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New method to analyze complex networks
To study what happens or could happen in extremely complex networks, such as in a pandemic or in Internet interactions, it is useful to simplify the system to make it manageable and to be able to
analyze it.
But how can one find the right vantage point to understand at a glance the salient features of the whole without losing sight of relevant connections?
A team of physicists including Guido Caldarelli, corresponding author of the study and professor of theoretical physics at Ca’ Foscari University Venice, has found a method to efficiently and
effectively ‘simplify’ the complex structure of the network. The result has been published in Nature Physics and is thus available to the international scientific community.
The scholars took their cue from the technique that won U.S. physicist Kenneth G. Wilson a Nobel Prize in 1982. Wilson was able to find a theory that could explain how phase transitions, such as the
freezing of the surface of a lake or the formation of a traffic column of cars, work.
He invented the mathematical technique of the renormalization group, which allows one to exploit a symmetry of nature (large is similar to small) to predict the behavior of certain systems. Part of
this method involves rescaling the cells in which the system is defined with larger and larger cells. At each step we merge both the cells of the system and the variables that make up the system (as
in the figure where we have depicted a spin system).
The knowledge of the system once the series of amalgamations is finished is able to tell us how the original system behaves at large distances and toward which fixed points the evolution of the
system is headed.
But how do we get the same advantage when the system is not made up of cells like a spreadsheet, but of nodes and relationships between them as is the case in our brains with neurons, in contagion
between infected and susceptible individuals, or with interactions on social media?
In real systems very often, if not always, interactions are characterized by the presence of a complex structure of connections that makes them very difficult to analyze.
The knowledge of the system once we finish the series of unifications is able to tell us how the original system behaves at great distances and toward what fixed points the evolution of the system is
But how do we get the same advantage when the system is not made up of cells like a spreadsheet, but of nodes and relationships between them as is the case in our brains with neurons, in contagion
between infected and susceptible individuals, or with interactions on social media?
In real systems very often, if not always, interactions are characterized by the presence of a complex structure of connections that makes them very difficult to analyze.
“Directly inspired by ideas from statistical physics,” Caldarelli explains, “we introduced a new renormalization group procedure that has proven essential for efficiently and elegantly discovering
the organization at multiple scales of complex networks and for detecting scale invariant features when present. It also defines a universal network scaling procedure that is on the one hand very
useful for analyzing large data sets and on the other hand shows us one of the fundamental symmetries of nature.”
Future applications the team will work on include filtering of experimental data masses, exploration of material space, and representation of information from historical archives.
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Unit 7
1. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data setsfor which such a procedure is not
appropriate. Use calculators, spreadsheets, and tablesto estimate areas under the normal curve.
2. 6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the
context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
3. Understand statistics as a processfor making inferences about population parameters based on a random sample from that population.
4. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
5. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
6. . Evaluate reports based on data
7. Describe events as subsets of a sample space (the set of outcomes) using characteristics(or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” | {"url":"http://algebraii2016spring.weebly.com/unit-7.html","timestamp":"2024-11-05T09:08:01Z","content_type":"text/html","content_length":"21987","record_id":"<urn:uuid:7dd18e72-916f-4974-8ff8-94262ad1c47c>","cc-path":"CC-MAIN-2024-46/segments/1730477027878.78/warc/CC-MAIN-20241105083140-20241105113140-00718.warc.gz"} |
Learn Real Analysis from Terence Tao's Book: Download the Pd
Learn Real Analysis from Terence Tao's Book: Download the Pdf for Free and Solve 13 Challenging Questions
Terence Tao Analysis 1 Pdf Free 13 question piece patis
If you are interested in learning real analysis, one of the best books you can find is Analysis I by Terence Tao. This book covers all the major topics of analysis in a simple, lucid, and rigorous
manner. It also provides many exercises and proofs that challenge and enhance your understanding of the subject. In this article, we will show you how to get the pdf version of this book for free,
how to use it effectively, and how to solve some of the most interesting questions in the book.
Terence Tao Analysis 1 Pdf Free 13 question piece patis
Who is Terence Tao?
Terence Tao is an Australian mathematician who is widely regarded as one of the greatest living mathematicians. He has made significant contributions to various fields of mathematics, such as
harmonic analysis, partial differential equations, combinatorics, number theory, and more. He has won many prestigious awards, such as the Fields Medal, the MacArthur Fellowship, the Breakthrough
Prize in Mathematics, and the Crafoord Prize. He is currently a professor of mathematics at UCLA and has written several books and papers on various topics.
What is Analysis 1?
Analysis I is a textbook on real analysis written by Terence Tao. It is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The book discusses the
basics of analysis, such as the construction of the number systems, set theory, limits, series, continuity, differentiation, integration, and more. The book also has appendices on mathematical logic
and the decimal system. The book is part of a two-volume series, with Analysis II covering topics such as metric spaces, topology, Fourier analysis, and Lebesgue integration.
Why is it important to learn real analysis?
Real analysis is one of the core branches of mathematics that studies the properties and behavior of real numbers, functions, sequences, series, limits, continuity, differentiation, integration, and
more. It provides the foundation for many other areas of mathematics and applications in science and engineering. Learning real analysis helps you develop logical thinking, abstract reasoning, and
rigorous proof skills. It also helps you appreciate the beauty and elegance of mathematics.
How to get the pdf for free?
Download from SpringerLink
One of the easiest ways to get the pdf version of Analysis I for free is to download it from SpringerLink. SpringerLink is a platform that provides access to millions of books and journals in various
disciplines. You can find the book by searching for its title or ISBN (978-981-10-1789-6) on the website. You can also use this link: https://link.springer.com/book/10.1007/978-981-10-1789-6. You can
download the entire book or individual chapters as pdf files. You can also read the book online or print it for personal use.
Download from Google Sheets
Another way to get the pdf version of Analysis I for free is to download it from Google Sheets. Google Sheets is a web-based spreadsheet application that allows you to create and edit spreadsheets
online. You can find the pdf file of the book by searching for its title or author on Google Sheets. You can also use this link: https://docs.google.com/viewer?a=v&pid=sites&srcid=
aGNtdXMuZWR1LnZufGxraGF8Z3g6NDVlODAwYjVlYTg1YzhjYg. You can download the pdf file or view it online. You can also copy and paste the content into a new spreadsheet or document.
Download from other sources
There are also other sources where you can get the pdf version of Analysis I for free, such as library websites, academic websites, torrent sites, etc. However, you should be careful about the
quality and legality of these sources. Some of them may have incomplete, corrupted, or pirated copies of the book. Some of them may also contain viruses, malware, or spyware that can harm your
computer or device. Therefore, you should always check the credibility and reputation of these sources before downloading anything from them.
How to use the pdf effectively?
Read the preface and introduction carefully
Before you start reading the book, you should read the preface and introduction carefully. These sections will give you an overview of the book's purpose, scope, structure, style, and prerequisites.
They will also give you some tips and advice on how to study the book effectively. For example, you will learn that the book is divided into 11 chapters, each covering a major topic of analysis. You
will also learn that the book is deeply intertwined with the exercises, as it is intended that you actively learn the material by proving several of the key results in the theory.
Follow the exercises and proofs step by step
One of the best ways to use the book effectively is to follow the exercises and proofs step by step. The book provides many exercises and proofs that challenge and enhance your understanding of the
subject. You should try to solve the exercises and understand the proofs on your own before looking at the solutions or hints. You should also check your answers and reasoning carefully and compare
them with the ones given in the book or online. This will help you develop logical thinking, abstract reasoning, and rigorous proof skills.
Review the main concepts and results regularly
Another way to use the book effectively is to review the main concepts and results regularly. The book covers a lot of material and it is easy to forget some of the details or get confused by some of
the notation or terminology. Therefore, you should review the main concepts and results regularly to reinforce your memory and understanding. You can use various methods to review, such as making
notes, flashcards, summaries, diagrams, etc. You can also use online resources, such as videos, podcasts, blogs, etc., to supplement your review.
What are the 13 questions and how to solve them?
Question 1: Prove that there is no largest natural number
To prove that there is no largest natural number, we can use a method called proof by contradiction. This method involves assuming that the opposite of what we want to prove is true and then showing
that this leads to a contradiction or absurdity.
Question 2: Prove that every natural number has a unique prime factorization
To prove that every natural number has a unique prime factorization, we can use a method called induction. This method involves proving that a statement is true for a base case (usually the smallest
or simplest case) and then showing that if it is true for any case, it is also true for the next case.
So let us prove that every natural number n > 1 has a unique prime factorization. The base case is n = 2, which is already a prime number and has a unique prime factorization of 2. Now suppose that
the statement is true for some natural number k > 1, that is, k has a unique prime factorization of p1^a1 * p2^a2 * ... * pm^am, where p1, p2, ..., pm are distinct prime numbers and a1, a2, ..., am
are positive integers. We want to show that the statement is also true for k+1.
There are two possibilities for k+1: either it is a prime number or it is not. If it is a prime number, then it has a unique prime factorization of k+1. If it is not a prime number, then it must have
at least one prime divisor q. Then we can write k+1 = q * r, where r is another natural number. By the induction hypothesis, r has a unique prime factorization of q1^b1 * q2^b2 * ... * qn^bn, where
q1, q2, ..., qn are distinct prime numbers and b1, b2, ..., bn are positive integers. Then we can write the prime factorization of k+1 as q * q1^b1 * q2^b2 * ... * qn^bn. This factorization is unique
because if there were another factorization of k+1 as p1^c1 * p2^c2 * ... * pm^cm, where p1, p2, ..., pm are distinct prime numbers and c1, c2, ..., cm are positive integers, then we would have q =
p1 or q = p2 or ... or q = pm by the fundamental theorem of arithmetic. But this would imply that k+1 has two different prime divisors, which contradicts our assumption that q is the only prime
divisor of k+1. Therefore, k+1 has a unique prime factorization.
By induction, we have proved that every natural number n > 1 has a unique prime factorization.
Question 3: Prove that there are infinitely many prime numbers
To prove that there are infinitely many prime numbers, we can use a method called proof by contradiction. This method involves assuming that the opposite of what we want to prove is true and then
showing that this leads to a contradiction or absurdity.
So let us assume that there are only finitely many prime numbers p1, p2, ..., pn. Then we can form a new natural number N by multiplying all these primes and adding one: N = p1 * p2 * ... * pn + 1.
Then N must have at least one prime divisor q. But then q must be equal to one of the primes p1, p2, ..., pn by the fundamental theorem of arithmetic. But then q divides both N and p1 * p2 * ... *
pn, which implies that q also divides N - p1 * p2 * ... * pn = 1. But this is impossible because no prime number can divide 1. Therefore, our assumption must be false and there are infinitely many
prime numbers.
Question 4: Prove that the set of rational numbers is countable
To prove that the set of rational numbers is countable, we can use a method called diagonalization. This method involves arranging the elements of the set in an infinite table and then listing them
in a diagonal order.
So let us consider the set of rational numbers Q = a/b : a and b are integers and b 0. We can arrange them in an infinite table as follows:
0 0 0 0 ... --- --- --- --- --- --- 0 0/1 -0/1 0/-1 -0/-1 ... 0 1/1 -1/1 1/-1 -1/-1 ... 0 2/1 -2/1 2/-1 -2/-1 ... 0 3/1 -3/1 3/-1 -3/-1 ... ... ... ... ... ... ... We can then list the elements of Q
in a diagonal order as follows:
Q = 0/1, 1/1, -0/1, 0/-1, -1/1, 2/1, -2/1, 1/-1, -0/-1, -1/-1, 3/1, -3/1, 2/-1, -2/-1, 3/-1, -3/-1, ... --- This shows that we can assign a natural number to each element of Q and vice versa.
Therefore, Q is countable.
Question 5: Prove that the set of real numbers is uncountable
To prove that the set of real numbers is uncountable, we can use a method called Cantor's diagonal argument. This method involves assuming that the set is countable and then constructing an element
that is not in the set by changing the digits in the diagonal of an infinite table.
So let us assume that the set of real numbers R is countable. Then we can list them in an infinite table as follows:
R = r_0 = d_00.d_01d_02d_03..., r_1 = d_10.d_11d_12d_13..., r_2 = d_20.d_21d_22d_23..., r_3 = d_30.d_31d_32d_33..., ... --- where each d_ij is a digit from 0 to 9. We can then construct a new real
number s by changing the digits in the diagonal of the table as follows:
s = d'_0.d'_1d'_2d'_3... --- where each d'_i is a digit from 0 to 9 that is different from d_ii. For example, we can choose d'_i = (d_ii + 1) mod 10. Then s is a real number that is different from
every r_i in the table. For example, s differs from r_0 in the first decimal place, from r_1 in the second decimal place, from r_2 in the third decimal place, and so on. This contradicts our
assumption that R is countable and that every real number is in the table. Therefore, our assumption must be false and R is uncountable.
Question 6: Prove that every bounded sequence has a convergent subsequence
To prove that every bounded sequence has a convergent subsequence, we can use a method called Bolzano-Weierstrass theorem. This theorem states that every bounded sequence has a subsequence that
converges to some limit in the same bound.
So let us consider a bounded sequence (a_n)_n=0^. This means that there exist two real numbers L and U such that L a_n U for all n. We can divide the interval [L,U] into two equal subintervals [L,
(L+U)/2] and [(L+U)/2,U]. Then at least one of these subintervals must contain infinitely many terms of (a_n)_n=0^. We can choose one such subinterval and call it [L_0,U_0]. We can also choose one
term of (a_n)_n=0^ that belongs to this subinterval and call it a_n_0. Then we can repeat this process for [L_0,U_0] and obtain another subinterval [L_1,U_1] that contains infinitely many terms of
(a_n)_n=0^ and another term a_n_1 that belongs to this subinterval. We can continue this process indefinitely and obtain a sequence of nested subintervals [L_k,U_k] and a sequence of terms (a_n_k)_k=
0^ such that:
• L L_k a_n_k U_k U for all k
• [L_k+1,U_k+1] [L_k,U_k] for all k
Then we can claim that (a_n_k)_k=0^ is a subsequence of (a_n)_n=0^ that converges to some limit L* in [L,U]. To prove this, we need to show that for any ε > 0, there exists a natural number K such
that a_n_k - L*
a_n_k - L* a_n_k - L_k + L_k - L* U_k - L_k + L_k - L* (U-L)/2^k + L_k - L*
Now we need to show that L_k - L* can be made arbitrarily small as k increases. To do this, we can use the fact that [L_k,U_k] is a nested sequence of closed intervals whose lengths tend to zero. By
the nested interval property, this implies that there exists a unique real number L* such that L* [L_k,U_k] for all k. Then we have:
L_k - L* U_k - L_k = (U-L)/2^k
which can be made arbitrarily small as k increases. Therefore, we have proved that a_n_k - L*
Question 7: Prove that every continuous function on a closed interval is bounded
To prove that every continuous function on a closed interval is bounded, we can use a method called extreme value theorem. This theorem states that every continuous function on a closed interval
attains its maximum and minimum values on that interval.
So let us consider a continuous function f on a closed interval [a,b]. By the extreme value theorem, there exist two points c and d in [a,b] such that f(c) f(x) f(d) for all x in [a,b]. Then we can
define two real numbers M and m as follows:
M = f(d)
m = f(c)
Then we have m f(x) M for all x in [a,b]. This means that f is bounded by M and m on [a,b]. Therefore, every continuous function on a closed interval is bounded.
Question 8: Prove that every polynomial function of odd degree has at least one real root
To prove that every polynomial function of odd degree has at least one real root, we can use a method called intermediate value theorem. This theorem states that if a function is continuous on a
closed interval and takes different signs at the endpoints of the interval, then it must have at least one zero in the interval.
So let us consider a polynomial function of odd degree p(x) = a_n x^n + a_n-1 x^n-1 + ... + a_1 x + a_0, where n is odd and a_n 0. We want to show that p(x) has at least one real root. To do this, we
can consider the limits of p(x) as x tends to positive and negative infinity:
lim_(x+) p(x) = lim_(x+) (a_n x^n + a_n-1 x^n-1 + ... + a_1 x + a_0)
= lim_(x+) (x^n (a_n + a_n-1/x + ... + a_1/x^(n-1) + a_0/x^n))
= lim_(x+) (x^n) * lim_(x+) (a_n + a_n-1/x + ... + a_1/x^(n-1) + a_0/x^n)
= (+) * a_n
= (+) * sign(a_n)
Similarly, we have:
lim_(x-) p(x) = (-) * sign(a_n)
Since n is odd, sign(a_n) is either +1 or -1. This means that p(x) takes different signs as x tends to positive and negative infinity. Therefore, by the intermediate value theorem, there must exist a
real number c such that p(c) = 0. This means that c is a real root of p(x). Therefore, every polynomial function of odd degree has at least one real root.
Question 9: Prove that the derivative of a constant function is zero
To prove that the derivative of a constant function is zero, we can use the definition of the derivative. The derivative of a function f at a point x is defined as:
f'(x) = lim_(h0) (f(x+h) - f(x))/h
If f is a constant function, then f(x) = c for some constant c and for all x. Then we have:
f'(x) = lim_(h0) (f(x+h) - f(x))/h
= lim_(h0) (c - c)/h
= lim_(h0) 0/h
= 0
Therefore, the derivative of a constant function is zero.
Question 10: Prove that the derivative of a linear function is its slope
To prove that the derivative of a linear function is its slope, we can use the definition of the derivative. The derivative of a function f at a point x is defined as:
f'(x) = lim_(h0) (f(x+h) - f(x))/h
If f is a linear function, then f(x) = mx + b for some constants m and b and for all x. Then we have:
f'(x) = lim_(h0) (f(x+h) - f(x))/h
= lim_(h0) ((m(x+h) + b) - (mx + b))/h
= lim_(h0) (mh)/h
= lim_(h0) m
= m
Question 11: Prove that the derivative of a product of two functions is the product of their derivatives plus the product of their functions and their derivatives
To prove that the derivative of a product of two functions is the product of their derivatives plus the product of their functions and their derivatives, we can use the definition of the derivative
and some algebraic manipulation. The derivative of a function f at a point x is defined as:
f'(x) = lim_(h0) (f(x+h) - f(x))/h
If f and g are two functions, then their product is another function h defined as h(x) = f(x) * g(x). Then we have:
h'(x) = lim_(h0) (h(x+h) - h(x))/h
= lim_(h0) ((f(x+h) * g(x+h)) - (f(x) * g(x)))/h
= lim_(h0) ((f(x+h) * g(x+h)) - (f(x+h) * g(x)) + (f(x+h) * g(x)) - (f(x) * g(x)))/h
= lim_(h0) (f(x+h) * (g(x+h) - g(x)) + g(x) * (f(x+h) - f(x)))/h
= lim_(h0) (f(x+h)/h * (g(x+h) - g(x)) + g(x)/h * (f(x+h) - f(x)))
= lim_(h0) (f(x+h)/h * lim_(h0) (g(x+h) - g(x))) + lim_(h0) (g(x)/h * lim_(h0) (f(x+h) - f(x)))
= f'(x) * g'(x) + g(x) * f'(x)
Therefore, the derivative of a product of two functions is the product of their derivatives plus the product of their functions and their derivatives.
Question 12: Prove that the derivative of a quotient of two functions is the quotient of their derivatives minus the quotient of their functions and their derivatives divided by the square of the
denominator function
To prove that the derivative of a quotient of two functions is the quotient of their derivatives minus the quotient of their functions and their derivatives divided by the square of the denominator
function, we can use the definition of the derivative and some algebraic manipulation. The derivative of a function f at a point x is defined as:
f'(x) = lim_(h0) (f(x+h) - f(x))/h
If f and g are two functions, then their quotient is another function h defined as h(x) = f(x)/g(x). Then we have:
h'(x) = lim_(h0) (h(x+h) - h(x))/h
= lim_(h0) ((f(x+h)/g(x+h)) - (f(x)/g(x)))/h
= lim_(h0) (((f(x+h)*g(x)) - (f(x)*g(x+h)))/(g(x+h)*g(x)))/h
= lim_(h0) ((f(x+h)/h - f(x)/h) * g(x) - (g(x+h)/h - g(x)/h) * f(x))/(g(x+h)*g(x))
= lim_(h0) ((f(x+h)/h - f(x)/h)/h * lim_(h0) g(x) - (g(x+h)/h - g(x)/h)/h * lim_ | {"url":"https://www.newbrunswicksmokeshop.com/group/express-smoke-shop-group/discussion/bc991fad-934b-44a3-bb0e-e90a5db31c5e","timestamp":"2024-11-14T22:15:30Z","content_type":"text/html","content_length":"1050528","record_id":"<urn:uuid:af217259-7c7d-4d87-ab9c-c28cabfcfd54>","cc-path":"CC-MAIN-2024-46/segments/1730477395538.95/warc/CC-MAIN-20241114194152-20241114224152-00306.warc.gz"} |
Browse the glossary using this index
Sampling error
The degree to which a sample might differ from the population.
Sampling method
The process of selecting some part of a population to observe and to estimate something of interest about the whole population (ex: the abundance of a rare or endangered species in the population
might be estimated by the pattern of detections from a sample of sites taken in the study region). These methods assume that each member of the population has a known non-zero probability of being
selected (probability sampling methods). They include simple random sampling, systematic sampling, and stratified sampling. Sampling error, which is the degree to which a sample might differ from the
population, could be calculated and results are reported plus or minus the sampling error.
The levels or sizes at which particular ecological entities or processes are considered. One distinction that is often made is between local, regional and biogeographic scales.
Scientific data
Facts obtained by making observations and measurements.
Scientific hypothesis
Educated guesses that attempt to explain scientific observations or scientific laws. It is the first step in the scientific method.
Scientific method
The way scientists gather and evaluate information; it involves observations, hypothesis formulation and testing.
Scientific or natural laws
Description of what scientists find happening in nature repeatedly in the same way without known exceptions. See scientific theories.
Scientific theories
Well-tested and widely accepted explanations of data and laws.
Significance test
A statistical procedure that when applied to a set of observations results in a probability value (p-value) relative to some hypothesis. Examples: Student’s t test, Wilcoxon’s test.
Simple random sampling
It considers that each member of the population has an equal and known chance of being selected by random sampling. This is mainly true for very large populations. | {"url":"https://medregion.scientificgame.unisalento.it/mod/glossary/view.php?id=147&mode=letter&hook=S&sortkey=&sortorder=asc","timestamp":"2024-11-07T11:57:42Z","content_type":"text/html","content_length":"46759","record_id":"<urn:uuid:225cd86f-ff89-4997-a527-30a338352e35>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00702.warc.gz"} |
Re: Dielectric constant of water from MSM and PME simulations
Re: Dielectric constant of water from MSM and PME simulations
On Fri, Oct 23, 2015 at 9:57 AM, Mattia Felice Palermo <
mattiafelice.palerm2_at_unibo.it> wrote:
> Dear Zhe,
> thank you very much for your accurate answer.
> > Could you specify how you calculate the dielectric constant?
> It has been computed with a inhouse program using the classical
> expression for the dielectric constant from the average dipole moment
> <M^2> as in your JCTC paper.
> > The dielectric constant of TIP3P-EW water is 89 (D. J. Price, C. L.
> > Brooks, J. Chem. Phys. 2004, 121, 10096), while you are getting 96.8
> > with PME and 83.3 with MSM. You can find the way we calculated the
> > dielectric constant on page 773 of our JCTC paper.
> We suspect that the higher value found in our simulation with PME might
> be related to the size of the sample (N=1000 in the TIP3P-EW original
> paper against N=11000 in our simulations). However the value is not far
> from the literature value of 89 (TIP3P-EW, model B) and from the
> value of 104 reported in your JCTC paper. We also checked other
> properties e.g. the oxygen-oxygen radial distribution function and
> the average module of the molecular dipole moment, and they are in
> agreement with the expected results for the model.
dear mattia,
some comments on this subject. it has been a long time, since i worked on
dielectric properties of water as a graduate student and later got a chance
to do some follow-up work in my spare time.
for your reference, please have a look at pages 18-21 of
the following points matter for computing the static dielectric constant
from dipolar fluctuations (NOTE: not the average but the fluctuations) :
- it is a *local* property. system size has very little to no impact. when
you sit down derive the expression of the fluctuation formula, you will
quickly see that the number of molecules will cancel out.
- it is a *slowly* converging property. most published data is simply not
fully converged.
- it is of monumental importance to use the correct fluctuation formula.
most likely you have used the one for ewald summation with conducting
boundary condition. in that case what you are simulating is effectively an
infinitely large sphere assembled from rectangular unit cells embedded in a
conducting dielectric (epsilon = infinity). i seriously doubt that this is
applicable to MSM. it would be more likely, that you need to derive the
fluctuation formula for a situation where epsilon is equal to the computed
epsilon. but don't take my word for it. these issues are extremely subtle
and i had to twist my brain quite hard for months to finally get a grip on
it and come up with consistent and convincing explanations for the
observations from my simulations.
on the notion of g(r) being reproduced. that means *nothing*. you need to
get them right, too. but with the same g(r) you can have very different
total system dipole fluctuations. the conducting boundary conditions of
commonly used ewald summation (and equivalent) actually enhances
fluctuations. if you switch to a vacuum embedding (epsilon = 0), then those
total dipole fluctuations are strongly suppressed, yet you can't tell a
difference from the g(r), as the average structure is practically
unaffected (you are looking at the second moment, after all, and the
average cancels out).
> > It is very surprising to see a dielectric constant of water to be
> > 258. How is the water structure? With such a large dielectric
> > constant, the water structure should be very unphysical.
> The first surprising fact is that the dielectric constant of bulk
> water differs if the MD simulations is carried out with PME and MSM
> methods. The dielectric constant of water with value 258 was obtained
> for a thin film of water supported on silicon dioxide and using the
> MSM method, while when using the PME method we obtain a dielectric constant
> of 91.5. Visual inspection of the samples through VMD did not show any
> unphysical structure of the water. We also computed the oxygen-oxygen
> radial distribution g(r)_O-O for the films, which you can find attached,
> and
> it does not show any significant difference between the two simulations.
based on my observations outlined above, i am not surprised. and more
importantly, you cannot easily transfer the method to other simulation
environments. you will need to derive the proper fluctuation formula for
such a situation as well..
> > Also, could you give us a little bit more details about your VDW
> > cutoff scheme? As reported in TIP3P-EW’s original paper, a model
> > that incorporates a long-range correction for truncated VDW will
> > give a dielectric constant of 76 instead of 89. Are you using the
> > same cutoff scheme for both PME and MSM?
> Yes we used the same cutoff scheme for both simulations. More in detail,
> these are the settings for the MSM simulations:
> cutoff 12.0
> switching on
> switchdist 10.0
> pairlistdist 14.0
> timestep 2.0
> nonbondedFreq 1
> fullElectFrequency 2
> stepspercycle 10
> langevin on
> langevinDamping 1
> langevinTemp 298.15
> LangevinPiston on
> LangevinPistonTarget 1.01325
> LangevinPistonPeriod 250
> LangevinPistonDecay 100
> LangevinPistonTemp 298.15
> cellBasisVector1 63.340 0.0 0.0
> cellBasisVector2 0.0 63.340 0.0
> cellBasisVector3 0.0 0.0 63.340
> rigidBonds all
> MSM yes
> The same setting were used for the PME simulations, except of course for
> the calculation of electrostatics:
> PME yes
> PMEGridSpacing 1.5
> Thank you very much for your help!
> P.s.: I changed the subject of this email to have all future
> contributions sorted in the same thread. Sorry for the confusion!
> --
> Mattia Felice Palermo - Ph.D.
> Università di Bologna
> Dipartimento di Chimica Industriale "Toso Montanari"
Dr. Axel Kohlmeyer akohlmey_at_gmail.com http://goo.gl/1wk0
College of Science & Technology, Temple University, Philadelphia PA, USA
International Centre for Theoretical Physics, Trieste. Italy.
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Perspectives on Black Holes: Astrophysical, Geometric, and Beyond General Relativity
2022 Theses Doctoral
Perspectives on Black Holes: Astrophysical, Geometric, and Beyond General Relativity
In this thesis, we consider three aspects of black holes. First, we examine a black hole boosted through a uniform magnetic field. We find that it can acquire an electric charge, just as a spinning
black hole in an ambient magnetic field can, though the gravito-electrodynamics upstage naive arguments about screening electric fields in determining the value of the charge accrued. We study the
chaotic behavior of the charged particles via their fractal basin boundaries.
Second, we study the vanishing of Love numbers for black holes from a geometric perspective and connect it to the existence of quasinormal modes in de Sitter space. Behind each phenomenon is a ladder
structure with a geometric/representation-theoretic origin which makes it possible to connect the asymptotic behavior of solutions at different boundaries.
Third, we model the formation of a black hole in dRGT massive gravity in a de Sitter background with a collapsing homogeneous and pressureless ball of dust or ``star''. We focus on several choices of
parameters corresponding to models of interest. We compute the position of the apparent horizon where it crosses the surface of the star, the Ricci curvature at the boundary, and the finite
correction to the curvature of the apparent horizon due to the graviton mass. We argue that our collapsing solutions cannot be matched to a static, spherically symmetric vacuum solution at the star's
surface, providing further evidence that physical black hole solutions in massive gravity are likely time-dependent.
• Berens_columbia_0054D_17624.pdf application/pdf 1.26 MB Download File
More About This Work
Academic Units
Thesis Advisors
Rosen, Rachel A.
Ph.D., Columbia University
Published Here
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Core JavaScript Guide 1.5: 6 Functions
Chapter 6 Functions
Functions are one of the fundamental building blocks in JavaScript. A function is a JavaScript procedure—a set of statements that performs a specific task. To use a function, you must first
define it; then your script can call it.
This chapter contains the following sections:
Defining Functions
A function definition consists of the function keyword, followed by
□ The JavaScript statements that define the function, enclosed in curly braces, { }. The statements in a function can include calls to other functions defined in the current application.
For example, the following code defines a simple function named square:
function square(number) {
return number * number;
The function square takes one argument, called number. The function consists of one statement that indicates to return the argument of the function multiplied by itself. The return statement
specifies the value returned by the function.
All parameters are passed to functions by value; the value is passed to the function, but if the function changes the value of the parameter, this change is not reflected globally or in the
calling function. However, if you pass an object as a parameter to a function and the function changes the object's properties, that change is visible outside the function, as shown in the
following example:
function myFunc(theObject) {
mycar = {make:"Honda", model:"Accord", year:1998};
x=mycar.make; // returns Honda
myFunc(mycar); // pass object mycar to the function
y=mycar.make; // returns Toyota (prop was changed by the function)
A function can be defined based on a condition. For example, given the following function definition:
if (num == 0)
function myFunc(theObject) {
the myFunc function is only defined if the variable num equals 0. If num does not equal 0, the function is not defined, and any attempt to execute it will fail.
In addition to defining functions as described here, you can also define Function objects, as described in "Function Object" on page 106.
A method is a function associated with an object. You'll learn more about objects and methods in Chapter 7, "Working with Objects."
A function can also be defined inside an expression. This is called a function expression. Typically such a function is anonymous; it does not have to have a name. For example, the function
square could have been defined as:
const square = function(number) {return number * number};
This is convenient when passing a function as an argument to another function. The following example shows the map function being defined and then called with an anonymous function as its first
function map(f,a) {
var result=new Array;
for (var i = 0; i != a.length; i++)
result[i] = f(a[i]);
return result;
map(function(x) {return x * x * x}, [0, 1, 2, 5, 10];
Defining a function does not execute it. Defining the function simply names the function and specifies what to do when the function is called. Calling the function actually performs the specified
actions with the indicated parameters. For example, if you define the function square, you could call it as follows.
