to comply with a correction to scaling to the residual free energy that is down by a factor 1/L, the scaling function D(c 1 , c 2 ) ought to exhibit the asymptotic behaviours respectively. Let us recall that the behaviour of the extrapolation D n=1 plotted in figure 8 was obtained by substituting [D 0 + D 1 ] =1 into equation (3.18). Therefore, the plotted extrapolated function does not approach its limiting value at c = ∞ as c −1/yc . This is because its asymptotic form contains the logarithmic term ∼ ln(c)/c mentioned above, evaluated at = 1. Hence, the deviation of the plotted extrapolation D n=1 from its value at c = ∞ varies (incorrectly) as ∼ ln(c)/c. For conciseness, we have refrained from designing alternative extrapolations into which the correct asymptotic large-c asymptotics is incorporated via appropriate exponentiation ansatzes.
Summary and Conclusions
Considering an O(n)-symmetric φ 4 model in film geometry, we investigated the fluctuation-induced forces produced by thermal fluctuations between the boundary planes of a film that is held at its bulk critical point. We restricted our attention to the case of generic non-symmetry-breaking boundary conditions. The interaction constants c j of the O(n) symmetric boundary termsc j φ 2 /2 included in the Hamiltonian were chosen to correspond to non-supercritical surface enhancements but otherwise allowed to take arbitrary values. Together with the restriction to the bulk critical temperature T c,∞ (or, more generally, to temperatures T ≥ T c,∞ ), this requirement guarantees that the O(n) symmetry is neither explicitly nor spontaneously broken. Whenever the symmetry φ → −φ is broken, the order-parameter profile φ does not vanish. As discussed in the introduction, this implies that a nonzero Casimir force is obtained even in mean-field theory -i.e., in the absence of fluctuations. Thus in these cases the Casimir force is not fully fluctuation induced but contains a non-fluctuating component. This applies, in particular, to binary liquid mixtures, for which beautiful direct measurements of the Casimir forces were accomplished recently [16,29,67]. A key motivation for excluding such symmetry breakdowns in the present investigation was the intention to keep the thermodynamic Casimir forces entirely fluctuation induced, making them share this crucial feature with the original QED Casimir force [1,4].
Our analysis was based on the field-theoretic RG approach in 4 − dimensions. The use of the expansion in studies of critical and near-critical Casimir forces has shortcomings that go beyond the familiar ones known from its application to critical behaviour in bulk and semi-infinite systems. The series expansions it yields for bulk and surface critical exponents as well as for other properties at bulk critical points -Taylor expansions in -are asymptotic. Naive extrapolations of such expansions to low orders in are not normally quantitatively reliable. However, quantitatively accurate results can be obtained by extending the expansions to sufficiently high orders, combining them with information from appropriate large-order results and using appropriate Borel-Padé resummation techniques [68,64,69,70]. The additional complication one encounters in the case of films is that = 4 − d ceases to be an appropriate expansion parameter when dealing with dimensional crossovers. (The adequate analogue of this parameter for the study of critical behaviour at the transition temperature T c,L of a film of finite thickness L and infinite extension in d−1 Cartesian directions would be 5 ≡ 5−d.) The limitations of the approach become particularly apparent when zero modes appear at zero-loop order at the bulk critical point, as happens for critical enhancement c 1 = c 2 = 0 of both boundary planes. Whenever this occurs, the expansion breaks down at the bulk critical temperature T c,∞ and becomes fractional, involving also powers of ln [43,46,47,48]. By contrast, the expansion remains (formally) intact at T c,∞ provided at least one of the (non-supercritical) enhancements c j is subcritical, although a similar breakdown clearly must occur at a temperature below T c,∞ .
Despite these deficiencies, the field-theoretic RG approach in 4 − dimensions has a number of appealing and valuable features. First of all, it lends itself to nontrivial checks of the scaling forms the residual free energy and the Casimir force are expected to have according to finite-size scaling theory and the RG approach. Since we performed a two-loop calculation which gave f res to order u, we were able to identify the ln(µL) contributions implied by the nontrivial O( ) term of the surface crossover exponent Φ in the scaling arguments (3.13) and thus verify the scaling forms (3.13) and (3.17) to first order in . Second, the fact that general properties such as the exponential decay in the disordered phase (see references [20,Sec. VI] and [43, Sec. IV.C]) and analyticity properties of the free-energy density f (see references [20,Sec. VII] and [43, Sec. IV.C]) must hold at any order of the small-expansion provides nontrivial checks of them. For the sake of clarity, it will be helpful to recall these analyticity properties. For given n and sufficiently large d, the film undergoes a sharp transition to an ordered phase at a temperature T c,L < T c,∞ . In the case of non-supercritical surface enhancements considered here, there should also be no surface transitions of the film at temperatures T ≥ T c,∞ (i.e. its surface layers should not exhibit long-range order). Consequently, the total free-energy density f must be analytic in temperature at T c,∞ . This requirement imposes conditions on the behaviour of the temperature dependent analogue of the scaling function of f res . We refer the reader to references [20,Sec. VII] and [43, Sec. IV.C] for details.
These analyticity requirements were found to be fulfilled by the two-loopexpansion results for anti-periodic, (O, O), and (O, sp) boundary conditions, but violated at O( ) for periodic and (sp, sp) boundary conditions [20]. Extension of the smallexpansion to O( 3/2 ) in the latter two cases via the effective-action approach outlined above increased the order at which a violation of analyticity requirements occurred to 3/2 [43]. Third, our analyses in the latter reference and above yield evidence of a shift of the point c 1 = c 2 = 0 at which the zero-mode field ϕ becomes critical at T c,∞ to an L-dependent location with c 1 + c 2 < 0. By analogy with the shift T c,∞ → T c,L of the transition temperature, such a shift is expected and in conformity with the required analyticity of f at bulk criticality.
One crucial problem one is faced with in studies of critical behaviour and dimensional crossover in films is the difficulty of obtaining accurate results for such shifts in d = 3 bulk dimensions by analytical methods. The reason is that fluctuations on all length scales between the microscopic one (lattice constant) and the bulk correlation length may contribute, as a result of which these shifts may acquire contributions that are non-analytic in the interaction constant [71,72,60,73]. Since we used RG-improved perturbation theory in 4− dimension at T c,∞ to determine the effective action H eff , our approach is not capable to capture such non-analytic contributions. It gave us a shift along the c 1 +c 2 axis of the point where the ϕ component of the order parameter becomes critical that was proportional to u * . This in turn implied a contribution to the critical Casimir force for critical surface enhancements c 1 = c 2 = 0 of the form (u * ) (3− )/2 . To make our results for the scaling functions D(c 1 , c 2 ) and D(c 1 , c 2 ) consistent with the fractional expansions at (c 1 , c 2 ) = (0, 0), we extended the effective-action approach of references [46] and [43] to nonzero values of c 1 + c 2 . We succeeded in achieving consistency with the results of these references for the case c 1 = c 2 = 0 and the fractional expansions. Furthermore, the effective-action approach turned out to be well-behaved for small . Nevertheless, its results must be taken with a grain of salt: they did not lend themselves easily to simple extrapolations to d = 3 dimensions that could be judged as clearly superior to those based on the conventional expansion.
Let us emphasise that our results exhibit a number of interesting and important qualitative features which may be expected to persist in quantitatively more accurate investigations, irrespective of the accuracy of our extrapolation to d = 3.
(i) Generalising previous work [19,20,37,43,47], they clearly demonstrate that critical Casimir forces can be attractive or repulsive depending on the values of the surface enhancement variables c j , even when the internal symmetry (Z 2 for n = 1 and O(n) for n > 1) is neither spontaneously nor explicitly broken.
(ii) They are in full accordance with -and hence corroborate -the scaling forms (3.14) and (3.17) of the residual free energy and Casimir force, respectively. This means that the Casimir amplitude becomes scale dependent.
(iii) As a further important observation we found that crossovers from attractive to repulsive forces and vice versa can occur if the surface interaction constants take appropriate values. In conjunction with (ii) this means that the critical Casimir force goes through zero at a certain thickness L 0 .
(iv) For the case of primary interest -the Ising bulk universality class with short-range interactions and d = 3 -we saw that for properly chosen surface enhancement values c 1 and c 2 , crossovers from attractive to repulsive and back to attractive behaviours should occur as L increases. It would certainly be worthwhile to check this prediction along with (iii) by Monte Carlo calculations.
(v) Finally, let us mention that crossover behaviours analogous to (iii) and (iv) should also be possible for three-dimensional O(n) systems with easy-axis spin anisotropies. Semi-infinite systems of this kind are known to have anisotropic analogues of the isotropic special transition [74,75], characterised by the coincidence of the transition temperature at which the easy-axis component of the order parameter at the surface becomes critical with the transition temperature T c,∞ of the n > 1 bulk system. Hence for finite thicknesses L, the surface interaction constants associated with a given easy axis on one or both boundary planes can be critically enhanced. This suggests that the mentioned analogues of (iii) and (iv) should occur. (Films involving different directions of easy axes on the two boundary planes would require separate analyses.) Appendix A. Calculation of the one-loop free-energy density f [1] Appendix A.1. Calculation based on the Abel-Plana summation formula To compute f [1] , we start from equation (3.28), differentiate this expression with respect toτ and compute the integral over p. This gives The expression in the second line of equation (A.1) varies ∼ L ∞ 0 dk (τ + k 2 ) (d−3)/2 in the large-L limit. We could subtract this bulk term to make the difference well defined. However, we are ultimately interested in the free-energy density f [1] (L;τ ,c 1 ,c 2 ). Term-by-term integration of the series for ∂τ f [1] increases the exponent (d − 3)/2 of the series coefficients by one. Hence, subtracting the limiting bulk contribution Lf [1] b would not suffice to render UV finite expressions for the free-energy density f [1] (L;τ ,c 1 ,c 2 ) in dimensions d 4. To obtain well-defined results for this quantity, we prefer to use analytical continuation in d, rather than making additional subtractions. We start by integrating the series in equation (A.1) term-wise, choosing the integration constant such that That the integration constant has been chosen correctly may not be obvious at this stage. However, once we will have analytically continued the above series (A.2) in d, one can confirm this choice by verifying that the resulting free-energy expressions reduce to known dimensionally regularised results atτ = 0+ in the limitsc 1 ,c 2 → 0 andc 1 ,c 2 → ∞. Furthermore, there are two other ways to arrive at expression (A.2), both of which indicate its consistency with general rules of dimensional regularisation. The first is to use the representation for the logarithm in the second line of equation (3.28), perform the integrations and take into account that integrals of pure powers such as (d−1) p 1 vanish in dimensional regularisation. Another way is to insert the partial-p identity (d − 1) −1 ∇ p · p into the integrand of the integral (d−1) p in the last line of equation (3.28) and integrate by parts, dropping the boundary terms at p = ∞.
According to the result (A.2) we must calculate -and analytically continue -a series of the form where κ m are the positive solutions to equation (2.21). Such series are generalisations of Epstein-Hurwitz ζ functions (see e.g. reference [76]). Let us assume that both C j ≥ 0 and C 1 + C 2 = 0. Then all κ m , m = 1, 2, . . . , ∞, are positive, and as we showed in section 2, non-degenerate. Hence the function ∂ κ ln R C 1 ,C 2 (κ) has a simple pole with residue 1 at each of these κ m . Since (κ 2 + b 2 ) a is regular at κ = κ m , the value of this function at κ m is given by the residue Res . But at κ = κ m R C 1 ,C 2 can be factorized as (A.7) Thus we have Since this function and the one appearing in S C 1 ,C 2 (a; b) are even in κ, we can extend the summation in equation (A.4) to all integer-valued m = 0, using κ −|m| = −κ |m| , and divide by 2. Since (κ 2 + b 2 ) a is regular at κ m , each term of this series can be expressed as (2πi) −1 times an integral dκ (κ 2 + b 2 ) a Υ C 1 ,C 2 (κ) along a contour that passes once around the pole at the respective κ m in a counter-clockwise fashion and contains no other singularities. If a < −1/2, the series S C 1 ,C 2 (a; b) converges and the integrand of the contour integral decays sufficiently fast as κ → ±∞ ± i0, so that the union of all these contour integrals can be deformed into a path γ 1 encircling all poles κ m with 0 = m ∈ Z (see figure A1). We now add and subtract integrals along the paths γ 2 and γ 3 depicted in this figure. Since the integrand is regular at all nonzero κ inside the region bounded by the closed path γ 1 ∪ γ 2 ∪ γ 3 , the integral along it is −2πi times the residue of the integrand at κ = 0. Furthermore, the integral along γ 2 approaches zero as the radius of the circle on which γ 2 is located tends to infinity. Hence we have (A.10) Figure A1. Paths in the complex κ-plane.
The factor (κ 2 + b 2 ) a implies that the integrand has branch cuts from ib to i∞ and from −ib to −i∞. In addition, the function g C 1 ,C 2 (κ) and hence Υ C 1 ,C 2 (κ) have poles at ±iC 1 and ±iC 2 , marked by yellow pentagons in figure A1. We move the path γ 3 infinitesimally close to the imaginary axes, passing around the poles ±C j along semicircles of radius δ → 0. The portions of γ 3 with Im κ > 0 and Im κ < 0 give identical contributions. Taking into account that the limiting values of the power on the right and left rim of the branch cut are lim Re κ→0± Im κ>0 one arrives at (A.12) Here P ∞ b dt means the principal value lim δ→0+ C>+δ dt, where C < and C > are the smaller and larger one of C 1 and C 2 , respectively, and b is assumed to be smaller than C < . The contribution in the second line results from the integrals along the semicircles.
In order that the integral P ∞ b dt exists, we must require a > −1 (to ensure convergence at the lower limit of integration) in addition to the original condition a < −1/2. In view of the behaviour of the integrand near the upper integration limit, we must have a < −1/2 (to guarantee convergence at the upper limit of integration). However, we can split off the limiting value lim κ→±i∞ N C 1 ,C 2 (κ)/R C 1 ,C 2 (κ) = ∓i, obtaining Since the first term vanishes at κ = iC j , the contribution it yields to the term in the second line of equation (A.12) vanishes, i.e. Res contributions to S C 1 ,C 2 (a; b) implied by the term −i in equation (A.13) can be represented as an integral along the original path γ 1 , namely where sgn(x) means the sign function. For a < −1/2, the latter integral is well defined and can be analytically computed. This gives where 2F1 , the regularised hypergeometric function, is an entire function related to the standard hypergeometric function 2 F 1 via 2F1 (α, β; γ; z) = 2 F 1 (α, β; γ; z)/Γ(γ). where I C 1 ,C 2 (a; b) represents the meromorphic function defined by the right-hand side of equation (A.15).
Equation (
A.17) provides the appropriate generalisations of the results of reference [20] for the special cases (C 1 , C 2 ) = (0, 0), (∞, ∞) and (0, ∞) to general nonnegative values of C 1 and C 2 . To check the consistency with Krech and Dietrich's results, let us work out the asymptotic behaviours in these limits. Straightforward analysis yields 19) and (A.20) approach infinity in the considered limits C j → ∞. These do not appear if one sets C 2 = ∞ and C 1 = C 2 = ∞ from the outset because the operations of analytic continuation and of taking these limits do not commute. (As long as a < 0, the subtracted terms approach zero as C j → ∞.) Note also that these terms contribute only to the excess surface densities f [1] s,j , but not to f [1] res . We now insert the above results (A.15) and (A.17) into equation (A.2), set a = (d − 1)/2, and take the limit b → 0 (i.e.τ → 0). The t-integral of equation (A.17) becomes ∞ 0 dt π g C 1 ,C 2 (it) t d−1 for such values of d. | 16,780.4 | 2011-10-06T00:00:00.000 | [
"Physics"
] |
Soluble receptors in cancer: mechanisms, clinical significance, and therapeutic strategies
Soluble receptors are soluble forms of receptors found in the extracellular space. They have emerged as pivotal regulators of cellular signaling and disease pathogenesis. This review emphasizes their significance in cancer as diagnostic/prognostic markers and potential therapeutic targets. We provide an overview of the mechanisms by which soluble receptors are generated along with their functions. By exploring their involvement in cancer progression, metastasis, and immune evasion, we highlight the importance of soluble receptors, particularly soluble cytokine receptors and immune checkpoints, in the tumor microenvironment. Although current research has illustrated the emerging clinical relevance of soluble receptors, their therapeutic applications remain underexplored. As the landscape of cancer treatment evolves, understanding and targeting soluble receptors might pave the way for novel strategies for cancer diagnosis, prognosis, and therapy.
