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It is even possible to have cases in which an experiment's results differ when the potentials are changed, even if no charged particle is ever exposed to a different field. One such example is the Aharonov–Bohm effect, shown in the figure. In this example, turning on the solenoid only causes a magnetic field B to exist... | Wikipedia - Introduction to gauge theory | null | null | null |
If one believed that the fields were the fundamental quantities, then one would expect that the results of the experiment would be unchanged. In reality, the results are different, because turning on the solenoid changed the vector potential A in the region that the electrons do pass through. Now that it has been estab... | Wikipedia - Introduction to gauge theory | null | null | null |
It is evident from the Quran that Adam was the father of contemporary humanity,: 21 but if there was sentient life before him is debated. According to some views, God created thirty times an Adam every 1000 years. After the downfall of each humanity, God left the world uninhabited for 50.000 years, then 50.000 inhabite... | Wikipedia - Adam in Islam | null | null | null |
: 195 The majority of scholars, however, rejects this opinion, but they agree that the jinn and animals have lived on earth before. According to the Majallat Al Azhar, nowhere within Islamic texts it is prescribed how long humans existed and every Muslim is free to think that is right, and that the notion of a young ea... | Wikipedia - Adam in Islam | null | null | null |
It is expected that ICSEng includes sessions on the following themes: Machine Learning / AI BigData (Data Mining, Data Warehouses, Sensor Networks, Data Classification, Regression) Intelligent Systems (Expert Systems, Artificial Intelligence, Neural Network, Fuzzy, Optimization Techniques, Hybrid Systems, Applications)... | Wikipedia - International Conference on Systems Engineering | null | null | null |
It is expected that a necessary condition for f(T) to make sense is f be defined on the spectrum of T. For example, the spectral theorem for normal matrices states every normal matrix is unitarily diagonalizable. This leads to a definition of f(T) when T is normal. One encounters difficulties if f(λ) is not defined for... | Wikipedia - Holomorphic functional calculus | null | null | null |
This is indeed the case. As another example, for f ( z ) = 1 ( z − 2 ) ( z − 5 ) {\displaystyle f(z)={\frac {1}{(z-2)(z-5)}}} the reasonable way of calculating f(T) would seem to be f ( T ) = ( T − 2 I ) − 1 ( T − 5 I ) − 1 . {\displaystyle f(T)=(T-2I)^{-1}(T-5I)^{-1}.\,} However, this expression is not defined if the ... | Wikipedia - Holomorphic functional calculus | null | null | null |
It is found only in the Arctic biomes in the Russian Federation, and it is the most common mammal on Severnaya Zemlya. Specimens were once found in England, but they are now extirpated. For the most part, lemmings of the genus Lemmus can coexist with those of genus Dicrostonyx. Arctic lemmings migrate when population d... | Wikipedia - Arctic lemming | null | null | null |
The disappearance of lemmings and the lemming cycles in the Arctic have shown that they are the causes of fluctuations in local breeding among geese and waders. Recovery of lemmings after years of low density is associated with a period of successful breeding and maintenance of their young in the snow.The diet of the A... | Wikipedia - Arctic lemming | null | null | null |
It is found that the anti-inflammatory lipid lipoxin A4 is an endogenous allosteric enhancer of the CB1 cannabinoid receptor. Lipoxin A4 enhance the affinity of anandamide at this receptor to exert cannabimimetic effects in the brain, by allosterically enhancing AEA signaling and thereby potentiating the effects of thi... | Wikipedia - Lipoxin A4 | null | null | null |
It is found, that the naturally occurring cannabinoid compound delta-9-tetrahydrocannabinol (THC: C21H30O2), appearing in Cannabis, increase NO production in neonatal cardiac cells through the induction of the inducible nitric oxide synthase (iNOS) activity in a CB2 receptor dependent manner, while increasing endotheli... | Wikipedia - Biological functions of nitric oxide | null | null | null |
It is frequently helpful in mathematics to refer to the elements of an array using subscripts. The subscripts can be integers or variables. The array takes the form of tensors in general, since these can be treated as multi-dimensional arrays. | Wikipedia - Index notation | null | null | null |