The preceding statement calls the function with an argument of five. The function executes its statements and returns the value twenty-five.
The arguments of a function are not limited to strings and numbers. You can pass whole objects to a function, too. The show_props function (defined in "Objects and Properties" on page 91) is an
example of a function that takes an object as an argument.
A function can even be recursive, that is, it can call itself. For example, here is a function that computes factorials:
function factorial(n) {
if ((n == 0) || (n == 1))
return 1
else {
var result = (n * factorial(n-1) );
return result
You could then compute the factorials of one through five as follows:
a=factorial(1) // returns 1
b=factorial(2) // returns 2
c=factorial(3) // returns 6
d=factorial(4) // returns 24
e=factorial(5) // returns 120
The arguments of a function are maintained in an array. Within a function, you can address the arguments passed to it as follows:
where i is the ordinal number of the argument, starting at zero. So, the first argument passed to a function would be arguments[0]. The total number of arguments is indicated by arguments.length.
Using the arguments array, you can call a function with more arguments than it is formally declared to accept. This is often useful if you don't know in advance how many arguments will be passed
to the function. You can use arguments.length to determine the number of arguments actually passed to the function, and then treat each argument using the arguments array.
For example, consider a function that concatenates several strings. The only formal argument for the function is a string that specifies the characters that separate the items to concatenate. The
function is defined as follows:
function myConcat(separator) {
var result="" // initialize list
// iterate through arguments
for (var i=1; i<arguments.length; i++) {
result += arguments[i] + separator
return result
You can pass any number of arguments to this function, and it creates a list using each argument as an item in the list.
// returns "red, orange, blue, "
myConcat(", ","red","orange","blue")
// returns "elephant; giraffe; lion; cheetah; "
myConcat("; ","elephant","giraffe","lion", "cheetah")
// returns "sage. basil. oregano. pepper. parsley. "
myConcat(". ","sage","basil","oregano", "pepper", "parsley")
See the Function object in the Core JavaScript Reference for more information.
JavaScript 1.3 and earlier versions. The arguments array is a property of the Function object and can be preceded by the function name, as follows:
JavaScript has several top-level predefined functions:
□ encodeURI, decodeURI, encodeURIComponent, and decodeURIComponent (all available with Javascript 1.5 and later).
The following sections introduce these functions. See the Core JavaScript Reference for detailed information on all of these functions.
eval Function
The eval function evaluates a string of JavaScript code without reference to a particular object. The syntax of eval is:
where expr is a string to be evaluated.
If the string represents an expression, eval evaluates the expression. If the argument represents one or more JavaScript statements, eval performs the statements. Do not call eval to evaluate an
arithmetic expression; JavaScript evaluates arithmetic expressions automatically.
isFinite Function
The isFinite function evaluates an argument to determine whether it is a finite number. The syntax of isFinite is:
where number is the number to evaluate.
If the argument is NaN, positive infinity or negative infinity, this method returns false, otherwise it returns true.
The following code checks client input to determine whether it is a finite number.
if(isFinite(ClientInput) == true)
/* take specific steps */
isNaN Function
The isNaN function evaluates an argument to determine if it is "NaN" (not a number). The syntax of isNaN is:
where testValue is the value you want to evaluate.
The parseFloat and parseInt functions return "NaN" when they evaluate a value that is not a number. isNaN returns true if passed "NaN," and false otherwise.
The following code evaluates floatValue to determine if it is a number and then calls a procedure accordingly:
if (isNaN(floatValue)) {
} else {
parseInt and parseFloat Functions
The two "parse" functions, parseInt and parseFloat, return a numeric value when given a string as an argument.
where parseFloat parses its argument, the string str, and attempts to return a floating-point number. If it encounters a character other than a sign (+ or -), a numeral (0-9), a decimal point, or
an exponent, then it returns the value up to that point and ignores that character and all succeeding characters. If the first character cannot be converted to a number, it returns "NaN" (not a
parseInt parses its first argument, the string str, and attempts to return an integer of the specified radix (base), indicated by the second, optional argument, radix. For example, a radix of ten
indicates to convert to a decimal number, eight octal, sixteen hexadecimal, and so on. For radixes above ten, the letters of the alphabet indicate numerals greater than nine. For example, for
hexadecimal numbers (base 16), A through F are used.
If parseInt encounters a character that is not a numeral in the specified radix, it ignores it and all succeeding characters and returns the integer value parsed up to that point. If the first
character cannot be converted to a number in the specified radix, it returns "NaN." The parseInt function truncates the string to integer values.
Number and String Functions
The Number and String functions let you convert an object to a number or a string. The syntax of these functions is:
where objRef is an object reference.
The following example converts the Date object to a readable string.
D = new Date (430054663215)
// The following returns
// "Thu Aug 18 04:37:43 GMT-0700 (Pacific Daylight Time) 1983"
x = String(D)
escape and unescape Functions
The escape and unescape functions let you encode and decode strings. The escape function returns the hexadecimal encoding of an argument in the ISO Latin character set. The unescape function
returns the ASCII string for the specified hexadecimal encoding value.
The syntax of these functions is:
These functions are used primarily with server-side JavaScript to encode and decode name/value pairs in URLs.
The escape and unescape functions do not work properly for non-ASCII characters and have been deprecated. In JavaScript 1.5 and later, use encodeURI, decodeURI, encodeURIComponent, and | {"url":"https://docs.huihoo.com/javascript/CoreGuideJS15/fcns.html","timestamp":"2024-11-12T02:18:48Z","content_type":"text/html","content_length":"45966","record_id":"<urn:uuid:b0b57191-9577-493f-b38d-7e868b7178d8>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.50/warc/CC-MAIN-20241112014152-20241112044152-00877.warc.gz"} |
Papel Semilogaritmico 4 Ciclos Pdf 25 Extra Quality | Change22
Papel Semilogaritmico 4 Ciclos Pdf 25 Extra Quality
LINK >> https://fancli.com/2tyL8A
What is Papel Semilogaritmico and How to Use It?
Papel semilogaritmico is a type of graph paper that has one axis with a logarithmic scale and another axis with a linear scale. It is used to plot data that has a wide range of values or that follows
an exponential or power law. For example, it can be used to plot the decay of radioactive substances, the growth of bacteria, or the response of electronic circuits.
Papel semilogaritmico can have different numbers of cycles on the logarithmic axis, depending on the range of values to be plotted. Each cycle represents a factor of 10 in the scale. For instance,
papel semilogaritmico 4 ciclos has four cycles on the logarithmic axis, meaning that it can plot data that spans four orders of magnitude.
To use papel semilogaritmico, you need to convert the data values on the logarithmic axis to their corresponding logarithms. For example, if you want to plot the value 1000 on the logarithmic axis,
you need to find its logarithm base 10, which is 3. Then you locate the point on the graph paper that corresponds to 3 on the logarithmic axis and 1000 on the linear axis. You can use a calculator or
a table of logarithms to find the logarithms of your data values.
Papel semilogaritmico 4 ciclos pdf 25 is a file name that suggests a pdf document containing papel semilogaritmico with four cycles on the logarithmic axis and 25 divisions on the linear axis. You
can download such a document from various online sources[^1^] [^2^] [^3^] or create your own using software tools.
Papel semilogaritmico is a useful tool for analyzing data that has a nonlinear relationship or that covers a wide range of values. It can help you visualize trends, patterns, and outliers in your
data and compare different data sets more easily.
Examples of Data Plotted on Papel Semilogaritmico
There are many examples of data that can be plotted on papel semilogaritmico to reveal patterns, trends, and relationships that may not be obvious on a linear scale. Here are some of them:
Phase diagram of water: A phase diagram shows the state of matter (solid, liquid, or gas) of a substance at different combinations of temperature and pressure. The phase diagram of water has a
logarithmic scale on the pressure axis and a linear scale on the temperature axis. This allows us to see the different regions where water exists as ice, liquid, or vapor, as well as the points where
phase transitions occur. For example, we can see that water boils at 100°C at normal atmospheric pressure (about 0.1 MPa), but at lower temperatures at higher altitudes (lower pressures). We can
also see that water can exist as a supercritical fluid above a certain critical point (374°C and 22.1 MPa), where there is no distinction between liquid and gas.
2009 "swine flu" progression: A semi-log plot can be used to track the progression of an epidemic or pandemic, such as the 2009 outbreak of H1N1 influenza (commonly known as "swine flu"). The plot
shows the cumulative number of confirmed cases or deaths on the logarithmic axis and the date on the linear axis. This allows us to see how fast the disease is spreading and whether it is following
an exponential growth curve or leveling off. For example, we can see that the 2009 swine flu pandemic had an initial exponential growth phase from April to June 2009, followed by a slower growth
phase until October 2009, when it reached its peak. The plot also shows the effect of interventions such as social distancing, vaccination, and antiviral drugs on slowing down or stopping the spread
of the disease.
Microbial growth: A semi-log plot can also be used to model the growth of bacteria or other microbes in a culture medium. The plot shows the number or mass of microbes on the logarithmic axis and the
time on the linear axis. This allows us to see the different phases of microbial growth: lag phase (when the microbes are adapting to the environment and preparing for division), exponential phase
(when the microbes are dividing rapidly), stationary phase (when the growth rate is balanced by the death rate due to nutrient depletion or waste accumulation), and death phase (when the death rate
exceeds the growth rate). The plot also shows how different factors such as temperature, pH, oxygen level, or antibiotics can affect the growth rate and duration of each phase. 061ffe29dd | {"url":"https://www.change22.com/forum/military-apparel-requests/papel-semilogaritmico-4-ciclos-pdf-25-extra-quality","timestamp":"2024-11-12T17:02:21Z","content_type":"text/html","content_length":"920627","record_id":"<urn:uuid:1f98f4d2-0e2e-405c-95c2-84ad5c47ac06>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00460.warc.gz"} |
Random Password Strength
Random passwords can be generated manually using everyday sources of randomness such as coins or dice. They can also be generated using a computer. However, using software to generate random
passwords is non trivial and requires a cryptographically strong pseudo random number generator. Also, just because a password is random, doesn't guarantee it's a strong password; it is possible,
although unlikely, that an easily guessable password is generated. If a weak password, such as a dictionary word or date, is generated it should be rejected.
Given a strong random password, how many attempts would it take an attacker to guess it? How do we calculate and specify the strength of such a password? In order to answer these questions we will
start by considering something called entropy.
In IT security, password entropy is the amount of randomness in a password or how difficult it is to guess. The entropy of a password is typically stated in terms of bits. For example, a known
password has zero bits of entropy, while a password with 1 bit of entropy would be guessed on the first attempt 50% of the time. A password with n bits of entropy would be as difficult to guess as an
n bit random quantity. Stated more generally, a password with n bits of entropy can be found in [2]^n attempts.
It was the mathematician Claude Shannon who first used the term entropy in information theory.
Calculating the entropy of a password
The entropy of a randomly selected password is based on its length and the entropy of each character. The entropy of each character is given by log-base-2 the size of the pool of characters the
password is selected from - see the formula below:
entropy per character = log[2](n)
password entropy = l * entropy per character
Where n is the pool size of characters and l is the length of the password.
Thus the entropy of a character selected at random from, say, the letters (a-z) would be log[2]26 or 4.7 bits. The table below gives the entropy per character for a number of different sized
character pools.
Table 1. Entropy Per Character for Character Pools
Character Pool Available Characters (n) Entropy Per Character
digits 10 (0-9) 3.32 bits
lower-case letters 26 (a-z) 4.7 bits
case sensitive letters and digits 62 (A-Z, a-z,0-9) 5.95 bits
all standard keyboard characters 94 6.55 bits
So, from the table above, we can see that a 20 character password chosen at random from the keyboard's set of 94 printable characters would have more than 128 bits (6.55 * 20) of entropy. A password
with this much entropy is infeasible to break by brute force (exhaustively working through all possible character combinations).
We can see how both the pool size of available characters and the password length affect the strength of the password; and that long random passwords are extremely strong. While these types of
passwords may be used by, say, one computer to authenticate to another computer, they are not much use to humans. Humans are notoriously bad at remembering passwords. A difficult to remember password
will have an adverse effect on security because the user will need to write it down somewhere - typically on a Post-it Note near to their computer.
User selected passwords
For many situations, a random password is not a practical approach and it is better to ask the user to select a memorable password that meets a number of criteria designed to increase the entropy of
the password. Below are some recommendations from NIST for passwords that are used to authenticate a user.
NIST estimate the following criteria for a user selected password yields 30 bits of entropy:
• a minimum of 8 characters, selected by users from an alphabet of 94 printable characters,
• should include at least one upper case letter, one lower case letter, one number and one special character,
• a dictionary is used to prevent users from including common words and
• permutations of the username as a password are prevented.
NIST recommend these password criteria are combined with mechanisms to mitigate against dictionary and brute force attacks and that passwords are changed on a regular basis.
Note the above recommendations are one example and it is important to examine your own security requirements carefully before deciding on a suitable password policy.
We welcome your feedback and/or corrections to this article.
Phil Ratcliffe: [email protected]
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Machine learning-based modeling of Syrian agricultural GDP trends: A comparative analysisMachine learning-based modeling of Syrian agricultural GDP trends: A comparative analysis | E-NAMTILA
Machine learning-based modeling of Syrian agricultural GDP trends: A comparative analysis
Khder Alakkari ^1*
1, Department of Statistics and Programming, Faculty of Economics, Tishreen University, Latakia, P.O. Box 2230, Syria
Manuscript link
This research examined the effectiveness of Autoregressive Integrated Moving Average (ARIMA), Neural Network Autoregressive (NNAR), and eXtreme Gradient Boosting (XGBoost) models in nowcasting and
forecasting the agricultural GDP of Syria, utilizing delayed time series data spanning from 1963 to 2022. The aim was to determine the most appropriate model for accurately representing the intrinsic
complexities and delays present in the data. The approach included an examination of descriptive statistics, autocorrelation functions, and the execution of stationarity tests. The evaluation of
model performance was conducted through the use of RMSE, MSE, and MAPE metrics. The findings revealed that the NNAR (3,2) model surpassed both ARIMA and XGBoost, showing the lowest error metrics and
illustrating its capacity to effectively capture non-linear relationships within the agricultural GDP series. The exceptional performance observed can be ascribed to the NNAR model’s adaptable
framework, which integrates autoregressive elements with neural networks. Projections extending to 2030, produced through the NNAR model, indicated a possible decrease in agricultural GDP,
underscoring the difficulties faced by the Syrian agricultural sector. The research suggests the necessity of ongoing monitoring, regular data updates, and additional analysis to enhance these
forecasts and guide strategies for the sector’s recovery and growth. It is essential to address the issue of delayed data publication by the Syrian Central Bureau of Statistics to improve the
timeliness and accuracy of future economic analyses and forecasts.
Keywords: GDP, Agricultural, Nowcasting, Forecasting, NNAR, Machine Learning
Agriculture Gross Domestic Product GDP, a crucial economic metric, denotes the aggregate value of products and services generated by a nation’s agriculture industry. This data is fundamentally a time
series, displaying patterns, seasonality, and volatility affected by climate change, technological progress, and governmental actions. Managing delayed time series creates additional complexity by
creating latencies between event occurrence and observation, hence affecting the precision of both nowcasting and forecasting. Analyzing and forecasting agricultural GDP amidst delays necessitates
advanced methodologies adept at managing and elucidating non-stationarity intricate connections within the data.
Time series analysis is essential for comprehending and forecasting the behavior of dynamic systems in diverse fields, such as economics, finance, and environmental research. Time series forecasting
has been widely utilized through traditional statistical methods, such as Autoregressive Integrated Moving Average (ARIMA) models. ARIMA models proficiently encapsulate the linear relationships and
autocorrelation inherent in the data [1][2]. However, these models may struggle to adapt to the intricate linkages and nonlinear patterns commonly found in real-world data. Hybrid models, exemplified
by the Neural Network Autoregressive (NNAR) model, have arisen as a more versatile approach by integrating the nonlinear capabilities of neural networks with the benefits of autoregressive models [3]
[4]. NNAR models are adept at illustrating the complex dynamics of time series data, particularly in contexts marked by substantial nonlinearity [5]. The capacity to handle high-dimensional data and
attain remarkable predictive accuracy has contributed to the popularity of machine learning methods such as eXtreme Gradient Boosting (XGBoost) [6]. XGBoost, founded on the principles of gradient
boosting decision trees, incrementally constructs an ensemble of weak learners to minimize a loss function and various regularization techniques are utilized to avert overfitting [7].
The agriculture sector in Syria has been a critical component of the economy, significantly contributing to employment and GDP. This sector was substantially affected by the persistent crisis, which
led to a decline in the overall productivity. However, Syria’s agricultural production function exhibits a long-term increase in returns to scale, with fixed capital being the most productive factor
This study aims to evaluate the efficacy of ARIMA, NNAR, and XGBoost models in predicting and forecasting Syrian agricultural GDP using lagged time series data. The optimal model for precisely
depicting the complexity and delays in the data is identified through a thorough evaluation methodology incorporating measures such as Root Mean Squared Error (RMSE), Mean Squared Error (MSE), and
Mean Absolute Percentage Error (MAPE). This research enhances the existing literature by examining the utilization of these models concerning agricultural GDP, offering significant insights for
policymakers, economists, and researchers interested in comprehending and forecasting the dynamics of this vital economic sector. The findings reported in this study will improve the accuracy of
agricultural GDP nowcasting and forecasting tools, thereby facilitating better decision-making in resource allocation, policy formulation, and risk management. This study builds on prior research by
thoroughly investigating the influence of delayed observations on the efficacy of various forecasting models. For that purpose, the delayed time series data will be statistically analyzed, the
autocorrelation structure will be investigated, and lead-lag correlations that may affect the accuracy of the forecast will be identified.
Materials and Methods
This section provides a comprehensive overview of the statistical tools and methodologies employed to achieve optimal predictions of the agricultural GDP series values in Syria from 1963 to 2022.
Consequently, its significance lies in understanding the real-time and prospective data for the variable. The data utilized in this study is sourced from the Syrian Central Bureau of Statistics –
National Accounts Division (Supplementary Table 1) [9].
A time series that displays trend and volatility is deemed non-stationary, affecting its values at various temporal points and rendering it unsuitable for long-term predictions. The enhanced
Dickey-Fuller test for time series is expressed by the subsequent equation [1]:
Where c: constant, α: coefficient on a time trend, : lag order of the autoregressive process. The augmented Dickey–Fuller test (ADF) test is carried out under the null hypothesis δ = 0 (not
stationary) against the alternative of δ < 0 (stationary). If the null hypothesis is not rejected, the first difference is performed to make the series stationary:
ARIMA model
Time series forecasting frequently employs ARIMA models, which characterize the autocorrelation present in the data [2]. These models are designated as Auto Regressive Integrated Moving Average (p, d
, q). The augmented Dickey–Fuller test (ADF) ascertains (d), while the autocorrelation function ρ(p) and the partial autocorrelation function R(p) ascertain (p) and (q) as follows:
The ARIMA (1,1,0) model with drift consists of an autoregressive term of order 1 (AR(1)), integrated of order 1 (I(1)), and no moving average term (MA(0)). The drift represents a constant term in the
differenced series. With y[t] representing the time series data at time , the ARIMA (1,1,0) model with drift can be written then as:
Where c is the drift (constant term), ϕ[1] is the autoregressive coefficient, ε[t] is the error term (white noise) with mean zero and constant variance σ^2, y[t-1], y[t-2]: are lagged values of the
series. The model parameters were selected using the auto.arima function, which automates the process of identifying the best-fitting ARIMA model by minimizing information criteria such as the Akaike
Information Criterion (AIC) and Bayesian Information Criterion (BIC). The function systematically explores different combinations of autoregressive (AR), integrated (I), and moving average (MA)
terms, choosing the model that best fits the training data. The automatic model selection process aims to minimize the following criterion [10]:
is the likelihood of the model, k is the number of parameters in the model, The auto.arima function compares models by varying the parameters p, d, and q, which represent the autoregressive order,
the degree of differencing, and the moving average order, respectively. The function identifies the model that minimizes AIC, balancing complexity and goodness of fit.
NNAR model
The NNAR (Neural Network Autoregressive) model is a sophisticated hybrid statistical and machine learning tool that integrates the capabilities of autoregressive models with the adaptability and
nonlinearity of neural networks. This method is particularly beneficial for time series forecasting, as it elucidates intricate patterns and dynamics.
The NNAR model enhances the conventional autoregressive model by integrating neural network components, enabling it to identify nonlinear correlations within the data. The fundamental concept is
utilizing historical data to forecast future values, wherein prior observations are inputted into a neural network that generates the predictions [5]. It is delineated by the subsequent components:
Autoregressive element: In the conventional autoregressive model, the future value of a time series is articulated as a linear amalgamation of preceding values. For the AR(p) model:
where y[t] represents the value at time t, ϕ denotes the coefficients, and ϵ[t] signifies the error term.
Neural Network Component: The NNAR model substitutes the linear combination with a neural network that use historical values as input to generate the future value. This enables the model to identify
more intricate, nonlinear associations. The NNAR (p,k,m) model can be formally articulated as follows: p: number of delayed observations (autoregressive variables), k: number of hidden layers, and m:
number of neurons in each hidden layer (Fig. 1).
Figure 1. components of a neural network (example). p: number of delayed observations (autoregressive variables), k: number of hidden layers, and m: number of neurons in each hidden layer
For the NNAR (3,2,1) model: p = 3: The model uses the last 3 observations to predict the next value. k = 2: There are two hidden layers. m = 1: The hidden layer contains a neuron (Fig. 2). According
to these components, the general formula for the NNAR (3,2,1) model is:
where ƒ is the neural network function. The neural network structure can be detailed as follows:
Figure 2. components of the neural network used in this study. p: number of delayed observations (autoregressive variables p=3), k: number of hidden layers (k=2), and m: number of neurons in each
hidden layer (m=1)
Input layer: Comprises the preceding three values (y[t-1], y[t-2], y[t-3]). Hidden layer: Includes a neuron. This neuron gets input from the preceding three observations, processes it via the
Rectified Linear Unit (ReLU) activation function, and generates an output x if x is positive; otherwise, it outputs 0. ReLU activation guarantees non-linearity, sparsity, and efficient gradient
propagation. The function is defined as follows:
Mathematically, the operations within the network can be described in terms of hidden layer calculations:
where g denotes the activation function, w[ji] represents the weights, and b[j] signifies the bias. The mathematical representation based on the computations of the output layer is:
where v[j]represents the weights linking the hidden layer to the output layer, and c is the bias term of the output cell. The NNAR (3,2,1) model adeptly integrates the historical autoregressive
element with the robust pattern recognition skills of neural networks. This combination enables the capture of both linear and nonlinear interactions.
XGBoost model
XGBoost (eXtreme Gradient Boosting) is a scalable machine learning framework for tree boosting, predicated on the ideas of gradient boosting decision trees (GBDT). It has emerged as one of the most
efficient algorithms for regression, classification, and ranking problems. The model aims to improve computational efficiency and predictive accuracy. The objective of XGBoost, akin to other gradient
boosting techniques, is to minimize a loss function by incrementally incorporating new models that rectify the faults of preceding models [7]. This can be expressed mathematically as:
Where: y[i] denotes the predicted value for observation i, ƒ[k] signifies a weak learner (specifically a decision tree in the context of XGBoost), x[i] represents the input features for observation i
, k indicates the number of iterations (trees), and ϵ is the error term. Each subsequent tree, f[k], is trained to minimize the residuals of the preceding model. The objective function in XGBoost
integrates the loss function L (which assesses the model’s fit to the data) and regularization terms Ω(ƒ[k]) (which regulate model complexity to prevent overfitting) [10]:
Where: L(y[i], ŷ[i]): denotes the loss function, specifically the squared error for regression in this context:
as the regularization term for tree k, where T denotes the number of leaves, w[j]^2 signifies the leaf weights, and γ and λ are the regularization parameters. The squared error loss is frequently
employed for regression problems:
Where: y[i] represents the actual value, and ŷ[i] denotes the anticipated value.
XGBoost employs an additive boosting methodology. In each iteration, a new decision tree is fitted to the residuals of the preceding tree:
Where: r[i]^(k)is the residual for observation i at iteration k, and ŷ[i] ^(k-1) represents the forecast from the preceding iteration. The new tree ƒ[k] is constructed to minimize these residuals,
and the model’s forecast is revised as follows:
Where η is the learning rate, controlling the contribution of each tree, XGBoost uses both L1 and L2 regularization to control overfitting:
L1 Regularization (Lasso) adds a penalty proportional to the absolute value of the leaf weights |w[j]|, whereas L2 Regularization (Ridge) adds a penalty proportional to the square of the leaf weights
w[j]^2. These regularizations are incorporated into the objective function to prevent overfitting by limiting the complexity of the trees [11].
XGBoost builds trees using a greedy algorithm that splits the data at each node to maximize the reduction in loss. It uses a process called “pruning” to stop growing trees when no significant
improvement in the objective function is observed.
Model evaluation metrics
For evaluating the model performance, the following metrics are used:
Root Mean Squared Error (RMSE):
Mean Squared Error (MSE):
Mean Absolute Percentage Error (MAPE):
Where n is the number of observations, y[t] is the actual value, and ŷ[t] is the predicted value.
The implementation of this research leveraged the statistical programming language R, specifically employing the RStudio environment. Several essential packages were utilized to facilitate the
analysis and model development including: forecast, xgboost, tseries, ggplot2, dplyr, Metrics, and caret.
Results and Discussion
This section involves the analysis of the time series of agricultural GDP in Syria and the estimation of the optimal model for data prediction. The initial step involves examining descriptive
statistics and the trajectory of the variable’s evolution through the analysis of autocorrelation functions, followed by a comparison of the performance metrics of the employed models, identifying
the attributes of the optimal model, and utilizing it for predictions up to the year 2030.
The descriptive statistics (Table 1) offer a preliminary analysis of the agricultural GDP data in Syria from 1963 to 2022, expressed in millions of Syrian pounds at constant prices. The mean
agricultural GDP during this period was approximately 143,287.1 million Syrian pounds, whereas the median was 122,226.7 million Syrian pounds, suggesting a marginally right-skewed distribution. The
significant disparity between the minimum (50,080.52) and maximum (293,756.0) values underscores considerable variations in agricultural production over time (Fig. 3). The standard deviation of
71,398.47 highlights the considerable variety within the dataset. The positive skewness (0.55) indicates that the distribution features a longer tail on the right, signifying the occurrence of
periods with very high agricultural GDP levels. The kurtosis score (2.08) is near the normal distribution’s kurtosis of 3, indicating a modest level of peakedness. The Jarque-Bera test for normalcy
produced a p-value of 0.08, somewhat exceeding the standard significance threshold of 0.05. This indicates that although there is some evidence of deviation from normality, it is insufficient to
unequivocally reject the null hypothesis of a normal distribution. The descriptive statistics indicate a time series marked by considerable variability, a propensity for positive skewness, and a
moderate degree of peakedness, establishing a basis for further study and modeling of Syria’s agricultural GDP series.
Table 1. Descriptive statistics of Syrian agricultural GDP data between 1963 and 2022. Mean, median, maximum, minimum, and standard deviation values are presented in million Syrian pounds.
Figure 3. Development of agricultural GDP in Syria during the period 1963-2022. GDP values are presented in million Syrian pounds.
An evident increasing trend in agricultural GDP, particularly from the early 1970s to the mid-2010s can be seen. This period was characterized by consistent growth, punctuated by occasional increases
and declines. However, the series exhibits significant volatility, particularly in the late 2010s and early 2020s (Fig. 3). The unpredictability is illustrated by the substantial decline in
agricultural GDP that occurred subsequent to 2015, which coincided with the onset of the Syrian conflict. The graph illustrates the instability and disruption that resulted from the conflict, as the
agriculture sector experienced a substantial decline during this period. Thus, the series appears to be non-stationary, suggesting that its statistical characteristics, such as mean and variance,
vacillate over time, particularly as a result of the substantial decline observed in recent years. The non-stationarity underscores the importance of employing appropriate statistical methods to
effectively evaluate and forecast the series.
Key insights into the temporal dependencies of the agricultural GDP series were elucidated by the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) (Fig. 4). The ACF
demonstrates a gradual decline, which suggests that past GDP values have a substantial impact on current values according to the fundamental principles outlined in time series analysis [12].
Therefore, a strong positive autocorrelation at lower delays is present. In contrast, the PACF exhibits a severe decline following the initial latency, with subsequent lags largely remaining within
the significance bounds. This indicates that the immediate past value is the primary indicator of the direct impact of past values [12]. These patterns indicate that the agricultural GDP series is
not random, exhibits temporal dependencies, and could potentially be modeled using an AR(1) process. The ACF’s gradual decay also suggests the possibility of non-stationarity, suggesting that
differencing techniques may be necessary to attain stationarity prior to the application of forecasting models.
Figure 4. Autocorrelation (A) and partial autocorrelation function (B) of Syrian agricultural GDP series.
The NNAR (3,2) model demonstrated superior performance across all three metrics, recording the lowest values for MAPE (5.70%), MSE (0.617), and RMSE (11857.71) (Fig. 5). This indicates that the NNAR
model is particularly adept at identifying the fundamental patterns and dynamics present in the agricultural GDP time series. This effectiveness can be attributed to its capacity to handle non-linear
relationships and its implementation of a neural network framework. The ARIMA (1,1,0) model exhibits a satisfactory level of accuracy, although it presents higher error values in comparison to NNAR.
The straightforward nature of this model may restrict its capacity to identify intricate relationships present in the data. The XGBoost model, however, demonstrated significantly elevated error
values, suggesting a less favorable performance in this particular context. This may be due to the model’s possible sensitivity to noise or overfitting, particularly in light of the dataset’s
relatively small sample size. The NNAR model demonstrates superior performance, which can be attributed to its flexible framework that effectively combines the advantages of autoregressive models and
neural networks. The autoregressive component identifies the natural temporal dependencies present in the time series, whereas the neural network component facilitates the learning of intricate
non-linear relationships within the data. This integrated method demonstrates notable advantages for time series of moderate length, specifically those containing between 30 and 100 observations,
while effectively managing the autocorrelation patterns commonly found in these series.
Figure 5. Comparison of root mean squared error (RMSE), mean squared error (MSE), and mean absolute percentage error (MAPE) as evaluation indicators of the tested Autoregressive Integrated Moving
Average (ARIMA), Neural Network Autoregressive (NNAR), and eXtreme Gradient Boosting (XGBoost) models in forecasting testing values of Syrian agricultural GDP series. A training set of 80% and
testing set of 20% were considered in training and evaluating each model.
Nine simulated trajectories (Series 1-9) of projected Syrian agricultural GDP, as forecasted by NNAR, were visualized (Fig. 6 A). The trajectories illustrate the intrinsic uncertainty associated with
NNAR forecasting, revealing a range of possible future scenarios. The variation noted beyond 2022 suggests an increasing level of uncertainty as the forecast period progresses further into the
future. The NNAR (3,2) forecasts (Fig. 6. B) offer a clearer representation of the model’s predictions. The black line illustrates the historical data, whereas the blue line represents the point
forecast produced by the NNAR model. The shaded blue regions denote prediction intervals, highlighting the uncertainty linked to the forecast. The darker blue region represents a greater degree of
confidence (80% to 95%), whereas the lighter blue region denotes a lesser degree of confidence. The prediction intervals expand as the forecast horizon lengthens, indicating an increase in
uncertainty regarding future GDP values. Both figures provide important insights into the projected path of agricultural GDP and the related uncertainties, facilitating informed decision-making and
risk evaluation.