INTRODUCTION
Soluble receptors are unique types of cellular receptors that exist in a soluble form.Receptors generally consist of a cytoplasmic domain, a transmembrane domain, and an extracellular domain.Soluble receptors are released into the extracellular space in the form of an extracellular domain lacking a transmembrane domain or bound to extracellular vesicles 1 .By binding to ligands in the extracellular environment, independent of their membrane-bound counterparts, soluble receptors can enhance or disrupt cellular signaling pathways 2 .They can also enter the circulation and elicit local and systemic effects by regulating cellular processes in various physiological conditions 3 .However, abnormal levels of these receptors in the circulation have been associated with disease severity across a range of conditions, including autoimmune diseases, diabetes, infectious diseases, and cancer [3][4][5][6] .
In cancer research, soluble receptors have recently generated interest due to their potential as biomarkers 5,7,8 , given their increased levels in the bodily fluids of patients.As biomarkers, they might offer benefits in early detection of cancer, prognosis estimation, and monitoring of treatment response.Beyond their diagnostic value, emerging evidence has demonstrated that soluble receptors are involved in cancer progression, metastasis, and escape from immune surveillance [9][10][11][12] .Specifically, soluble forms of cytokine receptors and immune checkpoints have been identified as key modulators in cancer pathogenesis.Although their clinical relevance in cancer has become increasingly apparent, their therapeutic use remains a budding field.Given the limitations of current cancer therapies, targeting soluble receptors is expected to open promising therapeutic avenues.
This review endeavors to dissect the complexities of soluble receptors in cancer.We will elucidate key mechanisms of soluble receptors, from their generation to their roles in cancer pathogenesis, with a particular focus on soluble cytokine receptors and soluble immune checkpoints.Additionally, we will delve into their clinical significance across multiple cancer types, reflecting on current research and existing therapeutic challenges.As our comprehension of soluble receptors evolves, this review highlights their potential as diagnostic/prognostic biomarkers and therapeutic targets in cancer.
GENERATION OF SOLUBLE RECEPTORS
Given the importance of soluble receptors in the development of various diseases, a comprehensive understanding of the mechanisms involved in their generation is essential for identifying potential therapeutic targets.Soluble receptors are known to be produced by several distinct molecular mechanisms, including (1) ectodomain shedding, (2) alternative mRNA splicing, and (3) extracellular vesicle release (Fig. 1).In this section, the generation of soluble receptors by each mechanism and clinical implications will be discussed.
Ectodomain shedding
Ectodomain shedding is a process in which transmembrane proteins exposed on the cell surface or cellular organelles are proteolytically cleaved and released by enzymes, called "sheddases" 13 .The cleaved extracellular domain (ectodomain) of a membrane-bound receptor is released into the extracellular space and transported in a soluble form.Enzymes known as ADAMs (a disintegrin and metalloproteinases), which are the bestcharacterized sheddases, are central to this process (ectodomain shedding).Within this ADAM family, ADAM10 and ADAM17, which have similar structures, are of particular interest, especially in the context of cancer research [14][15][16] .They consist of a catalytic metalloproteinase domain that functions in shedding, a disintegrin domain, a cysteine-rich domain, a transmembrane domain, and a C-terminal cytoplasmic domain that is involved in activity regulation.The short C-terminal fragment (CTF) that remains at the plasma membrane as a result of receptor cleavage is further processed by the γ-secretase protease complex to release the intracellular domain (ICD) fragment (Fig. 1a).Although most ICDs are degraded, some are translocated to several cellular compartments such as the nucleus and mitochondria where they are involved in intercellular signaling 17 .
Ectodomain shedding is known as a general mechanism for generating soluble forms of growth factor receptors and many types of cytokine receptors 18 .For instance, cytokine receptors cleaved by sheddases include class I cytokine receptors (e.g., IL-2 receptor, IL-6 receptor), the tumor necrosis factor (TNF) receptor superfamily, and the IL-1 receptor /Toll-like receptor superfamily 3,19,20 .Recent studies have indicated that serum levels of soluble receptors generated by proteolytic cleavage are correlated with disease severity in patients 4,14,21 .To date, considerable research has illuminated the mechanisms and roles of soluble receptors produced through ectodomain shedding.However, the underlying mechanisms governing shedding and soluble receptor generation remain elusive.
Alternative mRNA splicing
Soluble receptors can also be generated through alternative mRNA splicing, which can remove the exon encoding transmembrane domain of the receptor.When a full-length receptor is expressed, it exists in a form bound to the cell membrane through the transmembrane domain.However, when soluble form of the receptor lacking transmembrane region is expressed, it is secreted from the cell into the extracellular space (Fig. 1b).Recent studies have revealed that many soluble cytokine receptors are generated by alternative splicing as well as ectodomain shedding 19,[22][23][24] .TNF receptor 2 (TNFR2) can undergo alternative splicing to produce a soluble isoform that lacks exons 7 and 8, which encode transmembrane and cytoplasmic domains 25 .This soluble TNFR2 (sTNFR2) can be detected in human serum and its levels are elevated in patients with cancer and inflammatory diseases [26][27][28] .In addition to cytokine receptors, several inhibitory immune checkpoints have been shown to be released in a soluble form by alternative splicing.A soluble form of PD-1 (programmed death 1) is generated by alternative splicing of exon 3, which encodes the transmembrane domain of the PD-1 gene 29 .Another immune checkpoint CTLA-4 (cytotoxic T lymphocyte antigen 4) is also found in a soluble form lacking the transmembrane domain, encoded by exon 3 of CTLA-4 gene 30 .These soluble immune checkpoints can be detected in human serum and used as diagnostic markers in patients with various cancers 5,9,31 .
Extracellular vesicle release
Membrane-bound receptors are also released as components of extracellular vesicles such as microvesicles and exosomes.Although the receptor itself is not in a soluble form, it remains bound to the vesicle membrane.It is then released into the extracellular space, where it can still bind to its ligand (Fig. 1c).Some cytokine receptors such as TNF receptors (TNFR1 and TNFR2) and IL-6 receptor (IL-6R) have been detected on extracellular vesicles as full-length proteins [32][33][34] .These circulating vesicles can affect signaling pathways in other cell types.Additionally, it has been reported that tumor-derived exosomes can carry immunosuppressive or immunostimulatory molecules on their surface to mediate the function of immune cells in the tumor microenvironment 35 .ADAM proteases have also been found in extracellular vesicles such as exosomes 36,37 , suggesting that the ectodomain of receptors on the vesicle membrane might be cleaved and released by ADAM in these vesicles.However, shedding from extracellular vesicles remains largely unexplored.
It is noteworthy that extracellular vesicles such as exosomes can fuse with other cells 38 .This suggests that cells that do not normally express a particular receptor can express that receptor in its full-length upon fusion with such extracellular vesicles.It has been reported that extracellular vesicles containing full-length IL-6R can be fused with distant cells lacking IL-6R, inducing longterm intracellular signaling in target cells 39 .In cancers, microvesicles containing epidermal growth factor receptor variant III (EGFRvIII) are released from glioma cells and transferred to other cells lacking EGFRvIII, leading to a transformed phenotype 40 .Similarly, EGFR-containing exosomes can be transferred from primary gastric cancer cells to liver stromal cells and promote liver metastasis 41 .Therefore, extracellular vesicles with full-length receptors are critical for tumor progression.
SOLUBLE CYTOKINE RECEPTORS IN CANCER
Cytokines as messengers of the immune system can modulate immune responses by orchestrating cellular functions including cell proliferation, differentiation, and migration 42 .When receptors are bound by their respective cytokines, they initiate a series of intracellular signaling cascades.Numerous studies have reported that their dysregulation is closely associated with the pathogenesis of inflammatory diseases and cancer [42][43][44] .In the context of cancer, prolonged activated or suppressed signaling of certain cytokines can foster immune evasion in the tumor microenvironment 45,46 .Moreover, some cytokines and their receptors can be produced by tumor cells themselves, creating an autocrine loop that further enhances cell survival and proliferation 47,48 .
Cytokine receptors are found in membrane-bound form and soluble forms.Soluble forms of cytokine receptors can be released into the extracellular environment, which adds another layer of regulation.By binding freely to their respective ligands, they either enhance or reduce cytokine signaling depending on the context, thereby regulating tumor growth and the surrounding microenvironment 10,11,49 .Notably, levels of soluble cytokine receptors have been reported to be higher in serum of patients with various cancers than in that of healthy controls (Table 1).The next section will detail the mechanisms and clinical significance of representative soluble cytokine receptors, including the soluble forms of IL-2 receptor, IL-6 receptor, and TNF receptors.
Previous studies have reported that levels of sIL-2Rα are increased in patients with many cancers, including carcinoma and lymphoma [56][57][58] .Elevated sIL-2Rα level is correlated with high grade tumors and poor overall survival 56,59 , suggesting that it can be used as a non-invasive marker for the diagnosis and prognosis of cancer.Given that sIL-2R regulates immune responses, understanding its role in the tumor microenvironment can pave the way for novel anti-tumor therapies.Therefore, its clinical significance as a biomarker and a potential therapeutic target for cancer warrants further investigation.
Soluble IL-6R (sIL-6R)
The interleukin-6 (IL-6) signaling pathway is critical for various physiological processes, including inflammation, hematopoiesis, metabolism, and cancer 60 .The IL-6 receptor (IL-6R) exists in two forms: membrane-bound IL-6R and its soluble counterpart.In IL-6 classic signaling, IL-6 binds to membrane-bound IL-6R, inducing homodimerization of signal transducer protein gp130 (CD130) and activation of intracellular signaling cascades 61,62 .Soluble IL-6R (sIL-6R) can be generated by ectodomain shedding, alternative splicing, and release on extracellular vesicles 19 .sIL-6R retains its ability to bind to IL-6, forming the IL-6/sIL-6R complex.This complex then associate with membrane-bound gp130 homodimers, leading to intracellular signaling.This process is called IL-6 trans-signaling 63 .Notably, while IL-6 classic signaling through membrane-bound IL-6R is restricted to specific cell types such as hepatocytes and some lymphoid cells, IL-6 trans-signaling via sIL-6R can occur in all cells.It has been reported that gp130 is ubiquitously expressed in almost all cells except granulocytes 19 .
It is known that the IL-6-induced JAK/STAT3 signaling pathway drives the proliferation and survival of tumor cells 62 .Indeed, IL-6 trans-signaling has been reported to promote the development of pancreatic cancer and KRAS-driven lung adenocarcinoma 10,64 .In colitis-associated cancer (CAC), IL-6 and sIL-6R are produced by lamina propria myeloid cells.They stimulate the proliferation of premalignant intestinal epithelial cells, affecting early tumor formation 65,66 .During the late stages of CAC development, tumor-derived sIL-6R rather than membrane-bound IL-6R induces STAT3 activation and accelerates tumor growth 67,68 .In addition to signal transduction in tumor cells, IL-6 trans-signaling in immune cells affects tumor progression.It has been revealed that IL-6 trans-signaling via sIL-6R derived by myeloid cells attenuates CD4 + T helper type 1 (Th1) cell differentiation in tumor-bearing mice, leading to defective anti-tumor responses 69 .Moreover, IL-6 trans-signaling promotes immunosuppressive function of myeloid-derived suppressor cells (MDSCs) in breast cancer 70 .Given the role and significance of IL-6/sIL-6R trans-signaling in tumor progression, targeting this trans-signaling has therapeutic potential in many types of cancer.
Soluble TNFR (sTNFR)
Tumor necrosis factor (TNF) is a multifunctional cytokine that plays a role in homeostasis and disease pathogenesis 71 .TNF binds to two distinct receptors: TNF receptor 1 (TNFR1) and TNF receptor 2 (TNFR2).TNFR1 and TNFR2 have similar extracellular structures and are activated by both soluble and transmembrane TNF 26 .TNFR1 has an intracellular death domain and induces inflammation and tissue degeneration as well as programmed cell death.In contrast, TNFR2 lacks a death domain and mediates primarily homeostatic effects, including cell survival, proliferation, and tissue regeneration 71 .Both TNFR1 and TNFR2 can exist in soluble and membrane-bound forms.Soluble TNFRs are generated by proteolytic cleavage, synthesis via alternative mRNA splicing, or release in extracellular vesicles 3 .TNFRs are cleaved by ADAM17, also known as TACE (TNF-α converting enzyme) 72 .It has been shown that levels of soluble TNFR1 (sTNFR1) and soluble TNFR2 (sTNFR2) are increased in several diseases, including type 1 and type 2 diabetes with chronic kidney diseases 73,74 .
Previous studies have shown that the TNFR2-expressing Treg subset has a highly immunosuppressive function 75,76 .Additionally, TNFR2 has been reported to be expressed on CD8 + regulatory T cells (CD8 + Tregs) and CD8 + effector T cells, thus coordinating immune responses 77 .It is noteworthy that TNFR2 is increased in tumor-infiltrating Treg cells from human solid tumors 78 .In murine lung cancer and melanoma models, tumor growth in TNFR2deficient mice was significantly decreased compared to that in wild-type mice 79 .Levels of sTNFR2 in serum/plasma samples of several cancer patients are elevated, and such elevation has been found to be correlated with cancer development and poor overall survival 80 .These findings suggest that circulating sTNFR2 plays a pivotal role in the tumor microenvironment and can be used as a biomarker for cancer diagnosis and prognosis as well as cancer therapy.
SOLUBLE IMMUNE CHECKPOINTS IN CANCER
Immune checkpoints are paired receptor-ligand molecules that fine-tune the immune system to maintain immune homeostasis.Recently, immune checkpoints have gained attention in cancer immunotherapy, due to their exploitation by tumor cells rather than their protective role 81,82 .Overall, discovery of their roles in tumor immune evasion has paved the way for immune checkpoint blockade as a revolutionary therapeutic approach.In recent decades, antibodies targeting immune checkpoints, such as CTLA-4 and PD-1, have been actively developed and studied for cancer treatment 82 .However, clinical trials of immune checkpoint blockade to date have revealed limitations, as the percentage of patients who respond to such treatment is still low 83 .For example, although combination therapy with anti-PD-1 antibody nivolumab and anti-CTLA-4 antibody ipilimumab has been demonstrated to have therapeutic effects on overall survival outcomes in patients with advanced melanoma 84,85 , only a few patients can benefit from this treatment.Due to such limitations in the development of immunotherapies for cancer, an in-depth understanding of the mechanism of immune checkpoints has become necessary.
In addition to being expressed on cell membranes, immune checkpoints can be found in soluble form.Several studies have identified the source of specific soluble immune checkpoints.For example, soluble form of programmed cell death ligand 1 (sPD-L1) is reported to be produced by tumor cells or activated mature dendritic cells 86,87 .sPD-L1 can be generated via ectodomain shedding and binds to PD-1 to inhibit T cell responses 87,88 .Moreover, it has been reported that soluble CTLA-4 (sCTLA-4) is produced by Treg cells through alternative mRNA splicing 89 , and the spliced variant has also been detected in monocytes and immature dendritic cells 90 .Although the major sources of several soluble immune checkpoints have been identified in vitro, the molecular mechanisms responsible for the generation and physiological function of soluble immune checkpoints in vivo still require further investigation.