Special (and more familiar) cases are vectors (1d arrays) and matrices (2d arrays). The following is only an introduction to the concept: index notation is used in more detail in mathematics (particularly in the representation and manipulation of tensor operations). See the main article for further details. | Wikipedia - Index notation | null | null | null |
It is frequently important to know how much of a particular resource (such as time or storage) is theoretically required for a given algorithm. Methods have been developed for the analysis of algorithms to obtain such quantitative answers (estimates); for example, an algorithm which adds up the elements of a list of n ... | Wikipedia - Algorithmic method | null | null | null |
Therefore, it is said to have a space requirement of O ( 1 ) {\displaystyle O(1)} , if the space required to store the input numbers is not counted, or O ( n ) {\displaystyle O(n)} if it is counted. Different algorithms may complete the same task with a different set of instructions in less or more time, space, or 'eff... | Wikipedia - Algorithmic method | null | null | null |
It is frequently useful or required to manipulate the data being backed up to optimize the backup process. These manipulations can improve backup speed, restore speed, data security, media usage and/or reduced bandwidth requirements. | Wikipedia - Backup and disaster recovery appliance | null | null | null |
It is further argued that the degree to which economic status and inheritance is transmitted across generations determines one's life chances in society. Although many have linked one's social origins and educational attainment to life chances and opportunities, education cannot serve as the most influential predictor ... | Wikipedia - Inheritance law | null | null | null |
Lower amounts of human capital and inheritance can perpetuate inequality in the housing market and higher education. Research reveals that inheritance plays an important role in the accumulation of housing wealth. Those who receive an inheritance are more likely to own a home than those who do not regardless of the siz... | Wikipedia - Inheritance law | null | null | null |
As a result, mixed races might be excluded in inheritance privilege and are more likely to rent homes or live in poorer neighborhoods, as well as achieve lower educational attainment compared with whites in America. Individuals with a substantial amount of wealth and inheritance often intermarry with others of the same... | Wikipedia - Inheritance law | null | null | null |
A New York Times article reveals that the U.S. is the world's wealthiest nation, but "ranks twenty-ninth in life expectancy, right behind Jordan and Bosnia" and "has the second highest mortality rate of the comparable OECD countries". | Wikipedia - Inheritance law | null | null | null |
This has been regarded as highly attributed to the significant gap of inheritance inequality in the country, although there are clearly other factors such as the affordability of healthcare. When social and economic inequalities centered on inheritance are perpetuated by major social institutions such as family, educat... | Wikipedia - Inheritance law | null | null | null |
It is generally accepted that the foundations of modern chronology were laid by the humanist Joseph Scaliger. Isaac Newton in his work The Chronology of Ancient Kingdoms made one of the first attempts to revise the "Scaligerian chronology". In the twentieth century the "revised chronology" of Immanuel Velikovsky can be... | Wikipedia - Historical revisionist | null | null | null |
At the same time, contemporary non-academic researchers often propose a more radical revision. For example, the model of chronology reconstruction of the revisionist Andrei Stepanenko reduces the entire known written history to several centuries. At the same time, other non-academic revisionists, thanks to publicly ava... | Wikipedia - Historical revisionist | null | null | null |
It is generally agreed that to be considered "causal", the association between a biological factor and a disease (or other bad outcome) should be biologically coherent. That is to say, it should be plausible and explicable biologically according to the known facts of the natural history and biology of the disease in qu... | Wikipedia - Biological plausibility | null | null | null |
However, Austin Bradford Hill himself de-emphasized "plausibility" among the other criteria: It will be helpful if the causation we suspect is biologically plausible. But this is a feature I am convinced we cannot demand. What is biologically plausible depends upon the biological knowledge of the day. | Wikipedia - Biological plausibility | null | null | null |