Figure 6. Nowcasting and forecasting of Syrian agricultural GDP with uncertainty periods. Black line in both plots demonstrates historic data while Series (1-9) (A) and blue shaded (light and dark)
(B) represent NNAR forecasting results. GDP values are presented in million Syrian pounds.
Table 2 presents the projected values of Syrian agricultural GDP as anticipated by the NNAR model (up to 2030), together with the associated uncertainty estimates. The “Point Forecast” column
presents the most likely forecast of agricultural GDP for each year, determined using the NNAR model. The “Lo 80” and “Hi 80” columns indicate the 80% prediction interval, defining the range in which
the actual GDP value is expected to fall with 80% confidence. The “Lo 95” and “Hi 95” columns represent the 95% prediction interval, providing a broader range with heightened confidence. Forecasts
indicate that the agricultural GDP is projected to attain 60,397.07 million Syrian pounds by the year 2030. The anticipated reduction in agricultural GDP underscores possible difficulties confronting
the Syrian agricultural sector.
Table 2. Evaluation of NNAR nowcasting and forecasting of Syrian agricultural GDP with uncertainty periods up to 2030. GDP values are presented in million Syrian pounds.
The delay in data publication by the Syrian Central Bureau of Statistics presents a significant challenge for conducting timely economic analysis and forecasting. Although the title of the table
refers to “nowcasting,” it is important to recognize that the forecasts reach beyond the most recent data point, which is likely from 2022. The forecasts appear to be grounded in the historical data
that is accessible, along with the presumption that the existing trends and patterns will persist moving forward. Interpreting these forecasts requires careful consideration, acknowledging the
inherent limitations linked to data delays and the possibility of unexpected events influencing future agricultural GDP.
The estimated average annual growth rate, based on the point forecasts for the period 2022-2030, is -4.33. The anticipated reduction in agricultural GDP underscores possible difficulties confronting
the agricultural sector in Syria. Ongoing monitoring, the incorporation of updated data, and additional analysis are essential for enhancing these forecasts and guiding effective strategies aimed at
supporting the recovery and sustainable growth of the agricultural sector.
The NNAR model’s superior performance in forecasting Syrian agricultural GDP is consistent with earlier research that has shown the effectiveness of hybrid models in addressing the intricate dynamics
found in time series data. Previous studies have indicated that NNAR models surpass traditional ARIMA models in predicting water treatment plant influent characteristics [3], underscoring their
capacity to handle non-linear relationships frequently encountered in real-world data. Similarly, the advantages of NNAR compared to traditional modeling methods were highlighted in forecasting
COVID-19 data [4], highlighting its effectiveness for time series analysis. Other researches further supported this idea by illustrating the efficacy of NNAR models in forecasting food grain
production in India, surpassing the performance of conventional ARIMA, SutteARIMA, and Holt-Winters approaches [5]. This study’s comparison goes beyond traditional time series models to encompass
machine learning approaches such as XGBoost, an algorithm recognized for its predictive accuracy across multiple domains. Although XGBoost has demonstrated potential in time series applications,
including the forecasting of hemorrhagic fever with renal syndrome [6] and rainfall patterns [7], the current study emphasizes the possible limitations of relying solely on data-driven methods when
addressing complex economic data, which is marked by delayed observations and intrinsic structural factors. This research offers a distinctive contribution by focusing on the management of delayed
data in the context of agricultural GDP, in contrast to studies such as [13][14], which have investigated NNAR applications for up to date GDP modeling and Bitcoin forecasting. This approach is
particularly relevant in situations like Syria, where there are considerable limitations in data availability, as it is one of the main challenges identified by [15] in predicting regional
unemployment. Although neural network models are often regarded as superior in capturing non-linear relationships within timeseries, they may face obstacles in making precise future predictions due
to inconsistencies in the data, as illustrated by the example of rainfall data [16]. Consequently, it is essential to select suitable models that align with the characteristics of the datasets in
hand in order to obtain more accurate predictions.
This research addressed the challenge of delayed time series data, a prevalent issue in economic datasets, revealing a distinctive statistical aspect. The NNAR model demonstrates a notable capacity
to capture the delayed effects of historical agricultural GDP values on future trends. Its accurate forecasts, even in the presence of data lags, underscore its robustness and appropriateness for
practical applications, particularly in contexts where data availability may be limited. The emphasis on delayed time series and the proven effectiveness of NNAR in these contexts distinguishes this
study, providing important insights for economic forecasting and decision making in situations with limited data.
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Economics and Business. Hungarian Economists’ Society of Romania. 2018;21(135):66-78.
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Cite this article:
Alakkari, K. Machine learning-based modeling of Syrian agricultural GDP trends: A comparative analysis. DYSONA – Applied Science, 2025;6(1): 86-95. doi: 10.30493/das.2024.478968.1125 | {"url":"https://e-namtila.com/machine-learning-based-modeling-of-syrian-agricultural-gdp-trends-a-comparative-analysis/","timestamp":"2024-11-07T13:46:13Z","content_type":"text/html","content_length":"118303","record_id":"<urn:uuid:569a63db-f7dd-459c-b167-02023c6376d7>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00318.warc.gz"} |
half circle square footage calculator
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Understanding Fractions with Visual Aids - MathAndEnglishWorksheets.com
Introduction to Fractions
Fractions, a term that can make some students cringe. But, as a seasoned teacher, I’ve seen how visual aids can transform this complex concept into a simple, understandable one. Fractions are an
essential part of our daily lives. They help us divide pizza, measure ingredients for cooking, and even calculate distances.
What Are Fractions?
In simplest terms, fractions represent a part of a whole. They consist of two numbers: the numerator (top number) and the denominator (bottom number). The numerator indicates how many parts you have,
while the denominator tells you how many equal parts the whole is divided into.
Why Are Fractions Important?
Fractions are everywhere. They are used in cooking, shopping, construction, and even in understanding time. Mastering the concept of fractions is crucial for advancing in more complex math topics
like algebra and calculus.
Visual Aids for Understanding Fractions
Visual aids are a powerful tool for teaching fractions. They help students visualize the concept, making it easier to understand and remember. Here are some effective visual aids you can use:
Pizza Slices
One of the most relatable examples of fractions is a pizza. If you divide a pizza into eight equal slices, each slice represents 1/8 of the pizza. If you eat three slices, you’ve eaten 3/8 of the
pizza. This visual aid is effective because it’s something students can easily relate to.
Fraction Bars
Fraction bars are a great tool for comparing fractions. They are rectangular bars divided into equal parts. For example, a bar divided into four equal parts can represent 1/4, 2/4, 3/4, or 4/4. By
comparing different fraction bars, students can easily see which fraction is larger or smaller.
Number Lines
A number line is another effective visual aid for teaching fractions. It helps students understand the concept of fractions as numbers that fall between whole numbers. For example, the fraction 1/2
is halfway between 0 and 1 on a number line.
Practicing Fractions with Worksheets
Worksheets are a practical way to reinforce the concept of fractions. They provide students with the opportunity to practice what they’ve learned. At
, we offer a variety of worksheets designed to help students master fractions.
Benefits of Worksheets
Worksheets allow students to practice fractions at their own pace. They can solve problems, compare fractions, and even apply fractions to real-world scenarios. Worksheets also provide immediate
feedback, allowing students to identify and correct their mistakes.
Understanding fractions can be a challenge, but with the right tools and resources, it can be made simpler. Visual aids are a powerful way to teach fractions, making the concept more tangible and
relatable. Worksheets provide the necessary practice to reinforce the concept. Remember, practice makes perfect. So, don’t hesitate to use these resources to help your students master fractions. For
more tips and resources on teaching fractions, check out our blog post on
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Maximizing the Value of a Common ACT Math Strategy
Any student who has ever typed “ACT math tips” into an internet search bar is almost certainly familiar with the strategy of plugging in the answer choices on the ACT Math Section. The upside to this
strategy is clear: if students test each answer choice, they must eventually find the correct one. However, this method can often be quite time consuming and can even be ineffective on certain
problems. Much like any tool, this strategy will be most useful to students if they are able to understand not only how to use it, but how to do so effectively.
When does the strategy work?
Unfortunately, not all questions on the ACT allow students to test the answer choices. To determine if the strategy is viable for a given question, students can begin by looking at the structure of
the answer choices. Firstly, the answer must be in numerical form. While plugging in variables or expressions might be possible in some instances, it is often ineffective or might require the same
knowledge that would be necessary to solve the problem outright. Next, students should identify what the numbers in the answer choices represent. If they represent a variable found within the
problem, then the strategy should work. However, if the number represents something else (the number of solutions, the difference between two values, etc.), the strategy will not work for that
problem. Consider the following examples:
In example 1, the answer choices all represent different values of x. Since the value x is in the question itself, the answer choices can be plugged back into the equation until it produces a
mathematically true statement. In this case, the correct answer would be choice B. 3³ - 2(3) = 21 and 2(3)² + 2(3) = 24.
However, in example 2, the answer choices don’t represent any value found within the question. Instead, they measure the absolute value of the difference between the two solutions of the problem.
Therefore, there is no place for students to plug in the answer choices correctly. It’s also worth noting that the answer choices are designed to catch students relying on this strategy (or those who
don’t read the question carefully). If a student chose to plug in choice B for x in the equation, the equation would be correct, but it would not answer the question.
Where to Begin?
When students recognize that they can plug in the answer choices, should they simply plug in each answer choice randomly until they find the correct answer? They certainly could do so, but in order
to maximize the value of this strategy, it is often best to start with the answer choice of middle value. This often provides students with valuable information and can minimize the amount of choices
students need to plug in.
Students should note that answer choices typically are ordered by ascending value (Choice A < Choice B < Choice C, etc.). Because of this, the value of answer choice C is almost always between the
value of the other options. By testing answer C, students will find that if Sam has rented the bike for 5 hours, he would have paid $10 for the rental plus $3/hour for five hours, resulting in a
total of $25, which is greater than the $19 total he paid in the question. Not only does this prove that answer C is incorrect, it also shows that answers D and E must also be incorrect. If Sam were
to keep the bike out for longer than 5 hours, his total would continue to increase, but we know his total was actually less than the $25 we found in choice C. Therefore, the answer must be either A
or B. Next we can plug in either of the remaining choices: either it will be correct or it will eliminate all but one remaining answer. If the student plugs in choice B, they will find that he spent
$10 plus $3/hour for three hours, resulting in a total of $19; thus choice B must be correct.
Ultimately, plugging in the answer choices can be both useful to students as well as frustrating. Few students will ever grow to be confident in their math abilities as they “plug and chug” their way
through math sections; it’s time consuming and only partially effective. However, by mastering how and when to use the strategy to its fullest, students can actually use it to support their answers
and manage their time on difficult questions. | {"url":"https://info.methodlearning.com/blog/maximizing-the-value-of-a-common-act-math-strategy","timestamp":"2024-11-13T08:53:40Z","content_type":"text/html","content_length":"70460","record_id":"<urn:uuid:c2773f83-a9d4-448f-bb5c-e1d55f436606>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00433.warc.gz"} |
6.4 Conductors in Electrostatic Equilibrium - University Physics Volume 2 | OpenStax
By the end of this section, you will be able to:
• Describe the electric field within a conductor at equilibrium
• Describe the electric field immediately outside the surface of a charged conductor at equilibrium
• Explain why if the field is not as described in the first two objectives, the conductor is not at equilibrium
So far, we have generally been working with charges occupying a volume within an insulator. We now study what happens when free charges are placed on a conductor. Generally, in the presence of a
(generally external) electric field, the free charge in a conductor redistributes and very quickly reaches electrostatic equilibrium. The resulting charge distribution and its electric field have
many interesting properties, which we can investigate with the help of Gauss’s law.
The Electric Field inside a Conductor Vanishes
If an electric field is present inside a conductor, it exerts forces on the free electrons (also called conduction electrons), which are electrons in the material that are not bound to an atom. These
free electrons then accelerate. However, moving charges by definition means nonstatic conditions, contrary to our assumption. Therefore, when electrostatic equilibrium is reached, the charge is
distributed in such a way that the electric field inside the conductor vanishes.
If you place a piece of a metal near a positive charge, the free electrons in the metal are attracted to the external positive charge and migrate freely toward that region. The region the electrons
move to then has an excess of electrons over the protons in the atoms and the region from where the electrons have migrated has more protons than electrons. Consequently, the metal develops a
negative region near the charge and a positive region at the far end (Figure 6.34). As we saw in the preceding chapter, this separation of equal magnitude and opposite type of electric charge is
called polarization. If you remove the external charge, the electrons migrate back and neutralize the positive region.
The polarization of the metal happens only in the presence of external charges. You can think of this in terms of electric fields. The external charge creates an external electric field. When the
metal is placed in the region of this electric field, the electrons and protons of the metal experience electric forces due to this external electric field, but only the conduction electrons are free
to move in the metal over macroscopic distances. The movement of the conduction electrons leads to the polarization, which creates an induced electric field in addition to the external electric field
(Figure 6.35). The net electric field is a vector sum of the fields of $+q+q$ and the surface charge densities $−σA−σA$ and $+σB.+σB.$ This means that the net field inside the conductor is different
from the field outside the conductor.
The redistribution of charges is such that the sum of the three contributions at any point P inside the conductor is
Now, thanks to Gauss’s law, we know that there is no net charge enclosed by a Gaussian surface that is solely within the volume of the conductor at equilibrium. That is, $qenc=0qenc=0$ and hence
$E→net=0→(at points inside a conductor).E→net=0→(at points inside a conductor).$
Charge on a Conductor
An interesting property of a conductor in static equilibrium is that extra charges on the conductor end up on the outer surface of the conductor, regardless of where they originate. Figure 6.36
illustrates a system in which we bring an external positive charge inside the cavity of a metal and then touch it to the inside surface. Initially, the inside surface of the cavity is negatively
charged and the outside surface of the conductor is positively charged. When we touch the inside surface of the cavity, the induced charge is neutralized, leaving the outside surface and the whole
metal charged with a net positive charge.
To see why this happens, note that the Gaussian surface in Figure 6.37 (the dashed line) follows the contour of the actual surface of the conductor and is located an infinitesimal distance within it.
Since $E=0E=0$ everywhere inside a conductor,
Thus, from Gauss’s law, there is no net charge inside the Gaussian surface. But the Gaussian surface lies just below the actual surface of the conductor; consequently, there is no net charge inside
the conductor. Any excess charge must lie on its surface.
This particular property of conductors is the basis for an extremely accurate method developed by Plimpton and Lawton in 1936 to verify Gauss’s law and, correspondingly, Coulomb’s law. A sketch of
their apparatus is shown in Figure 6.38. Two spherical shells are connected to one another through an electrometer E, a device that can detect a very slight amount of charge flowing from one shell to
the other. When switch S is thrown to the left, charge is placed on the outer shell by the battery B. Will charge flow through the electrometer to the inner shell?
No. Doing so would mean a violation of Gauss’s law. Plimpton and Lawton did not detect any flow and, knowing the sensitivity of their electrometer, concluded that if the radial dependence in
Coulomb’s law were $1/r(2+δ)1/r(2+δ)$, $δδ$ would be less than $2×10−92×10−9$^1. More recent measurements place $δδ$ at less than $3×10−163×10−16$^2, a number so small that the validity of Coulomb’s
law seems indisputable.
The Electric Field at the Surface of a Conductor
If the electric field had a component parallel to the surface of a conductor, free charges on the surface would move, a situation contrary to the assumption of electrostatic equilibrium. Therefore,
the electric field is always perpendicular to the surface of a conductor.
At any point just above the surface of a conductor, the surface charge density $σσ$ and the magnitude of the electric field E are related by
To see this, consider an infinitesimally small Gaussian cylinder that surrounds a point on the surface of the conductor, as in Figure 6.39. The cylinder has one end face inside and one end face
outside the surface. The height and cross-sectional area of the cylinder are $δδ$ and $ΔAΔA$, respectively. The cylinder’s sides are perpendicular to the surface of the conductor, and its end faces
are parallel to the surface. Because the cylinder is infinitesimally small, the charge density $σσ$ is essentially constant over the surface enclosed, so the total charge inside the Gaussian cylinder
is $σΔAσΔA$. Now E is perpendicular to the surface of the conductor outside the conductor and vanishes within it, because otherwise, the charges would accelerate, and we would not be in equilibrium.
Electric flux therefore crosses only the outer end face of the Gaussian surface and may be written as $EΔAEΔA$, since the cylinder is assumed to be small enough that E is approximately constant over
that area. From Gauss’ law,
Electric Field of a Conducting Plate
The infinite conducting plate in
Figure 6.40
has a uniform surface charge density
on each of its faces. Note the plate has some finite thickness and therefore two surfaces. Use Gauss’s law to find the electric field outside the plate. Compare this result with that previously
calculated directly.
For this case, we use a cylindrical Gaussian surface, a side view of which is shown.
The flux calculation is similar to that for an infinite sheet of charge from the previous chapter with one major exception: The left face of the Gaussian surface is inside the conductor where
so the total flux through the Gaussian surface is
rather than 2
. Then from Gauss’ law,
and the electric field outside the plate is
This result is in agreement with the result from the previous section, and consistent with the rule stated above.
Electric Field between Oppositely Charged Parallel Plates
Two large conducting plates carry equal and opposite charges, with a surface charge density
of magnitude
as shown in
Figure 6.41
. The separation between the plates is
. What is the electric field between the plates?
Note that the electric field at the surface of one plate only depends on the charge on that plate. Thus, apply
with the given values.
The electric field is directed from the positive to the negative plate, as shown in the figure, and its magnitude is given by
$E=σε0=6.81×10−7C/m28.85×10−12C2/N m2=7.69×104N/C.E=σε0=6.81×10−7C/m28.85×10−12C2/N m2=7.69×104N/C.$
This formula is applicable to more than just a plate. Furthermore, two-plate systems will be important later.
A Conducting Sphere
The isolated conducting sphere (
Figure 6.42
) has a radius
and an excess charge
. What is the electric field both inside and outside the sphere?
The sphere is isolated, so its surface change distribution and the electric field of that distribution are spherically symmetrical. We can therefore represent the field as
. To calculate
), we apply Gauss’s law over a closed spherical surface
of radius
that is concentric with the conducting sphere.
is constant and
on the sphere,
For $r<Rr<R$, S is within the conductor, so $qenc=0,qenc=0,$ and Gauss’s law gives
as expected inside a conductor. If $r>Rr>R$, S encloses the conductor so $qenc=q.qenc=q.$ From Gauss’s law,
The electric field of the sphere may therefore be written as
Notice that in the region
, the electric field due to a charge
placed on an isolated conducting sphere of radius
is identical to the electric field of a point charge
located at the center of the sphere. The difference between the charged metal and a point charge occurs only at the space points inside the conductor. For a point charge placed at the center of the
sphere, the electric field is not zero at points of space occupied by the sphere, but a conductor with the same amount of charge has a zero electric field at those points (
Figure 6.43
). However, there is no distinction at the outside points in space where
, and we can replace the isolated charged spherical conductor by a point charge at its center with impunity.
Check Your Understanding 6.6
How will the system above change if there are charged objects external to the sphere?
For a conductor with a cavity, if we put a charge $+q+q$ inside the cavity, then the charge separation takes place in the conductor, with $−q−q$ amount of charge on the inside surface and a $+q+q$
amount of charge at the outside surface (Figure 6.44(a)). For the same conductor with a charge $+q+q$ outside it, there is no excess charge on the inside surface; both the positive and negative
induced charges reside on the outside surface (Figure 6.44(b)).
If a conductor has two cavities, one of them having a charge $+qa+qa$ inside it and the other a charge $−qb,−qb,$ the polarization of the conductor results in $−qa−qa$ on the inside surface of the
cavity a, $+qb+qb$ on the inside surface of the cavity b, and $qa−qbqa−qb$ on the outside surface (Figure 6.45). The charges on the surfaces may not be uniformly spread out; their spread depends upon
the geometry. The only rule obeyed is that when the equilibrium has been reached, the charge distribution in a conductor is such that the electric field by the charge distribution in the conductor
cancels the electric field of the external charges at all space points inside the body of the conductor.
• 1S. Plimpton and W. Lawton. 1936. “A Very Accurate Test of Coulomb’s Law of Force between Charges.” Physical Review 50, No. 11: 1066, doi:10.1103/PhysRev.50.1066
• 2E. Williams, J. Faller, and H. Hill. 1971. “New Experimental Test of Coulomb’s Law: A Laboratory Upper Limit on the Photon Rest Mass.” Physical Review Letters 26 , No. 12: 721, doi:10.1103/ | {"url":"https://openstax.org/books/university-physics-volume-2/pages/6-4-conductors-in-electrostatic-equilibrium","timestamp":"2024-11-06T20:58:59Z","content_type":"text/html","content_length":"479555","record_id":"<urn:uuid:29eca454-52c0-47f3-9a9d-10d5d6f57118>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00532.warc.gz"} |
What does the slope of a line tell you?
What does the slope of a line tell you?
Slope describes the steepness of a line. The slope of any line remains constant along the line. The slope can also tell you information about the direction of the line on the coordinate plane. Slope
can be calculated either by looking at the graph of a line or by using the coordinates of any two points on a line.
What is a distance vs time graph?
A distance-time graph shows how far an object has travelled in a given time. Distance is plotted on the Y-axis (left) and Time is plotted on the X-axis (bottom). A moving object is always
‘increasing’ its total length moved with time. ‘Curved lines’ on a distance time graph indicate that the speed is changing.
How do you type a horizontal line?
Follow these steps to insert a horizontal line in your document:
1. Put your cursor in the document where you want to insert the horizontal line.
2. Go to Format | Borders And Shading.
3. On the Borders tab, click the Horizontal Line button.
4. Scroll through the options and select the desired line.
5. Click OK.
What does a straight line on a graph mean physics?
time graph reveals pertinent information about an object’s velocity. For example, a small slope means a small velocity; a negative slope means a negative velocity; a constant slope (straight line)
means a constant velocity; a changing slope (curved line) means a changing velocity.
What is another name for slope in math?
Slope is the ‘steepness’ of the line, also commonly known as rise over run. We can calculate slope by dividing the change in the y-value between two points over the change in the x-value. of algebra
is the idea of slope.
What is the slope of all horizontal line?
The slope of a line is change in Y / change in X. The slope of a horizontal line = 0, not undefined. The slope of a vertical line = undefined.
What is the slope of a line graph?
The slope of a line is rise over run. Learn how to calculate the slope of the line in a graph by finding the change in y and the change in x.
What is distance-time graph 7?
Class 7 Physics Motion and Time. Distance-Time Graph. Distance-Time Graph. This is usually drawn as a line graph as it taken two variable quantities – Distance and Time. In a Distance-Time graph,
Distance is considered on the Y-axis (Vertical) and Time is considered on the X-axis (Horizontal).
What does slope mean?
the steepness
What is the acceleration of a horizontal line?
The slope of a horizontal line is zero, meaning that the object stopped accelerating instantaneously at those times. The acceleration might have been zero at those two times, but this does not mean
that the object stopped.
How do you describe a distance-time graph?
A distance-time graph shows how far an object has travelled in a given time. It is a simple line graph that denotes distance versus time findings on the graph. Distance is plotted on the Y-axis. Time
is plotted on the X-axis.
How do you make a horizontal straight line on a keyboard?
Press and hold the “Shift” key, then press and hold the hyphen “-” key, located two keys to the left of “Backspace” on a PC or “Delete” on a Mac. This creates a solid, horizontal straight line.
Release the hyphen key to stop the line.
What does the slope of a distance vs time graph tell you?
The slope of a distance-time graph represents speed. The steeper the slope is, the faster the speed. Average speed can be calculated from a distance-time graph as the change in distance divided by
the corresponding change in time.
Is horizontal up and down or side to side?
The terms vertical and horizontal often describe directions: a vertical line goes up and down, and a horizontal line goes across. You can remember which direction is vertical by the letter, “v,”
which points down.
How do I type a line symbol?
“|”, How can I type it?
1. Shift-\ (“backslash”).
2. German keyboard it is on the left together with < and > and the Alt Gr modifier key must be pressed to get the pipe.
3. Note that depending on the font used, this vertical bar can be displayed as a consecutive line or by a line with a small gap in the middle.
What is equation of the line?
The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you know two points that a line passes through, this page will show you how to find the
equation of the line.
What does a horizontal line mean on a distance time graph?
A distance-time graph tells us how far an object has moved with time. • The steeper the graph, the faster. the motion. • A horizontal line means the object is. not changing its position – it is not
moving, it is at rest.
What does a horizontal line mean in physics?
A horizontal line means the object is moving at a constant speed. • A downward sloping line means the object is slowing down. Distance/time graph. Speed(velocity)/time graph.
What do 3 vertical lines mean?
These three lines represent Shiva’s power that is threefold. These are action, knowledge and power of will. It is also said to symbolize Shiva’s trident or the divine trio of Shiva, Vishnu and
What is the vertical line symbol called?
The vertical bar, | , is a glyph with various uses in mathematics, computing, and typography. It has many names, often related to particular meanings: Sheffer stroke (in logic), pipe, vbar, stick,
vertical line, vertical slash, bar, pike, or verti-bar, and several variants on these names.
What is horizontal line in art?
5 Types of Lines in Art: Meaning and Examples Horizontal lines are straight lines parallel to the horizon that move from left to right. They suggest width, distance, calmness, and stability. Diagonal
lines are straight lines that slant in any direction except horizontal or vertical.
What is the velocity of a straight horizontal line?
Car 1 – Position and velocity graphs Constant velocity means the velocity graph is horizontal, equal to 11.11 m/s at all times. A constant velocity means the position graph has a constant slope (of
11.11 m/s). It’s a straight line sloping up, and starting below the origin.
How do you read a distance vs time graph?
Content statements:
1. A horizontal line means the object is stopped.
2. A straight diagonal line means the object is traveling at a constant speed.
3. The steeper the angle of the line, the faster the object is traveling.
4. An upward diagonal line means that the object is moving farther away from a specific point.
Are all horizontal lines parallel?
All horizontal lines are parallel. Parallel means that two or more lines can never intersect with one another. Horizontal lines are straight lines going from left to right without any angles, tilt,
rotation in terms of x & y axis, etc. Therefore, they should never intersect, which is the definition of parallel.
What’s a velocity?
The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is a physical vector quantity; both magnitude and direction
are needed to define it.
What is another name for a perfectly flat object?
A plane is a perfectly flat surface extending in all directions.
What is a horizontal line in math?
Horizontal Line Definition The meaning horizontal line is a straight line that is mapped from left to right and it is parallel to the X-axis in the plane coordinate system. In other words, the
straight line that does not make any intercept on the X-axis and it can have an intercept on Y-axis is called horizontal line.
What are 4 types of slopes?
Slopes come in 4 different types: negative, positive, zero, and undefined. as x increases. | {"url":"https://lynniezulu.com/what-does-the-slope-of-a-line-tell-you/","timestamp":"2024-11-07T06:59:20Z","content_type":"text/html","content_length":"52877","record_id":"<urn:uuid:e4222c45-51eb-49e0-bd3f-518b63d5ee75>","cc-path":"CC-MAIN-2024-46/segments/1730477027957.23/warc/CC-MAIN-20241107052447-20241107082447-00785.warc.gz"} |
Insert Delete GetRandom O(1)
Problem statement:
Implement the RandomizedSet class:
* RandomizedSet() Initializes the RandomizedSet object.
* bool insert(int val) Inserts an item val into the set if not present. Returns true if the item was not present, false otherwise.
* bool remove(int val) Removes an item val from the set if present. Returns true if the item was present, false otherwise.
* int getRandom() Returns a random element from the current set of elements (it's guaranteed that at least one element exists when this method is called). Each element must have the same probability
of being returned.
You must implement the functions of the class such that each function works in average O(1) time complexity.
Example 1:
[ "RandomizedSet ", "insert ", "remove ", "insert ", "getRandom ", "remove ", "insert ", "getRandom "]
[[], [1], [2], [2], [], [1], [2], []]
[null, true, false, true, 2, true, false, 2]
RandomizedSet randomizedSet = new RandomizedSet();
randomizedSet.insert(1); // Inserts 1 to the set. Returns true as 1 was inserted successfully.
randomizedSet.remove(2); // Returns false as 2 does not exist in the set.
randomizedSet.insert(2); // Inserts 2 to the set, returns true. Set now contains [1,2].
randomizedSet.getRandom(); // getRandom() should return either 1 or 2 randomly.
randomizedSet.remove(1); // Removes 1 from the set, returns true. Set now contains [2].
randomizedSet.insert(2); // 2 was already in the set, so return false.
randomizedSet.getRandom(); // Since 2 is the only number in the set, getRandom() will always return 2.
* -231 <= val <= 231 - 1
* At most 2 * 105 calls will be made to insert, remove, and getRandom.
* There will be at least one element in the data structure when getRandom is called.
Solution in C++
Solution in Python
Solution in Java
Solution in Javascript
Solution explanation
The algorithm uses a combination of both data structures, HashMap and ArrayList (or unordered_map and vector in C++). The HashMap is used to store the values and their corresponding indices in the
1. When inserting a value, we first check if the value is already present in the HashMap. If it's not present, we add the value to the HashMap with its index in the ArrayList, and also add the value
to the ArrayList.
2. When removing a value, we check if the value is present in the HashMap. If it's present, we swap the value to be removed with the last value in the ArrayList, update the HashMap with the new index
of the last value, and remove the last value from the ArrayList. After that, we remove the value from the HashMap.
3. To get a random value, we use the random function to generate a random index within the ArrayList's range and return the value at that index.
By using this combination of data structures, we are able to achieve average O(1) time complexity for each of the functions. | {"url":"https://www.freecodecompiler.com/tutorials/dsa/insert-delete-getrandom-o1","timestamp":"2024-11-07T13:55:45Z","content_type":"text/html","content_length":"41438","record_id":"<urn:uuid:862365c4-d3d2-49dc-bc45-37b748837140>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00200.warc.gz"} |
Using Ohm’s Law to Find the Potential Difference across a Resistor
Question Video: Using Ohm’s Law to Find the Potential Difference across a Resistor Physics • Third Year of Secondary School
A 2300 Ω resistor in a circuit has a current of 100 mA through it. What is the potential difference across the resistor?
Video Transcript
A 2300-ohm resistor in a circuit has a current of 100 milliamperes through it. What is the potential difference across the resistor?
In this exercise, we want to connect these three quantities of resistance, current, and potential difference. A great way to do this is through a relationship known as Ohm’s law. Ohm’s law says that
for a constant resistance value that resistance multiplied by the current through the resistor is equal to the potential difference across it.
In our case, we’re told what those current and resistance values are. So it’s just a matter of substituting in for those and calculating the voltage. The one thing we want to be careful for is to
consider the units in these values. Well, the value of the resistor is given in units of ohms, which is the base unit of resistance. The current we see is given in units of milliamperes, not amperes.
This means if we were to substitute in these values and then multiply through as is, we will get an answer for potential difference in units of millivolts. But if we want an answer in volts and we
do, then we’ll need to convert this value from milliamperes to amperes.
We know that 1000 milliamps is equal to one amp. And therefore, we can write 100 milliamperes as 100 times 10 to the negative third amps. And now, we see that the units when we multiply these two
values together will be amps times ohms; that is, volts. Taking this product, we find it’s equal to 230 volts. That is the potential difference across the resistor. | {"url":"https://www.nagwa.com/en/videos/719131471545/","timestamp":"2024-11-10T05:33:28Z","content_type":"text/html","content_length":"249543","record_id":"<urn:uuid:86a52a47-6eb4-44e5-9823-0c8c5538f38b>","cc-path":"CC-MAIN-2024-46/segments/1730477028166.65/warc/CC-MAIN-20241110040813-20241110070813-00029.warc.gz"} |
Why can t the capacitor be fully discharged
Why can t the capacitor be fully discharged
$begingroup$ Think of a capacitor as a spring. Charge is the displacement of the spring, current is the rate at which the spring moves. Voltage is the tension in the spring. Although the spring needs
to move at some time to generate a tension, the tension remains even when the spring is at rest.