Recent studies have shown that soluble forms of immune checkpoints can be detected in human serum or plasma and that elevated levels are associated with many cancer types 7,9,91,92 .Levels of these soluble immune checkpoints are not only simply increased in cancer patients but also correlated with the disease severity and prognosis of patients (Table 2).Moreover, high serum levels of soluble immune checkpoints are associated with resistance to several targeted cancer therapies in cancer patients [93][94][95] .These findings suggest the potential of using circulating immune checkpoints as biomarkers for the diagnosis and prognosis of various cancers.
TARGETING SOLUBLE RECEPTORS FOR CANCER THERAPY Therapeutics that directly target soluble receptors
Soluble receptors not only have the potential to be used as biomarkers for cancer diagnosis and prognosis, but can also be used as therapeutic targets in cancer treatment (Fig. 2).Direct targeting of soluble receptors or their pathways might be an effective therapeutic strategy to enhance anti-tumor responses.Although additional research is still needed, the clinical significance of increased soluble receptor levels in patients with various types of cancer provides sufficient evidence to support the development of novel cancer treatments by targeting these soluble receptors.Circulating levels of sIL-2Rα, one of the soluble cytokine receptors, have been shown to be correlated with progression of several types of cancer in previous studies [96][97][98] , with potential for use as a diagnostic and prognostic marker for cancer.However, considering that it is highly correlated not only with cancer but also with other diseases such as inflammatory diseases 3 , it can be used as an indicator to confirm the activation of T cells that produce sIL-2Rα in pathogenic conditions rather than simply as an indicator of cancer 49 .Therefore, when directly targeting soluble receptors as a cancer treatment strategy, it is important to conduct a precise analysis according to the characteristics of each cancer type and understand the molecular mechanism of each soluble receptor.To date, small-molecule compounds or monoclonal antibodies that directly target several soluble receptors have been developed, and research into the mechanism of how these substances affect the tumor microenvironment and their efficacy in both preclinical and clinical trials is ongoing.One of the therapeutic strategies being actively investigated is blocking IL-6 trans-signaling 99,100 .Some humanized monoclonal antibodies targeting IL-6R, such as tocilizumab and sarilumab, have been developed to inhibit IL-6 signaling.They are currently approved for treating arthritis or are in clinical trials for other diseases [101][102][103] .However, the problem with these antibodies is that they cannot distinguish between membrane-bound and soluble forms of IL-6R, inhibiting IL-6 classic signaling and transsignaling at the same time.An alternative IL-6 trans-signaling inhibitor that can be considered is a soluble gp130-Fc fusion protein (sgp130Fc, also known as olamkicept), which is a fusion protein of the extracellular portion of gp130 and the Fc region of a human IgG1 antibody 104 .IL-6 classic signaling maintains local homeostasis even under normal healthy conditions; under inflammatory conditions, however, local IL-6 classic signaling and trans-signaling as well as systemic trans-signaling are induced by high levels of IL-6 and sIL-6R in the blood 100 .Therefore, sgp130Fc, which selectively inhibits only trans-signaling without affecting IL-6 classic signaling, has high potential as a therapeutic agent for various diseases.As mentioned above, IL-6 transsignaling in various cancer types promotes tumor progression by suppressing anti-tumor responses of immune cells as well as increasing cell growth through signal transduction in tumor cells themselves.Surprisingly, blocking IL-6 trans-signaling with sgp130Fc has therapeutic effects on reducing tumor progression in murine cancer models, including murine colitis-associated cancer (CAC) 65,66 , lung adenocarcinoma 10 , and hepatocellular carcinoma (HCC) models 105,106 .However, few studies on blockade of IL-6 trans-signaling in cancer patients have been reported, despite its therapeutic effects in numerous preclinical cancer models.Therefore, additional clinical studies are needed before it can be used as a clinical tool for cancer treatment.
Another strategy to directly target soluble receptors for cancer treatment is to inhibit sTNFR.TNFR2-expressing Tregs are increased in the tumor microenvironment and have a high suppressive capacity in various cancers, including ovarian cancer, acute myeloid leukemia, and lung cancer [107][108][109] .It has been revealed that newly identified TNFR2 antagonistic monoclonal antibodies (TNFR2 antagonists) inhibit soluble TNFR2 secretion and Treg proliferation in vitro 110 .Of note, a TNFR2 antagonist has a greater effect on suppressing Tregs from the ascites fluid of ovarian cancer patients than Tregs from the peripheral blood of healthy donors 110 , suggesting the specificity of TNFR2 antagonists for the tumor microenvironment.Specifically, inhibiting the activity of tumor-residing Tregs through TNFR2 antagonism can increase proliferation of effector T cells in the tumor microenvironment and suppress tumor growth.Thus, it can be considered an engaging cancer therapy.
Modulation of ectodomain shedding
Inhibiting enzymes responsible for shedding of membrane-bound receptors can reduce levels of soluble receptors, which might also be a therapeutic strategy for cancer.Recent studies have shown that expression levels of ADAMs are increased in multiple cancer types 111,112 .Preclinical studies have reported that small-molecule compounds or monoclonal antibodies for modulating ADAMs inhibit migration, invasion, and growth of tumor cells 112 .For instance, treatment with Aderbasib (INCB7839), a small-molecule inhibitor of ADAM10/ADAM17, was reported to prevent growth of HER2 + human breast cancer in a mouse xenograft model 113 .INCB7839 has also been tested in clinical trials, with promising results in phase I/II trials of Trastuzumab-based HER2 + breast cancer therapy by inhibiting HER2 shedding (NCT01254136), and evaluated in phase I trials for recurrent or progressive high-grade gliomas (NCT04295759).
Targeting catalytic domains (metalloprotease domains) of the ADAM protease has so far failed due to highly conserved active sites among ADAM enzymes, resulting in unfavorable toxic effects.
Interestingly, recent studies have revealed that non-catalytic domains of ADAM10 and ADAM17, specifically a disintegrin domain and a cysteine-rich domain, can provide substrate specificity 114 .Through additional research, it is expected that inhibitors with increased specificity for other ADAM families with different structures will be developed, which will provide a way to overcome the limitations in ADAM inhibitor development.There are several ongoing clinical trials targeting specific ADAM proteases for cancer.The ADAM9-targeting antibody-drug conjugate IMGC936 has been tested in phase I/II trials for advanced solid tumors, such as non-squamous non-small cell lung cancer, triple-negative breast cancer, and colorectal cancer (NCT04622774).Therefore, targeting specific ADAM proteases may be a promising therapeutic strategy for cancer.
Enhancers of existing therapies: combination therapy
Understanding the interplay between soluble receptors and established therapeutic strategies can lead to more effective treatments.Despite the clinical success of current cancer immunotherapies, such as immune checkpoint blockade, a significant proportion of cancer patients still do not respond to treatment or are resistant to inhibitor treatment 115 .Of note, serum levels of soluble immune checkpoints are correlated with resistance to immunotherapy.In patients with advanced melanoma, anti-PD-1 antibody (pembrolizumab) monotherapy has been reported to increase serum levels of lymphocyte-activation gene 3 (sLAG3) in a disease progression group compared to a control group 95 .Additionally, serum PD-1 levels are increased in melanoma patients with disease progression, following combination treatment with anti-PD-1 antibody (nivolumab) plus anti-CTLA-4 antibody (ipilimumab) 95 .These recent findings suggest that targeting soluble immune checkpoints might be beneficial for immunotherapy-resistant cancer patients.Therefore, combination therapy with existing therapeutic strategies and inhibition of soluble receptors might be a solution to overcome the limitations of current treatments.
Challenges and future directions
Therapeutic strategies for cancer by inhibiting IL-6 trans-signaling should consider the effects of other IL-6 family members.The IL-6 family consists of IL-6, IL-11, and IL-27, all of which transduce signals using the gp130 receptor 20 .Of note, the IL-11 receptor (IL-11R) can also be detected in a soluble form.Levels of soluble IL-11R have been reported to be elevated in patients with gastric cancer 116 , suggesting possible effects of IL-11 trans-signaling in cancer progression in vivo.To reduce the potential of side effects, second-generation and third-generation variants have been developed from the previously developed sgp130Fc 100 .Indeed, the selectivity of inhibitors for IL-6 trans-signaling has gradually increased from the first-generation sgp130Fc to the secondgeneration variant sgp130 FLYR Fc and the third-generation variant cs130 Fly , but the effect on IL-11 trans-signaling has gradually decreased 117,118 .Therefore, increasing the selectivity of inhibitors targeting specific soluble receptor signaling will be of great help in reducing unwanted side effects in clinical studies.
In addition, several sheddase inhibitors are currently being developed for cancer treatment.While the specificity between ADAM family members has been addressed to some extent in the development of ADAM-targeted inhibitors, the fact that each ADAM can cleave a variety of substrates, including multiple cytokines, growth factors, and other membrane-bound receptors, may lead to detrimental side effects in clinical studies 18 .A recent study revealed that MEDI3622, a specific ADAM17 inhibitory antibody, has the potential to inhibit not only the HER pathway but also the EGFR pathway 119 .The researchers used combination therapy with MEDI3622 and the EGFR inhibitor cetuximab and found synergic effects resulting in complete tumor regression in an OE21 esophageal xenograft model 119 .Therefore, in future studies of sheddase inhibitors, it is necessary to first analyze expression of multiple substrates in each patient with a specific cancer type.
CONCLUSIONS
Soluble receptors have evolved as crucial players in cancer research.Their generation through various mechanisms, such as ectodomain shedding, alternative mRNA splicing, and extracellular vesicle release, underscores multifaceted ways in which they regulate cellular signaling pathways.Focusing on the roles of soluble cytokine receptors and soluble immune checkpoints, this review highlights the indispensable role of soluble receptors in cancer progression, metastasis, and immune evasion.Soluble receptors are detected at high levels in the blood of patients with various cancers.Given that soluble receptors are present in bodily fluids, they might provide a minimally invasive method for early diagnosis and prognosis of cancer.In addition to early cancer detection, directly targeting soluble receptors using smallmolecule compounds or monoclonal antibodies could be considered as cancer treatment strategies.The therapeutic potential of targeting these soluble receptors offers promising avenues for cancer treatment, and strategically combining therapies may enhance the efficacy of current strategies.Nevertheless, in the case of soluble immune checkpoints, how direct regulation of soluble immune checkpoints affects the tumor microenvironment has not yet been elucidated.Hence, it is evident that more studies are needed, especially in harnessing soluble receptors for cancer treatment.Future endeavors in this area should focus on improving therapeutic strategies, addressing identified challenges, and understanding the long-term implications of targeting soluble receptors in cancer.
Fig. 1
Fig. 1 Different mechanisms of soluble receptor generation.a Ectodomain shedding of a membrane-bound receptor.The substrate receptor is cleaved by an ADAM protease, resulting in release of a soluble receptor into the extracellular space.The remaining C-terminal fragment is further cleaved by the γ-secretase protease complex to generate an intracellular domain fragment.b Alternative splicing of a transcript encoding a receptor, generating either a membrane-bound receptor or a soluble receptor.c Release of a membrane-bound receptor in extracellular vesicles.This figure was created with BioRender.com.
Fig. 2
Fig. 2 Soluble receptors as biomarkers for cancer diagnosis and therapy.Targeting soluble receptors has benefits in cancer diagnosis, prognosis, and treatment.Considering that high levels of soluble receptors are detected in the bodily fluids of cancer patients and that such high levels are associated with disease severity, soluble receptors have the potential to be used as minimally invasive biomarkers for early detection and prognosis of cancer.Additionally, blocking soluble receptors through various therapeutic strategies can potentially improve the efficacy of current cancer treatment.This figure was created with BioRender.com.
Table 1 .
Biological functions of soluble cytokine receptors and clinical significance in cancer patients.
Table 2 .
Clinical significance of soluble immune checkpoints in cancer. | 6,249.6 | 2024-01-05T00:00:00.000 | [
"Medicine",
"Biology"
] |
Colored HOMFLY polynomials of knots presented as double fat diagrams
Many knots and links in S^3 can be drawn as gluing of three manifolds with one or more four-punctured S^2 boundaries. We call these knot diagrams as double fat graphs whose invariants involve only the knowledge of the fusion and the braiding matrices of four-strand braids. Incorporating the properties of four-point conformal blocks in WZNW models, we conjecture colored HOMFLY polynomials for these double fat graphs where the color can be rectangular or non-rectangular representation. With the recent work of Gu-Jockers, the fusion matrices for the non-rectangular [21] representation, the first which involves multiplicity is known. We verify our conjecture by comparing with the [21] colored HOMFLY of many knots, obtained as closure of three braids. The conjectured form is computationally very effective leading to writing [21]-colored HOMFLY polynomials for many pretzel type knots and non-pretzel type knots. In particular, we find class of pretzel mutants which are distinguished and another class of mutants which cannot be distinguished by [21] representation. The difference between the [21]-colored HOMFLY of two mutants seems to have a general form, with A-dependence completely defined by the old conjecture due to Morton and Cromwell. In particular, we check it for an entire multi-parametric family of mutant knots evaluated using evolution method.
Introduction
R-colored HOMFLY polynomials [1] are defined as the Wilson loop averages in 3d Chern-Simons theory [2] H L⊂M and for simply connected embedding space M = R 3 or S 3 it is an integer polynomial (i.e. all the coefficients are integer) of the variables q = exp 2πi κ+N and A = q N , where N parameterizes the gauge group SU (N ). Moreover, it can often be promoted to a positive integer superpolynomial [4]- [11], if one more parameter t is introduced: deviation from t = −1 can be considered as a β-deformation [12]. However, construction of superpolynomials is still a mystery, especially for non-rectangular representations R (i.e. when the corresponding Young diagram R is not rectangular), see [13,14,15]. In fact, even the colored HOMFLY polynomials are very difficult to find, and this enhances the difficulties of conceptual considerations.
Two recent achievements open a way to explicit calculation of the colored HOMFLY polynomials beyond rectangular representations. The first of them is evaluation of the 3-strand knot polynomials for representation 1 arXiv:1504.00371v1 [hep-th] 1 Apr 2015 [21] in [13,16] and of the underlying Racah matrices S andS, in [17]. The second is a conjectured expression [18,19,20] for the peculiar double fat tree diagrams, expressing the unreduced colored HOMFLY polynomials through the Racah matrices: (2) where the sum goes over representations X, which belong either to the product R ⊗R or to R ⊗ R, depending on the configuration and orientation of the diagram, and over additional indices a (µ) i = 1, . . . , m Xµ , appearing when X enters the product with a non-unit multiplicity m X . The weight factor is the product of quantum dimensions d X of X. Additional factors are just signs, σ = ±1, they appear only for non-trivial multiplicities and we ignore them for a while leaving until sec.7, though in fact σ are crucially important for non-rectangular R including R = [21].
We define the double fat tree diagrams as ordinary trees with vertices µ of arbitrary valencies k µ , e.g.
Let us consider a typical example of the double fat diagram of the knot. Suppose the usual knot diagram can be presented in the form i.e. in this concrete case it is three four-strand braids (propagators, or edges) connected by double lines into the vertex X, we call it the double fat diagram. In the field theory form, this particular diagram has a peculiar shape of a starfish with three fingers: d d X X µ X a1,a2,a3=1 σ X|a1,a2,a3 · d R 3 We always consider each edge in (3) being a 4-strand braid: Boxes in this picture denote vertical 2-strand braids of given lengths, which can be parallel or antiparallel, depending on the directions of arrows (which in their turn depend on parity of the lengths). The number of boxes in each propagator can be arbitrary. Each vertex µ in (3) is the cyclic junctions of k µ 4-strand braids: . . . X, a 1 X, a 2 X, a k−1
X, a k
With each such vertex µ one associates a representation X µ . The crucial feature of this construction is the selection rule for propagators: the two representations X,X at one end of the four-strand braid (5) differ by conjugation, while the additional indices a and b can be different. Thus, the propagator has two multi-indices Xab and Y cd: i.e. is a matrix element A Y cd,Xab, , while the matrix itself is made by the usual conformal block rule from the R-matrix T and the Racah matrix S.