To quote again from my Alfred Watson Memorial Lecture , there was "…no biological knowledge to support (or to refute) Pott's observation in the 18th century of the excess of cancer in chimney sweeps. It was lack of biological knowledge in the 19th that led to a prize essayist writing on the value and the fallacy of sta... | Wikipedia - Biological plausibility | null | null | null |
It is generally assumed that any extraterrestrial life that might exist will be based on the same fundamental biochemistry as found on Earth, as the four elements most vital for life, carbon, hydrogen, oxygen, and nitrogen, are also the most common chemically reactive elements in the universe. Indeed, simple biogenic c... | Wikipedia - Potentially habitable exoplanet | null | null | null |
Carbon has an unparalleled ability to bond with itself and to form a massive array of intricate and varied structures, making it an ideal material for the complex mechanisms that form living cells. Hydrogen and oxygen, in the form of water, compose the solvent in which biological processes take place and in which the f... | Wikipedia - Potentially habitable exoplanet | null | null | null |
These four elements together make up amino acids, which in turn are the building blocks of proteins, the substance of living tissue. In addition, neither sulfur (required for the building of proteins) nor phosphorus (needed for the formation of DNA, RNA, and the adenosine phosphates essential to metabolism) are rare. R... | Wikipedia - Potentially habitable exoplanet | null | null | null |
This can be partly explained by the fact that many of these elements, such as hydrogen and nitrogen, along with their simplest and most common compounds, such as carbon dioxide, carbon monoxide, methane, ammonia, and water, are gaseous at warm temperatures. In the hot region close to the Sun, these volatile compounds c... | Wikipedia - Potentially habitable exoplanet | null | null | null |
Outgassing of volatile compounds through the first volcanoes would have contributed to the formation of the planets' atmospheres. The Miller–Urey experiment showed that, with the application of energy, simple inorganic compounds exposed to a primordial atmosphere can react to synthesize amino acids.Even so, volcanic ou... | Wikipedia - Potentially habitable exoplanet | null | null | null |
Comets impacting with the Earth in the Solar System's early years would have deposited vast amounts of water, along with the other volatile compounds life requires, onto the early Earth, providing a kick-start to the origin of life. Thus, while there is reason to suspect that the four "life elements" ought to be readil... | Wikipedia - Potentially habitable exoplanet | null | null | null |
It is generally considered that as more advanced computing systems for analysis of data are built, the higher the value of dark data will be. It has been noted that "data and analytics will be the foundation of the modern industrial revolution". Of course, this includes data that is currently considered "dark data" sin... | Wikipedia - Dark data | null | null | null |
Technology advancements are helping to leverage this dark data affordably, thanks to young and innovative companies such as Datumize, Veritas or Lucidworks. Furthermore, many organisations do not realise the value of dark data right now, for example in healthcare and education organisations deal with large amounts of d... | Wikipedia - Dark data | null | null | null |
It is generally not advisable to repair study specimens, except perhaps for mechanical damage. Type specimens should – if at all possible – not be altered in any way. If foxing affects the study value of a specimen (e.g. in bird or mammal skins or in insects, where it might affect diagnostic coloration), this might rat... | Wikipedia - Foxing | null | null | null |
It is generally thought that the presence of carbonates in rock is strong evidence for the presence of liquid water. Recent observations of the planetary nebula NGC 6302 show evidence for carbonates in space, where aqueous alteration similar to that on Earth is unlikely. Other minerals have been proposed which would fi... | Wikipedia - Carbonate ion | null | null | null |