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Why doesn''t voltage drop to 0 when a capacitor becomes fully …
$begingroup$ Think of a capacitor as a spring. Charge is the displacement of the spring, current is the rate at which the spring moves. Voltage is the tension in the spring. Although the spring needs
to move at some time to generate a tension, the tension remains even when the spring is at rest.
How to Safely Discharge a Capacitor
How to discharge a capacitor in the most safely way. In this tutorial I''m going to show you several ways to discharge a capacitor. 1. Discharging the capacitor with a screwdriver. You might have
heard that one of the simplest ways to discharge the capacitor is by shorting its terminals, using a screwdriver or pliers.
How to Safely Discharge a Capacitor
How to discharge a capacitor in the most safely way. In this tutorial I''m going to show you several ways to discharge a capacitor. 1. Discharging the capacitor with a screwdriver. You might have
heard that …
How to Safely Discharge Capacitors
The capacitor is discharged once the bulb has fully dimmed. The main benefit of using a lightbulb (as opposed to a plain resistor) is that you have a visual indicator of the charge level in the
capacitor. With an Insulated Screwdriver. As mentioned above, sometimes people use an insulated screwdriver to discharge capacitors.
Charging and Discharging a Capacitor
However, so long as the electron current is running, the capacitor is being discharged. The electron current is moving negative charges away from the negatively charged plate and towards the …
Solved Discharging a capacitor. Strictly speaking, the
Strictly speaking, the equation for a discharging capacitor Q(t) = Qoe-t/RC implies that an infinite amount of time is required to discharge a capacitor completely. Yet, for prac- tical purposes, a
capacitor may be considered to be fully discharged after a finite length of time. To be specific, consider a capacitor with capacitance C
Why do Capacitors discharge?
If you''re asking about self-discharge (when nothing is connected to the capacitor), it''s because the dielectric between the capacitor plates is not perfectly non …
The RC Circuit
3. Why isn''t the time constant defined to be the time it takes the capacitor to become fully charged or discharged? 4. Explain conceptually why the time constant is larger for increased resistance.
5. What does an oscilloscope measure? 6. Why can''t we use a multimeter to measure the voltage in the second half of this lab? 7. Draw and label ...
RC Integrator Theory of a Series RC Circuit
As we have seen previously, the RC time constant reflects the relationship between the resistance and the capacitance with respect to time with the amount of time, given in seconds, being directly
proportional to resistance, R and capacitance, C. Thus the rate of charging or discharging depends on the RC time constant, τ = RC nsider the …
Capacitor Charge and Discharge Questions and Revision | MME
The capacitor at this stage should be fully discharged as no current has yet passed through the capacitor. Set the power supply to 10 : text{V}. Move the switch to position X, which will begin
charging the capacitor. You can tell when the capacitor is fully charged when the voltmeter reading reads 10 : text{V}.
How to Safely Discharge a Capacitor
Capacitors are electronic components found in almost every device containing a circuit board. Large capacitors can store enough charge to cause injuries, so they must be discharged properly. While
iFixit currently doesn''t sell a capacitor discharge tool, you can easily create your own.
When capacitor is fully charged.
A capacitor is fully charged when it cannot hold any more energy without being damaged and it is fully discharged if it is brought back to 0 volts DC across its terminals.You can also think of it as
the capacitor loses its charge, its voltage is dropping and so the electric field applied on the electrons decreases, and there is less force ...
5.19: Charging a Capacitor Through a Resistor
When the capacitor is fully charged, the current has dropped to zero, the potential difference across its plates is (V) (the EMF of the battery), and the energy stored in the capacitor (see Section
5.10) is …
How Long Does It Take to Discharge a Capacitor?
A fully charged capacitor discharges to 63% of its voltage after one time period. After 5 time periods, a capacitor discharges up to near 0% of all the voltage that it once had. ... This article
explains how long it takes to discharge a capacitor. This can be calculated using the RC time constant and waiting 5 time constants, which brings the ...
I wonder why I cannot charge a capacitor with alternating current?
Why can''t I charge the capacitor with AC? How do the plates block the flow of electrons with DC but not with AC. ... It will charge the capacitor on one half cycle and discharge it on the other
half. The net charge will be zero. Share. Cite. Improve this answer. Follow answered Sep 14, 2014 at 3:31. Ross Millikan Ross Millikan. 8,593 1 1 ...
circuit analysis
When the capacitor is fully charged (the parking lot is full of charges), and you connect a load (let''s say a resistor), the charges move from one side of the plate to the other through the resistor
(a current …
Discharging, Storage, and Disposal of Capacitors in Electronic …
power supply that remained energized by the capacitors on the supply. It was found that the capacitors were not discharged and the discharging circuitry on the card had failed. The circuit card did
not "look" to be physically damaged. CAPACITOR SAFETY: Capacitors are common components in electronic devices. They store
Capacitor Charge, Discharge and Time Constant Calculator
RC Time Constant Calculator. The first result that can be determined using the calculator above is the RC time constant. It requires the input of the value of the resistor and the value of the
capacitor.. The time constant, abbreviated T or τ (tau) is the most common way of characterizing an RC circuit''s charge and discharge curves.
Capacitor Charging & Discharging | Formula, Equations & Examples
Example: If a capacitor is fully charged to 10 V, calculate the time constant and how long it will take for the capacitor to fully discharge (equal to 5 time constants). The resistance of the ...
$begingroup$ The vertical wires in your two left hand diagrams will short-circuit the battery when you close the switch. The battery will get hot (perhaps dangerously so) and will quickly lose almost
all its stored energy. The wire can have almost zero voltage across it, even when the switch is closed and current is going through it, because its …
Capacitor Discharging
To discharge a capacitor, the power source, which was charging the capacitor, is removed from the circuit, so that only a capacitor and resistor can connected together in series. The capacitor drains
its voltage and …
My biggest problem is when I discharge a supercapacitor, let''s say 100F 2.7V, I use a boost converter, but all boost converters have a minimum input voltage of about 0.9V. But the capacitor still
has a lot of energy, about 40%. It is frustrating because I''m not able to use this energy so my real useful capacity of capacitor is only 60%.
Capacitor Charge and Discharge Questions and …
The capacitor at this stage should be fully discharged as no current has yet passed through the capacitor. Set the power supply to 10 : text{V}. Move the switch to position X, which will begin
charging the capacitor. …
What are the behaviors of capacitors and inductors at time t=0?
A fully discharged capacitor, having a terminal voltage of zero, will initially act as a short-circuit when attached to a source of voltage, drawing maximum current as it begins to build a charge.
Over time, the capacitor''s terminal voltage rises to meet the applied voltage from the source, and the current through the capacitor decreases ...
Charging and discharging capacitors
When a capacitor is discharged, the current will be highest at the start. This will gradually decrease until reaching 0, when the current reaches zero, the capacitor is fully discharged as there is
no charge stored across it. The rate of decrease of the potential difference and the charge will again be proportional to the value of the current.
Discharging a Capacitor (Formula And Graphs)
Key learnings: Discharging a Capacitor Definition: Discharging a capacitor is defined as releasing the stored electrical charge within the capacitor.; Circuit Setup: A charged capacitor is connected
in series with a resistor, and the circuit is short-circuited by a switch to start discharging.; Initial Current: At the moment the switch is …
Capacitor Transient Response | RC and L/R Time Constants
Because capacitors store energy in the form of an electric field, they tend to act like small secondary-cell batteries, being able to store and release electrical energy.A fully discharged capacitor
maintains zero volts across its terminals, and a charged capacitor maintains a steady quantity of voltage across its terminals, just like a battery.. When …
Can a capacitor charge and discharge at the same time?
Current can''t flow both ways at the same time in one conductor (wire). So if the load demands more than the supply can handle a capacitor will discharge but if the supply could handle the load then
the capacitor charges ? $endgroup$ ... How to let a capacitor be fully charged before being discharged by a load? 0.
Capacitor Discharging
Conversely, a smaller capacitance value leads to a quicker discharge, since the capacitor can''t hold as much charge, and thus, ... The time it takes for a capacitor to discharge 63% of its fully
charged voltage is equal to one time constant. After 2 time constants, the capacitor discharges 86.3% of the supply voltage. ...
If we charge a capacitor can we discharge it into a battery?
A single Maxwell (for instance) BCAP0350 2.7v ultra capacitor that''s about the size of a D cell has a capacity of 1300 Joules (1.3 x 10^3 J). It is extremely useful to use ultracaps to charge
batteries if the nature of the power source is intermittent and high current (say, at 35 to 175 Amps, also within spec of the one I listed).
Why do Capacitors discharge?
i am so confused why they discharge. Keeping always in mind that a capacitor stores electrical energy (and not electric charge), a capacitor in a circuit discharges when the attached circuit
''draws'' on the stored energy in the capacitor.
How to Discharge a Capacitor? Using Bleeder Resistor, …
There are a couple of techniques to properly discharge a capacitor. We will see the details for each technique one-by-one. No matter how we discharge the capacitor, never touch the leads of the
capacitor with your bare hands. Be extremely careful. Using a Metal Object (Screwdriver) This method is not the safest but it can …
circuit analysis
$begingroup$ it has to maintain the same voltage as before is incorrect ... think of the capacitor as a bucket with a 1cm hole in the bottom ... if you set the bucket in a lake, without submerging
the bucket fully, the water will flow into the bucket through the hole until the water in the bucket and the water outside of the bucket are at same level ....
Capacitor Discharge Time Calculator (with Examples)
How fast does a capacitor discharge? The speed at which a capacitor discharges depends on its capacitance and the resistor it is connected to. It depends on the RC time constant. In general, a
capacitor is considered fully charged when it reaches 99.33% of the input voltage. Conversely a cap is fully discharged when it loses the same amount of ...
Capacitor Discharge
When the capacitor is fully discharged, we speak of the steady state. This is the main difference between how capacitors behave in DC and AC circuits. The current change of a capacitor during
discharge. The figure …
5.18: Discharging a Capacitor Through a Resistor
If the capacitor is discharging, (dot Q) is negative. Expressed otherwise, the symbol to be used for the rate at which a capacitor is losing charge is (-dot Q). In Figure (V.)24 a capacitor is
discharging through a resistor, and the current as drawn is given by (I=-dot Q). The potential difference across the plates of the capacitor ...
10.14: Discharge of a Capacitor through an ...
The switch is closed, and charge flows out of the capacitor and hence a current flows through the inductor. Thus while the electric field in the capacitor diminishes, the magnetic field in the
inductor grows, and a back electromotive force (EMF) is induced in the inductor. Let (Q) be the charge in the capacitor at some time.
RC Integrator Theory of a Series RC Circuit
As we have seen previously, the RC time constant reflects the relationship between the resistance and the capacitance with respect to time with the amount of time, given in seconds, being directly …
The charge and discharge of a capacitor
The rate at which a capacitor can be charged or discharged depends on: (a) the capacitance of the capacitor) and (b) the resistance of the circuit through which it is …
5.19: Charging a Capacitor Through a Resistor
When the capacitor is fully charged, the current has dropped to zero, the potential difference across its plates is (V) (the EMF of the battery), ... It will discharge when the potential difference
across the electrodes is higher than a certain threshold. When an electric field is applied across the tube, electrons and positive ions ...
I wonder why I cannot charge a capacitor with alternating current?
Of course you can charge a capacitor with AC. The problem is that you keep changing how it is charged. While you apply a positive voltage to one plate, it will get a positive charge; half a cycle
later, it will attempt to get a negative charge; and so it continues.
Capacitor Charging & Discharging | Formula, Equations & Examples
The capacitor is fully charged when the voltage of the power supply is equal to that at the capacitor terminals. This is called capacitor charging; and the …
3.5: RC Circuits
capacitor fully charged, a long time after the switch is closed. When the capacitor has been allowed to charge a long time, it will become "full," meaning that the potential difference created by the
accrued charge balances the applied potential. In this case, the first and third terms of the Kirchhoff loop equation for the outer loop cancel ... | {"url":"https://piotrmorsztyn.pl/19704/07/2024.html","timestamp":"2024-11-08T05:05:42Z","content_type":"text/html","content_length":"35909","record_id":"<urn:uuid:eedffce3-4bcb-4bf7-a9d8-e1cedaa73041>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00676.warc.gz"} |
Mcelroy Fusion Pressure Chart
Mcelroy Fusion Pressure Chart - Web quickly find the right fusion pressure for your job. Certain repairs, warranty work, and inquiries may be directed, at mcelroy’s discretion, to an. Web use
mcelroy's fusion pressure calculator to quickly find the right fusion pressure for your job. Certain repairs, warranty work, and inquiries may be directed, at mcelroy’s discretion, to an. Web use
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McElroy TracStar® 500 Series 3 Fusion Machine
Web use mcelroy's fusion pressure calculator to quickly find the right fusion pressure for your job. Web mcelroy sliding fusion pressure calculator. 28 construction equipment pdf manual. Certain
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Using the McElroy Fusion Slide Calculator YouTube
Web mcelroy sliding fusion pressure calculator. Web use mcelroy's fusion pressure calculator to quickly find the right fusion pressure for your job. Quickly and easily determine the correct fusion
pressure, temperatures, and. Web mcelroy sliding fusion pressure calculator. With the aid of mcelroy's fusion pressure calculator, determining the proper fusion gauge pressure is.
Determining Drag Pressure on a McElroy Fusion Machine YouTube
28 construction equipment pdf manual. Don’t leave your fusions to chance. Web you can calculate your fusion pressure three ways. A simple way to perform a comprehensive. To properly fuse pipe the
McElroy McCalc® Fusion Pressure Calculator
To properly fuse pipe the fusion. • shift the selector valve down into the fusing position. Web mcelroy sliding fusion pressure calculator. 28 construction equipment pdf manual. Web don’t leave your
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Quickly determine fusion pressure with McCalc® calculator McElroy
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McElroy Pit Bull® 412 Fusion Machine
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pressure. To properly fuse pipe the fusion pressure must be. Web view and download mcelroy 28 operator's manual online.
McElroy MegaMc® 1648 Fusion Machine
Web page 5 pressure (shown above) tepa = total effective piston area drag = force required to move pipe example: To properly fuse pipe the fusion. Web use mcelroy's fusion pressure calculator to
quickly find the right fusion pressure for your job. Certain repairs, warranty work, and inquiries may be directed, at mcelroy’s discretion, to an. Web • use the.
McElroy Rolling 28 Fusion Machine
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McElroy TracStar® 900 Fusion Machine
To properly fuse pipe the fusion pressure must be. Web by selecting your mcelroy fusion machine and entering your pipe size and pressure requirements, the recommended theoretical gauge pressure may
be. Web use mcelroy's fusion pressure calculator to quickly find the right fusion pressure for your job. Web use mcelroy's fusion pressure calculator to quickly find the right fusion pressure.
Everything you need to know about McElroy Optimized Cooling™ McElroy
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requirements, the recommended theoretical gauge pressure may be. Web mcelroy sliding fusion pressure calculator. Certain repairs, warranty work, and inquiries may be directed, at mcelroy’s
discretion, to an. To properly fuse.
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example: To properly fuse pipe the fusion pressure must be. Our online calculator tool has a guide that breaks down each step. To properly fuse pipe the fusion. Web don’t leave your fusions to
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and. Web use mcelroy's fusion pressure calculator to quickly find the right fusion pressure for your job.
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A generalized Zakharov-Shabat equation with finite-band solutions and a soliton-equation hierarchy with an arbitrary parameter
In this paper, a generalized Zakharov-Shabat equation (g-ZS equation), which is an isospectral problem, is introduced by using a loop algebra G. From the stationary zero curvature equation we define
the Lenard gradients {g [j]} and the corresponding generalized AKNS (g-AKNS) vector fields {X[j]} and X[k] flows. Employing the nonlinearization method, we obtain the generalized Zhakharov-Shabat
Bargmann (g-ZS-B) system and prove that it is Liouville integrable by introducing elliptic coordinates and evolution equations. The explicit relations of the X[k] flows and the polynomial integrals
{H[k]} are established. Finally, we obtain the finite-band solutions of the g-ZS equation via the Abel-Jacobian coordinates. In addition, a soliton hierarchy and its Hamiltonian structure with an
arbitrary parameter k are derived.
Scopus Subject Areas
• Statistical and Nonlinear Physics
• Mathematics(all)
• Physics and Astronomy(all)
• Applied Mathematics
Dive into the research topics of 'A generalized Zakharov-Shabat equation with finite-band solutions and a soliton-equation hierarchy with an arbitrary parameter'. Together they form a unique | {"url":"https://scholars.hkbu.edu.hk/en/publications/a-generalized-zakharov-shabat-equation-with-finite-band-solutions","timestamp":"2024-11-12T00:37:21Z","content_type":"text/html","content_length":"55328","record_id":"<urn:uuid:08442227-9285-4d1b-a5f8-07899b4c38a4>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00027.warc.gz"} |
The Kissing Circles
There are some interesting figures below. You can see that we can put within a circle one or more circles of equal radius. The important property of these circles is that every consecutive circles
touch each other. Given the radius R of the larger circle and the number of small circles N of equal radius inside, you will have to find the radius of the smaller circles r, the area surrounded by
the kissing small circles (light blue) I and the area outside the kissing small circles but inside the larger circle (light green) E. FiguresforN =1,2,3,4,5,6 Input The input file will contain
several lines of inputs. Each line contains non-negative integers R (R ≤ 10000) and N (1 ≤ N ≤ 100) as described before. Input is terminated by end of file. Output For each line of input produce one
line of output. This one line contains three floating point numbers r, I and E as described before. The floating point numbers should have ten digits after the decimal point. The output will be
checked with special correction programs. So you wont have to worry about small precision errors. Sample Input 10 3 10 4 10 5 10 6 Sample Output 4.6410161514 3.4732652470 107.6854162259 4.1421356237
14.7279416563 83.8264899217 3.7019190816 29.7315551092 69.1625632742 3.3333333333 45.6568837582 59.0628713615 | {"url":"https://ohbug.com/uva/10283/","timestamp":"2024-11-03T17:31:39Z","content_type":"text/html","content_length":"2558","record_id":"<urn:uuid:732eaa2d-ada5-40d4-96b7-59b6b9cc334a>","cc-path":"CC-MAIN-2024-46/segments/1730477027779.22/warc/CC-MAIN-20241103145859-20241103175859-00553.warc.gz"} |
Liters to Moles Calculator
Introduction to liters to moles calculator
Liter and mole both are measurement units used to measure different concentrations of a substance. There are many physical methods to carry out these conversions but the easiest and quick method is
to use liters to moles calculator. This moles to liters calculator is 100% accurate and free to use. Here in this article, we will discuss the conversion of liters to moles.
What is liter?
A liter is the measurement unit that is used to measure different volumes of a gas or a liquid. Volume is the amount of space something takes up. It describes how much a container can hold or how
much gas can be filled in a container. Measuring cups, droppers, measuring cylinders, and beakers are all tools that can be used to measure volume. Other units for volume are milli liter and quartz.
A liter is used to measure larger volumes of gas.
Liters to moles formula
Mole is the SI unit of the large concentration of a substance. In the case of atoms, one mole is equal to 6.02 x 10^23 atoms while in the case of liters, one mole is equal to 22.4 liters at standard
temperature and pressure. Following is given the formula to convert liters to moles
Mole = Given Volume (in L) / 22.4 L
Volume in liters = Moles x 22.4 L
One can use these formulas to carry out liters to moles conversions and vice versa. Liters to moles calculator also uses the above formula. Let us solve the following example for practice
How to calculate the number of moles present in liters of nitrogen?
We can calculate the number of moles present in 29 liters of nitrogen (N[2]) gas.
The formula is
Moles = Given volume / 22.4 L
Moles = 29 / 22.4
Moles = 1.29
Answer; 29 liters of nitrogen (N2) gas contain 1.29 moles of nitrogen gas.
You can simply use moles to liters conversion calculator for carrying this calculations.
How to convert 2.5 moles of carbon dioxide gas to liters?
We can convert 2.5 moles of carbon dioxide (CO[2]) gas to liters.
The formula is
Liters = Moles x 22.4 L
Liters = 2.5 x 22.4
Liters = 56 L
Answer; 2.5 moles of carbon dioxide (CO[2]) gas is equal to 56 Liters of Carbon dioxide gas.
You can also use liters to moles calculator for liters to moles conversion free online.
Frequently Asked Questions
What is a Milli Liter and How many Milli Liters are Equal to one Liter?
A milli liter is the smallest unit of volume and one liter is equal to 1000 milli liters. A milli liter is denoted by mL.
How to convert 2500 mL to L?
L = given volume in mL / 1000
L = 2500 / 1000
L = 2.5
How to operate Liters to Moles Calculator?
Enter the given volume in the liter section and press the “calculate” button. The calculator would do the rest and your answer would appear on the screen.
Is moles to liters conversion calculator accurate?
Yes, volume to moles calculator is accurate when it comes to converting liters to moles. | {"url":"https://calculatores.com/liters-to-moles-calculator","timestamp":"2024-11-13T09:07:01Z","content_type":"text/html","content_length":"30167","record_id":"<urn:uuid:bd06cde7-8f02-4e3e-b5e7-c122e9af5b8a>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00671.warc.gz"} |
Relationship with Constant Angular Acceleration MCQ [PDF] Quiz Questions Answers | Relationship with Constant Angular Acceleration MCQs App Download & e-Book
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Relationship with Constant Angular Acceleration MCQ (PDF) Questions Answers Download
MCQ 1:
If θ is angular displacement, Ω angular velocity and α is angular acceleration, then by appropriate kinematic equation, Ωt-1/2αt^2=
1. θ
2. θ-θ[o]
3. θ+θ[o]
4. θ[o]
MCQ 2:
If x is the displacement, v is the velocity and a is acceleration at time t, then v^2=
1. v[o]^2+ax
2. v[o]^2+2ax
3. v[o]^2+2a(x-x[o])
4. v[o]^3`+2a(x-x[o])
MCQ 3:
If θ is angular displacement, Ω[o] is angular velocity at time t=0 and α is angular acceleration, then by appropriate kinematic equation, θ-θ[o]=
1. Ω[o]t+αt
2. Ω[o]t+1/2αt
3. Ω[o]t+1/2αt^2
4. Ω[o]+1/2αt^2
MCQ 4:
If θ is angular displacement, Ω[o] is angular velocity at time t=0 and α is angular acceleration, then by appropriate kinematic equation, Ω^2=
1. Ω[o]^2+2α(θ-θ[o])
2. Ω[o]+2α(θ-θ[o])
3. Ω[o]+1/2α(θ-θ[o])
4. Ω[o]+α(θ-θ[o])
MCQ 5:
Angular acceleration is denoted by
1. v
2. a
3. α
4. Ω
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Emergence and Incremental Probability
In 'Emergence and Incremental Impact', I argued (contra Kingston and Sinnott-Armstrong) that emergent properties do nothing to undermine the basic case for individual impact: they're just another
kind of threshold case, and thresholds are compatible with difference-making increments.
In that old post, I assumed counterfactual determinacy to make the case for there being some precise increment(s) that make a difference whenever a collection of increments together does. But while
revising my paper on collective harm, it occurred to me that the case becomes much more clear-cut when made in terms of probabilities.
Consider. Kingston & Sinnott-Armstrong object (p.179):
[T]he expected disvalue approach requires that the probability of dangerous events can themselves be increased (minutely) by the addition of relatively tiny emissions. But why should we assume
this? ... Emergence affects probability as it does other properties. While adding oil to an engine reduces the probability of a moving part failing, it is implausible that adding a molecule of
oil reduces that probability of failure by 1/10^25.
Why is this implausible? Suppose that adding a large drop of oil containing 10^23 molecules would reduce the probability of engine failure by at least 1/100. Now consider the sequence of possible
futures M[n] that consist in adding precisely n molecules of oil to the engine. By our initial supposition, the probability of engine failure in M[10^23] is at least 1/100 less than in M[0]. But then
it's logically impossible to assign probabilities of engine failure to each intermediate state in the sequence without some of those values in adjacent states differing by at least 1/10^25. ...
Of course, it may well be that adding only the first molecule of oil would indeed have a much lower than average chance of making a difference. But even if so, this merely ensures that some other
increments--namely, those in the threshold vicinity--have a correspondingly higher chance of making a difference. This is the familiar structure of expected-value reasoning in threshold cases. As
previously argued [in my paper], if we've no idea where the thresholds lie, or no special reason to expect ourselves to be disproportionately likely to be distant from them, then the mere existence
of such thresholds makes no difference to the expected value of our contribution: it remains equal to the average value of many such contributions. Nothing about emergent properties changes this
basic reasoning. But it does help to emphasize a crucial dialectical point, that the important question is not whether a single increment in isolation makes a difference (it need not), but rather
whether some increment in context does so (that is, given how many previous increments have already been made).
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Scientific RPN Calculator (with ATTINY85)
03-06-2018, 11:44 AM
Post: #4
Paul Dale Posts: 1,848
Senior Member Joined: Dec 2013
RE: Scientific RPN Calculator (with ATTINY85)
Nice device, the code looks very tight with plenty of space savers. I like \( \sqrt{x} = e^{\frac{ln (x)}{2}} \) and the common routine for both e^x and the trigonometric functions.
It also reaffirms the miracle of the HP 35 with its 7680 bits of ROM and the Sinclair Scientific with its 3520 bits of ROM.
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Inorganic Chemistry
Title: Inorganic Chemistry 1
Inorganic Chemistry
Bonding and Coordination Chemistry
Books to follow Inorganic Chemistry by Shriver
Atkins Physical Chemistry Atkins
C. R. Raj C-110, Department of Chemistry
Bonding in s,p,d systems Molecular orbitals of
diatomics, d-orbital splitting in crystal field
(Oh, Td). Oxidation reduction Metal Oxidation
states, redox potential, diagrammatic
presentation of potential data. Chemistry of
Metals Coordination compounds (Ligands
Chelate effect), Metal carbonyls preparation
stability and application. Wilkinsons catalyst
alkene hydrogenation Hemoglobin, myoglobin
oxygen transport
J.J. Thomson
When UV light is shone on a metal plate in a
vacuum, it emits charged particles (Hertz 1887),
which were later shown to be electrons by J.J.
Thomson (1899).
Light, frequency ?
Vacuum chamber
Collecting plate
Metal plate
(No Transcript)
Photoelectric Effect.
1. No electrons are ejected, regardless of the
intensity of the radiation, unless its frequency
exceeds a threshold value characteristic of the
2. The kinetic energy of the electron increases
linearly with the frequency of the incident
radiation but is independent of the intensity of
the radiation.
3. Even at low intensities, electrons are ejected
immediately if the frequency is above the
Major objections to the Rutherford-Bohr model
• We are able to define the position and velocity
of each electron precisely.
• In principle we can follow the motion of each
individual electron precisely like planet.
• Neither is valid.
Werner HeisenbergHeisenberg's name will always
be associated with his theory of quantum
mechanics, published in 1925, when he was only 23
• It is impossible to specify the exact position
and momentum of a particle simultaneously.
• Uncertainty Principle.
• ?x ?p ? h/4? where h is Planks Constant, a
fundamental constant with the value 6.626?10-34 J
h ? ½ mv2 ?
• KE 1/2mv2 h?- ?
• ? is the work function
• h? is the energy of the incident light.
• Light can be thought of as a bunch of particles
which have energy E h?. The light particles are
called photons.
If light can behave as particles,why not
particles behave as wave?
Louis de Broglie The Nobel Prize in Physics 1929
French physicist (1892-1987)
Louis de Broglie
• Particles can behave as wave.
• Relation between wavelength ? and the mass and
velocity of the particles.
• E h? and also E mc2,
• E is the energy
• m is the mass of the particle
• c is the velocity.
Wave Particle Duality
• E mc2 h?
• mc2 h?
• p h /? since ? c/?
• ? h/p h/mv
• This is known as wave particle duality
Flaws of classical mechanics
Photoelectric effect
Heisenberg uncertainty principle
limits simultaneous knowledge of conjugate
Light and matter exhibit wave-particle
duality Relation between wave and particle
properties given by the de Broglie relations
The state of a system in classical mechanics is
defined by specifying all the forces acting and
all the position and velocity of the particles.
Wave equation?Schrödinger Equation.
• Energy Levels
• Most significant feature of the Quantum
Mechanics Limits the energies to discrete
• Quantization.
The wave function
For every dynamical system, there exists a wave
function ? that is a continuous,
square-integrable, single-valued function of the
coordinates of all the particles and of time, and
from which all possible predictions about the
physical properties of the system can be obtained.
Square-integrable means that the normalization
integral is finite
If we know the wavefunction we know everything it
is possible to know.
d2 ? /dx2 8?2 m/h2 (E-V) ? 0 Assume V0
between x0 xa Also ? 0 at x 0 a
d2?/dx2 8?2mE/h2 ? 0
d2?/dx2 k2? 0 where k2 8?2mE/h2
Solution is ? C cos kx D sin kx
• Applying Boundary conditions
• ? 0 at x 0 ? C 0
• ? ? D sin kx
An Electron in One Dimensional Box
• ?n D sin (n?/a)x
• En n2 h2/ 8ma2
• n 1, 2, 3, . . .
• E h2/8ma2 , n1
• E 4h2/8ma2 , n2
• E 9h2/8ma2 , n3
Characteristics of Wave Function
He has been described as a moody and impulsive
person. He would tell his student, "You must not
mind my being rude. I have a resistance against
accepting something new. I get angry and swear
but always accept after a time if it is right."
Characteristics of Wave Function What Prof.
Born Said
• Heisenbergs Uncertainty principle We can never
know exactly where the particle is.
• Our knowledge of the position of a particle can
never be absolute.
• In Classical mechanics, square of wave amplitude
is a measure of radiation intensity
• In a similar way, ?2 or ? ? may be related to
density or appropriately the probability of
finding the electron in the space.
The wave function ? is the probability amplitude
Probability density
The sign of the wave function has not direct
physical significance the positive and negative
regions of this wave function both corresponds to
the same probability distribution. Positive and
negative regions of the wave function may
corresponds to a high probability of finding a
particle in a region.
Characteristics of Wave Function What Prof.
Born Said
• Let ? (x, y, z) be the probability function,
• ?? d? 1
• Let ? (x, y, z) be the solution of the wave
equation for the wave function of an electron.
Then we may anticipate that
• ? (x, y, z) ? ?2 (x, y, z)
• choosing a constant in such a way that ? is
converted to
• ? (x, y, z) ?2 (x, y, z)
• ? ??2 d? 1
The total probability of finding the particle is
1. Forcing this condition on the wave function is
called normalization.
• ??2 d? 1 Normalized wave function
• If ? is complex then replace ?2 by ??
• If the function is not normalized, it can be done
by multiplication of the wave function by a
constant N such that
• N2 ??2 d? 1
• N is termed as Normalization Constant
Eigen values
• The permissible values that a dynamical variable
may have are those given by
• ?? a?
• - eigen function of the operator ? that
corresponds to the observable whose permissible
values are a
• ? -operator
• ? - wave function
• a - eigen value
?? a?
If performing the operation on the wave function
yields original function multiplied by a
constant, then ? is an eigen function of the
operator ?
? e2x and the operator ? d/dx
Operating on the function with the operator d
?/dx 2e2x constant.e2x
e2x is an eigen function of the operator ?
• For a given system, there may be various possible
• As most of the properties may vary, we desire to
determine the average or expectation value.