Interchanging m α and l α at each level α inside every fingeris a mutation transform (provided one considers only the tree diagrams), and in fact one can perform a mutation to change m α , l α → m α + k α , l α − k α with any k α . In result, for symmetric representations R, the HOMFLY polynomial depends only on the sums m α + l α , however, for generic R dependencies on m α and l α are separated.
Beyond the rectangular R, additional indices a and b are added to X, still there are just two independent S-matrices, S andS, from which all other are made by various conjugations. Whatever is R, the first lines in the Racah matrices S andS are always made from the quantum dimensions: This property is crucial for self-consistency of (2) when an edge is a tadpole. Then the role of the end-vertex (with the sum over the corresponding X) is to imitate gluing of the caps like with a singlet representation 0 ∈ R ⊗R, or XX = δ 1X (12) Relations (10) ensure that each tadpole (end-edge of a branch in the tree, which we call finger) is nothing but the matric element A ab 1X . Because of this in what follows we omit the cycles at the end-edges of the branches. Additional universally applicable simplifications emerge from the elementary S, T -matrix identities, like the celebrated (ST ) 3 = 1 in the case of R = [1] for SU q (2), for its generalization to arbitrary representations of SU q (N ) see (62).
The set of fat-tree diagrams is very big. According to [19], it contains at least all the knots from the Rolfsen table [21] (with the possible exception of 10 161 ), we do not know any proved example of knot beyond this family. 4 Most importantly, many complicated knots (with many intersections) look quite simple when represented as double fat graphs, in particular a lot of interesting examples already get into the three-finger set, i.e. have k = 3. As already mentioned, there are plenty of obvious mutants already within the starfish family (defined in (31), see below) and even among the pretzel knots [22], what makes it especially interesting for the studies of [21]-colored polynomials, which are the simplest to distinguish some mutants.
At the same time, eq.(2) describing the colored HOMFLY polynomials for the fat tree diagrams is by no means a trivial formula. Its origins are not immediately clear neither from the conformal block [3,23] nor from the Reshetikhin-Turaev [24,25,26] approaches to knot/link polynomials, despite (2) is clearly very much in the spirit of these both. Anyhow, there is a lot of evidence, coming from direct applying the RT/conformal block method [18,19,20] and its advanced versions like the evolution [27], cabling [16] and differential expansion [15] methods, which supports this formula in the case of symmetric representations, and we add more in this paper for the case of representation [21]. Moreover, eq.(2) looks typical for topological field theories (like the Hurwitz model in [28,29]) and it can serve as a basis of a new intuition and calculus in knot theory, involving a kind of pant decomposition of link diagrams.
When we write "vertices" and "propagators" in (2) we actually make a choice between two dual interpretations of this kind of formulas: one could instead do the opposite and treat the circles in (3) as loops and assign the edges to vertices. Within this framework, the tree diagrams are no longer trees but contain loops, however, the overlapping loops are still absent. Technically this is not very convenient, because we get unit propagators, simple universal loop factors d −1/2 X and an infinite variety of complicated vertices (5). This is why in the present, largely technical text we make use of the first interpretation. However, conceptually the second one can be more much closer in spirit to the common language of string theory, and provides a useful intuitive vision.
The paper is organized as follows. In the first part we describe the elementary building blocks for double far graphs and explain how to construct knots out of them. In the second part we first describe some peculiarities of representation theory especially related to the first non-trivial mixed representation [21], and then consider the colored HOMFLY polynomials in representation [21] for various knots. In particular, we check that these HOMFLY polynomials do differ between the notorious Conway-Kinoshita-Terasaka (KTC) mutant pair, in accordance with expectations [30], moreover, the manifest difference between their HOMFLY polynomials is in complete agreement with [31]. We also discuss other mutant pairs, in particular, find a difference between the HOMFLY polynomials of a whole 2-parametric family of mutants. However, representation [21] turns out not to be enough to differ between another set of mutants. Some more explicit HOMFLY polynomials in representation [21] for various knots is listed in the Appendix, where one can find also a table that describes the features of all knots with not more than 10 intersections relevant for this paper.
Note that all answers for the HOMFLY polynomials in representation [21] in this paper for the knots that have a three braid representation we compared with the results obtained by the cabling method of [13,16]. Besides, we made a few self-consistency checks, see s.7.4.
Throughout the paper we use the notation [n] both for the quantum number and for the representation (e.g., [21]). Hopefully this would not lead to a misunderstanding. Other our notations are and d R is the quantum dimension of the representation R.
Part I Diagrammar 2 Chern-Simons evolution Expression (6) for each propagator (5) in (2) is usually interpreted as the ordinary time evolution in Chern-Simons theory, which is provided by monodromies of conformal block made from R-matrices T of three types (depending on the pair of adjacent strands that it acts on) and Racah matrices S, see [3] for the original idea and [23,19,20] for recent applications. In the case of arbitrary representation R there is a whole variety of S matrices and eq.(6) needs to be formulated more accurately. This section describes our notation, which will be used in the rest of the text. S is a matrix, with two peculiar multi-indices Xab and Y cd, which are collections of square matrices of different sizes, depending on irreducible representations X and Y . Two more potentially convenient notation are The punctured line helps to illustrate the meaning of indices, it indicates that, after applying the Racah matrix S, the representation R 1 becomes close to R 4 . Note that the initial state Xab stands to the right/bottom of the final Y cd, but representations are ordered oppositely: from the left to the right and from the top to the bottom. When we write explicit matrices in sec.6, the left/upper indices (like Y cd) label rows, while the right/bottom (Xab) -columns.
The composition of two evolutions gives the identity: If combined with unitarity of S (orthogonality when S is real), this implies: Note that S converts two parallel braids into two antiparallel, whileS converts antiparallel into antiparallel: Operators T describe crossing of two adjacent strands and are much simpler than S. The only delicate point is that there are three different pairs of adjacent strands in the 4-strand braid and therefore there are three different T -matrices, which we denote T + , T 0 and T − . Also, the two intersecting strands can be either parallel or antiparallel, what we denote by T andT respectively. This brings the number of different T -insertions in (6) to six.
One can promote these operators to matrices of the same type as S: The eigenvalues are the standard ones in the theory of cut-and-joinŴ -operators [29] and the same which appear in the Rosso-Jones formula [32,6]: All X 's take values ±1. We usually omit the indices ±, 0 of T later on, since these T 's are all the same as matrices.
Pretzel fingers and propagators
Our next goal is to classify different types of expressions (6) for the propagator (5) -according to the possible number and parities of parameters n α , m α and l α and to directions of strands (arrows). A special role is played by the terminal branches in the tree (3), which we call fingers. They are represented by matrix elements A ab 1X = A 0,Xab , and all the T -matrices standing to the very left of all S can be omitted. According to (18), the last (most left) S in such matrix element can be eitherS or S but not S † .
In this section we begin from the simplest possible types of propagators and fingers, belonging to the pretzel type. For pretzels all m α = l α = 0 and there is just one parameter n in each of the k of the fingers. Still, there are propagators and thus fingers of three different kinds, depending on directions of arrows and the parity of n. In the case of pretzels, the notation with bars is sufficient to distinguish between all these cases, still we add explicit indices par, ea, oa to avoid any confusion: The choice of S-matrices in above examples is easy to understand from (18), one should remember that S converts parallel states (from R ⊗ R) into antiparallel (from R ⊗R), while S † acts in the opposite direction, andS relates antiparallel to antiparallel.
In the final expressions (boxed) we suppressed most indices, thus implying that we deal with matrices in extended space, where basis is labeled by the multi-index Xab. We explain the details of this formalism in sec.6, while in sec.5 we use the symbolical notation: just X for the multi-index and X for appropriate contractions, including non-trivial sign-factors σ (which is symbolized by the bar over the sum).
In the case of propagators there are three more option, but they can not be closed non-trivially and do not show up in the pretzel family and in the remaining parts of the present paper.
Other building blocks 4.1 Non-pretzel fingers
Generalization to arbitrary non-pretzel fingers and propagators (5) with arbitrary parameters m α , l α , n α is exhaustively described by (6), one just needs to put appropriate S and T matrices for the given choice of arrows, like we did for the pretzel fingers in sec.3. Since this is straightforward we do not provide this additional list.
What is more important, some diagrams, which do not a priori look like (5), actually belong to this family, and this is the reason for the double fat graph description to cover so many different knots and links. In this section, we mention just two examples of this kind, exploited in our further considerations.
Horizontal loop
The first example is simple: It is nearly obvious that this is just the non-pretzel finger with parameters n 1 = m 2 = l 2 = ±1 (signs and the types of S and T matrices depend on the types of intersection and directions of arrows). No S-matrix identities are needed to get an expression for it. One could easily insert a horizontal braid of arbitrary length and consider a sequence of such horizontal loops:
Horizontal braid
The isolated horizontal braid is nothing but the pretzel finger. The type of the finger depends on orientation of lines and the parity of m.
More interesting is the horizontal braid located in between the two middle lines in the double fat propagator: This is a contraction of three blocks, where the middle one is exactly (4.3). Schematically, it is In fact there are seven versions of this relation, for different arrow directions and different parities of m. Four of them describe even m:
Odd antiparallel pretzel knots
More generally, if there is any odd number of odd antiparallel fingers, If the number of fingers is even, we get links rather than knots.
Pure parallel pretzel knots
If the pretzel knot is made from the parallel fingers only, their number should be even and exactly one length should be even, otherwise we get a link rather than a knot. The answer for the HOMFLY polynomial is
Mixed parallel-antiparallel pretzel knots
The remaining family of the pretzel links/knots contains even number of parallel fingers and odd number of antiparallel, which have even lengths. The corresponding HOMFLY polynomial is
Non-pretzel fingers
Now let us consider a few non-pretzel examples.
Knot 10 71 . Its HOMFLY polynomial is With the help of (63) the last matrix element can be changed for The last two factors in the sum are already familiar A par (p) and A par (q) from (22), while the new one is (like all the sums inside particular fingers, this is an ordinary matrix multiplication without any sign σ-factors).
The third finger is
and Configuration (44) is not always a knot: it can also be a link with two or even three components: p q r # of link components even even odd 1 odd even even 1 odd odd odd 1 even even even 2 even odd odd 2 odd even odd 2 odd odd even 2 even odd even 3 Among knots, the notable members of the three-finger family are the thick knots 10 124 and 10 139 , which also have pretzel realizations: 10 124 = (5, 1, 3, 1) and 10 139 = (4, 2, 3, 1).
Generic four-box 3-strand braids beyond starfish family
For s = 1 the braid (42) can not be converted by the Reidemeister moves to a starfish configuration. Instead, it is equivalent to where the propagator is actually performing an operation like (14) on antiparallel strands, i.e. is represented by the matrixS. According to (2), the corresponding HOMFLY polynomial is
Diagrams with non-tadpole propagators
In the case of (51) and (52) not all the pretzel fingers are contracted directly, an additional propagator appears on the way and our basic formula (2) involves two independent summations.
The ppS block
A new building block appearing in (52) is This expression remains the same ifS is transposed,S XY −→S Y X . The number of parallel fingers in this building block can exceed two (but needs to be even), however, for our purposes below, the two will be enough.
For the 4-box 3-strand braid one can rewrite (52) as
Double braids
In fact, propagator can be less trivial than in (52). Important generalization is provided by the horizontal braid (27): The right two lines in the second block do not change the representation, the left part of this block is just the Pretzel finger A eg 1Z . The type of S-matrices and the Pretzel finger depends on the directions of arrows and on the parity of the braid length m.
The simplest application of (54) is to the double braids of [27], which has also the pretzel representation (−1, 2k, m).
Pretzel fingers connected via horizontal braid
More interesting is the situation when pretzel fingers appear from both sides of the horizontal braid: The central block is just the horizontal braid, antiparallel of length 2, described by the corresponding version of (54). Therefore, the reduced HOMFLY polynomial for the diagram (55) with even m is The four external fingers involve parallel braids, while that of the even length m in the propagator is antiparallel. The fat tree is the same (51), only the internal propagator is more sophisticated. Mutation is a permutation of p and q or of r and s.
At s = 0 the parallel finger A par If additionally q = 0, we obtain a composite knot, made out of two 2-strand constituents: All formulas in this part work immediately for the fundamental and symmetric representations. They were tested in various representations from this set. Since the Racah matrices are explicitly known for all symmetric representations [34], [20, 2nd paper], there is no problem to make further tests in this direction. In all these cases all the σ-factors are unities, and there is no need to deal specifically with overlined sums. The same formulas continue to work for representation [21], but then some σ-factors are −1. Expressions for R = [21] are rather involved, because such are the Racah matrices, explicitly calculated in [17], and we describe them in the next section.
Part II Examples 6 Racah matrices 6
.1 Generalities
The Racah matrices relate the two expansions and that is, it is a linear operator When the vector spaces W are one-dimensional ("no multiplicities" case), one can represent this linear operator as a matrix with indices P ∈ R 1 ⊗R 2 and S ∈ R 2 ⊗R 3 . When W are multidimensional, there is no distinguished any basis and the concrete form of the Racah matrix depends on conventions, and on four additional indices labeling the bases in the four W -spaces for each given pair P and S. For the purposes of knot (rather than link) theory, all the four representations R 1 , R 2 , R 3 , Q are either R or its conjugateR. In result, there are two essentially different Racah matrices: • S S,c,d|P,a,b with P ∈ R ⊗ R, but S ∈ R ⊗R, and •S S,c,d|P,a,b with both P, S ∈ R ⊗R. These are the only two kinds of the Racah matrices that show up in our discussion of the double fat tree diagrams.
Note that S is essentially asymmetric, whileS can be symmetric, and actually is in the multiplicity-free case.
Another important fact is that the singlet representation 0 ∈ R ⊗ R, but 0 / ∈ R ⊗ R (except for the case of N = 2), therefore, the matrix elements 1X in (2) can not have S † at the very left, but only S orS. In general, as we already saw earlier, (18) S converts the parallel strands into antiparallel, whileS antiparallel to antiparallel. Our fingers never contain three parallel strands, thus these two types of relations are sufficient for our consideration. However, beyond this paper the third Racah matrix connecting the parallel strands to parallel (it was called "mixing matrix" in [25]) plays a big role. Actually, it is much simpler: it does not depend on N (i.e. on A). For symmetric representations, it coincides with restrictions of both S andS to N = 2, but for more complicated representations the story is a little more involved.
The Racah matrices S are always unitary and satisfy (10). There are also additional non-trivial relations like [35,17] which are the implication of In more detail, with indices restored: An important application of this identity is the possibility of shifting any pretzel finger of length 1 to any position [22] at any representation R, though permutations of arbitrary fingers are not a symmetry of the knot.
The simplest symmetric representations
For symmetric representations R, there are no multiplicities, no indices a, b, c, d and the Racah matrices are canonically defined.
• When R is the fundamental representation R = [1], they are given by (8) and (9), or in a generalizable notation, • Similarly, for representation R = [3] and so on.