It is generally well established that any quantum mechanical measurement can be reduced to a set of yes–no questions or bits that are either 1 or 0. RQM makes use of this fact to formulate the state of a quantum system (relative to a given observer!) in terms of the physical notion of information developed by Claude Sh... | Wikipedia - Relational quantum mechanics | null | null | null |
Any yes/no question can be described as a single bit of information. This should not be confused with the idea of a qubit from quantum information theory, because a qubit can be in a superposition of values, whilst the "questions" of RQM are ordinary binary variables. Any quantum measurement is fundamentally a physical... | Wikipedia - Relational quantum mechanics | null | null | null |
By extension, any physical interaction may be seen to be a form of quantum measurement, as all systems are seen as quantum systems in RQM. A physical interaction is seen as establishing a correlation between the system and the observer, and this correlation is what is described and predicted by the quantum formalism. B... | Wikipedia - Relational quantum mechanics | null | null | null |
It is hard to determine how widely OpenBSD is used, because the developers do not publish or collect usage statistics. In September 2005, the BSD Certification Group surveyed 4330 individual BSD users, showing that 32.8% used OpenBSD, behind FreeBSD with 77%, ahead of NetBSD with 16.3% and DragonFly BSD with 2.6%. Howe... | Wikipedia - OpenBSD | null | null | null |
It is hard to diagnose essential tremor and differentiate it from other types of tremor. The burst discharge patterns of EMG signals is compared to the frequency and amplitude of videotaped tremors to evaluate and diagnose essential tremor. | Wikipedia - Electrophysiological techniques for clinical diagnosis | null | null | null |
It is harder to see a trend in a noisy time series. For example, if the true series is 0, 1, 2, 3 all plus some independent normally distributed "noise" e of standard deviation E, and we have a sample series of length 50, then if E = 0.1 the trend will be obvious; if E = 100 the trend will probably be visible; but if E... | Wikipedia - Linear trend estimation | null | null | null |
It is helpful to find a layout of minimum size when designing a VLSI circuit. Such a problem can often be modeled as a graph embedding problem. The objective is to find an embedding for which the layout area is minimized. Finding the minimum layout area is also NP-hard. An approximation algorithm has been introduced an... | Wikipedia - Approximate max-flow min-cut theorem | null | null | null |
It is heterotrophic, obtaining nutrients externally instead of synthesizing them by an internal process such as photosynthesis. It is an omnivorous grazer, consuming various types of tiny organisms from its environment. It eats phytoplankton such as minute algaes. It has been observed eating Nannochloris oculata and Mi... | Wikipedia - Oxyrrhis marina | null | null | null |
It often eats the coccolithophore Cricosphaera elongata, and, in experimental situations, readily eats Tetraselmis suecica, Isochrysis galbana, and Rhodomonas sp. Some of these food items are relatively large, as large as the O. marina cell itself. | Wikipedia - Oxyrrhis marina | null | null | null |
It is selective in its grazing, showing clear preferences for certain food taxa. It can also pick certain individuals over others, as evidenced by its preference for virus-infected Emiliana huxleyi cells over healthy cells. It is cannibalistic, as well. | Wikipedia - Oxyrrhis marina | null | null | null |
It feeds by phagocytosis, totally engulfing its prey. It has been observed spinning one of its flagella in such a way that it creates a current, pulling the item closer so it can seize it. It is also raptorial, approaching and pouncing on the prey item, especially when the item is a protist. | Wikipedia - Oxyrrhis marina | null | null | null |
O. marina can sense and respond to certain chemicals that are exuded by algal prey.The locomotion of the O. marina cell is helical due to the simultaneous movement of its two flagella. It mostly swims in a straight line, but it makes turns when it detects food.In terms of reproduction, O. marina is isogamous, with repr... | Wikipedia - Oxyrrhis marina | null | null | null |
O. marina may also affect the environment by producing dimethyl sulfide, which is released when it grazes on some prey types, such as E. huxleyi.Predators of O. marina include protozoa such as the ciliate Strombidinopsis jeokjo, copepods such as Acartia tonsa and rotifers. The mixotrophic flagellate Prymnesium parvum i... | Wikipedia - Oxyrrhis marina | null | null | null |