• We know
• ?? a?
• Multiply both side of the equation by ?
• ??? ?a?
• To get the sum of the probability over all space
• ? ??? d? ? ?a? d?
• a constant, not affected by the order of
Removing a from the integral and solving for a
a ? ??? d?/ ? ?? d?
? cannot be removed from the integral.
a lt? ?? ?? gt/ lt? ?? gt
Chemical Bonding
• Two existing theories,
• Molecular Orbital Theory (MOT)
• Valence Bond Theory (VBT)
• Molecular Orbital Theory
• MOT starts with the idea that the quantum
mechanical principles applied to atoms may be
applied equally well to the molecules.
(No Transcript)
Simplest possible moleculeH2 2 nuclei and 1
• Let the two nuclei be labeled as A and B wave
functions as ?A ?B.
• Since the complete MO has characteristics
separately possessed by ?A and ?B,
• ? CA?A CB?B
• or ? N(?A ? ?B)
• ? CB/CA, and N - normalization constant
This method is known as Linear Combination of
Atomic Orbitals or LCAO
• ?A and ?B are same atomic orbitals except for
their different origin.
• By symmetry ?A and ?B must appear with equal
weight and we can therefore write
• ?2 1, or ? 1
• Therefore, the two allowed MOs are
• ? ?A ?B
For ?A ?B we can now calculate the energy
• From Variation Theorem we can write the energy
function as
• E ??A?B ?H ??A?B?/??A?B ??A?B?
Looking at the numerator E ??A?B ?H
??A?B?/??A?B ??A?B?
• ??A?B ?H ? ?A?B? ??A ?H ??A?
• ??B ?H ??B?
• ??A ?H ??B?
• ??B ?H ??A?
• ??A ?H ? ?A? ??B ?H ??B? 2??A?H ??B?
ground state energy of a hydrogen atom. let us
call this as EA
??A ?H ? ?A? ??B ?H ??B? 2??A?H ??B?
• ??A ?H ? ?B? ??B ?H ??A? ?
• ? resonance integral
? Numerator 2EA 2 ?
Looking at the denominator E ??A?B ?H
??A?B?/??A?B ??A?B?
• ??A?B ??A?B? ??A ??A?
• ??B ??B?
• ??A ??B?
• ??B ??A?
• ??A ??A? ??B ??B? 2??A ??B?
??A ??A? ??B ??B? 2??A ??B?
?A and ?B are normalized, so ??A ??A? ??B ??B?
??A ??B? ??B ??A? S, S Overlap integral.
? Denominator 2(1 S)
Summing Up . . . E ??A?B ?H ??A?B?/??A?B
Numerator 2EA 2 ?
Denominator 2(1 S)
E (EA ?)/ (1 S) Also E- (EA - ?)/ (1 S)
E EA ?
S is very small ? Neglect S
Energy level diagram
EA - ?
Linear combination of atomic orbitals
Rules for linear combination
1. Atomic orbitals must be roughly of the same
2. The orbital must overlap one another as much
as possible- atoms must be close enough for
effective overlap.
3. In order to produce bonding and antibonding
MOs, either the symmetry of two atomic orbital
must remain unchanged when rotated about the
internuclear line or both atomic orbitals must
change symmetry in identical manner.
Rules for the use of MOs When two AOs mix,
two MOs will be produced Each orbital can
have a total of two electrons (Pauli principle)
Lowest energy orbitals are filled first
(Aufbau principle) Unpaired electrons have
parallel spin (Hunds rule) Bond order ½
(bonding electrons antibonding electrons)
Linear Combination of Atomic Orbitals (LCAO)
The wave function for the molecular orbitals can
be approximated by taking linear combinations of
atomic orbitals.
c extent to which each AO contributes to the MO
?AB N(cA ?A cB?B)
?2AB (cA2 ?A2 2cAcB ?A ?B cB2 ?B 2)
Overlap integral
Probability density
Constructive interference
cA cB 1
?g N ?A ?B
?2AB (cA2 ?A2 2cAcB ?A ?B cB2 ?B 2)
density between atoms
electron density on original atoms,
The accumulation of electron density between the
nuclei put the electron in a position where it
interacts strongly with both nuclei.
Nuclei are shielded from each other
The energy of the molecule is lower
Destructive interference Nodal plane
perpendicular to the H-H bond axis (en density
0) Energy of the en in this orbital is higher.
• The electron is excluded from internuclear region
? destabilizing
(No Transcript)
Molecular potential energy curve shows the
variation of the molecular energy with
internuclear separation.
Looking at the Energy Profile
• Bonding orbital
• called 1s orbital
• s electron
• The energy of 1s orbital
• decreases as R decreases
• However at small separation, repulsion becomes
• There is a minimum in potential energy curve
11.4 eV 109 nm
LCAO of n A.O ? n M.O.
Location of Bonding orbital 4.5 eV
The overlap integral
• The extent to which two atomic orbitals on
different atom overlaps the overlap integral
S gt 0 Bonding
S lt 0 anti
Bond strength depends on the degree of overlap
S 0 nonbonding
(No Transcript)
(No Transcript)
(No Transcript)
Homonuclear Diatomics
• MOs may be classified according to
• (i) Their symmetry around the molecular axis.
• (ii) Their bonding and antibonding character.
• ?1s? ?1s? ?2s? ?2s? ?2p? ?y(2p) ?z(2p)
??y(2p) ??z(2p)??2p.
dx2-dy2 and dxy
g- identical under inversion
u- not identical
Place labels g or u in this diagram
First period diatomic molecules
Bond order 1
Bond order ½ (bonding electrons antibonding
Diatomic molecules The bonding in He2
?1s2, ?1s2
Bond order 0
Molecular Orbital theory is powerful because it
allows us to predict whether molecules should
exist or not and it gives us a clear picture of
the of the electronic structure of any
hypothetical molecule that we can imagine.
(No Transcript)
Second period diatomic molecules
?1s2, ?1s2, ?2s2
Bond order 1
Diatomic molecules Homonuclear Molecules of the
Second Period
?1s2, ?1s2, ?2s2, ?2s2
Bond order 0
MO diagram for B2
Li 200 kJ/mol F 2500 kJ/mol
Same symmetry, energy mix- the one with higher
energy moves higher and the one with lower energy
moves lower
MO diagram for B2
Paramagnetic ?
General MO diagrams
O2 and F2
Li2 to N2
Orbital mixing Li2 to N2
Bond lengths in diatomic molecules
(No Transcript)
From a basis set of N atomic orbitals, N
molecular orbitals are constructed. In Period 2,
The eight orbitals can be classified by symmetry
into two sets 4 ? and 4 ? orbitals.
The four ? orbitals from one doubly degenerate
pair of bonding orbitals and one doubly
degenerate pair of antibonding orbitals.
The four ? orbitals span a range of energies, one
being strongly bonding and another strongly
antibonding, with the remaining two ? orbitals
lying between these extremes.
To establish the actual location of the energy
levels, it is necessary to use absorption
spectroscopy or photoelectron spectroscopy.
(No Transcript)
Distance between b-MO and AO
Heteronuclear Diatomics.
• The energy level diagram is not symmetrical.
• The bonding MOs are closer to the atomic
orbitals which are lower in energy.
• The antibonding MOs are closer to those higher in
c extent to which each atomic orbitals
contribute to MO
If cA?cB the MO is composed principally of ?A
1s 1 2s, 2p 7
? c1 ?H1s c2 ?F2s c3 ?F2pz
Largely nonbonding
2px and 2py
1?2 2?21?4
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A converse to a theorem of Gross, Zagier, and Kolyvagin
Let E be a semistable elliptic curve over Q. We prove that if E has non-split multiplicative reduction at at least one odd prime or split multiplicative reduction at at least two odd primes, then
(Formula Presented) We also prove the corresponding result for the abelian variety associated with a weight 2 newform f of trivial character. These, and other related results, are consequences of our
main theorem, which establishes criteria for (Formula Presented) where V is the p-adic Galois representation associated with f, that ensure that (Formula Presented) The main theorem is proved using
the Iwasawa theory of V over an imaginary quadratic field to show that the p-adic logarithm of a suitable Heegner point is non-zero.
All Science Journal Classification (ASJC) codes
• Statistics and Probability
• Statistics, Probability and Uncertainty
• Birch-swinnerton-dyer conjecture
• Heegner points
• Iwasawa theory
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conic optimization
\(\) We introduce a family of symmetric convex bodies called generalized ellipsoids of degree \(d\) (GE-\(d\)s), with ellipsoids corresponding to the case of \(d=0\). Generalized ellipsoids (GEs)
retain many geometric, algebraic, and algorithmic properties of ellipsoids. We show that the conditions that the parameters of a GE must satisfy can be checked in strongly polynomial … Read more | {"url":"https://optimization-online.org/tag/conic-optimization/","timestamp":"2024-11-03T17:18:24Z","content_type":"text/html","content_length":"111424","record_id":"<urn:uuid:645b924c-17e9-4a41-84e7-db093554ac1a>","cc-path":"CC-MAIN-2024-46/segments/1730477027779.22/warc/CC-MAIN-20241103145859-20241103175859-00166.warc.gz"} |
Linear Suffix Array
One article out of three thousands is beautiful. "
Simple Linear Work Suffix Array Construction
" (Juha Karkkainen and Peter Sanders, 2003) is a simple and elegant linear algorithm for building suffix array in linear time. Back in 2003, When I saw the article the very first time back, I
thought: "
This is a recursive diamond
Suffix Arrays
(SA) are a powerfull tool used in many different fields such as
string matching
, and many others. A suffix array A of T is just a sorted array of suffixes of T. To avoid quadratic space we store only the indices of the suffixes, instead of full suffixes of T. Given SA(T), one
can search for occurrences of P directly on the suffix array using binary search in O(|P| lg |T|) time. This can be improved to O(|P| + lg |T|).
SA were originally
Gene Myers
(ex-Celera) and
Udi Manber
(now at Google). For more than a decade, the direct construction of suffix array was O(N^2). SA were built in linear time indirectly by
an intermediate
suffix tree
(which are expensive from the point of view of memory). SA is equivalent to an in-order traversal of the leaves of the suffix tree.
Here a succint description of the algorithm:
1. Sort Σ, the alphabet of the T in linear time by using radix sort;
2. Replace each letter in the text with its rank among the letters in the text;
3. Divide the text T into 3 parts:
• T0 = < (T[3i ], T[3i + 1], T[3i + 2]) , i>=0 . . . >
• T1 = < (T[3i + 1], T[3i + 2], T[3i + 3]) , i=0>
• T2 = < (T[3i + 2], T[3i + 3], T[3i + 4]) , i >= 0 >
4. Recurse on the concatenation of T0 and T1. When this recursive call returns, we get T0 and T1 sorted in a suffix array. After that, we need is to sort the suffixes of T2, and merge them with the
old suffixes to get suffixes of T. This is the point where the algorithm become a diamond: the construction of the suffixes of T2 and the linear merge.
5. Note that by construction T2[i:] = T[3i+2:]= (T[3i+2], T[3i+3:]) = (T[3i+2], T0[i+1:]). Therefore we can have T2[i:] from the already built To[i+1]
6. Merge the sorted suffixes of T0, T1, and T2. Remember that suffixes of T0 and T1 are already sorted, so comparing a suffix from T0 and a suffix from T1 takes constant time. To compare against a
suffix from T2, we decompose it again to get a suffix from either T0 or T1;
Since this sorting and merging is done in linear time, we get a recursion formula T(n)=T(2/3n)+O(n), which gives linear time. You can prove it by substitution -- intuitively note that 2/3
C++ code for suffix array
contained therein. It is neat, simple and instructive.
2 comments:
1. That's a really nice algorithm!
2. Two new linear SA algorithms are available at http://www.cs.sysu.edu.cn/nong/, faster and simple too... | {"url":"http://codingplayground.blogspot.com/2009/03/linear-suffix-array.html","timestamp":"2024-11-07T16:59:45Z","content_type":"application/xhtml+xml","content_length":"133984","record_id":"<urn:uuid:f12aaec7-a81c-4cb1-a043-5bbb98a1fdc8>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00760.warc.gz"} |
2023 Applicant Profiles and Admissions Results
Re: 2023 Applicant Profiles and Admissions Results
*will update after cycle
Applying to Where:
Stanford - Rejected 2/10
Berkeley - Rejected 2/13
Cornell - Rejected 2/2
Carnegie Mellon - Rejected 3/28
UT Austin - Rejected 4/20
Minnesota - Waitlisted 2/16 -> Accepted (MS) 4/19
Washington - Rejected 2/3
Maryland - Rejected 4/23
Rice - Rejected 2/8
Ohio State - Waitlisted 2/24 -> Accepted 4/3
Texas A&M - Accepted 2/15
USC - Accepted 4/3
Colorado - Rejected 4/20
Boston University - Rejected 3/2
LSU - Accepted 2/14
UC Riverside - Accepted 4/5
Oregon State - Accepted 3/7
University of Houston - Accepted 3/18
Baylor - Submitted -> withdrawn
Last edited by colton on Sun Apr 23, 2023 9:51 am, edited 23 times in total.
Re: 2023 Applicant Profiles and Admissions Results
Last edited by hilberthotel on Thu Feb 09, 2023 11:16 am, edited 1 time in total.
Re: 2023 Applicant Profiles and Admissions Results
hilberthotel wrote: ↑
Tue Feb 07, 2023 12:42 pm
Undergrad + Graduate Institution: Tier 1 Indian
Major(s): Math
GPA: 3.1
Math GPA: 3.8(in-person math - 4)
Masters's GPA: 3.6
Program Applying: Pure Math
Applying to Where:
GRE - 169/164/3
mGRE - 860
Grad courses taken - Algebraic Geometry, Algebraic Number Theory, Cryptography, Stochastic Processes, Advanced Probability, Commutative Algebra, Statistical Inference, Galois Theory, Measure
Theory, Coding Theory, Advanced Operations Research, Calculus on Manifolds and Data Science.
Brown - Submitted
Dartmouth - Rejected
Boston College- Submitted
UIC - Submitted(email by graduate directors to confirm interest)
Indiana- Submitted(1st open house invite)
UMass Amherst- Submitted
UArizona - Submitted
Oklahoma(Only one guy) - Submitted
Temple(Only one guy) - Waitlisted
Stevens - Submitted
When did you hear from Temple?
Re: 2023 Applicant Profiles and Admissions Results
inaicecream wrote: ↑
Tue Feb 07, 2023 1:05 pm
hilberthotel wrote: ↑
Tue Feb 07, 2023 12:42 pm
Undergrad + Graduate Institution: Tier 1 Indian
Major(s): Math
GPA: 3.1
Math GPA: 3.8(in-person math - 4)
Masters's GPA: 3.6
Program Applying: Pure Math
Applying to Where:
GRE - 169/164/3
mGRE - 860
Grad courses taken - Algebraic Geometry, Algebraic Number Theory, Cryptography, Stochastic Processes, Advanced Probability, Commutative Algebra, Statistical Inference, Galois Theory, Measure
Theory, Coding Theory, Advanced Operations Research, Calculus on Manifolds and Data Science.
Brown - Submitted
Dartmouth - Rejected
Boston College- Submitted
UIC - Submitted(email by graduate directors to confirm interest)
Indiana- Submitted(1st open house invite)
UMass Amherst- Submitted
UArizona - Submitted
Oklahoma(Only one guy) - Submitted
Temple(Only one guy) - Waitlisted
Stevens - Submitted
When did you hear from Temple?
I emailed them asking for an update.
Re: 2023 Applicant Profiles and Admissions Results
Institution: Well-known(ish) LAC
GPA: Top 10% of my class (for anonymity and since we have severe grade deflation)
Major: Mathematics
Type of Student: domestic white male
Research: One summer in experimental particle physics, paid, but no real production. One program similar to PolyMath, that was essentially an unpaid REU, a final report, unpublished. One NSF REU
(with people on this thread considering it a top choice) with a publication, and submission to a top journal. International REU with a pretty famous mentor, publication upcoming.
Coursework: (all undergrad level) Linear Algebra, Vector Calculus, Discrete Structures, Algebraic Combinatorics, Abstract Algebra, Complex Analysis, Topology, Real Analysis, Galois Theory, Discrete
Geometry, Algebraic Topology, Independent Study on combinatorics, Algebraic Geometry, Commutative Algebra and Homological Algebra, and Real Functions and Measures (the last 3 were done “abroad”
virtually), and a senior thesis in combinatorics.
Other: I worked as a tutor for all the classes I’ve taken and a course assistant/grader for a sizable subset of those classes. I’ve also been a drop-in tutor, note taker, and lab TA for intro
Program Applying: Pure Math/Applied Math PhD (Except Cambridge)
No GREs
Applied (in order of hearing back):
Cambridge Part III: Conditional Acceptance 12/14
Harvard SEAS: Interview 12/22 --> Reject 2/6
UChicago: Reject 1/13
Yale: Reject 1/20
BMS Phase I: Interview/Invitation to Berlin 1/20-->Waitlist
Harvard: Reject 1/27
Northwestern: Reject 1/28 (Expected, my SOP wasn't really that great)
Cornell: Reject 1/30
UCLA: Reject 2/1
UMN: Acceptance 2/2
Princeton: Reject 2/3
Washington: Reject 2/3
Dartmouth: Reject 2/6
JHU: Reject 2/8
UIUC: Acceptance 2/8
Brown: Reject 2/9
U Oregon: Acceptance 2/9
Stanford: Reject 2/10
Berkeley: Reject 2/13
Caltech: Reject 2/13
UNL: Acceptance 2/16
Utah: Waitlist 2/16
Some forgotten dates:
MIT: Reject
Stony Brook: Reject
Columbia: Reject
Wisconsin: Reject
Ohio State: Waitlist
Things I'm waiting on (that there might be hope):
Fulbright: Semi-Finalist
UT Austin
Last edited by physicsofcomica on Thu Mar 09, 2023 6:35 pm, edited 5 times in total.
Re: 2023 Applicant Profiles and Admissions Results
physicsofcomica wrote: ↑
Tue Feb 07, 2023 3:50 pm
Institution: Well-known(ish) LAC
GPA: Top 10% of my class (for anonymity and since we have severe grade deflation)
Major: Mathematics
Type of Student: domestic white male
Research: One summer in experimental particle physics, paid, but no real production. One program similar to PolyMath, that was essentially an unpaid REU, a final report, unpublished. One NSF REU
(with people on this thread considering it a top choice) with a publication, and submission to a top journal. International REU with a pretty famous mentor, publication upcoming.
Coursework: (all undergrad level) Linear Algebra, Vector Calculus, Discrete Structures, Algebraic Combinatorics, Abstract Algebra, Complex Analysis, Topology, Real Analysis, Galois Theory,
Discrete Geometry, Algebraic Topology, Independent Study on combinatorics, Algebraic Geometry, Commutative Algebra and Homological Algebra, and Real Functions and Measures (the last 3 were done
“abroad” virtually), and a senior thesis in combinatorics.
Other: I worked as a tutor for all the classes I’ve taken and a course assistant/grader for a sizable subset of those classes. I’ve also been a drop-in tutor, note taker, and lab TA for intro
Program Applying: Pure Math/Applied Math PhD (Except Cambridge)
No GREs
Applied (in order of hearing back):
Cambridge Part III: Conditional Acceptance 12/14
Harvard SEAS: Interview 12/22 --> Reject 2/6
UChicago: Reject 1/13
Yale: Reject 1/20
BMS Phase I: Interview/Invitation to Berlin 1/20
Harvard: Reject 1/27
Northwestern: Reject 1/28 (Expected, my SOP wasn't really that great)
Cornell: Reject 1/30
UCLA: Reject 2/1
UMN: Acceptance 2/2
Princeton: Reject 2/3
Washington: Reject 2/3
Dartmouth: Reject 2/6
Hi, could you please elaborate on what conditional acceptance from Cambridge part 3 means?
Re: 2023 Applicant Profiles and Admissions Results
Undergrad Institution: a midwest big state in China transferred to a midwest big state in the US
Major(s): Math with Honors, Data Science
Minor(s): none
GPA: 3.46/4.0 (freshman in China); 4.0/4.0 (US)
Math GPA: not displayed on the transcript
Type of Student: International Asian Male
GRE Revised General Test: didn't submit except for UCs who "strongly recommend" it
Q: 169 (97%?)
V: 151 (49%?)
W: don't remember
GRE Subject Test in Mathematics: didn't submit except for UCs who "strongly recommend" it
M: 860 (87%)
TOEFL Score: Waived thanks to a US degree
Program Applying: Pure Math
Research Experience: One year of reading with faculty, a summer REU at home university (no publication, just a poster presented at symposiums), and two directed readings with graduate students. All
in harmonic analysis & analytic number theory
Awards/Honors/Recognitions: Departmental scholarships, dean list every semester, first prize in Chinese College Mathematics Competition (CMC 2020, before transfer)
Pertinent Activities or Jobs: Course assistant (tutor) of multiple advanced courses for two years (excellent feedback, an additional teaching letter submitted to some of the places), grader for
measure theory, analysis II, and topology I.
Math Courses Taken: Almost all undergrad courses, all taken with honors; almost all graduate courses in analysis/PDE. 6 grad courses on the transcript, auditing more after applications to save some
tuition (high for international!). Many talks in seminars and topic courses in the department (many thanks!!). Regular coding + applied math courses for the DS major.
Any Miscellaneous Points that Might Help:
Applying to Where: (in the order of hearing back)
UPenn - Invited 1.10 to the Open House on 2.2-3, informal acceptance by email 2.7, formal letter 2.22. Attending!!!!!!!
Chicago - Rejected 1.14
Yale - Rejected 1.20
JHU - Accepted 2.2, open house on 3.10. declined
Princeton - Rejected 2.3
UMN, Purdue, Northwestern, UIUC, UCSD - Withdrawn 2.8
UBC - email to inquire about the missing letter and interest, withdrawn
Stanford - Rejected 2.10
UCB - Rejected 2.13
Home university - Rejected 2.20
MIT - Rejected 2.21
UCLA - Waitlisted 3.3 (sent an email inquiry and was told I'm on the waitlist) Rejected 3.20 (right after their open house I guess?)
Brown - Rejected 3.10
Duke - Rejected 3.17
Duke - Rejected 4.12 They are a scam for application fee this year.
Last edited by Yufei on Sat Apr 29, 2023 12:49 pm, edited 13 times in total.
Re: 2023 Applicant Profiles and Admissions Results
brumer_stark wrote: ↑
Tue Feb 07, 2023 4:06 pm
physicsofcomica wrote: ↑
Tue Feb 07, 2023 3:50 pm
Institution: Well-known(ish) LAC
GPA: Top 10% of my class (for anonymity and since we have severe grade deflation)
Major: Mathematics
Type of Student: domestic white male
Research: One summer in experimental particle physics, paid, but no real production. One program similar to PolyMath, that was essentially an unpaid REU, a final report, unpublished. One NSF
REU (with people on this thread considering it a top choice) with a publication, and submission to a top journal. International REU with a pretty famous mentor, publication upcoming.
Coursework: (all undergrad level) Linear Algebra, Vector Calculus, Discrete Structures, Algebraic Combinatorics, Abstract Algebra, Complex Analysis, Topology, Real Analysis, Galois Theory,
Discrete Geometry, Algebraic Topology, Independent Study on combinatorics, Algebraic Geometry, Commutative Algebra and Homological Algebra, and Real Functions and Measures (the last 3 were
done “abroad” virtually), and a senior thesis in combinatorics.
Other: I worked as a tutor for all the classes I’ve taken and a course assistant/grader for a sizable subset of those classes. I’ve also been a drop-in tutor, note taker, and lab TA for intro
Program Applying: Pure Math/Applied Math PhD (Except Cambridge)
No GREs
Applied (in order of hearing back):
Cambridge Part III: Conditional Acceptance 12/14
Harvard SEAS: Interview 12/22 --> Reject 2/6
UChicago: Reject 1/13
Yale: Reject 1/20
BMS Phase I: Interview/Invitation to Berlin 1/20
Harvard: Reject 1/27
Northwestern: Reject 1/28 (Expected, my SOP wasn't really that great)
Cornell: Reject 1/30
UCLA: Reject 2/1
UMN: Acceptance 2/2
Princeton: Reject 2/3
Washington: Reject 2/3
Dartmouth: Reject 2/6
Hi, could you please elaborate on what conditional acceptance from Cambridge part 3 means?
As long as I graduate with “First Class Honors” which in the US means a GPA of 3.7>.
Re: 2023 Applicant Profiles and Admissions Results
physicsofcomica wrote: ↑
Tue Feb 07, 2023 3:50 pm
Institution: Well-known(ish) LAC
GPA: Top 10% of my class (for anonymity and since we have severe grade deflation)
Major: Mathematics
Type of Student: domestic white male
Research: One summer in experimental particle physics, paid, but no real production. One program similar to PolyMath, that was essentially an unpaid REU, a final report, unpublished. One NSF REU
(with people on this thread considering it a top choice) with a publication, and submission to a top journal. International REU with a pretty famous mentor, publication upcoming.
Coursework: (all undergrad level) Linear Algebra, Vector Calculus, Discrete Structures, Algebraic Combinatorics, Abstract Algebra, Complex Analysis, Topology, Real Analysis, Galois Theory,
Discrete Geometry, Algebraic Topology, Independent Study on combinatorics, Algebraic Geometry, Commutative Algebra and Homological Algebra, and Real Functions and Measures (the last 3 were done
“abroad” virtually), and a senior thesis in combinatorics.
Other: I worked as a tutor for all the classes I’ve taken and a course assistant/grader for a sizable subset of those classes. I’ve also been a drop-in tutor, note taker, and lab TA for intro
Program Applying: Pure Math/Applied Math PhD (Except Cambridge)
No GREs
Applied (in order of hearing back):
Cambridge Part III: Conditional Acceptance 12/14
Harvard SEAS: Interview 12/22 --> Reject 2/6
UChicago: Reject 1/13
Yale: Reject 1/20
BMS Phase I: Interview/Invitation to Berlin 1/20
Harvard: Reject 1/27
Northwestern: Reject 1/28 (Expected, my SOP wasn't really that great)
Cornell: Reject 1/30
UCLA: Reject 2/1
UMN: Acceptance 2/2
Princeton: Reject 2/3
Washington: Reject 2/3
Dartmouth: Reject 2/6
Is UMN for Minnesota?
Re: 2023 Applicant Profiles and Admissions Results
FieldsMedalist wrote: ↑
Tue Feb 07, 2023 6:28 pm
physicsofcomica wrote: ↑
Tue Feb 07, 2023 3:50 pm
Institution: Well-known(ish) LAC
GPA: Top 10% of my class (for anonymity and since we have severe grade deflation)
Major: Mathematics
Type of Student: domestic white male
Research: One summer in experimental particle physics, paid, but no real production. One program similar to PolyMath, that was essentially an unpaid REU, a final report, unpublished. One NSF
REU (with people on this thread considering it a top choice) with a publication, and submission to a top journal. International REU with a pretty famous mentor, publication upcoming.
Coursework: (all undergrad level) Linear Algebra, Vector Calculus, Discrete Structures, Algebraic Combinatorics, Abstract Algebra, Complex Analysis, Topology, Real Analysis, Galois Theory,
Discrete Geometry, Algebraic Topology, Independent Study on combinatorics, Algebraic Geometry, Commutative Algebra and Homological Algebra, and Real Functions and Measures (the last 3 were
done “abroad” virtually), and a senior thesis in combinatorics.
Other: I worked as a tutor for all the classes I’ve taken and a course assistant/grader for a sizable subset of those classes. I’ve also been a drop-in tutor, note taker, and lab TA for intro
Program Applying: Pure Math/Applied Math PhD (Except Cambridge)
No GREs
Applied (in order of hearing back):
Cambridge Part III: Conditional Acceptance 12/14
Harvard SEAS: Interview 12/22 --> Reject 2/6
UChicago: Reject 1/13
Yale: Reject 1/20
BMS Phase I: Interview/Invitation to Berlin 1/20
Harvard: Reject 1/27
Northwestern: Reject 1/28 (Expected, my SOP wasn't really that great)
Cornell: Reject 1/30
UCLA: Reject 2/1
UMN: Acceptance 2/2
Princeton: Reject 2/3
Washington: Reject 2/3
Dartmouth: Reject 2/6
Is UMN for Minnesota?
Re: 2023 Applicant Profiles and Admissions Results
I received an email from Berkeley few hours ago. It seems like an unofficial offer. Anyone the same situation as me? Can't believe this is true
Re: 2023 Applicant Profiles and Admissions Results
Any update from UIC?
Several people posted they got email from grad office asking if they are still interested. Did they hear any updates?
Re: 2023 Applicant Profiles and Admissions Results
WDDYz wrote: ↑
Wed Feb 08, 2023 3:44 am
I received an email from Berkeley few hours ago. It seems like an unofficial offer. Anyone the same situation as me? Can't believe this is true
what did the email say specifically? i haven't received any such thing but sounds like a good thing!
Re: 2023 Applicant Profiles and Admissions Results
Isthisacamera wrote: ↑
Wed Feb 08, 2023 5:41 am
Any update from UIC?
Several people posted they got email from grad office asking if they are still interested. Did they hear any updates?
I also got that email on the 28th of Jan. So far have heard nothing since
Re: 2023 Applicant Profiles and Admissions Results
corkquark wrote: ↑
Wed Feb 08, 2023 11:54 am
Isthisacamera wrote: ↑
Wed Feb 08, 2023 5:41 am
Any update from UIC?
Several people posted they got email from grad office asking if they are still interested. Did they hear any updates?
I also got that email on the 28th of Jan. So far have heard nothing since
Judging by how many people who've received it and the fact that some acceptances have been out, you can probably safely assume we're on a waitlist rn.
Re: 2023 Applicant Profiles and Admissions Results
corkquark wrote: ↑
Wed Feb 08, 2023 11:54 am
WDDYz wrote: ↑
Wed Feb 08, 2023 3:44 am
I received an email from Berkeley few hours ago. It seems like an unofficial offer. Anyone the same situation as me? Can't believe this is true
what did the email say specifically? i haven't received any such thing but sounds like a good thing!
Basically it told me that official offer will come a few weeks later, and invites me to the open house.
Re: 2023 Applicant Profiles and Admissions Results
Helpmepls wrote: ↑
Wed Feb 08, 2023 1:10 pm
corkquark wrote: ↑
Wed Feb 08, 2023 11:54 am
Isthisacamera wrote: ↑
Wed Feb 08, 2023 5:41 am
Any update from UIC?
Several people posted they got email from grad office asking if they are still interested. Did they hear any updates?
I also got that email on the 28th of Jan. So far have heard nothing since
Judging by how many people who've received it and the fact that some acceptances have been out, you can probably safely assume we're on a waitlist rn.
Are you sure some acceptances have been out?
I only know of one at Grad Cafe which might be a prof unofficially telling an applicant or someone trolling.
I went to the Indiana open house yesterday and their early decision process was described to us. It was exactly the same as the UIC email we got.
Re: 2023 Applicant Profiles and Admissions Results
hilberthotel wrote: ↑
Wed Feb 08, 2023 2:21 pm
Helpmepls wrote: ↑
Wed Feb 08, 2023 1:10 pm
corkquark wrote: ↑
Wed Feb 08, 2023 11:54 am
I also got that email on the 28th of Jan. So far have heard nothing since
Judging by how many people who've received it and the fact that some acceptances have been out, you can probably safely assume we're on a waitlist rn.
Are you sure some acceptances have been out?
I only know of one at Grad Cafe which might be a prof unofficially telling an applicant or someone trolling.
I went to the Indiana open house yesterday and their early decision process was described to us. It was exactly the same as the UIC email we got.