Representation [21]
In the case of R = [21] there are seven different items X in the decomposition 19 The corresponding dimensions and eigenvalues are (68) with non-trivial multiplicity m Adj = 2, however this makes the Racah matrices 10 × 10, since X m 2 X = 6 · 1 + 1 · 2 2 = 10. They are explicitly found in [17]. The pure antiparallel matrixS is Here we again encounter one item with multiplicity two, and the parallel → antiparallel Racah matrix S is This matrix is obtained from that of [17] by transposition to make it consistent with (10) and thus with our representation of knots. Also minor (always allowed) conjugations are performed in (70) and (73) to get rid of unnecessary minuses and imaginary units. Diagonalized R-matricesT and T are read off from the last columns of (69) and (72): and In these S-and T -matrices the index X runs from 1 to 7, and for X = 7 there are additional indices a i which take two values, which we substitute as 7 11 Then contractions in (2) for the simplest double-fat graph (31) can be rewritten as follows: It is the underlined term that breaks the permutation symmetry between different A (i) in the original product down to just cyclic symmetry, and it is the one that distinguishes mutants. When all A (i) 9 or A (i) 10 are vanishing, the symmetry is preserved and mutants remain indistinguished by the [21]-colored HOMFLY.
σ-factors and other technicalities
Since eq.(2) is a kind of a conjecture/educated guess, and was so far well tested only for symmetric representations where no multiplicities (indices a, b, c, . . .) arise, there is no reason to insist that contractions (76) are exactly correct. In fact, they are not: for complicated enough knots, (2) with rule (76) does not produce polynomials in representation [21] and, in result, fails to reproduce the known answers. Both these problems are cured by switching to σ, which is allowed to take the values ±1 only, but is not obligatory identical unity.
The procedure at the moment is to adjust theses sign factors for a given knot so that the answer for HOMFLY is a Laurent polynomial in A and q. This choice is either unique, or the answer does not depend on allowed choices. In our examples, the sign ambiguity appears only when one of the fingers is pretzel of length one and some matrix elements simply vanish, thus the sign in front of them is just irrelevant. No general rule is found yet for a priori determination of σ, except for some simple families of double fat diagrams it is available, in this technical section we describe what is already known.
3 fingers
In the simplest case of 3 fingers we use the following notation: First of all, it is always the case that σ 111 = σ 222 = 1. Now, it turns out that the two relevant sets of signs of the remaining σ's, appearing in the right formulas are either all equal to -1: or only two σ abc equal to -1. Depending on the order of fingers, it can be either σ 112 and σ 221 or two other pairs obtained by cyclic permutations from these, we will always choose the order in such a way that the first pattern is realized: However, the choice between the two possibilities depends on the type of knot. As to the naive option it also sometimes happens to provide right answers, but only when some of the pretzel lengths are unit and identities (63) relate (80) to (78)-(79). It deserves mentioning that (79) explicitly breaks the cyclic symmetry between A, B and C, thus one can expect that it is relevant when such a symmetry is absent, say in the case of two parallel and one antiparallel pretzel fingers. Accidentally or not, three parallel pretzel fingers is an impossible configuration, while for three antiparallel pretzel fingers the non-diagonal terms are just vanishing.
More fingers
Similarly, for 4-finger parallel pretzel knots the relevant choice is At last, for the 5-finger pretzel knot with one antiparallel finger (for the sake of definiteness, it is the first finger) the proper choice is Thus, we learn, first, that always σ 11...1 = σ 22...2 = 1 and, second, there is a symmetry of simultaneous replace 1 ↔ 2 in all indices. Specifically for the parallel pretzel knots (they exist only for the even number of fingers), there is also an additional symmetry: all sign factors obtained by a cyclic permutation are the same.
Sign dependence on knots
This list of relevant sign choices is not necessarily complete, but it is necessary and sufficient for all the examples that we studied so far. With these sign prescriptions, H [21] for knots are polynomials (otherwise denominators can occur) and coincide with the previously known answers from [13,16,17,33], when they are available. If talking about the concrete knots, among the starfish configurations, all the 3-finger configurations we checked so far are described by (79) (with the distinguished of the three fingers put third) for exception of knot 10 71 , when (78) is realized, and all the 4 parallel finger and (one antiparallel + 4 parallel) finger configurations satisfy the rules described in ss.7.1.2.
As for the double sum configurations (see the Appendix), 10 152 is described by (79) in the both sums, 10 153 is described by (79) in the sum over pretzel fingers and (78) in the second sum. At last, 10 154 is described by (78) in the both sums.
At last, the three sum configuration, (56) is described by (78) in the internal sum in (55) and (79) in the two sums within the ppS-blocks.
Explicit calculations in the pretzel case
After the matrices S, T and the sign factors σ are explicitly known, it is straightforward to insert them into formulas of sec.5 and obtain the colored HOMFLY polynomials in representation [21] for an enormous set of knots. Numerous tricks are needed to make software running fast enough on ordinary computers, but by now this is a routine in knot theory and we do not dwell upon these details. In fact, the answers themselves are huge, thus it makes no sense to list them all, especially given the (large) number of examples. Therefore, we just enumerated the classes of diagrams, and in the Appendix we list explicit examples. Here, for illustrative purposes, we present some general discussion of the pretzel case. A vast set of concrete examples can be found again in the Appendix.
Even antiparallel
This finger depends on the even parameter n and is given by the matrix element Again, the unitarity A Y X (0) = δ Y X makes this choice natural as compared with those with additional insertions of Λ.
For n = 0, this matrix element is just δ X,1 . For n = ±2, the matrix elements of A ea 1X with X + 9, 10 are very simple, similarly to the parallel case: The simplest check to be made is for the Hopf link, which can be represented both through parallel and antiparallel braid: This is the reduced HOMFLY invariant, and since it describes a link, it is not a polynomial. Any combinations of even antiparallel fingers only provide links, not knots. The simplest knot family involving such fingers is P r(n 1 , n 2 ,m), where two of the three fingers are parallel. Then = X d 4 [12] d
Odd antiparallel
This finger depends on the odd parameter n and is given by the matrix element This time n is odd and cannot vanish, therefore there is no obstacle for inserting Λ and writing S † T n ΛS 1X instead, however, this does not actually affect the answers, at least in the cases discussed here.
Elementary calculation or application of identity (62) gives that at n = ±1 where X belongs to the parallel sector, X ∈ R ⊗ R. Once again, this immediately provides the answers for the trefoil: For other values of n these matrix elements are multiplied by polynomials: In particular, this means that the odd antiparallel fingers vanish at X = 9, 10 for all values n, which means that odd antiparallel Pretzel mutants are undistinguishable by the colored HOMFLY polynomials in representation [21]. The polynomials P themselves are, however, somewhat involved. For instance, The twist knots are pretzel T w k = P r(1,1, 2k − 1) i.e. are made from three odd antiparallel fingers: Because the off-diagonal terms in (76) vanish for odd antiparallel fingers, there is no difference between 8 X=1 and X . The answers for twist knots reproduce those from [16,17] and [33]. Other members of the same three-finger family are:
Checks
All answers for the HOMFLY polynomials in representation [21] in this paper for the knots that have a three braid representation we compared with the results obtained by the cabling method of [13,16]. Besides, there are five types of self-consistency checks one can currently make to test our answers. The first four are true for all our examples, the fifth one is more tedious and was only partly verified.
Alexander polynomials for 1-hook representations
As conjectured in [36] a "dual" factorization property holds at A = 1, i.e. for the Alexander polynomials, but only for representations R described by single-hook diagrams: Representation [21] belongs to this class. Neither any meaning, nor generalizations of this remarkable factorization property is currently available.
Jones polynomials
For SU q (2), i.e. for A = q 2 all two-line Young diagrams [r 1 r 2 ] get equivalent to the single-line [r 1 − r 2 ], in particular, [21] gets indistinguishable from [1]. This means that
The weak form of differential expansion
Expressions for colored knot polynomials are extremely complicated, but in fact they have a lot of hidden structure and satisfy a lot of non-trivial relations. Understanding of these structures nicknamed "differential expansions" [36,27,15] because their first traces were observed in [4] devoted to the study of Khovanov-Rozansky "differentials" is still very poor. In its weakest possible form, the differential expansion conjecture implies for representation [21] that [13,33] H and H R are the reduced HOMFLY polynomials. In other words certain linear combination of H [21] and H [1] should vanish at A = q ±2 , i.e. in the case of sl (2).
Despite the restriction to SU q (2) is the same as in the previous test, this one looks independent.
Quasiclassical expansion and Vassiliev invariants
Differential expansions from the previous paragraph are examples of cleverly-structured quasiclassical expansions in parameters like , where q = e and A = q N or z = {q} = q − 1/q. The most structured expansion of this type, known so far is the Hurwitz-style formula [39] for reduced colored HOMFLY: Here ϕ R (∆) are characters of the universal symmetric group (defined as in [29]), l(∆) is the number of lines in the Young diagram ∆ and the coefficients of generalized special polynomials Σ K ∆,k (A) are made from the Vassiliev invariants.
This formula includes (102) as a particular case and is also closely related to (105). It imposes non-trivial restrictions on the coefficients of colored polynomials. As already mentioned, we made only a few simple checks of our answers with this formula, and it is very interesting to extend them in order to understand what are the really independent "degrees of freedom" in H [21] , as compared to those already captured by the colored HOMFLY polynomials in symmetric representations. This study can be also helpful for superpolynomial extensions of the [21]-colored knot polynomials, which still remains a complete mystery.
Mutants
Of special interest among the newly available answers are those for the pairs of mutants, i.e. knots related by the mutation transformation, which are inseparable by knot polynomials in symmetric representations.
Generalities
Mutation in knot theory is the transformation of link diagram, when one cuts a sub-diagram with exactly four external legs, rotate and glue it back to the original position. Within the Reshetikhin-Turaev approach, it is clear that cutting corresponds to decomposition of knot polynomial in the channel R 1 ⊗ R 2 and mutation is a rotation in the spaces of intertwining operators W Q R1R2 : R 1 ⊗ R 2 → Q. If these spaces are one-dimensional, like in the case of rectangular representations R 1 = R 2 orR 1 = R 2 , the mutation does not affect the corresponding HOMFLY polynomial. Thus, mutants can be distinguished by colored HOMFLY polynomials in non-rectangular representations, the first of which is R = [21]. The difference H mutant1 [21] − H mutant2 [21] = {q} 11 [21] (q 2 ) = (108) = {q} 4 · {Aq 3 } 2 {Aq 2 }{A}{A/q 2 }{A/q 3 } 2 · A γ · M mutant [21] (q 2 ) has the universal prefactor. The differentials D ±2 and D 0 appear in it because the Alexander and the Jones polynomials at A = 1 and A = q 2 are not affected by the mutation and, thus, the difference should vanish for SU q (N ) with N = 0 and N = 2, i.e. at the corresponding values of A = q N and, since the Young diagram [21] is symmetric, at A = q −N (due to the level-rank duality, [6,8,36]. Vanishing for SU q (3) follows from a more involved argument of ref. [30]. There are no factors D 1 D −1 , because we consider the reduced HOMFLY polynomial, which is equal to the original unreduced one divided by d 21 = D1D0D−1 [3] . The additional A-independent factor {q} 4 seems to be typical for all non-diagonal terms considered in this paper, and this provides an explanation for power 11 in (108). In all examples, which we managed to analyze, M mutant (q 2 ) is, indeed, a function of q only, with no A-dependence.
Examples of mutants
Of these, the KTC pair is most famous. However, the simplest are pretzel ones: there are two such pairs close to the bottom of above list, see also eq.(111) below. For enumeration of mutants with up to 16 intersections see [40].
KTC mutants
The Kinoshita-Terasaka (11n42) and Conway (11n34) knots (KTC mutants) are respectively M (3, −2|2| − 3, 2) and M (3 − 2|2|2, −3). Both knots have representations with 11-intersection, but for our purposes the realization with 12 intersections is more convenient, These diagrams are already easy to bring to the form (55) with (p, q, r, s) = (3, −2, −3, 2) and (3, −2, 2, −3) for 11n42 and 11n34 respectively. Their HOMFLY are: 2 2 We use here the notation from [19]. Matrix lists the coefficients of a polynomial in A 2 and q 2 by the following rule: Changing m = 2 −→ m = −2 simply switches between these two polynomials. At q = 1 both these polynomials are cubes of the special polynomial, H [21] (q = 1) = H [1] (q = 1) At A = q 2 both reproduce the same Jones and at A = 1 the Alexander polynomial, which in this particular case is just unity, The first terms of the differential expansion (see ss.7.4) in the classical limit, A = q N , q = e , are In accordance with [30], the difference between the two polynomials shows up in the order 11 , which is related to the power 11 of {q} in (108). The complete difference is [2] [7] and z = q − q −1 = {q}. It perfectly matches the result of [31]. The difference could actually be calculated for three-cabled knots (because symmetric and antisymmetric representations [3] and [111] do not contribute to it), what allows one to make calculations with the help of the ordinary skein relations. However, the answers for individual H [21] could not be obtained in that way.
Other mutant pairs
In the list (109) of 11-intersection mutant pairs there are four more pairs, for which the fat tree description is already provided. In fact, from this point of view they belong exactly to the same class as the KTC mutants, just some intersection signs are different. The differences are H 11n36 [21] − H 11n44 [21] = A −9 [ Somewhat surprisingly, some differences are the same for different pairs: for 11n36/11n44 and 11n41/11n47, as well as for 11n39/11n45 and 11n151/11n152. The same phenomenon one could observe for the pretzel mutants: the differences are the same for pairs: 11n71/11n75 and 11n76/11n78; 11a47/11a44, 11a57/11a231 and 11n73/11n74 (in the latter case the three differences coincide), see ss.8.3. The entire HOMFLY are, of course quite different, see the Appendix.
It remains to be seen, if the remaining pairs in (109) possess a double fat tree description.
Evolution method in application to mutant families
Of course, most interesting are not just particular knots, but entire families, depending on various parameters. The way to study this kind of problems is provided by the evolution method of [6,27]. For its application to knot polynomials in representation [21] see [33], but there only the simplest family of twist knots was considered (the torus knots were described in this way in arbitrary representation [32,5,6,7], but this is a much simpler exercise, because of the clear algebraic nature of the torus family). We briefly remind this story and then extend consideration to the first mutant-containing family.
9.1 Twist knots [16,17,33] The [21]-colored HOMFLY for generic twist knots was obtained by the evolution method in [33]: This example is already quite interesting for the study of differential expansion [15] beyond (anti)symmetric representations, however, this family does not contain mutant pairs and, hence, is not representative enough.
4-finger pretzel knots
The simplest multi-parametric family containing mutant pairs is the four-parallel-finger pretzels P r(n 1 , n 2 , n 3 , n 4 ) with even n 1 and n 2 , n 3 , n 4 odd. In this case, one has H P r(n1,n2,n3,n4) [21] − H P r(n1,n2,n4,n3) and For generic even values of n 1 expression is more complicated: The r.h.s. of (126) is actually a Laurent polynomial in q. This formula is obtained by the evolution method of [27] w.r.t. the variables n 2 , n 3 , n 4 , and it has the structure predicted by the general expression (108) for mutants. Also it vanishes whenever any of n 2 , n 3 , n 4 is unity, because for the pretzel knots unit length always commutes with any other length due to identities like (63). Eqs.(111)-(112) in ss.8.3 are particular cases of (126).
Conclusion
In this paper we continued the study of the double fat tree realization of link diagrams, for which HOMFLY polynomials are described by an absolutely new and impressively effective formula (2). This formula looks like coming from some new quantum field theory, which should still be found and explored.
In the present paper we focus on another property of (2), which actually reduces evaluation of nearlyarbitrary knot polynomials to that for the two-bridge knots. It goes without saying that this overcomes most calculational complexities in knot/link theory. As an immediate illustration, we calculate a number of [21]colored polynomials, and actually can now do this for almost arbitrary given example. Among other things this is used to explicitly illustrate/validate old expectations about the mutant pairs: they are indeed sometimes (but not always!) distinguished/separated by the [21]-colored polynomials. For instance, the KTC mutant pair can be resolved by these polynomials, but the pretzel mutants made from antiparallel fingers of odd lengths can not.