It is hypothesized that introducing cognitive dissonance into machine learning may be able to assist in the long-term aim of developing 'creative autonomy' on the part of agents, including in multi-agent systems (such as games), and ultimately to the development of 'strong' forms of artificial intelligence, including a... | Wikipedia - Cognitive dissonance theory | null | null | null |
It is illegal for a practicing engineer to jeopardize public safety in any way. This means that an engineer must hold herself or himself to the highest level of technical and moral conduct reasonable or suffer litigation if an engineering system fails causing harm to the public, including maintenance technicians. Breac... | Wikipedia - Engineering law | null | null | null |
It is implicit in the above treatment that the data points are all given equal weight. Technically, the objective function U = ∑ i w i ( Y i − y i ) 2 {\displaystyle U=\sum _{i}w_{i}(Y_{i}-y_{i})^{2}} being minimized in the least-squares process has unit weights, wi = 1. When weights are not all the same the normal equ... | Wikipedia - Savitzky–Golay smoothing filter | null | null | null |
. , w m ) {\displaystyle W={\text{diag}}(w_{1},w_{2},...,w_{m})} , an analytical solution to the normal equations can be written down. For example, with a quadratic polynomial, J T W J = ( m ∑ w i ∑ w i z i ∑ w i z i 2 ∑ w i z i ∑ w i z i 2 ∑ w i z i 3 ∑ w i z i 2 ∑ w i z i 3 ∑ w i z i 4 ) {\displaystyle \mathbf {J^{T}... | Wikipedia - Savitzky–Golay smoothing filter | null | null | null |
A set of convolution coefficients may then be derived as C = ( J T W J ) − 1 J T W . {\displaystyle \mathbf {C} =\left(\mathbf {J^{T}W} \mathbf {J} \right)^{-1}\mathbf {J^{T}W} .} Alternatively the coefficients, C, could be calculated in a spreadsheet, employing a built-in matrix inversion routine to obtain the inverse... | Wikipedia - Savitzky–Golay smoothing filter | null | null | null |
This set of coefficients, once calculated and stored, can be used with all calculations in which the same weighting scheme applies. A different set of coefficients is needed for each different weighting scheme. It was shown that Savitzky–Golay filter can be improved by introducing weights that decrease at the ends of t... | Wikipedia - Savitzky–Golay smoothing filter | null | null | null |
It is important for the computer to be able to evaluate the value of the pieces on the board so it can assess whether or not a capture or exchange would be desirable. Assessing the relative value of pieces is an area of ongoing Arimaa research. Some currently used systems are DAPE and FAME. | Wikipedia - Computer Arimaa | null | null | null |
It is important physically that in general U ( ⋅ ) {\displaystyle U(\cdot )} does not have to be an ordinary representation of G {\displaystyle G} ; it may not be possible to choose the phase factors in the definition of U ( g ) {\displaystyle U(g)} to eliminate the phase factors in their composition law. An electron, ... | Wikipedia - Particle physics and representation theory | null | null | null |
Actually, if H {\displaystyle {\mathcal {H}}} is finite dimensional, then regardless of the group G {\displaystyle G} , every projective unitary representation of G {\displaystyle G} comes from an ordinary unitary representation of G ~ {\displaystyle {\tilde {G}}} . If H {\displaystyle {\mathcal {H}}} is infinite dimen... | Wikipedia - Particle physics and representation theory | null | null | null |
Fortunately, in the crucial case of the Poincaré group, Bargmann's theorem applies. (See Wigner's classification of the representations of the universal cover of the Poincaré group.) The requirement referred to above is that the Lie algebra g {\displaystyle {\mathfrak {g}}} does not admit a nontrivial one-dimensional c... | Wikipedia - Particle physics and representation theory | null | null | null |
This is the case if and only if the second cohomology group of g {\displaystyle {\mathfrak {g}}} is trivial. In this case, it may still be true that the group admits a central extension by a discrete group. But extensions of G {\displaystyle G} by discrete groups are covers of G {\displaystyle G} . | Wikipedia - Particle physics and representation theory | null | null | null |
For instance, the universal cover G ~ {\displaystyle {\tilde {G}}} is related to G {\displaystyle G} through the quotient G ≈ G ~ / Γ {\displaystyle G\approx {\tilde {G}}/\Gamma } with the central subgroup Γ {\displaystyle \Gamma } being the center of G ~ {\displaystyle {\tilde {G}}} itself, isomorphic to the fundament... | Wikipedia - Particle physics and representation theory | null | null | null |