Yeah, so I received an acceptance from UIC (lol I was the one who posted that on grad cafe). I got that email from the DGS with the questions about my interest and updates on 1/28 and then on 2/6 I
got an email from the DGS saying that they are making me an offer (haven't gotten the official letter yet) with university fellowship.
Hope this helps clarify a bit. I don't know anything about other offers they're making.
Re: 2023 Applicant Profiles and Admissions Results
Helpmepls wrote: ↑
Wed Feb 08, 2023 1:10 pm
corkquark wrote: ↑
Wed Feb 08, 2023 11:54 am
Isthisacamera wrote: ↑
Wed Feb 08, 2023 5:41 am
Any update from UIC?
Several people posted they got email from grad office asking if they are still interested. Did they hear any updates?
I also got that email on the 28th of Jan. So far have heard nothing since
Judging by how many people who've received it and the fact that some acceptances have been out, you can probably safely assume we're on a waitlist rn.
Gotchu, thanks that makes sense!
Re: 2023 Applicant Profiles and Admissions Results
WDDYz wrote: ↑
Wed Feb 08, 2023 1:58 pm
corkquark wrote: ↑
Wed Feb 08, 2023 11:54 am
WDDYz wrote: ↑
Wed Feb 08, 2023 3:44 am
I received an email from Berkeley few hours ago. It seems like an unofficial offer. Anyone the same situation as me? Can't believe this is true
what did the email say specifically? i haven't received any such thing but sounds like a good thing!
Basically it told me that official offer will come a few weeks later, and invites me to the open house.
Oh nice, congrats!
Re: 2023 Applicant Profiles and Admissions Results
emptiest.set wrote: ↑
Wed Feb 08, 2023 2:36 pm
hilberthotel wrote: ↑
Wed Feb 08, 2023 2:21 pm
Helpmepls wrote: ↑
Wed Feb 08, 2023 1:10 pm
Judging by how many people who've received it and the fact that some acceptances have been out, you can probably safely assume we're on a waitlist rn.
Are you sure some acceptances have been out?
I only know of one at Grad Cafe which might be a prof unofficially telling an applicant or someone trolling.
I went to the Indiana open house yesterday and their early decision process was described to us. It was exactly the same as the UIC email we got.
Yeah, so I received an acceptance from UIC (lol I was the one who posted that on grad cafe). I got that email from the DGS with the questions about my interest and updates on 1/28 and then on 2/6
I got an email from the DGS saying that they are making me an offer (haven't gotten the official letter yet) with university fellowship.
Hope this helps clarify a bit. I don't know anything about other offers they're making.
This makes me optimistic about the fellowship shortlist part. If you were offered a fellowship, it certainly wasn't a waitlist email
I am sad about not getting the fellowship, but makes me positive about an early offer
Edit - Congratulations on the offer!
Re: 2023 Applicant Profiles and Admissions Results
Undergrad Institution: Top 50 state school
Major(s): Mathematics
Minor(s): N/A
GPA: 4
Math GPA: 4
Program Applying: Pure Mathematics PhD
Research Experience: Two publications, one prestigious REU, senior thesis in progress
Awards/Honors/Recognitions: Departmental scholarships
Pertinent Activities or Jobs: TA for graduate algebra
Math Courses Taken: 15 graduate courses (Diff Top, Alg Top, Alg Geo, NT, Rep Theory).
Applying to Where:
1. Duke: Accepted
2. UChicago: Rejected
3. Stanford: Rejected
4. UCSD: Withdrawn
5. UWash: Accepted (Declined)
6. Columbia: Accepted
7. Michigan: Accepted
8. UC Berkeley: Accepted
9. Wisconsin-Madison: Accepted (Declined)
10. Johns Hopkins: Rejected
11. Northwestern: Rejected
12. UPenn: Invited to open house
13. Brown: Rejected
14. Utah: Withdrawn
15. UIUC: Accepted (Declined)
Last edited by fieldwithoneelement on Sun Mar 05, 2023 1:08 pm, edited 6 times in total.
Re: 2023 Applicant Profiles and Admissions Results
hilberthotel wrote: ↑
Wed Feb 08, 2023 3:05 pm
emptiest.set wrote: ↑
Wed Feb 08, 2023 2:36 pm
hilberthotel wrote: ↑
Wed Feb 08, 2023 2:21 pm
Are you sure some acceptances have been out?
I only know of one at Grad Cafe which might be a prof unofficially telling an applicant or someone trolling.
I went to the Indiana open house yesterday and their early decision process was described to us. It was exactly the same as the UIC email we got.
Yeah, so I received an acceptance from UIC (lol I was the one who posted that on grad cafe). I got that email from the DGS with the questions about my interest and updates on 1/28 and then on
2/6 I got an email from the DGS saying that they are making me an offer (haven't gotten the official letter yet) with university fellowship.
Hope this helps clarify a bit. I don't know anything about other offers they're making.
This makes me optimistic about the fellowship shortlist part. If you were offered a fellowship, it certainly wasn't a waitlist email
I am sad about not getting the fellowship, but makes me positive about an early offer
Edit - Congratulations on the offer!
Thanks, and good luck, I hope you get an offer too!!
Re: 2023 Applicant Profiles and Admissions Results
fieldwithoneelement wrote: ↑
Wed Feb 08, 2023 4:01 pm
Undergrad Institution: Top 50 state school
Major(s): Mathematics
Minor(s): N/A
GPA: 4
Math GPA: 4
Program Applying: Pure Mathematics PhD
Research Experience: Two publications, one prestigious REU, senior thesis in progress
Awards/Honors/Recognitions: Departmental scholarships
Pertinent Activities or Jobs: TA for graduate algebra
Math Courses Taken: 15 graduate courses (Diff Top, Alg Top, Alg Geo, NT, Rep Theory).
Applying to Where:
1. Duke: Accepted (and will almost definitely attend)
2. UChicago: Rejected
3. Stanford:
4. UCSD:
5. UWash: Accepted
6. Columbia:
7. Michigan:
8. UC Berkeley: Accepted
9. Wisconsin-Madison:
10. Johns Hopkins: Rejected
11. Northwestern:
12. UPenn: Invited to open house
13. Brown:
14. Utah:
15. UIUC: Accepted
May I ask you why or how you decided to go to Duke? I have trouble deciding where to go.
Re: 2023 Applicant Profiles and Admissions Results
crepant wrote: ↑
Wed Feb 08, 2023 8:39 pm
fieldwithoneelement wrote: ↑
Wed Feb 08, 2023 4:01 pm
Undergrad Institution: Top 50 state school
Major(s): Mathematics
Minor(s): N/A
GPA: 4
Math GPA: 4
Program Applying: Pure Mathematics PhD
Research Experience: Two publications, one prestigious REU, senior thesis in progress
Awards/Honors/Recognitions: Departmental scholarships
Pertinent Activities or Jobs: TA for graduate algebra
Math Courses Taken: 15 graduate courses (Diff Top, Alg Top, Alg Geo, NT, Rep Theory).
Applying to Where:
1. Duke: Accepted (and will almost definitely attend)
2. UChicago: Rejected
3. Stanford:
4. UCSD:
5. UWash: Accepted
6. Columbia:
7. Michigan:
8. UC Berkeley: Accepted
9. Wisconsin-Madison:
10. Johns Hopkins: Rejected
11. Northwestern:
12. UPenn: Invited to open house
13. Brown:
14. Utah:
15. UIUC: Accepted
May I ask you why or how you decided to go to Duke? I have trouble deciding where to go.
High stipend + not too expensive cost of living + Low student to faculty ratio. Most importantly, alignment of faculty with my own mathematical interests.
Re: 2023 Applicant Profiles and Admissions Results
Those who heard from Stanford and/or MIT, was it via email?
Re: 2023 Applicant Profiles and Admissions Results
Scholar wrote: ↑
Thu Feb 09, 2023 12:27 am
Those who heard from Stanford and/or MIT, was it via email?
Yes. (From Stanford)
Re: 2023 Applicant Profiles and Admissions Results
Undergrad Institution: large state school
Major(s): Mathematics
Minor(s): Physics
GPA: 3.93 / 4
GREs : N/A
Program Applying: Pure Mathematics PhD
Research Experience: Some research in physics, led to conference talk(s), undergrad thesis, and publication in progress. Started on a projcet in my field for my masters. No REUs
Awards/Honors/Recognitions: deans list
Pertinent Activities or Jobs: TA for calculus, grader.
Math Courses Taken: Usual undergrad coursework, grad numerical analysis, plus grad algebra, algebraic topology, differential geometry sequences, some reading and special topics courses.
Interests: Low dimensional topology, knot theory, geometry, mathematical physics (TQFTs, strings, GR), TDA.
Any Miscellaneous Points that Might Help Organized a student seminar in low dimensional topology. Various misc. talks. Combined B.S./M.S. track. Tetris god.
Mega Reach:
UC Berkeley - rejected (2/13)
Princeton - rejected
Stanford - rejected (2/10)
Match + reach:
Rutgers - unofficially admitted! (2/8), officially admitted (2/9)
NC State - plan to withdraw
Duke - invited to interview Rejected
UVA - Waitlisted (3/8)
Rice - rejected (3/15)
UT Austin - plan to withdraw
U Michigan - no interview Rejected
U Oregon - admitted! (2/9)
Georgia Tech - Waitlisted upon inquiry
U Iowa - plan to withdraw
Last edited by McFloery on Wed Apr 05, 2023 2:36 am, edited 15 times in total.
Re: 2023 Applicant Profiles and Admissions Results
fieldwithoneelement wrote: ↑
Wed Feb 08, 2023 4:01 pm
Undergrad Institution: Top 50 state school
Major(s): Mathematics
Minor(s): N/A
GPA: 4
Math GPA: 4
Program Applying: Pure Mathematics PhD
Research Experience: Two publications, one prestigious REU, senior thesis in progress
Awards/Honors/Recognitions: Departmental scholarships
Pertinent Activities or Jobs: TA for graduate algebra
Math Courses Taken: 15 graduate courses (Diff Top, Alg Top, Alg Geo, NT, Rep Theory).
Applying to Where:
1. Duke: Accepted (and will almost definitely attend)
2. UChicago: Rejected
3. Stanford:
4. UCSD:
5. UWash: Accepted
6. Columbia:
7. Michigan:
8. UC Berkeley: Accepted
9. Wisconsin-Madison:
10. Johns Hopkins: Rejected
11. Northwestern:
12. UPenn: Invited to open house
13. Brown:
14. Utah:
15. UIUC: Accepted
May I ask about when did you hear from Berkeley? Is it an official offer?
Re: 2023 Applicant Profiles and Admissions Results
WDDYz wrote: ↑
Thu Feb 09, 2023 6:15 am
fieldwithoneelement wrote: ↑
Wed Feb 08, 2023 4:01 pm
Undergrad Institution: Top 50 state school
Major(s): Mathematics
Minor(s): N/A
GPA: 4
Math GPA: 4
Program Applying: Pure Mathematics PhD
Research Experience: Two publications, one prestigious REU, senior thesis in progress
Awards/Honors/Recognitions: Departmental scholarships
Pertinent Activities or Jobs: TA for graduate algebra
Math Courses Taken: 15 graduate courses (Diff Top, Alg Top, Alg Geo, NT, Rep Theory).
Applying to Where:
1. Duke: Accepted (and will almost definitely attend)
2. UChicago: Rejected
3. Stanford:
4. UCSD:
5. UWash: Accepted
6. Columbia:
7. Michigan:
8. UC Berkeley: Accepted
9. Wisconsin-Madison:
10. Johns Hopkins: Rejected
11. Northwestern:
12. UPenn: Invited to open house
13. Brown:
14. Utah:
15. UIUC: Accepted
May I ask about when did you hear from Berkeley? Is it an official offer?
Two days ago. They said the official letter would come in the coming weeks. Funding letter would come early March
Re: 2023 Applicant Profiles and Admissions Results
KelsyF wrote: ↑
Tue Dec 20, 2022 1:44 am
Undergrad Institution: Top 30 Big U with liberal arts feeling
Major(s):Applied Math
Math GPA:3.90
Type of Student: International Asian Female
GRE Revised General Test: *only submitted to non-optional programs
Q: 168 (90%)
V: 153 (58%)
W: 3.5 (38%)
GRE Subject Test in Mathematics: *only submitted to U-Washington
M: 550 (25%)
TOEFL Score: waived
Program Applying: Applied Math
Research Experience: summer 10-week full-time research and honor thesis at home university (climate modeling, numerical analysis, probability theory, rare events, stochastic process), 2 poster
presentation + 1 oral presentation, attended 2 conferences for graduate school
Awards/Honors/Recognitions:research fellowship at home university, dean's list every semester, 2 travel grants
Pertinent Activities or Jobs: tutor in Calc1-2 and ODE for only one semester
Math Courses Taken: taking modern algebra, fluid dynamics, differential geometry and graduate level real analysis next semester; A in intro real analysis, complex analysis, PDE, numerical
methods, numerical linear algebra, math modeling, discrete dynamical systems, but I had a C+ in linear algebra II
Any Miscellaneous Points that Might Help: at least two strong rec letters, one recommender is alumnus of U-Arizona and he sent my info to UofA (most of his research students I knew got an offer
from UofA), one recommender is alumnus of Northwestern, female and first-gen college student
Any Other Info That Shows Up On Your App and Might Matter: I was double majored in applied math and finance and planned to apply for fin math/fin engineering programs. I dropped the finance major
and started to do applied math research super late.
Applying to Where: *apply for math Ph.D. if no applied math program offered
Colorado Boulder - Applied Math Ph.D. Submitted 12/01 admitted 2/7
U Washington - Applied Math Ph.D. Submitted 12/01 admitted to Master 1/25
U Minnesota Twin Cities - Math Ph.D. Submitted 12/15 admitted 2/2
U Wisconsin Madison - Math Ph.D. Submitted 12/15
Georgia Tech - Math Ph.D. Submitted 12/15
U Michigan Ann Arbor - AIM Math Ph.D. Submitted 12/15
U Texas Austin - CSEM Ph.D. Submitted 12/15
U Maryland College Park - AMSC Ph.D. Submitted 12/15
Northwestern - ESAM Ph.D. Submitted 12/19
UC Davis - Applied Math Ph.D. Submitted 12/25 admitted 1/26
Boston U - Math Ph.D. Submitted 12/26
U Arizona - Applied Math Ph.D. Submitted 12/30 interview 2/2
U Pitts - Math Ph.D. Submitted 1/2
Georgetown - Applied Math Ph.D. Submitted 1/1
*Home University - Math master (terminating pure math master program with funding) Submitted 1/15 interview 1/30
U Penn - AMCS master Submitted 2/1
What did they say in your interview at Arizona? Anything technical? Did they say when decisions will be released? Congrats btw!
Re: 2023 Applicant Profiles and Admissions Results
hilberthotel wrote: ↑
Wed Feb 08, 2023 3:05 pm
emptiest.set wrote: ↑
Wed Feb 08, 2023 2:36 pm
hilberthotel wrote: ↑
Wed Feb 08, 2023 2:21 pm
Are you sure some acceptances have been out?
I only know of one at Grad Cafe which might be a prof unofficially telling an applicant or someone trolling.
I went to the Indiana open house yesterday and their early decision process was described to us. It was exactly the same as the UIC email we got.
Yeah, so I received an acceptance from UIC (lol I was the one who posted that on grad cafe). I got that email from the DGS with the questions about my interest and updates on 1/28 and then on
2/6 I got an email from the DGS saying that they are making me an offer (haven't gotten the official letter yet) with university fellowship.
Hope this helps clarify a bit. I don't know anything about other offers they're making.
This makes me optimistic about the fellowship shortlist part. If you were offered a fellowship, it certainly wasn't a waitlist email
I am sad about not getting the fellowship, but makes me positive about an early offer
Edit - Congratulations on the offer!
Perhaps there is a case for optimism yet! I saw the gradcafe post and sorta just assumed if some acceptances are out and many people received the email, then a conservative estimate is that I'd be on
a waitlist. Congrats emtiest.set!
Re: 2023 Applicant Profiles and Admissions Results
crepant wrote: ↑
Thu Feb 09, 2023 12:46 am
Scholar wrote: ↑
Thu Feb 09, 2023 12:27 am
Those who heard from Stanford and/or MIT, was it via email?
Yes. (From Stanford)
Yes. (From MIT) MIT sent its official letter of admission directly via email. No status update via portal.
Re: 2023 Applicant Profiles and Admissions Results
wjvr46 wrote: ↑
Tue Feb 07, 2023 12:08 am
veenzaan wrote: ↑
Mon Feb 06, 2023 12:32 pm
wjvr46 wrote: ↑
Thu Jan 19, 2023 5:39 pm
Undergrad Institution: Big state US
Major(s): Mathematics
GPA: 3.67
Math GPA: 4.0
Type of Student: White, International, Male
Program Applying: Pure Math: Analysis
Research Experience: Currently working with a professor on PDEs, and software engineering internship in sophomore year
Awards/Honors/Recognitions: Few scholarships, dean's list.
Pertinent Activities or Jobs: Grader for Linear Algebra and tutors
Math Courses Taken: Graduate Level courses: Real Analysis, and Topology.
Any Miscellaneous Points that Might Help: Good recommendation letters.
Applying to Where: (Color use here is welcome)
School - Rice
School - OSU
School - Texas AM
School - UT Austin
School - UVA
School - Vanderbilt
School - University of Tennessee
School - University of Florida (Accepted 02/03)
School - Notre Dame
School - University of Houston
School - University of Kentucky
School - University of Alabama
Hi, is the acceptance from University of Florida (Gainesville) or Florida State University (Tallahassee)? Congratulations!
Hello and congratulations on your admission to UF! I'm curious, how were you notified of the acceptance?
Re: 2023 Applicant Profiles and Admissions Results
gzero wrote: ↑
Tue Sep 06, 2022 9:14 am
Non Super-Reach
I will not attend any of these, but won't withdraw my applications. I'm interested to see where I would have got in, and hopefully the info will be of some use.
Please withdraw your applications if you know for a fact you wouldn't attend.
Re: 2023 Applicant Profiles and Admissions Results
Current Undergrad Institution: Commuter state school
Major(s): Mathematics
Minor(s): Education/honors college
GPA: 3.327 by now lmao
Math GPA: why do yall think my GPA's so low!
Type of Student: Domestic, Female, Asian, first grad student in family
Program Applying: Pure Mathematics PhD (discrete, algebraic geometry, geometric group theory, discrete analysis, etc)
Research Experience: One REU with conference poster session, ongoing thesis
Awards/Honors/Recognitions: full scholarship, honors for a while, honors college, one fellowship
Pertinent Activities or Jobs: Tutored for college algebra, precalc, calc 1+2, "TA'd" (we had a diff name and payrate) for calc 1 for a year
Math Courses Taken: the usual, nothing to write home about (real and complex analysis, group and ring theory algebra, geometry, discrete, ODEs)
Any Miscellaneous Points that Might Help: funky thesis!!!
Applying to Where: (assume all math phd unless noted, submitted all on 12/10/22 unless noted)
TUFTS - update: they submitted a master's application on my behalf as of 2/15 ???
Update 2: UNOFFICIAL MASTER’S ADMIT AS OF 2/26 @ 9pm EST (lmao)
Georgia Tech - REJECTED 1/27/23 (email to check portal)
MIT - REJECTED 2/21/23 (email, direct)
UMA - 1/15
UNH - REJECTED 2/23 (email to check portal)
NORTHEASTERN - 1/15
Wesleyan - 1/15
Salem State (Masters in math) - 1/15
Smith College (Post bacc) (not yet applied, waiting to hear back first)
Updated: 2/27/23
Last edited by uhoh.spaghettio on Mon Feb 27, 2023 12:22 pm, edited 2 times in total.
Re: 2023 Applicant Profiles and Admissions Results
macmath7 wrote: ↑
Tue Jan 17, 2023 11:24 pm
Undergrad Institution: Small Catholic Liberal Arts School
Major(s): Mathematics and Computer Science
Minor(s): Italian
GPA: 3.82/4.00
Math GPA:
Type of Student: White Domestic Female (Domestic/International (Country?), Male/Female?, Minority?)
GRE Revised General Test:
Q: xxx (xx%)
V: xxx (xx%)
W: x.x (xx%)
GRE Subject Test in Mathematics:
M: xxx (xx%)
TOEFL Score: (xx = Rxx/Lxx/Sxx/Wxx) (if applicable)
Program Applying: Pure Math
Research Experience: Participated in an REU between my sophomore and junior year, did not result in a paper or publication, however my work is being used in further research. Also did research
with a professor at my university on group structure on elliptic curves
Awards/Honors/Recognitions: Member and officer of Upsilon Pi Epsilon, received one of the highest degree scholarships from my school. Dean's list every semester except my first (college started
off tough).
Pertinent Activities or Jobs: Have tutored since sophomore year of high school and works as a tutor for all math classes at my institution in multiple places at the school.
Math Courses Taken: Calc 1, Calc 2, Calc 3, Linear Algebra, Real Analysis, Abstract Algebra 1, Abstract Algebra 2, Complex Analysis, Geometric Algebra, Differential Geometry, Applied Math, Proof
writing course, as well as other independent study classes.
Any Miscellaneous Points that Might Help: I'm a woman so hopefully that will help me a bit.
Any Other Info That Shows Up On Your App and Might Matter: I didn't get great grades in a few of my classes due to some extenuating circumstances. Some of that is going to be addressed in my
Applying to Where:
any news from tufts, brandeis, umass?
Re: 2023 Applicant Profiles and Admissions Results
Undergrad Institution: A Southeast Asian university (arguably the best for maths in the country), ranked 401-450 (by subject in mathematics) globally
Major(s): Maths (with integrated master's)
Minor(s): -
GPA: 3.97/4.00 (undergrad), 4.00/4.00 (master's)
Math GPA:
Type of Student: International Asian Male
GRE Revised General Test: N/A
GRE Subject Test in Mathematics: N/A
IELTS Score: (8.0 = R8.5/L8.5/S7.5/W7.0)
Program Applying: Probability & Stochastic Analysis (Pure & Applied)
Research Experience: A summer research programme in stochastic analysis (or winter? Because it was held by an Australian university)
Awards/Honors/Recognitions: Graduated with a distinction (cum laude in my country), research award as stated above, full undergraduate scholarship, integrated bachelor's/master's scholarship in the
same university, some maths competitions
Pertinent Activities or Jobs: Tutor & TA in several maths courses (calculus, real analysis, etc.)
Math Courses Taken: All compulsory ones (linear algebra, real analysis, etc.), measure theory, financial maths, Fourier analysis, functional analysis, some actuarial science courses
Any Miscellaneous Points that Might Help: My supervisor for the aforementioned research experience said he was pleased with my performance in the programme & wrote a good recommendation letter for me
Any Other Info That Shows Up On Your App and Might Matter:
Applying to Where:
Oxford - Random Systems CDT / Already had my interview on 2nd February, now waiting for the outcome
Imperial - Random Systems CDT / Applied in late December, no news as of yet
University of Edinburgh/Heriot-Watt University (joint) - MAC-MIGS CDT / Applied very late in early Match
Cambridge - MASt Part III in Mathematical Statistics / Conditional offer on 9th February, waiting for funding outcome
Last edited by borelcantelli on Mon Mar 13, 2023 10:28 am, edited 1 time in total.
Re: 2023 Applicant Profiles and Admissions Results
Has anyone been rejected/waitlisted at UPenn? I saw one offer on gradcafe but haven't seen rejection/waitlist decisions.
Re: 2023 Applicant Profiles and Admissions Results
brumer_stark wrote: ↑
Sat Feb 11, 2023 1:05 pm
Has anyone been rejected/waitlisted at UPenn? I saw one offer on gradcafe but haven't seen rejection/waitlist decisions.
I don’t think rejections went out yet. People have only received unofficial offers. Bridge Applicants haven’t heard anything yet either. It’s just the waiting game for the rest of us now.
Re: 2023 Applicant Profiles and Admissions Results
inaicecream wrote: ↑
Sat Feb 11, 2023 1:48 pm
brumer_stark wrote: ↑
Sat Feb 11, 2023 1:05 pm
Has anyone been rejected/waitlisted at UPenn? I saw one offer on gradcafe but haven't seen rejection/waitlist decisions.
I don’t think rejections went out yet. People have only received unofficial offers. Bridge Applicants haven’t heard anything yet either. It’s just the waiting game for the rest of us now.
Yeah I haven’t heard from them either. I applied to the bridge fellowship as well.
Re: 2023 Applicant Profiles and Admissions Results
Undergrad Institution : International qs ranking around 250th
Masters institution : US news 50th private
Major(s) : Math
Minor(s) : Computer science
GPA : 3.6
Math GPA : 3.74
Type of Student : International Asian Male
GRE Revised General Test : 330
Q : 169
V : 161
W :3.5
TOEFL Score: 101 = R27/L22/S24/W28
Program Applying: Computational Math: image processing, combinatorics
Research Experience: Not much research, no publications, several PhD courses taken with presentation on some topics at the last of each semester
Math Courses Taken: analysis, algebra, real analysis, ode, numerical analysis, differential geometry, control, signal processing, communication
Any Miscellaneous Points that Might Help: Due to personal reasons, my reseach background is weak, so I applied almost all the computational math phd programs I can find, approximately 15 schools, US
news ranking 10-50
Any Other Info That Shows Up On Your App and Might Matter: completing two masters in math and computer science at same time, computer science program focused on architecture and signal processing
Applying to Where:
UPenn - AMCS - Rejected 3/8
University of Michigan - AIM - Rejected 3/27
Northwestern - ESAM - Rejected 3/29
Notre Dame - ACMS - Pending on
UC-Davis - Applied Math - Pending on
Stony Brook - CAM - Admitted 3/13
Michigan State - CMSE Interviewed 1/23 - Admitted 2/7
Rutgers - mathematical sciences - Pending on
UW Madison - Math - Rejected 2/20
Duke - Math - Rejected 3/17
University of Illinois Urbana-Champaign - Math - Rejected 3/16
UCSB - Math - Pending on
Penn State - Math - Rejected 3/13
Last edited by Kolmogorov on Wed Mar 29, 2023 12:07 pm, edited 10 times in total.
Re: 2023 Applicant Profiles and Admissions Results
Anyone heard from stony brook (pure math)?
Re: 2023 Applicant Profiles and Admissions Results
I suspect we won't hear from Stony brook for another couple weeks...their applications were due on the 15th of January lol
Re: 2023 Applicant Profiles and Admissions Results
xbq22 wrote: ↑
Mon Feb 13, 2023 2:24 pm
I suspect we won't hear from Stony brook for another couple weeks...their applications were due on the 15th of January lol
Yes, but I'm guessing most of their applications came before 01/01 since that was the deadline for full consideration for fellowships. I think this is historically around when they start sending
early acceptances and then continue for about a month. Also, Indiana said they would be getting back to some people this week, and their applications were due on 01/15, so it's not unreasonable.
Re: 2023 Applicant Profiles and Admissions Results
Boplicity wrote: ↑
Mon Feb 13, 2023 3:17 pm
xbq22 wrote: ↑
Mon Feb 13, 2023 2:24 pm
I suspect we won't hear from Stony brook for another couple weeks...their applications were due on the 15th of January lol
Yes, but I'm guessing most of their applications came before 01/01 since that was the deadline for full consideration for fellowships. I think this is historically around when they start sending
early acceptances and then continue for about a month. Also, Indiana said they would be getting back to some people this week, and their applications were due on 01/15, so it's not unreasonable.
Oh shit, idk if i submitted my application in time for that. Did not know there was a first deadline :/
Re: 2023 Applicant Profiles and Admissions Results
xbq22 wrote: ↑
Mon Feb 13, 2023 5:13 pm
Boplicity wrote: ↑
Mon Feb 13, 2023 3:17 pm
xbq22 wrote: ↑
Mon Feb 13, 2023 2:24 pm
I suspect we won't hear from Stony brook for another couple weeks...their applications were due on the 15th of January lol
Yes, but I'm guessing most of their applications came before 01/01 since that was the deadline for full consideration for fellowships. I think this is historically around when they start
sending early acceptances and then continue for about a month. Also, Indiana said they would be getting back to some people this week, and their applications were due on 01/15, so it's not
Oh shit, idk if i submitted my application in time for that. Did not know there was a first deadline :/
Purdue had this exact same deadline thing where if you submit by Jan 1, your app gets consideration for fellowships. I didn't apply to Stony Brook but my guess is that while your app might not be
considered for fellowships, you definitely will be considered for other financial aid packages such as TAships if you receive an admit
Re: 2023 Applicant Profiles and Admissions Results
I have held out on doing this for so long but I think it's time to write up my own thingy here.
Undergrad Institution: Well known, not ivy, not amazing for math research but not bad either (though my advisor has told me that he knows of no one who has gotten into a T10 program from this
institution in the last 15 years
Majors: Double majored in math and physics
GPA: 3.83
Math GPA: 4.0
Type of student Domestic White Male
GRE Did not take
Program Applying: Pure Math, mainly focused on geometry and mathematical physics
Research Experience: Two research projects in physics, no publications, writing an honours thesis on the geometry of gauge theory that is essentially a textbook (currently sits at 180 pages)
Math Courses Taken: Multi, Odes, Linear Algebra I and II, Differential Geometry of curves and surfaces, discrete maths, Real Analysis I/II.
Graduate Courses Taken: Grad QM I and II, Grad EM, Quantum Field Theory I and II, Mathematical Physics, Differential topology I and II, Graduate Algebra I and II, Topics in Geometry (I suspect my
lack of a complex analysis course, and my heavier slant towards physics is hurting me mildly here)
Any Miscellaneous Points that Might Help: 2 of my letters of recommendation should be very strong, another two should be good. I have given talks on gauge theory, and Yang-Mills theory in both the
physics and math departments as well.
Applying to where: (in no particular order)
Harvard: Rejected
Caltech: Rejected
UCLA: Rejected
Duke: No interview (yet at least)Rejected
UPenn: No Open House InviteRejected
Oxford: No interview (yet at least) rejected
UC Berkely: Rejected (this one hurt me
Stanford: Rejected
MIT: Rejected
Stony Brook: Rejected (this one was also painful. I got hopeful when I wasn't in the first round of rejections)
Washington: Rejected
Princeton: Rejected
UT Austin:
Oregon State
University of OregonAccepted!
UPittAccepted! Rejected Offer
NC StateAccepted! Rejected Offer
Cambridge Part ThreeAwaiting approval by PAO. Acceptance! Most likely will attend if Stony Brook doesn't work out. (I have been told that this is a good thing so we shall see at least). It was a good
sign! If you get the awaiting approval by PAO, and don't here anything for longer than two weeks, email them and they might send an official offer. That's what I did.
Last edited by xbq22 on Thu Mar 30, 2023 7:52 pm, edited 6 times in total.
Re: 2023 Applicant Profiles and Admissions Results
xbq22 wrote: ↑
Mon Feb 13, 2023 5:48 pm
I have held out on doing this for so long but I think it's time to write up my own thingy here.
Undergrad Institution: Well known, not ivy, not amazing for math research but not bad either (though my advisor has told me that he knows of no one who has gotten into a T10 program from this
institution in the last 15 years
Majors: Double majored in math and physics
GPA: 3.83
Math GPA: 4.0
Type of student Domestic White Male
GRE Did not take
Program Applying: Pure Math, mainly focused on geometry and mathematical physics
Research Experience: Two research projects in physics, no publications, writing an honours thesis on the geometry of gauge theory that is essentially a textbook (currently sits at 180 pages)
Math Courses Taken: Multi, Odes, Linear Algebra I and II, Differential Geometry of curves and surfaces, discrete maths, Real Analysis I/II.