Of greatest importance for knot theory are now three questions: • How large is the double fat tree family: what are the knots/links beyond it (if any?), and what is the way to find a double fat tree realization of a given knot/link?
• What is the origin of (2) and its effective field theory interpretation? What could be the meaning of quantization and loop diagrams in this effective theory.
• What is the β-deformation of (2), i.e. can this powerful formula be lifted to the super-and Khovanov-Rozansky polynomials?
Added to these could be two obvious technical next steps: • to extend the double fat trees made from 4-strand braids propagators to to arbitrary braids. The need for this for knot theory depends on the answer to the very first question, however, the problem itself can have its own value, especially because of its relation to multi-point conformal blocks. Since (2) is going to provide a new look at all this set of subjects, its generalizations are valuable in arbitrary directions.
• to develop a systematic calculus for colored knots in arbitrary representations, beyond symmetric and [21]. As clear from the present text, this is actually a problem of calculating the simplest Racah matrices describing the 2-bridge knots. If one really does not need the multi-bridge extension for most of knot theory, this technical problem acquires a new value, and hopefully will be solved in the near future, at least to a certain extent.
Calculations in the case of representation [21] are quite involved and can be performed in slightly different ways. In particular, such technically independent exercise for the KTC mutants is reported in a parallel paper [41].
Here we list examples of knots from the Rolfsen table of [21], for which the [21]-colored HOMFLY are now available.
A list of knots with up to 10 intersections
We start from the table which contains some relevant information about the knots up to 10 intersections.
The left part of the table lists the previously known cases: • For the torus knots, the arbitrary colored HOMFLY polynomial is given by the Rosso-Jones formula [32].
• For three-strand knots, the [21]-colored HOMFLY polynomials can be calculated by the cabling method of [16] on ordinary computers. When the number of strands is three, we explicitly give a braid word, only instead of τ a1 1 τ a2 2 τ a3 1 . . . we write the sequence a 1 , a 2 , a 3 , . . . • For two-bridge knots the knowledge of Racah matrices S andS from [17] is sufficient: eq.(2) in this case reduces to an obvious matrix element A 11 . The corresponding answers are available from [17]. When the number of bridges is two, we explicitly give an S − T word.
The right part of the table lists the cases which are available only now, by the method of the present paper, these knots are boldfaced in the first column. Numerous intersections between the left and right parts of the table are important for checking our conjecture (2).
An exhaustive list of the pretzel knots up to 10 intersections is borrowed from the third paper of ref. [20]. They are distinguished from generic double fat tree knots only by simplicity of computer calculations, what is actually quite important.
The starfish cases are also usually simple enough: they still involve just one sum over representations (all pretzel knots are automatically starfish). The cases with two and three propagators involve two and three such sums and are considerably more difficult for computers. A search for maximally simple representations are therefore important from this point of view, and hopefully the table can be significantly improved.
The right part of the table is currently incomplete, but it seems all the knots with 10 or less intersections to fit into it (with the possible exception of 10 161 , which is anyhow present in the left part of the table).
In addition to this table, answers are available for some explicitly identified mutants with 11 intersections.
Some thin knots
A lot of explicit examples with less than nine intersections can be found in [16] and [17]. Here we add the only 8-intersection knot 8 15 which was not present in those lists (it is pretzel, but possesses also a simpler triple-finger realization), and a couple of 10-intersection knots: and
The first thick knots
Thick are the knots, for which the fundamental superpolynomials are not obtained from HOMFLY by a change of variables and Khovanov homologies have non-trivial entries off critical diagonals (marked in red in [21]). In most cases, these superpolynomials have more terms than the HOMFLY polynomial (though this discrepancy can often be eliminated by switching to differential expansion a la [15]). The first thick knots in the Rolfsen The next have eleven and more intersections.
3-strand cases
Five of these are 3-strand and therefore the answers for H [21] are easily available by the methods of [16]: Moreover, two of these are torus knots, 8 19 = T orus [3,4] and 10 124 = T orus [3,5], and therefore arbitrary colored HOMFLY polynomials for them are available: provided by the Rosso-Jones formula [32,6].
4-parallel pretzel finger cases
Three of the above thick knots are of the pretzel type and are described by the simple formulas: and H P r(n1,n2,n3,n4) R These three cases are 3-strand (and thus already known)
Realizations from [19]
According to [18] and [19], seven thick knots from [4] can be realized just as triple-finger starfish diagrams: H 942 10 145 is the only example in our thick-knot set, where summation is over representations X ∈ R ⊗ R, i.e. in the parallel sector. This summation is insensitive to the choice of parameters ξ in sec.7, thus there is no overline in this case.
H 10145 [21] = Three knots are more complicated, their HOMFLY polynomials are represented by double sums, at best: | 11,627 | 2015-04-01T00:00:00.000 | [
"Mathematics"
] |
Optical Filters with Asymmetric Transmittance Depending on the Incident Angle, Produced Using Liquid Crystalline Ink (Louver LC Filters)
In many situations in everyday life, sunlight levels need to be reduced. Optical filters with asymmetric transmittance dependent on the incident angle would be useful for sunglasses and vehicle or architectural windows, among others. Herein, we realized the production of optical filters, called “louver filters”, comprising HAN-type LC film produced using liquid crystalline ink with dichroic dyes. For the formation of the HAN-type LC film, the liquid crystalline ink was aligned on a rubbed polyimide layer and polymerized by UV irradiation. Two kinds of filters are proposed: one is a filter composed of HAN-type LC film and a polarizer, and the other is composed of two HAN-LC films with a half-wave plate between them. The dependence of the asymmetric transmittance on the incident angle was confirmed for these filters. The dependence changed depending on the pretilt angle of the alignment layers. Photographs taken with the optical filters displayed their effectiveness.
Introduction
Control of light strength is important for all circumstances in life.In the case of windows for buildings and cars, or in sunglasses, only the light from above should be blocked out; light from the front or from below need not be blocked.For these situations, optical films for which transmittance varies depending on the direction are desirable.However, the optical films produced so far have been optically isotropic, and the transmittance does not vary with angle.
Concerning optical films of which the transmittance varies depending on the incident angle, several kinds of films have been commercialized for peeping prevention of flat panel displays [1,2].These films possess minute layered structures perpendicular or oblique to the film plane.These films must be used by attaching to the displays.In the case of the applications of these films to windows or glasses, the light scattering occurs to make the films opaque.To prevent the light scattering, the size of the layered structures must be less than the light wavelength.On the other hand, it was reported that by using a liquid crystalline solution containing liquid crystalline monomer and dichroic dye, polarizers can be formed [3].In this method, the dichroic dye alignment direction was controlled by liquid crystalline materials.The dichroic dye exists homogeneously in the film and light scattering does not occur.Concerning the molecular arrangement of the liquid crystal, not only the azimuth angle but also the polar angle can be controlled.By controlling both the azimuth angle and polar angle of dichroic dye in the film, the optical filters with asymmetric transmittance depending on the incident angle without light scattering could be realized.
The authors proposed optical devices using liquid crystal devices (LCDs) with asymmetric transmittance [4,5].For these devices, hybrid alignment nematic (HAN) LCDs [6][7][8][9][10][11][12] and LCDs of high pretilt parallel alignment with dichroic dye were used.Combinations of one of these LCDs and a polarizer or two of these LCDs and a half-wave plate could realize effectively asymmetric transmittance dependent on the incident angle.By using LCDs, the properties can be changed by applying an electric voltage.However, for use in the windows of buildings and cars or in sunglasses, optical filters composed of film materials would be more appropriate than LCDs.These HAN-type films could be produced by printing liquid crystalline ink containing liquid crystal monomer and dichroic dye on rubbed polyimide layers.
It is known that in the interface between liquid crystal (LC) materials and air, the LC molecules tend to align perpendicular to the surface of the interface [13].Therefore, by placing an LC layer on a rubbed alignment layer for homeotropic alignment, an HAN molecular arrangement can be formed spontaneously.Furthermore, by using LC monomers as LC materials and irradiating them with ultraviolet (UV) light, polymer films possessing an HAN-type structure (Figure 1) can be formed [14][15][16][17][18][19][20][21][22][23].
optical filters with asymmetric transmittance depending on the incident angle light scattering could be realized.
The authors proposed optical devices using liquid crystal devices (LCD asymmetric transmittance [4,5].For these devices, hybrid alignment nematic LCDs [6][7][8][9][10][11][12] and LCDs of high pretilt parallel alignment with dichroic dye we Combinations of one of these LCDs and a polarizer or two of these LCD half-wave plate could realize effectively asymmetric transmittance dependent o cident angle.By using LCDs, the properties can be changed by applying an voltage.However, for use in the windows of buildings and cars or in sunglasse filters composed of film materials would be more appropriate than LCD HAN-type films could be produced by printing liquid crystalline ink containin crystal monomer and dichroic dye on rubbed polyimide layers. It is known that in the interface between liquid crystal (LC) materials and LC molecules tend to align perpendicular to the surface of the interface [13].T by placing an LC layer on a rubbed alignment layer for homeotropic alignment, molecular arrangement can be formed spontaneously.Furthermore, by using L mers as LC materials and irradiating them with ultraviolet (UV) light, polym possessing an HAN-type structure (Figure 1) can be formed [14][15][16][17][18][19][20][21][22][23]. Figure 2 shows the structure of an optical filter using an HAN-type LC fi polarizer, along with the mechanism for the dependence of the transmittance o cident angle [4,5].In the case of the optical filters shown in Figure 2, the s-wave sorbed by the polarizer.The p-waves in the direction perpendicular to the molec of the dichroic dye are absorbed.On the other hand, the p-waves in the direction to the molecular axis of the dye pass through the film.As a result, dependen transmittance on the incident angle becomes possible.When using a polar transmittance of the filter is less than 50%.Figure 2 shows the structure of an optical filter using an HAN-type LC film and a polarizer, along with the mechanism for the dependence of the transmittance on the incident angle [4,5].In the case of the optical filters shown in Figure 2, the s-waves are absorbed by the polarizer.The p-waves in the direction perpendicular to the molecular axis of the dichroic dye are absorbed.On the other hand, the p-waves in the direction parallel to the molecular axis of the dye pass through the film.As a result, dependence of the transmittance on the incident angle becomes possible.When using a polarizer, the transmittance of the filter is less than 50%.
In Figure 3, the structure of an optical film made using two HAN-type LC films with a half-wave plate between them is shown.The LC alignment direction or rubbing direction on the alignment film of each HAN-type LC film is the same.The angle between the alignment direction and the optical axis of the half-wave plate is set at 45 degrees.The polar angle of the dye molecules changes through the LC layer.The average polar angle of the molecules is shown [4].
Figure 4 shows the mechanism realizing the dependence of the transmittance on the incident angle when using the structure shown in Figure 3 [4].The incident light parallel to the dye's molecular axis passes through the films with little absorption.On the other hand, the p-waves of incident light perpendicular to the dye molecular axis are absorbed by the dye; however, the s-waves of the incident light pass through the film without absorption.By passing through a half-wave plate, p-waves and s-waves are exchanged.In the second LC film, the p-waves exchanged with the s-waves are absorbed by the dichroic dyes.According to this mechanism, the incident light perpendicular to the LC molecules or dichroic dyes is absorbed, while the incident light parallel to them passes through the films with little absorption.In the optical filter shown in Figure 3, no polarizer is used.Thus, the transmittance could be more than 50%.In Figure 3, the structure of an optical film made using two HAN-type LC with a half-wave plate between them is shown.The LC alignment direction or ru direction on the alignment film of each HAN-type LC film is the same.The an tween the alignment direction and the optical axis of the half-wave plate is set at grees.The polar angle of the dye molecules changes through the LC layer.The a polar angle of the molecules is shown [4].In Figure 3, the structure of an optical film made using two HAN-type LC with a half-wave plate between them is shown.The LC alignment direction or r direction on the alignment film of each HAN-type LC film is the same.The an tween the alignment direction and the optical axis of the half-wave plate is set at grees.The polar angle of the dye molecules changes through the LC layer.The a polar angle of the molecules is shown [4].
Figure 3.The structure of an optical film using two HAN-type LC films and a half-wave p tween them.The LC alignment directions of the two HAN-type LC films are the same.Th between the LC alignment directions and the optical axis of the half-wave plate is set at 45 d Figure 4 shows the mechanism realizing the dependence of the transmittance incident angle when using the structure shown in Figure 3 [4].The incident light p to the dye's molecular axis passes through the films with little absorption.On th hand, the p-waves of incident light perpendicular to the dye molecular axis are ab by the dye; however, the s-waves of the incident light pass through the film with sorption.By passing through a half-wave plate, p-waves and s-waves are exchan the second LC film, the p-waves exchanged with the s-waves are absorbed by chroic dyes.According to this mechanism, the incident light perpendicular to molecules or dichroic dyes is absorbed, while the incident light parallel to them
HAN LC Film2
Half-wave plate Figure 3.The structure of an optical film using two HAN-type LC films and a half-wave plate between them.The LC alignment directions of the two HAN-type LC films are the same.The angle between the LC alignment directions and the optical axis of the half-wave plate is set at 45 degrees.
We call these filters "louver LC filters".This name refers to the fact that these optical filters are composed of films produced from liquid crystalline ink and to the dependence of the transmittance on the incident angle.films with little absorption.In the optical filter shown in Figure 3, no polarizer is used.Thus, the transmittance could be more than 50%.We call these filters "louver LC filters".This name refers to the fact that these optical filters are composed of films produced from liquid crystalline ink and to the dependence of the transmittance on the incident angle.
Materials
RMM28B (Merck KGaA, Darmstadt, Germany Rahway, NJ, USA) [21][22][23] was used as the LC monomer.RMM28B is in a solid state at room temperature.With heating, it enters the LC state at 53 °C.At temperatures higher than 76 °C, it is in both an LC state and a liquid state.With cooling, the LC state is maintained at room temperature.However, after 1 h, it returns to a solid state.RMM28B contains a photoinitiator of polymerization, Irugacure 907 (<10%).For the dichroic dye, NKX-4173 (Hayashibara Co., Ltd., Okayama, Japan) was used.
Preparation of the Liquid Crystalline Ink
Quantities of 200.5 mg of LC monomer RMM28B, 4.0 mg (2 wt% relative to the RMM28B) of dichroic dye NKX-4713, and 328.1 mg of toluene were placed in a sample bottle.The weight proportion of the solid was 38%.The bottle was placed on a hot plate with a magnetic stirrer function.The mixture was stirred at 100 °C for 60 min to obtain a homogeneous black solution.
The state of the solution was observed from 25 to 110 °C using an Olympus BX50 polarizing microscope, (Olympus Co., Tokyo, Japan) a Mettler Toledo FP90, and a hot stage (Mettler-Toledo International, Tokyo,Japan).The solution showed a nematic LC state from 25 to 106 °C.Solutions containing 1, 3, and 5 wt% of dichroic dye NKX-4713 were also prepared.
Formation of Alignment Layers with a Small Pretilt Angle
A layer of SE-150 polyimide solution (Nissan Chemical Co., Tokyo, Japan) with a pretilt angle of 4 degrees was formed via 3000 rpm rotation spin coating on a glass plate of dimensions 20 mm × 25 mm area and 0.7 mm thickness.The formed layer was heated at 200 °C for 1 h to obtain polyimide film 0.1 µm thick.The surface of the layer was rubbed with a cotton velvet cloth attached to a 40 mm diameter roller rotating at 1000 rpm using
Materials
RMM28B (Merck KGaA, Darmstadt, Germany) [24][25][26] was used as the LC monomer.RMM28B is in a solid state at room temperature.With heating, it enters the LC state at 53 • C. At temperatures higher than 76 • C, it is in both an LC state and a liquid state.With cooling, the LC state is maintained at room temperature.However, after 1 h, it returns to a solid state.RMM28B contains a photoinitiator of polymerization, Irugacure 907 (<10%).For the dichroic dye, NKX-4173 (Hayashibara Co., Ltd., Okayama, Japan) was used.