It is important to assess current climate data and design in preparation of changes or threats to the environment. Resilience plans and passive design strategies can differ based on climates that are too hot. Here are general climate responsive design strategies based on three different climatic conditions: | Wikipedia - Resilience (engineering and construction) | null | null | null |
It is important to be aware that there are competing conventions regarding the "direction of the edges" in the Cuntz-Krieger relations. Throughout this article, and in the way that the relations are stated above, we use the convention first established in the seminal papers on graph C*-algebras. The alternate conventio... | Wikipedia - Graph C*-algebra | null | null | null |
It is important to distinguish the paradigm of a lexeme from a morphological pattern. In the context of an inflecting language, an inflectional morphological pattern is not the explicit list of inflected forms. A morphological pattern usually references a prototypical class of inflectional forms, e.g. ring as per sing.... | Wikipedia - Morphological pattern | null | null | null |
It is important to know that taxa lists derived by conventional (morphological) identification are not, and maybe never will be, directly comparable to taxa lists derived from barcode based identification because of several reasons. The most important cause is probably the incompleteness and lack of accuracy of the mol... | Wikipedia - Taxonomic resolution | null | null | null |
It is important to note that bcrypt is not a key derivation function (KDF). For example, bcrypt cannot be used to derive a 512-bit key from a password. At the same time, algorithms like pbkdf2, scrypt, and argon2 are password-based key derivation functions - where the output is then used for the purpose of password has... | Wikipedia - Bcrypt | null | null | null |
In this scenario, bcrypt is stronger than pbkdf2, scrypt, and argon2. PBKDF2: pbkdf2 is weaker than bcrypt. The commonly used SHA2 hashing algorithm is not memory-hard. | Wikipedia - Bcrypt | null | null | null |
SHA2 is designed to be extremely lightweight so it can run on lightweight devices (e.g. smart cards). This means PBKDF2 is very weak for password storage, as commodity SHA-2 hashing hardware that can perform trillions of hashes per second is easily procured scrypt: scrypt is weaker than bcrypt for memory requirements l... | Wikipedia - Bcrypt | null | null | null |
argon2: bcrypt is more lightweight than Argon2. This may pose a problem for some web applications where usage of Argon2 would require lowering the security parameters to an unacceptable level in order to still be performant. Specifically, Argon2 is less secure than bcrypt for run times less than 1 second (i.e., for com... | Wikipedia - Bcrypt | null | null | null |
Argon2 does not match or surpass bcrypt's strength until exceeding ~1000ms runtimes. This may be unsuitable for password hashing, but is perfectly acceptable for key-derivation. | Wikipedia - Bcrypt | null | null | null |
In some cases, Argon2 is recommended over bcrypt, if the security parameters are high enough. pufferfish2 is an evolution of bcrypt that uses a tunable memory footprint (like scrypt and argon2), rather than the fixed 4 KB memory footprint of bcrypt. Similar to scrypt or argon2, pufferfish2 gains its difficulty by using... | Wikipedia - Bcrypt | null | null | null |
Unlike scrypt and argon2, pufferfish2 only operates in a CPU core's L2 cache. While scrypt and argon2 gain their memory hardness by randomly accessing lots of RAM, pufferfish2 limits itself to just the dedicated L2 cache available to a CPU core. This makes it even harder to implement in custom hardware than scrypt and ... | Wikipedia - Bcrypt | null | null | null |
It is important to note that orthology relationships in public databases typically represent gene-level orthology and do not provide information concerning conserved alternative splice variants. Databases that contain and/or detect orthologous relationships include: | Wikipedia - Phylogenetic inference using transcriptomic data | null | null | null |
It is important to note that there are key trade-offs between VANs and Direct EDI, and in many instances, organizations exchanging EDI documents can in fact use both in concert, for different aspects of their EDI implementations. For example, in the U.S., the majority of EDI document exchanges use AS2, so a direct EDI ... | Wikipedia - Electronic Data Interchange | null | null | null |