Graduate Courses Taken: Grad QM I and II, Grad EM, Quantum Field Theory I and II, Mathematical Physics, Differential topology I and II, Graduate Algebra I and II, Topics in Geometry (I suspect my
lack of a complex analysis course, and my heavier slant towards physics is hurting me mildly here)
Any Miscellaneous Points that Might Help: 2 of my letters of recommendation should be very strong, another two should be good. I have given talks on gauge theory, and Yang-Mills theory in both
the physics and math departments as well.
Applying to where: (in no particular order)
Harvard: Rejected
Caltech: Rejected
UCLA: Rejected
Duke:No interview (yet at least)
UPenn:No Open House Invite
Oxford:No interview (yet at least)
UC Berkely:
Stanford: Rejected
Stony Brook:
UT Austin:
Oregon State
University of OregonAccepted!
NC StateAccepted!
Cambridge Part ThreeAwaiting approval by PAO (I have been told that this is a good thing so we shall see at least).
When did you hear from Pitt?
Re: 2023 Applicant Profiles and Admissions Results
inaicecream wrote: ↑
Mon Feb 13, 2023 6:44 pm
xbq22 wrote: ↑
Mon Feb 13, 2023 5:48 pm
I have held out on doing this for so long but I think it's time to write up my own thingy here.
Undergrad Institution: Well known, not ivy, not amazing for math research but not bad either (though my advisor has told me that he knows of no one who has gotten into a T10 program from this
institution in the last 15 years
Majors: Double majored in math and physics
GPA: 3.83
Math GPA: 4.0
Type of student Domestic White Male
GRE Did not take
Program Applying: Pure Math, mainly focused on geometry and mathematical physics
Research Experience: Two research projects in physics, no publications, writing an honours thesis on the geometry of gauge theory that is essentially a textbook (currently sits at 180 pages)
Math Courses Taken: Multi, Odes, Linear Algebra I and II, Differential Geometry of curves and surfaces, discrete maths, Real Analysis I/II.
Graduate Courses Taken: Grad QM I and II, Grad EM, Quantum Field Theory I and II, Mathematical Physics, Differential topology I and II, Graduate Algebra I and II, Topics in Geometry (I
suspect my lack of a complex analysis course, and my heavier slant towards physics is hurting me mildly here)
Any Miscellaneous Points that Might Help: 2 of my letters of recommendation should be very strong, another two should be good. I have given talks on gauge theory, and Yang-Mills theory in
both the physics and math departments as well.
Applying to where: (in no particular order)
Harvard: Rejected
Caltech: Rejected
UCLA: Rejected
Duke:No interview (yet at least)
UPenn:No Open House Invite
Oxford:No interview (yet at least)
UC Berkely:
Stanford: Rejected
Stony Brook:
UT Austin:
Oregon State
University of OregonAccepted!
NC StateAccepted!
Cambridge Part ThreeAwaiting approval by PAO (I have been told that this is a good thing so we shall see at least).
When did you hear from Pitt?
I think last Thursday I heard from pitt, u of o, and my Cambridge portal opened. | {"url":"https://mathematicsgre.com/viewtopic.php?f=1&t=5886&sid=f0f669ed14d06647843eadaca29409af&start=100","timestamp":"2024-11-13T18:46:06Z","content_type":"text/html","content_length":"223488","record_id":"<urn:uuid:75a01d81-b6c7-4c1f-8513-fed8147a46e4>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00447.warc.gz"} |
C++ Multisets are like sets, in that they are associative containers containing a sorted set of objects, but differ in that they allow duplicate objects.
Multiset Constructors default methods to allocate, copy, and deallocate multisets
Multiset Operators assign and compare multisets
begin returns an iterator to the beginning of the multiset
clear removes all elements from the multiset
count returns the number of elements matching a certain key
empty true if the multiset has no elements
end returns an iterator just past the last element of a multiset
equal_range returns iterators to the first and just past the last elements matching a specific key
erase removes elements from a multiset
find returns an iterator to specific elements
insert inserts items into a multiset
key_comp returns the function that compares keys
lower_bound returns an iterator to the first element greater than or equal to a certain value
max_size returns the maximum number of elements that the multiset can hold
rbegin returns a reverse_iterator to the end of the multiset
rend returns a reverse_iterator to the beginning of the multiset
size returns the number of items in the multiset
swap swap the contents of this multiset with another
upper_bound returns an iterator to the first element greater than a certain value
value_comp returns the function that compares values | {"url":"http://ld2010.scusa.lsu.edu/cppreference/wiki/stl/multiset/start","timestamp":"2024-11-07T06:32:09Z","content_type":"application/xhtml+xml","content_length":"6785","record_id":"<urn:uuid:bc8715c8-5e62-4d87-ac85-f096425364fd>","cc-path":"CC-MAIN-2024-46/segments/1730477027957.23/warc/CC-MAIN-20241107052447-20241107082447-00288.warc.gz"} |
Digital Math Resources
Display Title
MATH EXAMPLES--The Median
MATH EXAMPLES--The Median
This set of tutorials provides 40 examples of calculating the median. NOTE: The download is a PPT file.
Common Core Standards CCSS.MATH.CONTENT.6.SP.B.4, CCSS.MATH.CONTENT.6.SP.A.3
Grade Range 6 - 12
Curriculum Nodes • Probability and Data Analysis
• Data Analysis
Copyright Year 2014
Keywords data analysis, tutorials, measures of central tendency, mode, average | {"url":"https://www.media4math.com/library/math-examples-median","timestamp":"2024-11-06T17:11:49Z","content_type":"text/html","content_length":"60851","record_id":"<urn:uuid:669c510d-9c70-4bda-843f-626fa4cbf799>","cc-path":"CC-MAIN-2024-46/segments/1730477027933.5/warc/CC-MAIN-20241106163535-20241106193535-00350.warc.gz"} |
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Hardness of Noise-Free Learning for Two-Hidden-Layer Neural Networks (Conference Paper) | NSF PAGES
null (Ed.)
We give the first statistical-query lower bounds for agnostically learning any non-polynomial activation with respect to Gaussian marginals (e.g., ReLU, sigmoid, sign). For the specific problem of
ReLU regression (equivalently, agnostically learning a ReLU), we show that any statistical-query algorithm with tolerance n−(1/ϵ)b must use at least 2ncϵ queries for some constant b,c>0, where n is
the dimension and ϵ is the accuracy parameter. Our results rule out general (as opposed to correlational) SQ learning algorithms, which is unusual for real-valued learning problems. Our techniques
involve a gradient boosting procedure for "amplifying" recent lower bounds due to Diakonikolas et al. (COLT 2020) and Goel et al. (ICML 2020) on the SQ dimension of functions computed by two-layer
neural networks. The crucial new ingredient is the use of a nonstandard convex functional during the boosting procedure. This also yields a best-possible reduction between two commonly studied models
of learning: agnostic learning and probabilistic concepts.
more » « less | {"url":"https://par.nsf.gov/biblio/10478031-hardness-noise-free-learning-two-hidden-layer-neural-networks","timestamp":"2024-11-07T10:55:19Z","content_type":"text/html","content_length":"243369","record_id":"<urn:uuid:411560c1-1c51-4b3f-a8e0-3913ba1744c9>","cc-path":"CC-MAIN-2024-46/segments/1730477027987.79/warc/CC-MAIN-20241107083707-20241107113707-00737.warc.gz"} |
Printable Multiplication Chart 1-20 | Multiplication Chart Printable
Printable Multiplication Chart 1-20
Free Printable Multiplication Chart 1 20 Table PDF
Printable Multiplication Chart 1-20
Printable Multiplication Chart 1-20 – A Multiplication Chart is an useful tool for youngsters to learn how to multiply, separate, as well as locate the smallest number. There are numerous usages for
a Multiplication Chart.
What is Multiplication Chart Printable?
A multiplication chart can be used to assist kids discover their multiplication truths. Multiplication charts been available in many kinds, from complete page times tables to solitary web page ones.
While specific tables serve for offering pieces of details, a complete page chart makes it much easier to review truths that have currently been grasped.
The multiplication chart will typically include a leading row and a left column. The top row will have a checklist of products. When you want to find the product of two numbers, pick the very first
number from the left column and the 2nd number from the top row. Move them along the row or down the column up until you get to the square where the two numbers fulfill when you have these numbers.
You will after that have your product.
Multiplication charts are valuable discovering tools for both children and grownups. Printable Multiplication Chart 1-20 are offered on the Internet as well as can be printed out and laminated for
Why Do We Use a Multiplication Chart?
A multiplication chart is a diagram that demonstrates how to increase 2 numbers. It usually includes a top row and also a left column. Each row has a number representing the item of both numbers. You
pick the initial number in the left column, relocate down the column, and then pick the 2nd number from the top row. The item will certainly be the square where the numbers satisfy.
Multiplication charts are useful for numerous factors, including assisting children learn exactly how to divide and also simplify portions. Multiplication charts can additionally be useful as desk
resources since they offer as a consistent tip of the student’s development.
Multiplication charts are likewise beneficial for helping trainees remember their times tables. As with any type of skill, memorizing multiplication tables takes time and also practice.
Printable Multiplication Chart 1-20
10 Best Free Printable Multiplication Chart 1 20 Printablee
Satisfactory Multiplication Table 1 20 Printable Hudson Website
Tables 1 To 20 PDF Multiplication Table Multiplication Chart
Printable Multiplication Chart 1-20
If you’re looking for Printable Multiplication Chart 1-20, you’ve come to the ideal location. Multiplication charts are readily available in various styles, consisting of full size, half dimension,
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Multiplication charts as well as tables are essential tools for youngsters’s education. These charts are terrific for use in homeschool math binders or as classroom posters.
A Printable Multiplication Chart 1-20 is a valuable tool to strengthen mathematics realities and can aid a youngster discover multiplication rapidly. It’s likewise a great tool for miss checking and
learning the times tables.
Related For Printable Multiplication Chart 1-20 | {"url":"https://multiplicationchart-printable.com/printable-multiplication-chart-1-20-2/","timestamp":"2024-11-11T16:18:14Z","content_type":"text/html","content_length":"42663","record_id":"<urn:uuid:2eafc909-a198-4ba0-bb34-4702f2355262>","cc-path":"CC-MAIN-2024-46/segments/1730477028235.99/warc/CC-MAIN-20241111155008-20241111185008-00266.warc.gz"} |
Bandwidth Math and Connection Speed Needed - The PowerPoint Blog
Bandwidth Math and Connection Speed Needed
There are 5 Categories of Internet Connections:
1. 5+ Mbps = Very High Broadband
2. 1-5 Mbps = High Broadband
3. 786 Kbps = Fast Broadband
4. 384 Kbps = Standard Broadband
5. 56 Kbps = Dial-up
To figure the bandwidth a viewer will need to view the streaming media file with perfect playback, we need to work through these formulas (one for a Standard Web Server, one for a Streaming Server
(note: Streaming Servers are overviewed a few posts from now).
A: Figuring Bandwidth Needs From A Standard Server. Here things are easy because we get to figure things directly in ‘bandwidth’ math using bits not bytes.
1. Figure “Bits Per Second”
Video Height x Video Width x Frame Rate (fps) = Bits/second (Kbps)
eg. (320 x 240 video dimensions) x 15 fps = 1,152,000 Bits/second
2. Convert Bits Per Second (Kbps) to Megabits Per Second (Mbps)
Bps (Total from #1) / 1,024 (1 Mbps = 1,024 Kbps) = Needed Connection Speed
eg. 1,152,000 Kbps / 1,024 = 1,125 Mbps (so the person watching should have a, category 2, high broadband connection)
B: Figuring Bandwidth Needs From A Streaming Media Server. Here there are a few extra steps because streaming servers encode everything in Bytes Per Second (Bps), which needs to then be converted to
Kbps to know the bandwidth need.
1. Figure Total Bits Per Second
Video Height x Video Width x Frame Rate (fps) = Total Bits/second
eg. (320 x 240 video dimensions) x 15 fps) = 1,152,000 Bits/second
2. Figure the Bytes Per Second (Bps)
Bps (total from #1) / 8 = Bps (divide by 8 because there are 8 bits in 1 byte)
eg. ((320 x 240 x 15) / 8) = 144,000 Bps
3. Convert Bps to Kbps
Bps (total from #2) / 1,000 = Kilobytes/second (Kbps)
eg. 144,000 Bps / 1000 = 1,152Kbps (which is rounded to 1.2 Mbps)
These formulas do not take into account your server’s bandwidth limitations, the number of simultaneous viewers, network congestion or a host of other variables. Now we know how to anticipate the
needed connection speed for our streaming media.
Up next are some of the ways we can make a larger bandwidth file playback smooth on a low bandwidth connection.
– Troy @ TLC | {"url":"https://thepowerpointblog.com/bandwidth_math_and_connection_speed_need/","timestamp":"2024-11-07T07:05:57Z","content_type":"text/html","content_length":"44858","record_id":"<urn:uuid:d8294de7-dd7b-4c2b-8f26-8b7a52b161c0>","cc-path":"CC-MAIN-2024-46/segments/1730477027957.23/warc/CC-MAIN-20241107052447-20241107082447-00775.warc.gz"} |
helper class for time complexity checks during test runs
helper macros for coroutines
a vector class that cannot be moved while it is not empty
The code in this file is used to construct an lts in fsm format.
O(m log n)-time branching bisimulation algorithm.
O(m log n)-time branching bisimulation algorithm similar to liblts_bisim_dnj.h which does not use bunches, i.e., partitions of transitions. This algorithm should be slightly faster, but in
particular use less memory than liblts_bisim_dnj.h. Otherwise the functionality is exactly the same.
O(m log n)-time stuttering equivalence algorithm.
Author(s): # Carlos Gregorio-Rodriguez, Luis LLana, Rafael Martinez-Torres.
Header file for the simulation preorder algorithm.
This file defines an algorithm for weak bisimulation, by calculating the transitive tau closure and apply strong bisimulation afterwards. In order to apply this algorithm it is advisable to first
apply a branching bisimulation reduction.
This file contains lts_convert routines that translate different lts formats into each other.
add your file description here.
Header file for hash table data structure used by the simulation preorder algorithm. | {"url":"https://mcrl2.org/web/doxygen/dir_b5d9ad585618aece95f4a58a30c943a2.html","timestamp":"2024-11-05T09:07:51Z","content_type":"application/xhtml+xml","content_length":"18591","record_id":"<urn:uuid:e337e63e-3987-4db6-aaed-4c589db59a75>","cc-path":"CC-MAIN-2024-46/segments/1730477027878.78/warc/CC-MAIN-20241105083140-20241105113140-00684.warc.gz"} |
how many cubic yards in a tri axle dump truck
Source: bing.com
Tri axle dump trucks are commonly used in the construction industry for hauling and transporting materials such as gravel, sand, and dirt. These trucks are designed to carry heavy loads and have a
large capacity, but many people are unsure about how many cubic yards they can hold.
Source: bing.com
What is a Cubic Yard?
Before we dive into the capacity of a tri axle dump truck, we need to understand what a cubic yard is. A cubic yard is a unit of measurement used for measuring volume. It is equal to 27 cubic feet or
764.5 liters. To put that into perspective, a standard washing machine holds about 3 cubic feet of laundry.
Source: bing.com
What is a Tri Axle Dump Truck?
A tri axle dump truck is a heavy-duty truck that has three axles, one in the front and two in the rear. The rear axles are powered by the engine and help distribute the weight of the load. These
trucks are commonly used in construction sites to haul and transport materials such as dirt, sand, and gravel.
Source: bing.com
Capacity of a Tri Axle Dump Truck
The capacity of a tri axle dump truck depends on the size of the truck and the material being hauled. On average, a tri axle dump truck can hold anywhere from 16 to 20 cubic yards of material.
However, some trucks can carry up to 25 cubic yards of material.
Source: bing.com
Factors That Affect the Capacity
Several factors can affect the capacity of a tri axle dump truck. These include:
• The size and weight of the truck
• The size and weight of the load
• The type of material being hauled
• The terrain and road conditions
Why is it Important to Know the Capacity?
Knowing the capacity of a tri axle dump truck is important for several reasons. For one, it helps ensure that you are not overloading the truck, which can lead to safety hazards and fines. It also
helps you plan and estimate the number of trips needed to transport the required amount of material.
Source: bing.com
How to Calculate the Volume of Material
To calculate the volume of material that can be held by a tri axle dump truck, you need to know the length, width, and height of the bed. The formula for calculating the volume is:
Volume = Length x Width x Height
Let’s say the length of the bed is 20 feet, the width is 8 feet, and the height is 4 feet. Using the formula above, we can calculate the volume:
Volume = 20 x 8 x 4 = 640 cubic feet
To convert cubic feet to cubic yards, we divide the volume by 27:
640 ÷ 27 = 23.7 cubic yards
So, a tri axle dump truck with a bed measuring 20 x 8 x 4 feet can hold approximately 23.7 cubic yards of material.
In conclusion, a tri axle dump truck can hold anywhere from 16 to 25 cubic yards of material, depending on its size and the type of material being hauled. It is important to know the capacity of the
truck to avoid safety hazards and fines. By calculating the volume of the bed, you can estimate the amount of material that can be transported in one trip. | {"url":"https://www.truckstrend.com/how-many-cubic-yards-in-a-tri-axle-dump-truck","timestamp":"2024-11-10T18:05:34Z","content_type":"text/html","content_length":"81265","record_id":"<urn:uuid:53360fab-9578-4155-aa80-d0e3c29735ac>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00411.warc.gz"} |
On continual leakage of discrete log representations
Let double-struck G be a group of prime order q, and let g [1],...,g[n] be random elements of double-struck G. We say that a vector x = (x[1],...,x[2]) ∈ ℤ [q]^n is a discrete log representation of
some some element y ∈ double-struck G (with respect to g[1],...,g[n]) if g[1]^x1⋯g[n]^xn = y. Any element y has many discrete log representations, forming an affine subspace of ℤ[q]^n. We show that
these representations have a nice continuous leakage-resilience property as follows. Assume some attacker A(g [1],...,g[n], y) can repeatedly learn L bits of information on arbitrarily many random
representations of y. That is, A adaptively chooses polynomially many leakage functions f[i] : ℤ[q] ^n → {0,1}^L, and learns the value f[i](x [i]), where x[i] is a fresh and random discrete log
representation of y. A wins the game if it eventually outputs a valid discrete log representation x* of y. We show that if the discrete log assumption holds in double-struck G, then no polynomially
bounded A can win this game with non-negligible probability, as long as the leakage on each representation is bounded by L ≈ (n - 2) log q = (1 - 2/n)·|x|. As direct extensions of this property, we
design very simple continuous leakage-resilient (CLR) one-way function (OWF) and public-key encryption (PKE) schemes in the so called "invisible key update" model introduced by Alwen et al. at
CRYPTO'09. Our CLR-OWF is based on the standard Discrete Log assumption and our CLR-PKE is based on the standard Decisional Diffie-Hellman assumption. Prior to our work, such schemes could only be
constructed in groups with a bilinear pairing. As another surprising application, we show how to design the first leakage-resilient traitor tracing scheme, where no attacker, getting the secret keys
of a small subset of decoders (called "traitors") and bounded leakage on the secret keys of all other decoders, can create a valid decryption key which will not be traced back to at least one of the
Publication series
Name Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Number PART 2
Volume 8270 LNCS
ISSN (Print) 0302-9743
ISSN (Electronic) 1611-3349
Other 19th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2013
Country/Territory India
City Bengaluru
Period 12/1/13 → 12/5/13
ASJC Scopus subject areas
• Theoretical Computer Science
• General Computer Science
Dive into the research topics of 'On continual leakage of discrete log representations'. Together they form a unique fingerprint. | {"url":"https://nyuscholars.nyu.edu/en/publications/on-continual-leakage-of-discrete-log-representations","timestamp":"2024-11-12T16:49:27Z","content_type":"text/html","content_length":"59794","record_id":"<urn:uuid:c8789221-8f77-4a43-9926-dcc1d1d382c2>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00602.warc.gz"} |
Fast and Parallel Processing
Paul Gader’s Ph.D. research, finished in 1986, was on parallel algorithms for Discrete Fourier Transforms and General Linear Transforms. He states, “The idea back then was that image processing could
not be performed on general purpose CPUs. Therefore, researchers were investigating special image processing architectures. One was the so-called Massively Parallel Processor that would have a
rectangular array of simple processors that could communicate only with their neighbors. There was a desire for automating the mapping of algorithms that required global computation to sequences of
local calculations.”
Professor Gader investigated mathematical methods for doing that. He explains:
In the case of linear transformations, the problem could be a considered a matrix factorization problem. First consider the problem for a linear, or 1D, array of processors:
Figure 1. A linear array with 4 nodes. The neighbors of node \(x_1\) are nodes
\(x_1\) and \(x_2\), of node \(x_2\) are nodes \(x_1\), \(x_2\), \(x_3\), etc.
The neighbors of a node in the array are defined to be the node itself and the nodes immediately to the left and right of the node. At the ends, these are just the node on the left (at the right end)
or the node on the right. Given a transformation, \(\mathbf{y} = \mathbf{Ax}\), where \(\mathbf{A}\) is a full \(M\times M\) matrix, the problem is to find a sequence of matrices \(\mathbf{A_1}, \
mathbf{A_2}, \dots, \mathbf A_{M-1}\) such that each \(\mathbf A\) is tri-diagonal with \(\mathbf A = \mathbf{A_1}\mathbf{A_2}\ldots\mathbf A_{M-1}\). For any solution, \(\mathbf y = \mathbf A_1\
mathbf A_2\ldots\mathbf A_{M-1}\mathbf x\).
For example, let
\(\mathbf A = \begin{bmatrix}
0.67 &2.33 &0.00 &-0.33\\
1.00 &0.67 &2.00 &0.00\\
-1.33 &0.67 &0.67 &1.67\\
0.33 &-1.33 &0.33 &2.00
Then \(\mathbf A = \mathbf A_1\mathbf A_2\mathbf A_3\) where
\(\mathbf A_1 =
3 &-1 & 0 & 0\\
-1 & 3 &-1 & 0\\
0 &-1 & 3 &-1\\
0 & 0 &-1 & 3
\mathbf A_2 =
0.33 &0.33 &0.00 &0.00\\
0.33 &0.33 &0.33 &0.00\\
0.00 &0.33 &0.33 &0.33\\
0.00 &0.00 &0.33 &0.33
\mathbf A_3 =
2 & 1 & 0 & 0\\
-1 & 2 & 1 & 0\\
0 &-1 & 2 & 1\\
0 & 0 &-1 & 2
At each node in the linear array, the calculations \(\mathbf y_1 = \mathbf A_3\mathbf x\), \(\mathbf y_2 = \mathbf A\mathbf y_1\), and \(\mathbf y_3 = \mathbf A\mathbf y_2\) only require data only
from their immediate neighbors in the array. Conceptually, a 2D array of processors leads to the same problem except the tri-diagonal matrix has to have a block format to account for neighbors in
both the horizontal and vertical directions.
For example, one algorithm/architecture, referred to as a systolic algorithm/architecture, can process sequences of linear transforms, including Fourier transforms, at very high data rates.
A sequence of signals, \(z_1\), …, \(z_t\), can be presented to the processor array. Once the array is filled, the Fourier transform of one signal is produced at each time step.
A systolic network for computing sequences of 5-point Fourier transforms. This can be done for arbitrary N-point Fourier transforms.
Want to know more? Click on these links:
Bidiagonal Factorization of Fourier Matrices and Systolic Algorithms for Computing Discrete Fourier Transforms
Necessary and Sufficient Conditions for the Existence of Local Matrix Decompositions
Tridiagonal Factorizations of Fourier Matrices and Applications to Parallel Computations of Discrete Fourier Transforms
Bidiagonal Factorizations of Fourier Matrices and Systolic Algo- rithms for Computing Discrete Fourier Transforms
Necessary and Sufficient Conditions for the Existence of Local Matrix Decompositions
Tridiagonal Factorizations of Fourier Matrices and Applications to Parallel Computations of Discrete Fourier Transforms
In these papers, Paul Gader didn’t construct parallel algorithms but used group theory to help construct Superfast FFTs:
A Variant of the Gohberg-Semencul Formula Involving Circulant Matrices
Displacement Operator Based Decompositions of Matrices Using Circulants or Other Group Matrices
Professor Gader also worked on factorization of nonlinear transformations based on mathematical morphology as described in:
Local Decompositions of Gray-Scale Morphological Templates
Separable Decompositions and Approximations of Greyscale Mor-phological Templates
Keywords: Fast Fourier Transforms, Parallel Fast Fourier Transforms, Graphics Processing Units, GPUs, Matrix Factorization. | {"url":"https://faculty.eng.ufl.edu/computing-for-life/research/fast-and-parallel-processing/","timestamp":"2024-11-06T15:15:29Z","content_type":"text/html","content_length":"88206","record_id":"<urn:uuid:d05fc342-e666-4237-bd0d-6348021cb90d>","cc-path":"CC-MAIN-2024-46/segments/1730477027932.70/warc/CC-MAIN-20241106132104-20241106162104-00173.warc.gz"} |
Consort Flow Diagram Template
Consort Flow Diagram Template - Consort 2010 checklist (word) full bibliographic reference. Randomized (n= ) analysed (n= ) excluded from analysis (give reasons) (n= ) allocated to intervention (n=
). Web the flow diagram can be accessed via the original published paper by following the pubmed links in the full bibliographic reference section of this web page. The text boxes can be modified by
clicking on them. The text boxes can be m odified by clicking on. Web sample template for the consort diagram showing the flow of participants through each stage of a randomized trial. Schulz kf,
altman dg, moher d, for the consort group. Web 1 sample template for the consort diagram showing the flow of partici pants thr ough each stage of a randomized trial. Web consort 2010 flow diagram
consort 2010 flow diagram enrollment assessed for eligibility (n= ) allocated to intervention.
Consort flow chart.
Web 1 sample template for the consort diagram showing the flow of partici pants thr ough each stage of a randomized trial. The text boxes can be m odified by clicking on. Randomized (n= ) analysed (n
= ) excluded from analysis (give reasons) (n= ) allocated to intervention (n= ). Web sample template for the consort diagram showing the flow.
Revised template of the CONSORT diagram showing the flow of
Schulz kf, altman dg, moher d, for the consort group. Web consort 2010 flow diagram consort 2010 flow diagram enrollment assessed for eligibility (n= ) allocated to intervention. Web sample template
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Deficit reduction through growth
Jan 25 2011
Deficit reduction through growth
This blog post seeks to answer the question: what economic growth rate does the UK need to sustain in order to reduce the deficit to zero?
This seems like a relevant question at the moment, and I’ve not seen a straightforward calculation of the answer – so I thought I’d give it a go myself. The idea being that even if the end result is
not particularly informative the thinking behind getting the end result is useful.
The key parameter of interest here is the gross domestic product (GDP): the amount of goods and services produced in a year in the UK; it’s a measure of how wealthy we are as a nation, how it
increases with time is a measure of economic growth. Also important are the deficit (how much the government’s annual spending exceeds its income) and debt (how much the government is borrowing).
Inflation means that the GDP can appear to grow each year with no increase in real economic activity, therefore I decided to use “inflation adjusted” GDP figures. I also preferred to use annual GDP
figures rather than quarterly ones.
To model this I took a starting point of a known GDP, debt, deficit and government spend which I then propagated forwards in time: I made the GDP grow by a fixed percentage each year, and assumed
that government spending would be flat (I’m using GDP adjusted for inflation so I think this is reasonable). Assuming that the total tax take is a fixed proportion of GDP I can calculate the deficit
and hence increasing debt in each year, I add the debt servicing cost to the government spending in each. Since I’m doing everything else in the absence of inflation I’ve used a debt servicing rate
of 2% rather than the 5% implied by a £43bn debt interest cost in 2010 – this makes my numbers a bit inconsistent.
I’ve put the calculation in a spreadsheet here.
Given this model my estimate is that the UK would need to sustain GDP growth of 4.8% per year until 2020 in order to reduce the deficit to 0%. This 4.8% GDP growth brings in approximately an
additional £30bn in taxes for each year for which the growth is 4.8%. During this time the debt would rise to nearly 80% of GDP and so the cost of servicing the debt will double. These numbers seem
plausible and fit with other numbers I’ve heard knocking around.
To get a feel for how GDP has varied in the past, this is the data for inflation adjusted annual GDP growth in the UK since 1950:
The red line shows the “target” 4.8% GDP growth, and the blue bars the actual growth in the economic, adjusted for inflation. The data comes from here. What’s notable is that GDP growth has rarely
hit our target and what’s worse, over the last 40 years there have been four recessions (where GDP growth is negative), so the likelihood must be that another recession before or around 2020 is to be
In real-life we are actually using a combination of GDP, government spending cuts and tax increases to bring down the deficit. These calculations indicate 0.5% GDP growth is approximately £7bn per
year which is equivalent to a couple of pence on basic rate (see here) or about 1% of government spending (see here).
Doing this calculation is revealing because it highlights why there is an emphasis on cuts in government spending as a means of reducing the deficit. This had been a bit of a mystery to me with the
figure of 80:20 cuts to taxes ratio being widely quoted as some sort of optimum, although there is some indication of other countries working with a ratio closer to 50:50. The thing is that when you
cut your spending, you are in control. You can set a target for reduction and have a fair degree of confidence you can hit that target and show you have hit that target relatively quickly and easily.
On the contrary relying on growth in GDP, or taxes, is a rather more unpredictable exercise: taxes because the amount of tax raised depends on the GDP.
The Office for Budget Responsibility (OBR) published uncertainty bounds for it’s future predictions of GDP in their pre-budget report last year (see p10 and Annex A in this report), their central
forecast is for growth of 2.5% but by 2014 (i.e. in only 4 years) they estimated only a 30% chance that it lay between 1.5% and 3.5% actually they only claim a 40% chance of being in that range for
this year (2011).
At the risk of being nearly topical, GDP is reported to have shrunk by 0.5% in the last quarter of last year, 2010. This is largely irrelevant to this post, although forecasts for GDP were growth of
~0.5% which supports the idea that GDP is not readily predictable. It’s worth noting that the ONS will revise this figure at monthly intervals until they get all the data in – the current estimate is
based on 40% of the data being available.
Given this abysmal ability to predict GDP I suspect that there is little governments can do to influence the growth in GDP. It would be interesting to estimate the influence government policy has
relative to prevailing global economic conditions, and what timelags there might be between policy changes and growth.
I think these calculations are illustrative rather than definitive, and what I’d really like is for someone to point to some better calculations! | {"url":"https://ianhopkinson.org.uk/2011/01/deficit-reduction-through-growth/","timestamp":"2024-11-06T18:20:28Z","content_type":"text/html","content_length":"88785","record_id":"<urn:uuid:1719e542-df95-4b10-bf23-e17b0e140641>","cc-path":"CC-MAIN-2024-46/segments/1730477027933.5/warc/CC-MAIN-20241106163535-20241106193535-00792.warc.gz"} |
GMAT Syllabus 2023, Section & Subject Wise Syllabus - Check Here
Latest Applications Open 2024:
The GMAT is the online test, which is organized by the Graduate Management Admission Council (GMAC) and the GMAT is completely known as the Graduate Management Admission Test.
There are various graduate management programs available for the candidates in which include MBA, Master of Finance, and Master of Accountancy programs, so those candidates are interested to get
admission, they can fill the application form of GMAT online mode.
There are many of candidates who may appear for the examination of GMAT every year to complete their graduate management programs. The candidates have to apply online mode.
The candidates can get the complete information on the GMAT through this article which includes GMAT Syllabus, Exam Pattern, Exam Centers, etc.