Preparation of the Liquid Crystalline Ink
Quantities of 200.5 mg of LC monomer RMM28B, 4.0 mg (2 wt% relative to the RMM28B) of dichroic dye NKX-4713, and 328.1 mg of toluene were placed in a sample bottle.The weight proportion of the solid was 38%.The bottle was placed on a hot plate with a magnetic stirrer function.The mixture was stirred at 100 • C for 60 min to obtain a homogeneous black solution.
The state of the solution was observed from 25 to 110 • C using an Olympus BX50 polarizing microscope, (Olympus Co., Tokyo, Japan) a Mettler Toledo FP90, and a hot stage (Mettler-Toledo International, Tokyo, Japan).The solution showed a nematic LC state from 25 to 106 • C. Solutions containing 1, 3, and 5 wt% of dichroic dye NKX-4713 were also prepared.
Preparation of HAN-Type LC Films 2.3.1. Formation of Alignment Layers with a Small Pretilt Angle
A layer of SE-150 polyimide solution (Nissan Chemical Co., Tokyo, Japan) with a pretilt angle of 4 degrees was formed via 3000 rpm rotation spin coating on a glass plate of dimensions 20 mm × 25 mm area and 0.7 mm thickness.The formed layer was heated at 200 • C for 1 h to obtain polyimide film 0.1 µm thick.The surface of the layer was rubbed with a cotton velvet cloth attached to a 40 mm diameter roller rotating at 1000 rpm using a PM-50 rubbing machine (EHC Co., Tokyo, Japan).The distance between the polyimide layer surface and the roller was set to be 0.4 mm shorter than the length of the velvet fiber.
HAN-Type Layer Formation by Spin Coating
A solution of LC monomer and dichroic dye (1 wt%) was coated on the surface of an SE-150 alignment layer on a glass plate by rotation at 3000 rpm using a spin coater.Just before use, the solution was heated to 40 • C while stirring with a magnetic stirrer.The layer was heated at 55 • C for 1 min and was irradiated with 28.7 mW/cm 2 365 nm UV light for 1 min.The layer thickness was 3.6 µm.For the HAN-type layer produced by spin coating, two areas possessing opposite polar angle directions were observed.The two areas separated at the center of the rotation.By using the same methods, layers containing 2, 3, and 5 wt% dichroic dye were formed.The layer thicknesses were 4.2, 3.2, and 3.8 µm, respectively.HAN-type layers were also prepared on the high-pretilt-angle alignment layers.Optical measurements were carried out in the area in which the polar angle was formed in the same direction as the pretilt angle.
HAN-Type LC Layer Formation Using a Film Applicator
A polyethylene terephthalate (PET) film (95 mm × 95 mm, 0.125 mm thickness) was fixed on a glass plate (100 mm × 100 mm, 0.7 mm thickness) using polyimide tapes.A solution of SE-5291 polyimide (Nissan Chemical Co.) was coated on this film by 3000 rpm spin-coating rotation.The layer was heated at 90 • C for 45 min to obtain a polyimide layer.The surface on the polyimide layer was rubbed as described in Section 2.3.1.The pretilt angle of SE-5291 is 6 degrees [28].A solution of LC monomer and dichroic dye (5 wt% relative to the LC monomer) was coated on the obtained alignment layer using an SA-201 Baker-type film applicator and a PI-1210 auto film applicator (Tester Sangyo Co., Ltd., Saitama, Japan).
Just before use, the solution was heated to 40 • C. The coating direction was set parallel and opposite to the rubbing direction.The layer thickness and the bar speed of the applicator were set to 20 µm and 50 mm/s, respectively.The applicator was warmed to 55 • C before use.The obtained layer was heated to 55 • C for 1 min.The substrate with the formed LC monomer layer was set in a vacuum using a vacuum vessel with quartz glass (MUVPBQ-150, AITEC SYSTEM Co., Ltd., Kanagawa, Japan).UV light (365 nm, 28.7 mW/cm 2 ) was irradiated through the quartz glass for two minutes.The layer thickness was measured using a VK9710/VK9700 laser microscope (KEYENCE Co., Osaka, Japan) and found to be 9 µm.
Combination of Two LC Films
The combination of two LC films and a half-wave plate shown in Figure 3 was formed by using two LC films on glass or PET film substrate.In the case of a glass substrate, an upper glass substrate was placed on another LC film, and the rubbing direction on each substrate was set to be the same.In the case of a PET substrate, each PET substrate was placed on the outside of the two LC films, because PET substrate has the quality of birefringence.The rubbing directions were set to be parallel and opposite.The direction of the half-wave plate extension axis was set at 45 degrees to the rubbing direction.Pureace@R-270 polycarbonate film (film thickness 67 µm, TEIJIN Ltd., Tokyo, Japan) was used as the half-wave plate.The retardation of this film was measured and found to be 267 nm using 579 nm light.
Measurement of the Incident Angle Dependence of the Transmittance
The dependence of the transmittance of the optical filters on the incident angle was measured using an RETS-100 optical property measurement system (Otsuka Electronic Co., Osaka, Japan).The transmittance of the single LC films was measured using polarized light (p-waves in Figure 2) with a polarizer.Transmittance without a polarizer was taken as 100%.
The transmittance of the two LC films in Figure 3 was measured using nonpolarized light without a polarizer.The relationship between the sign of the incident angle and the direction of the polar angle of the LC monomer is shown in Figure 5.
Measurement of the Incident Angle Dependence of the Transmittance
The dependence of the transmittance of the optical filters on the incident angle was measured using an RETS-100 optical property measurement system (Otsuka Electronic Co., Osaka, Japan).The transmittance of the single LC films was measured using polarized light (p-waves in Figure 2) with a polarizer.Transmittance without a polarizer was taken as 100%.
The transmittance of the two LC films in Figure 3 was measured using nonpolarized light without a polarizer.The relationship between the sign of the incident angle and the direction of the polar angle of the LC monomer is shown in Figure 5.
Measurement of the Pretilt Angles of the Alignment Layers
In order to measure the alignment layers' pretilt angles, LC cells with parallel but opposite rubbing directions were prepared.The distance between the alignment layers was set to 20 μm.The pretilt angle was measured using the PAS-301 pretilt-angle measurement system (Elsicon Co., Newark, DE, USA).
HAN-Type LC Layers Formed by Spin Coating
Figure 6 shows the photographs from the direction of negative incident angle shown in Figure 5.In the case of spin coating, two kinds of uniform HAN-type LC alignment regions were formed.In particular, in the case of a low-pretilt-angle alignment layer, the boundary between the regions was at the center of the rotation (Figure 6a).
Measurement of the Pretilt Angles of the Alignment Layers
In order to measure the alignment layers' pretilt angles, LC cells with parallel but opposite rubbing directions were prepared.The distance between the alignment layers was set to 20 µm.The pretilt angle was measured using the PAS-301 pretilt-angle measurement system (Elsicon Co., Newark, DE, USA).
HAN-Type LC Layers Formed by Spin Coating
Figure 6 shows the photographs from the direction of negative incident angle shown in Figure 5.In the case of spin coating, two kinds of uniform HAN-type LC alignment regions were formed.In particular, in the case of a low-pretilt-angle alignment layer, the boundary between the regions was at the center of the rotation (Figure 6a).Opposite dependence of the transmittance on the incident angle was observed each region (Figure 7).In the area deemed regular, the LC molecular polar angle dir tion was the same as the pretilt-angle direction on the alignment layer.In the a Opposite dependence of the transmittance on the incident angle was observed in each region (Figure 7).In the area deemed regular, the LC molecular polar angle direction was the same as the pretilt-angle direction on the alignment layer.In the area deemed irregular, the LC molecular polar angle direction was opposite to the pretilt-angle direction.However, the values of transmittance dependent on the incident angle in two regions were the same (Figure 7a).In Figure 6a, the difference between the dark area and the light area shows the transmittance contrast between the positive and negative directions shown in Figure 5. Opposite dependence of the transmittance on the incident angle was observed in each region (Figure 7).In the area deemed regular, the LC molecular polar angle direction was the same as the pretilt-angle direction on the alignment layer.In the area deemed irregular, the LC molecular polar angle direction was opposite to the pretilt-angle direction.However, the values of transmittance dependent on the incident angle in two regions were the same (Figure 7a).In Figure 6a, the difference between the dark area and the light area shows the transmittance contrast between the positive and negative directions shown in Figure 5.With the use of a 25-degree pretilt-angle alignment layer, the irregular regions were reduced (Figure 6b).In Figure 7b, the dependence of the transmittance on the incident angle in the regular area was as expected for a high-pretilt-angle alignment layer [4].However, dependence was not observed in the irregular area.
During the spin-coating process, centrifugal force is applied to the solution in a liquid crystal state.In the LC layer, migration of the solution near the substrate surface is limited; however, near the interface with the air, the solution flows toward the outside of the rotation.As a result, the polar angle direction is reversed around the center of the rotation, although the alignment direction is parallel to the rubbing direction.In the case of a low pretilt angle, the effect of the pretilt angle is limited.The polar angle distribution is determined by the centrifugal force.However, in the case of a high pretilt angle, the effect of the pretilt angle increases.The expected LC molecular arrangements for each case are shown in Figure 8a,b.limited; however, near the interface with the air, the solution flows toward the outside of the rotation.As a result, the polar angle direction is reversed around the center of the rotation, although the alignment direction is parallel to the rubbing direction.In the case of a low pretilt angle, the effect of the pretilt angle is limited.The polar angle distribution is determined by the centrifugal force.However, in the case of a high pretilt angle, the effect of the pretilt angle increases.The expected LC molecular arrangements for each case are shown in Figure 8a
Observed Defects in the Case of LC Layer Formation Using a Baker-Type Film Applicator
HAN-type LC film was formed using a Baker-type film applicator as detailed in Section 3.4.Some defects were observed where uniform layer formation was hindered.We call this type of defect "tilt reverse" [29,30].In these defects, the direction of the polar angle was opposite to that in the regular area.From the direction in which light passes unhindered through the film, tilt reverse is observed as dark spots.From the opposite direction, tilt reverse is observed as bright spots in the dark area.By using a polarized microscope, the defects were observed as spots surrounded by linear defects.These defects are expected to form when irregular flow of the LC solution occurs, for example, around particles or on a deformed alignment layer surface.
Dependence of the Transmittance on the Incident Angle for a HAN-Type LC Layer Using Low-Pretilt-Angle Alignment Layers, Observed by Polarized Light
The dependence of the transmittance on the incident angle for HAN-type LC film on a glass substrate using polarized light parallel to the LC alignment direction is shown in Figure 9. Transmittance increases monotonically from +45 degrees to −45 degrees.The degree of the dependences of the transmittance on the incident angles for 2%, 3%, and 5% does not show the difference.However, the one for 1% is much smaller.
Observed Defects in the Case of LC Layer Formation Using a Baker-Type Film Applicator
HAN-type LC film was formed using a Baker-type film applicator as detailed in Section 3.4.Some defects were observed where uniform layer formation was hindered.We call this type of defect "tilt reverse" [29,30].In these defects, the direction of the polar angle was opposite to that in the regular area.From the direction in which light passes unhindered through the film, tilt reverse is observed as dark spots.From the opposite direction, tilt reverse is observed as bright spots in the dark area.By using a polarized microscope, the defects were observed as spots surrounded by linear defects.These defects are expected to form when irregular flow of the LC solution occurs, for example, around particles or on a deformed alignment layer surface.
Dependence of the Transmittance on the Incident Angle for a HAN-Type LC Layer Using Low-Pretilt-Angle Alignment Layers, Observed by Polarized Light
The dependence of the transmittance on the incident angle for HAN-type LC film on a glass substrate using polarized light parallel to the LC alignment direction is shown in Figure 9. Transmittance increases monotonically from +45 degrees to −45 degrees.The degree of the dependences of the transmittance on the incident angles for 2%, 3%, and 5% does not show the difference.However, the one for 1% is much smaller. .Dependence of the transmittance on the incident angle using polarized light for HAN-type LC films on glass substrate (see Figures 2 and 5).The HAN-type LC films were produced by spin coating.The dependence in the regular region is shown.The light wavelength was 550 nm.The film widths were 3.6 μm (1%), 4.2 μm (2%), 3.2 μm (3%), and 3.8 μm (5%).The pretilt angle of the alignment layer was 4 degrees.
Figure 10 shows the dependence of the transmittance on the incident angle using polarized light for HAN-type LC films on PET substrates.It shows a similar tendency to that indicated in Figure 9.The dependence can be explained by the mechanism shown in Figure 2. Incident light from the + direction shown in Figure 5 proceeds in the direction perpendicular to the dichroic dye molecular axis and is efficiently absorbed by the dye.On the other hand, incident light from the − direction proceeds parallel to the dye mo- Transmittance (%) Incident Angle (degree) 1% 2% 3% 5% Figure 9. Dependence of the transmittance on the incident angle using polarized light for HAN-type LC films on glass substrate (see Figures 2 and 5).The HAN-type LC films were produced by spin coating.The dependence in the regular region is shown.The light wavelength was 550 nm.The film widths were 3.6 µm (1%), 4.2 µm (2%), 3.2 µm (3%), and 3.8 µm (5%).The pretilt angle of the alignment layer was 4 degrees.
Figure 10 shows the dependence of the transmittance on the incident angle using polarized light for HAN-type LC films on PET substrates.It shows a similar tendency to that indicated in Figure 9.The dependence can be explained by the mechanism shown in Figure 2. Incident light from the + direction shown in Figure 5 proceeds in the direction perpendicular to the dichroic dye molecular axis and is efficiently absorbed by the dye.On the other hand, incident light from the − direction proceeds parallel to the dye molecular axis, and the absorption is therefore limited.The slopes of the graphs for the concentrations from 2% to 5% do not change, but that for 1% decreases considerably.
Figure 9. Dependence of the transmittance on the incident angle using polarized light for HAN-type LC films on glass substrate (see Figures 2 and 5).The HAN-type LC films were produced by spin coating.The dependence in the regular region is shown.The light wavelength was 550 nm.The film widths were 3.6 μm (1%), 4.2 μm (2%), 3.2 μm (3%), and 3.8 μm (5%).The pretilt angle of the alignment layer was 4 degrees.
Figure 10 shows the dependence of the transmittance on the incident angle using polarized light for HAN-type LC films on PET substrates.It shows a similar tendency to that indicated in Figure 9.The dependence can be explained by the mechanism shown in Figure 2. Incident light from the + direction shown in Figure 5 proceeds in the direction perpendicular to the dichroic dye molecular axis and is efficiently absorbed by the dye.On the other hand, incident light from the − direction proceeds parallel to the dye molecular axis, and the absorption is therefore limited.The slopes of the graphs for the concentrations from 2% to 5% do not change, but that for 1% decreases considerably.
Figure 10.Dependence of the transmittance on the incident angle using polarized light for HAN-type LC films on PET substrate (see Figures 2 and 5).The light wavelength was 550 nm.The pretilt angle of the alignment layer was 2 degrees.
To explain the mechanism, the LCD structure shown in Figure 11 Transmittance (%) Incident Angle (degree) 4% 3% 2% 1% Figure 10.Dependence of the transmittance on the incident angle using polarized light for HAN-type LC films on PET substrate (see Figures 2 and 5).The light wavelength was 550 nm.The pretilt angle of the alignment layer was 2 degrees.