Due to the fact that many organizations first starting out with EDI often do so to meet a customer or partner requirement and therefore lack in-house EDI expertise, a VAN can be a valuable asset. However, VANs may come with high costs. VANs typically charge a per-document or even per-line-item transaction fee to proces... | Wikipedia - Electronic Data Interchange | null | null | null |
This is the predominant reason why many organizations also implement an EDI software solution or eventually migrate to one for some or all of their EDI. On the other hand, implementing EDI software can be a challenging process, depending on the complexity of the use case, technologies involved and availability of EDI e... | Wikipedia - Electronic Data Interchange | null | null | null |
It is important to note that traditional database encryption techniques normally encrypt and decrypt the contents of a database. Databases are managed by "Database Management Systems" (DBMS) that run on top of an existing operating system (OS). This raises a potential security concern, as an encrypted database may be r... | Wikipedia - Database encryption | null | null | null |
EFS can encrypt data that is not part of a database system, which implies that the scope of encryption for EFS is much wider when compared to a system such as TDE that is only capable of encrypting database files. Whilst EFS does widen the scope of encryption, it also decreases database performance and can cause admini... | Wikipedia - Database encryption | null | null | null |
It is important to obtain some indication about how generalizable the results are. While this is often difficult to check, one can look at the stability of the results. Are the results reliable and reproducible? There are two main ways of doing that. | Wikipedia - Data Analytics | null | null | null |
Cross-validation. By splitting the data into multiple parts, we can check if an analysis (like a fitted model) based on one part of the data generalizes to another part of the data as well. Cross-validation is generally inappropriate, though, if there are correlations within the data, e.g. with panel data. | Wikipedia - Data Analytics | null | null | null |
Hence other methods of validation sometimes need to be used. For more on this topic, see statistical model validation. | Wikipedia - Data Analytics | null | null | null |
Sensitivity analysis. A procedure to study the behavior of a system or model when global parameters are (systematically) varied. One way to do that is via bootstrapping. | Wikipedia - Data Analytics | null | null | null |
It is instructive to first consider the time reversal symmetry pair of puzzles RBB and RRB. As it turns out, these two puzzles are the simplest to solve in that their recursive algorithms depend only one on the other, and not on other variations of the puzzle. In contrast, solutions for the semi-colored variations (whe... | Wikipedia - Magnetic Tower of Hanoi | null | null | null |
Next, it is assumed that the algorithms are optimal for n − 1, and using this assumption, it is shown that they are optimal for n. Beginning with the RBB(n) algorithm, it is clear that before disk 1 can be placed on the D post, it must first be on the S post (which is the only post colored Red), and the rest of the dis... | Wikipedia - Magnetic Tower of Hanoi | null | null | null |
Next, it is shown that from this state the final solution can only be reached via an intermediate state where all n − 1 disks are on the S post. For disk 2 to be placed on the D post, it must first be on the S post (the only Red post), while the other n − 2 disks must be on the I post. However, before disk 3 can be pla... | Wikipedia - Magnetic Tower of Hanoi | null | null | null |
This reasoning can proceed through all the disks, each of which must first be on the S post before passing to the I post, thus showing that the solution must pass through an intermediate state where all n − 1 disk are on the S post. To achieve this intermediate state, it is necessary to use an optimal algorithm which t... | Wikipedia - Magnetic Tower of Hanoi | null | null | null |
This of course is just the RBB(n − 1) algorithm. Similar reasoning can be applied to show that the RRB(n) algorithm above is optimal. Solving algorithms can also be written, and their optimality proved, for other time-reversal pairs of the puzzles, namely: The RBN and NRB pair The RNB and BNR pair The RNN and NNB pairT... | Wikipedia - Magnetic Tower of Hanoi | null | null | null |