To explain the mechanism, the LCD structure shown in Figure 11 is considered.For simplicity, the polar angle of the LC molecule is assumed to be 45 degrees.Incident angles of 45 degrees and −45 degrees are considered.By the Lambert-Beer law, the transmittance at incident angles of +45 degrees and −45 degrees for p-waves T +45 and T −45 can be expressed by the equations below.The passing distances l +45 and l −45 for both incident angles are the same value, l. ε p and ε s are the absorption coefficients of polarized light vibrating parallel and perpendicular to the molecular long axis of the dye.The dependence of the transmittance on the incident angle can then be estimated as the value T −45 − T +45 : The equation above shows that the dependence of the transmittance on the incident angle depends on the film thickness and on the concentration and ε p − ε s value of the dye.It also shows that in the case of a high concentration or thick film, the change in the dependence due to change in the concentration or the thickness becomes small.In Figures 9 and 10, the change in the dependence from 1% to 2% is larger than that from 2% to 5%.To obtain high dependence, the use of a high concentration of the dye and a thick film would be effective.However, these values cannot be changed freely, because the transmittance varies depending on these values.The most effective way to obtain high dependence would then be the use of dye possessing a large ε p − ε s value.
Furthermore, the degree of alignment or order parameter of the LC material is important.The degree of liquid crystal alignment depends on the LC material, the alignment layer, and the process of film formation.These factors can improve the dependence of the transmittance on the incident angle.
Relationship between the Alignment Layer Pretilt Angle and the Dependence of the Transmittance on the Incident Angle
Figure 12 shows the dependence of the transmittance of HAN-type LC films, made using alignment layers with different pretilt angles, on the incident angle of polarized light.For alignment layers with pretilt angles of 4, 6, and 17 degrees, the transmittance increases from 45 degrees to −45 degrees monotonically.The transmittance at 45 degrees takes almost the same value for these three films.However, as the pretilt angle increases, the dependence of the transmittance on the incident angle increases.On the other hand, in the case of a pretilt angle of 27 degrees, the transmittance peaks at −20 degrees.Figure 12 shows that a 17-degree pretilt angle is preferable for HAN-type LC films.Dependence of the transmittance of HAN-type LC films, made using alignment layers with different pretilt angles, on the incident angle of polarized light (see Figures 2 and 5).The concentration of the dichroic dye was 5%.
Combination of Two HAN-Type LC Films and a Half-Wave Plate
Figures 13 and 14 show the transmittance dependences on the incident angle for the combination of two HAN-type LC films (1% of dye concentration) and a half-wave plate shown in Figure 3, alongside that for single HAN-type LC film (1% of dye concentration) with a polarizer.The transmittances for negative incident angles are more than 50% Transmittance (%) Incident Angle (degree)
4°6°17°27°
Figure 12.Dependence of the transmittance of HAN-type LC films, made using alignment layers with different pretilt angles, on the incident angle of polarized light (see Figures 2 and 5).The concentration of the dichroic dye was 5%.
Combination of Two HAN-Type LC Films and a Half-Wave Plate
Figures 13 and 14 show the transmittance dependences on the incident angle for the combination of two HAN-type LC films (1% of dye concentration) and a half-wave plate shown in Figure 3, alongside that for single HAN-type LC film (1% of dye concentration) with a polarizer.The transmittances for negative incident angles are more than 50% and 43%, respectively.These values cannot be achieved by the filters with a polarizer.In Figure 13, at +45 • the transmittance of two LC films and a half-wave plate is much higher than the one of an LC film with a polarizer, because p-wave from the direction of +θ cannot be absorbed sufficiently due to the low dye concentration and thin film thickness compared with a polarizer.
Figure 12.Dependence of the transmittance of HAN-type LC films, made using alignment layers with different pretilt angles, on the incident angle of polarized light (see Figures 2 and 5).The concentration of the dichroic dye was 5%.
Combination of Two HAN-Type LC Films and a Half-Wave Plate
Figures 13 and 14 show the transmittance dependences on the incident angle for the combination of two HAN-type LC films (1% of dye concentration) and a half-wave plate shown in Figure 3, alongside that for single HAN-type LC film (1% of dye concentration) with a polarizer.The transmittances for negative incident angles are more than 50% and 43%, respectively.These values cannot be achieved by the filters with a polarizer.In Figure 13, at +45° the transmittance of two LC films and a half-wave plate is much higher than the one of an LC film with a polarizer, because p-wave from the direction of +θ cannot be absorbed sufficiently due to the low dye concentration and thin film thickness compared with a polarizer.In Figure 14, the transmittance of two LC films and a half-wave plate is similar to those for the one of an LC film with a polarizer.It shows the result that can be expected by the mechanism shown in Figure 4.In both Figures 13 and 14, the maximum values can be observed around −20°.This phenomenon could be observed for the devices using In Figure 14, the transmittance of two LC films and a half-wave plate is similar to those for the one of an LC film with a polarizer.It shows the result that can be expected by the mechanism shown in Figure 4.In both Figures 13 and 14, the maximum values can be observed around −20 • .This phenomenon could be observed for the devices using LCDs [4].With a large incident angle, the transmittance could decrease as the optical path extends.As a result, the maximum transmittance could be observed at an incident angle smaller than 45 degrees.In the case of two LC films and a half-wave plate, the maximum values could be observed at smaller incident angles than that for an LC film with a polarizer, because the optical path doubles.
Figures 15 and 16 show the transmittance dependences on the incident angle for the filters using HAN-type LC films (5% of dye concentration).In both figures, in the region of positive incident angle, the transmittances of the two LC films with a half-wave plate are the same as those for an LC film with a polarizer.This result can be expected by the mechanism shown in Figure 4.However, in the region of negative incident angle, the transmittances of the two LC films with a half-wave plate are similar to the ones for an LC film with a polarizer.The result cannot be explained by the mechanism shown in Figure 4.This could be explained by two factors: the order parameter of the LC film is not enough and the polar angle is distributed from 0 • to 90 • for HAN-LC film.In the case of high concentration of the dichroic dye, the incident light from −45 • would be absorbed by the dyes at the distributed polar and azimuth angles.To realize a function of two LC films with a half-wave plate, as shown in Figure 4, the appropriate concentration of the dichroic dye should be important.A wide variety of applications can be expected for these filters.For architectural window applications, the preferable transmittance could be varied depending on the area or the purpose of the usage.When the high transmittance is preferable, the filter with two LC films and a half-wave plate could be selected.For car side windows and sunglasses, relatively low transmittance would be required.For these products, the filter of one LC film with a polarizer could be selected.
Figure 15.Dependence of the transmittance on the incident angle for a combination of two HAN-type LC films on glass substrates and a half-wave plate, shown in Figure 3, and that for a single HAN-type LC film with a polarizer.The concentration of the dichroic dye was 5%.
Figure 16.Dependence of the transmittance on the incident angle for a combination of two HAN-type LC films on PET substrates and a half-wave plate, shown in Figure 3, and that for a single HAN-type LC film with polarizer.The concentration of the dichroic dye was 5%.
A wide variety of applications can be expected for these filters.For architectural window applications, the preferable transmittance could be varied depending on the area or the purpose of the usage.When the high transmittance is preferable, the filter with two LC films and a half-wave plate could be selected.For car side windows and sunglasses, relatively low transmittance would be required.For these products, the filter of one LC film with a polarizer could be selected.Figure 16.Dependence of the transmittance on the incident angle for a combination of two HAN-type LC films on PET substrates and a half-wave plate, shown in Figure 3, and that for a single HAN-type LC film with polarizer.The concentration of the dichroic dye was 5%.
Applications
Louver LC filters are optical filters through which the transmittance varies depending on the incident angle.With this property, the louver LC filters could be applied to sunglasses and windows, among others.Figures 17-19 show photographs taken with and without a louver LC filter.The louver LC filter was composed of HAN-type LC film and a polarizer, as shown in Figure 2.With a louver LC filter, the total light strength decreases.However, the photograph brightness is maintained automatically.Figure 17b clearly shows that the strength of the light decreases only from the upper side.In Figures 18 and 19, with a louver LC filter, the lower parts of the photographs look brighter.Figure 18 shows that by looking through the louver LC filter, we could read the documents more clearly than we could by using conventional sunglasses.In Figure 17, the scenery in the lower part can be observed more brightly and precisely than it can without a louver LC filter.
Applications
Louver LC filters are optical filters through which the transmittance varies depending on the incident angle.With this property, the louver LC filters could be applied to sunglasses and windows, among others.Figures 17-19 show photographs taken with and without a louver LC filter.The louver LC filter was composed of HAN-type LC film and a polarizer, as shown in Figure 2.With a louver LC filter, the total light strength decreases.However, the photograph brightness is maintained automatically.Figure 17b clearly shows that the strength of the light decreases only from the upper side.In Figures 18 and 19, with a louver LC filter, the lower parts of the photographs look brighter.Figure 18 shows that by looking through the louver LC filter, we could read the documents more clearly than we could by using conventional sunglasses.In Figure 17, the scenery in the lower part can be observed more brightly and precisely than it can without a louver LC filter.
Conclusions
In this article, optical filters with transmittance dependent on the incident angle, made using liquid crystalline ink, are proposed.We refer to this optical filter as a "louver LC filter".For louver LC filters, HAN-type LC films produced from an LC monomer and dichroic dye were used.Two kinds of louver filters are proposed: one is composed of a HAN-type LC film and a polarizer, and the other is composed of two HAN-type LC films with a half-wave plate between them.By using these louver LC filters, the light strength from the upper side can be reduced preferentially.This property is appropriate for sunglasses, windows in cars and buildings, and other applications.
Patents
Patent WO2021256499A1, Optical element and eyewear, has been filed.
Conclusions
In this article, optical filters with transmittance dependent on the incident angle, made using liquid crystalline ink, are proposed.We refer to this optical filter as a "louver LC filter".For louver LC filters, HAN-type LC films produced from an LC monomer and dichroic dye were used.Two kinds of louver filters are proposed: one is composed of a HAN-type LC film and a polarizer, and the other is composed of two HAN-type LC films with a half-wave plate between them.By using these louver LC filters, the light strength from the upper side can be reduced preferentially.This property is appropriate for sunglasses, windows in cars and buildings, and other applications.
Figure 1 .
Figure 1.Polymer film possessing an HAN-type LC structure.
Figure 1 .
Figure 1.Polymer film possessing an HAN-type LC structure.
Materials 2023 ,Figure 2 .
Figure 2. The structure of an optical filter using an HAN-type LC film and a polarizer, a mechanism for the dependence of the transmittance on the incident angle.
Figure 3 .Figure 4 Figure 2 .
Figure 3.The structure of an optical film using two HAN-type LC films and a half-wave p tween them.The LC alignment directions of the two HAN-type LC films are the same.Th between the LC alignment directions and the optical axis of the half-wave plate is set at 45 d
Figure 2 .
Figure 2. The structure of an optical filter using an HAN-type LC film and a polarizer, mechanism for the dependence of the transmittance on the incident angle.
Figure 4 .
Figure 4.The mechanism realizing the dependence of the transmittance on the incident angle when using the structure shown in Figure 3 [1].
Figure 4 .
Figure 4.The mechanism realizing the dependence of the transmittance on the incident angle when using the structure shown in Figure 3 [4].
Figure 5 .
Figure 5.The relationship between the LC monomer polar angle direction and the sign of the incident angle.
Figure 5 .
Figure 5.The relationship between the LC monomer polar angle direction and the sign of the incident angle.
Figure 6 .
Figure 6.Photographs of LC layers formed by spin coating: (a) low-pretilt-angle alignment la (dark area, irregular region; light area, regular region); (b) high-pretilt-angle alignment layer (d area, irregular region; light area, regular region).The arrow shows the direction of the rubb process.
Figure 6 .
Figure 6.Photographs of LC layers formed by spin coating: (a) low-pretilt-angle alignment layer (dark area, irregular region; light area, regular region); (b) high-pretilt-angle alignment layer (dark area, irregular region; light area, regular region).The arrow shows the direction of the rubbing process.
Figure 6 .
Figure 6.Photographs of LC layers formed by spin coating: (a) low-pretilt-angle alignment layer (dark area, irregular region; light area, regular region); (b) high-pretilt-angle alignment layer (dark area, irregular region; light area, regular region).The arrow shows the direction of the rubbing process.
Figure 7 .Figure 7 .
Figure 7.The dependence of the transmittance on the incident angle in regular and irregular regions (a) with a low-pretilt-angle alignment layer or (b) with a high-pretilt-angle alignment layer.
Figure 8 .
Figure 8.The LC molecular arrangements in a HAN-type LC film produced by spin coating with a low-pretilt-angle alignment layer (a) or with a high-pretilt-angle alignment layer (b).
Figure 8 .
Figure 8.The LC molecular arrangements in a HAN-type LC film produced by spin coating with a low-pretilt-angle alignment layer (a) or with a high-pretilt-angle alignment layer (b).
Materials 2023 , 17 Figure 9
Figure 9. Dependence of the transmittance on the incident angle using polarized light for HAN-type LC films on glass substrate (see Figures2 and 5).The HAN-type LC films were produced by spin coating.The dependence in the regular region is shown.The light wavelength was 550 nm.The film widths were 3.6 μm (1%), 4.2 μm (2%), 3.2 μm (3%), and 3.8 μm (5%).The pretilt angle of the alignment layer was 4 degrees.
is considered.For simplicity, the polar angle of the LC molecule is assumed to be 45 degrees.Incident angles of 45 degrees and −45 degrees are considered.By the Lambert-Beer law, the trans-
Materials 2023 ,Figure 11 .Figure 11 .
Figure 11.An LCD structure in which the polar angle of the LC molecule is a constant value of θ.The passing distances l+45 and l−45 for both incident angles are the same value, l. and are the absorption coefficients of polarized light vibrating parallel and perpendicular to the molecular long axis of the dye.The dependence of the transmittance on the
Materials 2023 , 17 Figure 12 .
Figure12.Dependence of the transmittance of HAN-type LC films, made using alignment layers with different pretilt angles, on the incident angle of polarized light (see Figures2 and 5).The concentration of the dichroic dye was 5%.
Figure 13 .Figure 13 . 17 Figure 14 .
Figure13.Dependence of the transmittance on the incident angle for a combination of two HAN-type LC films on glass substrates and a half-wave plate, shown in Figure3, and that for a single HAN-type LC film with a polarizer.The concentration of the dichroic dye was 1%.
Figure 14 .
Figure14.Dependence of the transmittance on the incident angle for a combination of two HAN-type LC films on PET substrates and a half-wave plate, shown in Figure3, and that for a single HAN-type LC film with polarizer.The concentration of the dichroic dye was 1%.
17 Figure 15 .Figure 15 .
Figure15.Dependence of the transmittance on the incident angle for a combination of two HAN-type LC films on glass substrates and a half-wave plate, shown in Figure3, and that for a single HAN-type LC film with a polarizer.The concentration of the dichroic dye was 5%.
Figure 17 .
Figure 17.Photographs of a white wall without a louver LC filter (a) and with a louver LC filter (b).The louver LC filter was composed of HAN-type LC film and a polarizer.
Figure 17 .
Figure 17.Photographs of a white wall without a louver LC filter (a) and with a louver LC filter (b).The louver LC filter was composed of HAN-type LC film and a polarizer.
Figure 17 .
Figure 17.Photographs of a white wall without a louver LC filter (a) and with a louver LC filter (b).The louver LC filter was composed of HAN-type LC film and a polarizer.
Figure 18 .
Figure 18.Photographs of scenery and a book without a louver LC filter (a) and with a louver LC filter (b).
Figure 18 .Figure 19 .
Figure 18.Photographs of scenery and a book without a louver LC filter (a) and with a louver LC filter (b).Materials 2023, 16, x FOR PEER REVIEW 15 of 17
Figure
Figure Photographs of a view from a high building without a louver LC filter (a) and with a louver LC filter (b). | 11,166.4 | 2023-08-01T00:00:00.000 | [
"Physics"
] |