Full details of these algorithms and proofs of their optimality can be found in.To conclude this section, the solving algorithm of the fully free NNN puzzle is listed. The proof of optimality can also be found in. Move the smallest n − 1 disk from S to I via D, using the RNN(n − 1) algorithm Move disk 1 from S to D. Mo... | Wikipedia - Magnetic Tower of Hanoi | null | null | null |
It is invariant to the imaging mode: which means, that it uses the same algorithm irrespective of the imaging mode present, whereas, frequency domain methods require changes depending on the mode and geometry. Ambiguous azimuth aliasing usually occurs when the Nyquist spatial sampling requirements are exceeded by frequ... | Wikipedia - Synthetic-aperture radar | null | null | null |
It matches the space/time filter: uses the information about the imaging geometry, to produce a pixel-by-pixel varying matched filter to approximate the expected return signal. This usually yields antenna gain compensation. With reference to the previous advantage, the back projection algorithm compensates for the moti... | Wikipedia - Synthetic-aperture radar | null | null | null |
It is known that the Strongly Connected Steiner Subgraph problem is W-hard parameterized by the number k {\displaystyle k} of terminals, and also does not admit an O ( log 2 − ε n ) {\displaystyle O(\log ^{2-\varepsilon }n)} -approximation in polynomial time (under standard complexity assumptions). However a 2-approx... | Wikipedia - Parameterized approximation algorithm | null | null | null |
It is known that the outer automorphism group for a simple Lie algebra g {\displaystyle {\mathfrak {g}}} is isomorphic to the group of diagram automorphisms for the corresponding Dynkin diagram in the classification of Lie algebras. The only algebras with non-trivial outer automorphism group are therefore A n ( n ≥ 2 )... | Wikipedia - Lie algebra automorphism | null | null | null |
It is known that the spectral mapping theorem holds for the polynomial functional calculus: for any polynomial p, σ(p(T)) = p(σ(T)). This can be extended to the holomorphic calculus. To show f(σ(T)) ⊂ σ(f(T)), let μ be any complex number. By a result from complex analysis, there exists a function g holomorphic on a nei... | Wikipedia - Holomorphic functional calculus | null | null | null |
{\displaystyle f(z)-f(\mu )=(z-\mu )g(z).\,} According to the homomorphism property, f(T) − f(μ) = (T − μ)g(T). Therefore, μ ∈ σ(T) implies f(μ) ∈ σ(f(T)). For the other inclusion, if μ is not in f(σ(T)), then the functional calculus is applicable to g ( z ) = 1 f ( z ) − μ . {\displaystyle g(z)={\frac {1}{f(z)-\mu }}.... | Wikipedia - Holomorphic functional calculus | null | null | null |
It is known to form mixed-species colonies. Other species that it will roost with include Dobson's horseshoe bat and the Pomona roundleaf bat. During January, individuals have been observed in a state of torpor. Their average generation time is 7.5 years. | Wikipedia - Andaman horseshoe bat | null | null | null |
It is known to produce the isoflavone irilone, and several analytical studies have been made from the rhizomes. | Wikipedia - Iris germanica | null | null | null |
It is lengthy process as the number of iterations m {\displaystyle m} in decoder algorithm takes is {\displaystyle } Zemor's decoding algorithm finds it difficult to decode erasures. A detailed way of how we can improve the algorithm isgiven in. | Wikipedia - Zemor's decoding algorithm | null | null | null |
It is less clear what purpose biominerals serve in bacteria. One hypothesis is that cells create them to avoid entombment by their own metabolic byproducts. Iron oxide particles may also enhance their metabolism. | Wikipedia - Biomineralization | null | null | null |
It is likely that Brazil has retained the technological capacity and knowhow to produce and deliver a nuclear weapon. Experts at the Los Alamos National Laboratory have concluded that in view of its previous nuclear activities, Brazil is in a position to produce nuclear weapons within three years. If Brazil decided to ... | Wikipedia - Brazil and weapons of mass destruction | null | null | null |
It is more generally possible to define the Heisenberg group of a locally compact abelian group K, equipped with a Haar measure. Such a group has a Pontrjagin dual K ^ {\displaystyle {\hat {K}}} , consisting of all continuous U ( 1 ) {\displaystyle U(1)} -valued characters on K, which is also a locally compact abelian ... | Wikipedia - Heisenberg group | null | null | null |
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