GMAT Syllabus 2023
The GMAT Syllabus may include various topics, which cover four sections as Analytical Writing Assessment, Integrated Reasoning, Quantitative and Verbal.
Latest Applications For Various UG & PG Courses Open 2024
It is the four sections of the GMAT. The candidates have to study that four sections to give the examination of GMAT and with the help of the syllabus, candidates will be able to do better
preparation for the examination.
Four Broad Sections of GMAT
The GMAT is a three-and-a-half-hour test carrying a maximum score of 800 points. The entire GMAT syllabus is divided into four broad sections:
• Analytical Writing Assessment (AWA)
• Integrated Reasoning (IR)
• Quantitative
• Verbal
Analytical Writing Assessment (AWA)
This is the first section of the GMAT and test-takers need to finish this section in 30 minutes. This is an essay section where the test taker needs to write an analysis of the presented argument.
In the AWA section, the GMAT Checks
• Candidates writing skills and abilities
• Clarity and logic in the argument
• The overall relevance of your essay with respect to the given topic
Integrated Reasoning
The IR section consists of 12 questions of 4 types:
• Multi-source reasoning
• Graphics interpretation
• Table analysis
• Two-part analysis
In the IR section, the GMAT looks for skills related to the following:
• Deciphering relevant information presented in text, numbers, and graphics
• Assessing appropriate information from different sources
• Combining and arranging information to observe relationships among them and solving complex problems to arrive at a correct interpretation
Quant Syllabus
The quant may include various topics, which is given below
• Number Systems & Number Theory
• Multiples and factors
• Fractions
• Decimals
• Percentages
• Averages
• Powers and roots
• Profit & Loss
• Simple & Compound Interest
• Speed, Time, & Distance
• Pipes, Cisterns, & Work Time
• Ratio and Proportion
• Mixtures & Alligation
• Descriptive statistics
• Sets
• Probability
• Permutation & Combination
• Monomials, polynomials
• Algebraic expressions and equations
• Functions
• Exponents
• Arithmetic & Geometric Progression
• Quadratic Equations
• Inequalities and Basic statistics
• Lines and angles
• Triangles
• Quadrilaterals
• Circles
• Rectangular solids and Cylinders
• Coordinate geometry
This is the third section on the GMAT. The test-takers will be provided with 41 verbal questions that need to be solved in 75 minutes.
In the Verbal section of the GMAT, the test takers are assessed for
Latest Applications For Various UG & PG Courses Open 2024
• Reading and understanding the written material
• Reasoning out and appraising the arguments
• Rectifying the written material in accordance with standard written English
GMAT Exam Pattern
The GMAT Exam Pattern has mentioned below-
GMAT Test Section Number of Questions Question Types Timing
Analytical Writing Assessment 1 Topic Analysis of Argument 30 Minutes
Multi-Source Reasoning
Integrated Reasoning 12 Questions Graphics Interpretation 30 Minutes
Two-Two Part Analysis
Table Analysis
Quantitative 37 Questions Data Sufficiency 75 Minutes
Problem Solving
Reading Comprehension
Verbal 41 Questions Critical Reasoning 75 Minutes
Sentence Correction
Total Exam Time 3hrs, 30 minutes
If you have any other Questions related to GMAT Syllabus 2023, you may ask your Queries by commenting below.
Hi Guys, I am Sandeep Co-founder of IASpaper and UPSCToday Staying in Mumbai (India) and pursuing graduation in Computer Science and Engineering from Mumbai University. I love helping Aspirants.
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How to Write Li in Roman Numerals: A Quick Guide
In Roman numerals, “L” represents the value 50, and “I” represents the value 1. To write the number 51 in Roman numerals, we need to combine these two symbols.
To write 51 in Roman numerals, we can use the subtractive principle, where a smaller numeral is placed before a larger numeral to subtract its value. So, we can write 51 as “LI,” which means 50 + 1 =
Here’s a quick guide to writing 51 in Roman numerals:
• Start with the largest Roman numeral that is less than or equal to the number you want to write. In this case, the largest Roman numeral less than 51 is “L,” which represents 50.
• Write “L” first, followed by “I” to represent the remaining value of 1. So, we get “LI,” which represents 50 + 1 = 51.
In conclusion, the Roman numeral for the number 51 is written with the symbols “LI,” which translate to “50 plus 1.” The Roman numeral system is an ancient numerical system that is still used today
for a variety of reasons, including the numbering of book chapters, the representation of numbers on clock faces, and the indication of the years on structures.
see also
A Step-by-Step Guide to Writing MCMXXXVI in Words
How to Write 2005 in Roman Numerals: A Step-by-Step Guide
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Why Mathematics? - Department of Mathematics Blog
Why Mathematics?
Making it count Student experience 18 July 2018
Why Mathematics?
For over 4 years, I’ve been asked similar questions over a thousand times :
“ Why did you choose mathematics?”
“Are you an idiot?”
“Are you crazy?”
A large number of people, even some maths students, usually feel confused why students are willing to choose maths as their major. Mathematics, which is a difficult and challenging subject for
students, seems like a ridiculous choice to some. Having been a maths student for more than 4 years, I’d like to share my feelings on the subject with you.
Firstly, the greatest advantage of maths learning is the ability of logical thinking. For example, as a maths student, sometimes you need to deal with a lot of data and find internal logical
connections and this will improve your analysis ability. Furthermore, after repeating the same steps many times, your logical-thinking ability will be strengthened. As everyone knows, logical
thinking is a very important ability for your future career.
Secondly, almost every mathematics student is a quick learner. Since maths students usually need to solve some difficult questions which they are not familiar with, they need to learn related
theorems, algorithms or coding language in a short period. Thus, you need to learn and understand new things quickly. This ability will help you a lot in your future career.
Finally, the most important thing is to be hard-working. Studying maths will push you to be hard-working and help you to cultivate good study habits, which will play an important role for your whole
life. To some extent, this will decide the probability of your future success.
I used to study mathematics and applied mathematics for my Bachelor degree and I am studying MSc Mathematical Finance at the University of Manchester now. This program at the University of Manchester
has a high world-ranking which is an important reason for my choice. What’s more, after studying here for one year, I found this is really a worthy program, since it’s a good combination of Maths and
Finance. You can learn not only the key theorems in finance, but also the translation and practical application by mathematical methods, which will make the theorems more impressive and attractive.
One week ago, I finished my final exams of the second semester and that is the hardest time in the whole semester. Have you ever seen Manchester at 3 or 4am? If you don’t like drinking, you may
answer “No”. However, it’s normal for a maths student in the exam period. If possible, I hope that I could spend all the 24 hours revising since no course is easy for our major. Although the revision
period is painful, the sense of achievement you can get after your exam is fantastic! And this is the reason why maths students think maths is a charming subject!
In other words, do not hesitate to be a mathematics student since there are so many benefits you can obtain. Come and join the School of Mathematics!
alan turing buildingmathsMScPostgraduateStephanieuniversity
Related posts | {"url":"https://www.sites.se.manchester.ac.uk/maths-blog/2018/07/18/why-mathematics/","timestamp":"2024-11-09T07:09:14Z","content_type":"text/html","content_length":"46891","record_id":"<urn:uuid:857e22f6-515c-4f3b-9908-366dd53d30ce>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.30/warc/CC-MAIN-20241109053958-20241109083958-00761.warc.gz"} |
Parallelogram 80761 - math word problem (80761)
Parallelogram 80761
Construct a parallelogram ABCD if a=5 cm, height to side a is 5 cm, and angle ASB = 120 degrees. S is the intersection of the diagonals.
Correct answer:
Did you find an error or inaccuracy? Feel free to
write us
. Thank you!
You need to know the following knowledge to solve this word math problem:
Units of physical quantities:
Themes, topics:
Grade of the word problem:
We encourage you to watch this tutorial video on this math problem:
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/MAT/LAW57 (BARLAT3)
Block Format Keyword This law describes plasticity hardening by a user-defined function and can be used only with shell elements.
This is an elasto-plastic orthotropic law for modeling anisotropic materials in forming processes especially aluminum alloys. This material law must be used with property set type /PROP/TYPE9
(SH_ORTH) or /PROP/TYPE10 (SH_COMP).
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW57/mat_ID/unit_ID or /MAT/BARLAT3/mat_ID/unit_ID
${\rho }_{i}$
E $u$
fct_ID[E] E[inf] C[E]
r[00] r[45] r[90] C[hard] m
${\epsilon }_{p}^{max}$ ${\epsilon }_{t}$ ${\epsilon }_{m}$ F[cut] F[smooth]
Repeat the next line for each plasticity function
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_ID[i] Fscale[i] ${\stackrel{˙}{\epsilon }}_{i}$
Field Contents SI Unit Example
Material identifier.
(Integer, maximum 10 digits)
Unit identifier.
(Integer, maximum 10 digits)
Material title.
(Character, maximum 100 characters)
Initial density.
${\rho }_{i}$ $\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\
(Real) right]$
Young's modulus.
E $\left[\text{Pa}\right]$
Poisson's ratio.
Function identifier for the scale factor of Young's modulus, when Young's modulus is function of the plastic
strain. 11
fct_ID[E] Default = 0: in this case the evolution of Young's modulus depends on E[inf] and C[E].
Saturated Young's modulus for infinitive plastic strain.
Parameter for Young's modulus evolution.
Lankford parameter 0 degree.
Default = 1.0 (Real)
Lankford parameter 45 degrees.
Default = 1.0 (Real)
Lankford parameter 90 degrees.
Default = 1.0 (Real)
Hardening coefficient.
= 0
Hardening is full isotropic model.
= 1
C[hard] Hardening uses the kinematic Prager-Ziegler model.
= between 0 and 1
Hardening is interpolated between the two models.
Barlat parameter.
= 2.0
Reduces to Hill's law.
= 6.0 (Default)
m Body Centered Cubic (BCC) material.
= 8.0
Face Centered Cubic (FCC) material.
Failure plastic strain.
${\epsilon }_{p}^{max}$
Default = 1.0 x 10^30 (Real)
Tensile failure strain at which stress starts to reduce.
${\epsilon }_{t}$
Default = 1.0 x 10^30 (Real)
Maximum tensile failure damage strain at which the stress in element is set to zero.
${\epsilon }_{m}$
Default = 2.0 x 10^30 (Real)
Cutoff frequency for the strain rate filtering.
F[cut] $\text{[Hz]}$
Default = 10000 Hz (Real)
Smooth strain rate option flag.
= 0 (Default)
F[smooth] No strain rate smoothing.
= 1
Strain rate smoothing active.
Plasticity curves i^th function identifier.
Scale factor for i^th function.
Default set to 1.0 (Real)
${\stackrel{˙}{\epsilon }}_{i} Strain rate for i^th function.
$ $\left[\frac{\text{1}}{\text{s}}\right]$
Example (Steel)
unit for mat
g mm ms
#- 2. MATERIALS:
# RHO_I
# E NU
206000 .3
#FUNCT_IDE EINF CE
# r00 r45 r90 C_hard m
1.79 1.51 2.27 0 0
# EPSP_max EPS_T EPS_M Fcut Fsmooth
# funct_ID Fscale_i EPS_i
#- 3. FUNCTIONS:
# X Y
.1 320
.5 480
1.2 600
1. The anisotopic yield criteria F for plane stress is defined by:
$F=a{|{K}_{1}+{K}_{2}|}^{m}+a{|{K}_{1}-{K}_{2}|}^{m}+c{|2{K}_{2}|}^{m}-2{{\sigma }_{y}}^{m}=0$
${\sigma }_{y}$ is the yield stress
${K}_{1}=\frac{{\sigma }_{xx}+h{\sigma }_{yy}}{2}$ and ${K}_{2}=\sqrt{{\left(\frac{{\sigma }_{xx}-h{\sigma }_{yy}}{2}\right)}^{2}+{p}^{2}{\sigma }_{xy}^{2}}$
2. Angles for Lankford parameters are defined with respect to orthotropic direction 1. The material constants a, c, h, and p are obtained from the three Lankford parameters:
$\begin{array}{l}a=2-2\sqrt{\frac{{r}_{00}}{1+{r}_{00}}}\sqrt{\frac{{r}_{90}}{1+{r}_{90}}}\\ c=2-a\\ h=\sqrt{\frac{{r}_{00}}{1+{r}_{00}}}\sqrt{\frac{1+{r}_{90}}{{r}_{90}}}\end{array}$
Material constant p is calculated by solving:
$\frac{2m\cdot {\sigma }_{y}{}^{m}}{\left(\frac{\partial F}{\partial {\sigma }_{xx}}+\frac{\partial F}{\partial {\sigma }_{yy}}\right){\sigma }_{45}}-1-{r}_{45}=0$
3. If the last point of the first (static) function equals 0 in stress, the default value of ${\epsilon }_{p}^{max}$ is set to the corresponding value of ${\epsilon }_{p}$.
4. If ${\epsilon }_{p}$ (plastic strain) reaches ${\epsilon }_{p}^{\mathrm{max}}$, in one integration point, the corresponding shell element is deleted.
5. If the largest principal strain ${\epsilon }_{1}>{\epsilon }_{t}$, the stress is reduced using the following relation:
$\sigma =\sigma \left(\frac{{\epsilon }_{m}-{\epsilon }_{1}}{{\epsilon }_{m}-{\epsilon }_{t}}\right)$
6. If ${\epsilon }_{1}>{\epsilon }_{m}$, the stress is reduced to 0 (but the element is not deleted).
7. The maximum number of curves is 10.
8. If $\stackrel{˙}{\epsilon }\le {\stackrel{˙}{\epsilon }}_{n}$, the yield is interpolated between f[n] and f[n-1].
9. If $\stackrel{˙}{\epsilon }\le {\stackrel{˙}{\epsilon }}_{1}$, function f[1] is used.
10. Above ${\stackrel{˙}{\epsilon }}_{\mathrm{max}}$, yield is extrapolated.
Figure 1.
11. The evolution of Young's modulus:
□ If fct_ID[E] > 0, the curve defines a scale factor for Young's modulus evolution with equivalent plastic strain, which means the Young's modulus is scaled by the function $\mathrm{f}\left({\
overline{\epsilon }}_{p}\right)$:
$E\left(t\right)=E\cdot \mathrm{f}\left({\overline{\epsilon }}_{p}\right)$
The initial value of the scale factor should be equal to 1 and it decreases.
□ If fct_ID[E] = 0, the Young's modulus is calculated as:
$E\left(t\right)=E-\left(E-{E}_{inf}\right)\left[1-\mathrm{exp}\left(-{C}_{E}{\overline{\epsilon }}_{p}\right)\right]$
Where, E and E[inf] are respectively the initial and asymptotic value of Young's modulus, and ${\overline{\epsilon }}_{p}$ is the accumulated equivalent plastic strain.
Note: If fct_ID[E] = 0 and C[E] = 0, Young's modulus, E is kept constant.
12. The parameters F[smooth] and F[cut] allows you to enable a strain-rate filtering. Three cases can be set:
□ If F[smooth] = 0 and F[cut] = 0.0, the strain-rate filtering is turned off.
□ If F[smooth] = 1 and F[cut] = 0.0, the strain-rate filtering uses a default cutoff frequency of 10 kHz.
□ If F[cut] ≠ 0, F[smooth] is automatically set to 1 and the strain-rate filtering uses the cutoff frequency given by you. | {"url":"https://help.altair.com/hwsolvers/rad/topics/solvers/rad/mat_law57_barlat3_starter_r.htm","timestamp":"2024-11-10T09:36:09Z","content_type":"application/xhtml+xml","content_length":"177558","record_id":"<urn:uuid:19d6f255-a0fd-46e7-be96-002d81ff93b5>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00277.warc.gz"} |
Rate-Dependent Hysteresis Model of a Giant Magnetostrictive Actuator Based on an Improved Cuckoo Algorithm
School of Mechatronic Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
Mechatronics T&R Institute, Lanzhou Jiaotong University, Lanzhou 730070, China
Engineering and Technology Research Center of Logistics and Transportation Equipment Information of Gansu Province, Lanzhou 730000, China
Gansu Logistics and Transportation Equipment Industry Technology Center, Lanzhou 730000, China
Author to whom correspondence should be addressed.
Submission received: 10 September 2023 / Revised: 16 October 2023 / Accepted: 23 October 2023 / Published: 26 October 2023
A rate-dependent asymmetric Prandtl–Ishilinskii (RAPI) model was proposed to tackle the serious rate-dependent hysteresis nonlinearity of the giant magnetostrictive actuator(GMA) output. First, a
polynomial function was introduced based on the PI model, and hysteresis factors were introduced to the Play operator, which accurately described the asymmetrical characteristic of the actuator
output. On this basis, rate-dependent parameters were added to establish a rate-dependent RAPI model. Second, an improved cuckoo search (ICS) algorithm was proposed to solve the difficulty in the
parameter identification of the RAPI model. For the ICS algorithm, the algorithm stability and optimization accuracy were improved using the adaptive step (AS) strategy and bird’s nest disturbance
strategy. Then, the effectiveness of the ICS algorithm was tested by comparing it with other parameter identification algorithms. Finally, the rate-dependent RAPI model was verified by combining the
output data of the giant magnetostrictive actuator under different frequencies. The results show that the rate-dependent RAPI model exhibits a higher accuracy than the PI model, thus verifying the
effectiveness of the rate-dependent RAPI model.
1. Introduction
A giant magnetostrictive actuator, a new-type actuator with giant magnetostrictive materials as the drive element, is a power output device with the magnetostrictive effect, accompanied by the
advantages of a high output frequency, strong stability, and large output force [
]. In recent years, the increasing speed of high-speed trains has increased the vibration of the train due to the irregularities of the track. The application of a giant magnetostrictive actuator to
a train’s active suspension allows for different damping forces to be output based on the disturbance excitation of distinct lines, thereby lessening train vibration and enhancing the stability and
comfort of the train operation. Therefore, the application of a super magnetostrictive actuator in train active suspension has a good prospect.
Due to the serious hysteresis nonlinearity of the giant magnetostrictive actuator output, however, it is difficult to control the precise output, which greatly limits the practical application of
giant magnetostrictive actuators [
]. The hysteresis characteristic of a giant magnetostrictive actuator can be expressed by a hysteresis model, and establishing an accurate hysteresis model has become a significant foundation for
solving hysteresis nonlinearity. At present, hysteresis models are generally divided into two types: physical models and phenomenological models, the former of which mainly include the J-A model [
] and the free energy model [
] and the latter of which include the Preisach model [
], the Prandtl–Ishilinskii (PI) model [
], and neural network models [
]. In application, the J-A model and the free energy model require high-precision experimental data and more model parameters. The Preisach model is characterized by dual integrals and a complicated
solving process, thus restricting its application. The solution precision of neural network models excessively relies upon the accuracy of experimental data. Over the other methods, the PI model
integrates the advantages of a small calculated quantity, high flexibility, and easy identification and solution. In this study, therefore, a giant magnetostrictive actuator was subjected to
hysteresis modeling based on the PI model.
The PI model was put forward by Prandtl et al. to model magnetic materials. In the process of popularization, the basic PI model has been improved by research scholars and applied in various fields.
Zhong, Y. [
] introduced a cubic polynomial into the primary function of the PI model to construct an enhanced PI model, endowing the model with asymmetry so that it could describe the magnetic hysteresis
phenomenon within a wider range and identify model parameters using the moth–flame algorithm. The results showed that the fitting accuracy of the improved PI model is significantly higher than that
of the classical PI model under high frequencies. Zhao, X.H. [
] divided hysteresis nonlinearity into a linear module and a nonlinear model, described the nonlinear model with the PI model, replaced the linear model with an electromechanical transfer function,
and finally connected the PI model with the transfer function in series to form a dynamic hysteresis model and solve the inverse model. The results manifested that the designed dynamic PI model
displays good performance within 0–50 Hz. Tang, H.B. [
] improved the PI model by adding a dead-zone operator and introducing a frequency function. It was then experimentally verified that the improved model is much better than the classical PI model and
can fit the GMM output curve well within 80 Hz. Pan, Y. [
] optimized the parameters of the classical PI model using the sequential quadratic programming algorithm, added a shift operator to make the model asymmetric, and improved the rate dependence of the
model through the series ARX model given the shortcomings of the asymmetric PI model. Finally, it was verified that the model has a good fitting effect on hysteresis curves above 200 Hz, but the
improving effect on low-frequency hysteresis curves is not evident. Subhash Rakheja et al. [
] established a rate-dependent PI model based on the memoryless function of the dead-zone operator and compared the comprehensive PI model data and the actual output. The comparison results revealed
that the improved model can describe the nonlinear hysteresis characteristics in a wide range of excitation amplitudes and frequencies. Dargahi et al. [
] described the hysteresis curve of the magnetorheological elastomer using the improved generalized PI model and replaced the original equal interval distribution with the threshold distribution
function. The results showed that the improved generalized model can accurately characterize the hysteresis characteristics of magnetorheological materials under different loading conditions and
magnetic field ranges. Peng et al. [
] applied the PI model to the hysteresis nonlinear modeling of a giant magnetostrictive actuator, proposed a rate-dependent modified PI model, and then identified the parameters of the model by using
the constrained least squares method. The results showed that, within a certain frequency range, the rate-dependent modified PI model could effectively describe the hysteresis characteristics of the
giant magnetostrictive actuator. Xiao et al. [
] modified the classical PI model and used the least square method to identify parameters of the modified PI model. The results show that the modified PI model can reduce the modeling error, but the
model accuracy is still not guaranteed under a high frequency. Nie, L.L. et al. [
] established a rate-dependent asymmetric hysteresis RDAPI model by introducing a dynamic envelope function into the play operator of the PI model and then combined with other improved PI models to
characterize the rate-dependent and asymmetric hysteresis behavior of the piezoelectric micro-positioning level. Experiments show that the accuracy of the RDAPI model is improved significantly. On
this basis, a robust adaptive control method is proposed. Wang, W. et al. [
] improved the Play operator in the PI model to an asymmetric operator, established an asymmetric API model, and optimized the parameters of the API model, which reduced the number of parameters and
maintained a high accuracy. The experimental results show that the compensator based on this model can effectively suppress the hysteresis of the piezoelectric actuator.
In summary, the parameter identification and hysteresis modeling techniques for the magnetostrictive actuator based on the PI model are still immature. In this paper, aiming at the rate-dependent
asymmetric hysteresis characteristics of the output curve of the active suspension magnetostrictive actuator, a rate-dependent asymmetric PI (RAPI) model was constructed by adding auxiliary functions
based on the PI model, which can accurately describe the hysteresis curve of the output of the magnetostrictive actuator. In order to solve the problem of the RAPI model having multiple parameters
that are difficult to identify, an improved cuckoo search (ICS) algorithm was proposed, which has higher optimization accuracy and stability compared to traditional algorithms. Finally, through
comparative experiments with the PI model, it is verified that the RAPI model effectively improves the fitting accuracy of the actuator’s hysteresis curve. Based on the RAPI model, precise dynamic
control of the giant magnetostrictive actuator can be further achieved, which is of great significance for the practical application of the magnetostrictive actuator in the active suspension of
2. Rate-Dependent Asymmetric PI Model
2.1. PI Model
In the PI model, the hysteresis of the output is generally described by the weighted superposition of the Play operator [
]. The basic Play operator is defined as follows:
] is assumed to be the set of all continuous piecewise functions in the definitional domain of [0,
], in which 0 =
… <
, and the output of the Play operator is:
$F r [ u ( t ) ] = f r u ( t ) , F r [ u ( t − 1 ) ]$
$f r ( u ( t ) , F r [ u ( t − 1 ) ] ) = max { u ( t ) − r , min ( u ( t ) + r , F r [ u ( t − 1 ) ] ) }$
Here, F[r] [u(0)] is the output of a single Play operator at the initial moment; F[r] [u(t)] denotes the output of a single Play operator at time t, in which u(t) stands for the input signal at time
t; F[r] [u(t − 1)] represents the output of the Play operator at the time before t. r is the threshold of the Play operator.
The output of the PI model is obtained through the weighted superposition of multiple Play operators with different thresholds and the summation with the input linear function, with the following
output formula:
$P I ( t ) = α u ( t ) + ∑ i = 1 n P r i F r i u ( t )$
Here, PI(t) is the output of the PI model; u(t) denotes the input of the PI model; α is the weight of the input; n represents the number of Play operators in the PI model; P[ri] stands for the weight
of each Play operator.
2.2. Asymmetric PI (API) Model
The Play operator of the PI model is centrosymmetric, and the output of giant magnetostrictive actuators is characterized by asymmetric hysteresis, leading to a big error in the description of the
asymmetric hysteresis curve by the PI model. Therefore, the PI model should be improved to make up for this deficiency. If introduced into the PI model, high-order polynomials, which are generally
asymmetric, can endow the model with the ability to fit asymmetric curves. In this study, the linear function in the PI model was substituted by a polynomial function as follows:
$G u t = a 0 + a 1 u t + a 2 u t 2 + a 3 u t 3 + a 4 u t 4 + … a n u t n$
Despite the asymmetry of the model output thanks to the polynomial function, the model details were not described, so the hysteresis factor
was introduced into the model to optimize the operator Play. The improved expression is as follows:
$F r , β u t = max { u ( t ) − β r , min ( u ( t ) + β r , F r , β [ u ( t − 1 ) ] ) }$
)] is the output of the improved Play operator at the current moment;
− 1)] stands for the output of the operator at the previous moment. The value of
could change the output amplitude and output gap of the Play operator, thus affecting the output of the asymmetric PI model. With the above improvements combined, the asymmetric PI model is expressed
as shown in Formula (7).
$A P I u t = G u t + ∑ i = 1 n P r i F r i , β i u t$
2.3. RAPI Model
A study [
] has shown that when the excitation frequency is greater than 5 Hz, the hysteresis characteristics of giant magnetostrictive actuators will be affected by the frequency, showing rate-dependent
hysteresis characteristics. Since the PI model is rate-independent, and neither the added hysteresis factor nor the auxiliary function contain frequency parameters, rate dependence processing is
required for the asymmetric PI model.
The current rate-dependent hysteresis modeling methods can be divided into two types: separated rate-dependent hysteresis models and overall rate-dependent hysteresis models. The separated
rate-dependent hysteresis models divide the hysteresis nonlinearity of the system into rate-independent hysteresis links of giant magnetostrictive materials and linear time invariant links consisting
of other components, which are then respectively modeled and connected in series so as to establish an integral system model. Overall rate-dependent hysteresis models do not differentiate the system
and establish a holistic model. Given that the model accuracy of separated modeling will be reduced under the high input frequency, the asymmetric PI model was improved in terms of the aspect of rate
dependence through the overall modeling method. Moreover, the coefficient c of the weighted Play operator sum was added, and a frequency function specific to the auxiliary function
)] and the hysteresis factor
was constructed:
$R A P I u t = G f u t + c f ∑ i = 1 n P r i F r i , β r i f u t$
$G f u t = a 0 f + a 1 ( f ) u t + a 2 f u t 2 + a 3 f u t 3 + ⋯ + a n f u t n$
$F f = k 1 , n × f + k 2 , n n = c , β , a 1 , a 2 , … a n$
Here, c(f), β(f), a[0](f)… a[n] (f) denote frequency-related parameters. The parameter values were identified by combining the output under different frequencies, and the unknown parameters in
Formula (9) were acquired through curve fitting. Then, each frequency function was substituted into Formula (8) so as to obtain the rate-dependent RAPI model.
3. Improved CS Algorithm
3.1. CS Algorithm
With the development of meta-heuristic optimization algorithms in recent years, such new-type optimization algorithms as the artificial fish swarm algorithm [
], CS algorithm [
], and grey wolf algorithm [
] have been developed by researchers and gradually applied to the field of parameter identification [
]. Therein, the CS algorithm has been widely used by virtue of a few control parameters and a strong global optimization ability. The CS algorithm is a meta-heuristic optimization algorithm proposed
by Yang et al., imitating the predation (Levy flight) and brooding behavior (discovery probability (Pa)) of cuckoos. The algorithm assumes the following conditions for simulation:
• There was only one bird egg in each nest, and the eggs were randomly distributed.
• In each evolution, the bird egg with the highest fitness was reserved.
• Under a fixed number of bird’s nests, the host bird abandoned the cuckoo eggs at Pa, and the eliminated nests would be replaced by new nests.
Based on the above assumptions, the iterative formula for the CS algorithm is as follows:
$X i t + 1 = X i t + α ⊗ L e v y λ$
$α = α 0 × X i t − X b e s t t$
$X i ( t + 1 )$
is the position of the
-th bird’s nest in the
+ 1 iteration;
$X i t$
stands for the position of the
-th bird’s nest in the
-th iteration;
$X b e s t t$
represents the best bird’s nest for the
-th iteration;
is the factor that controls the step of cuckoo movement, usually taken as 0.01; ⨂ is the product of vectors;
) is a random number that obeys the Levy distribution, which is solved by the following formula:
$L e v y λ = Φ × μ ν 1 / β$
was taken as 1.5, Φ through the following formula:
$Φ = τ 1 + β sin π × β 2 β τ 1 + β 2 × 2 β − 1 2 1 β$
is the standard Gamma function. Based on the above formula, the formula of the CS algorithm is as follows:
$X i t + 1 = X i t + α 0 × Φ × μ ν 1 β × X i t − X b e s t t$
When the bird’s nests were updated according to Levy flight, the host bird would still abandon some nests as per Pa if it found the cuckoo’s eggs, and a random number distributed in [0, 1] was
generated through the rand function and compared with Pa. Stochastically biased walk was adopted for the nests whose random number was greater than Pa, while the nests satisfying < Pa were kept
unchanged. The random preference formula is as follows:
$X i t + 1 = X i t + r X j t − X k t$
$X j t$ and $X k t$ are two random nests of the t-th generation, and r is a random number following a normal distribution.
The Cuckoo Search algorithm has a simple iterative process and a small number of control parameters. However, it also has limitations: the step size and discovery probability during the optimization
process remain constant, which leads to the inability of the Cuckoo Search algorithm to balance global search and local exploration. For complex problems, it cannot rely on Levy flights to escape
from local optima.
3.2. CS Algorithm Optimization
3.2.1. Adaptive Step (AS) Strategy
In the CS algorithm,
is the step coefficient, which directly determines the flight distance of the bird’s nest in each iteration. Since
is taken as 0.01 in the standard CS algorithm, the flight distance of the bird’s nest is relatively fixed, resulting in an imbalance between global search and local development. By analyzing the step
formula, it can be concluded that under a rather lower
value, the iteration range of the algorithm is small, accompanied by a high search accuracy and a low convergence rate. When the
value is rather higher, the iterative step of the algorithm increases, along with an enlarged search scope and low convergence accuracy [
]. Based on the above analysis, an AS function was proposed in this study and substituted into the following formula:
$w = 2 × ( − w max − w min K max × K ) + w max − w min K K max + exp ( − 12 × K K max − 6 ) + w max$
$X i ( t + 1 ) = X i t + w × α ⊗ L e v y λ$
According to the experiment,
= 0.8 is the minimum value of the inertia factor;
= 2 is the maximum value of the inertia factor;
is the number of iterations; and
is the maximum number of iterations, which was set to
= 1000. The change in the
value is displayed in
Figure 1
After the AS function was introduced, the algorithm was able to search globally at a large step in the initial stage of iterations and search locally at a small step in the later stage, showing an
initially declining, then rising, and finally declining trend on the whole. This not only conformed to the algorithm optimization law but also contributed to the strong population diversity of the
algorithm in the middle and later stages.
3.2.2. Bird’s Nest Disturbance Strategy
Although the standard CS algorithm can jump out of the local optimal solution to a certain extent with the help of the Levy flight strategy in the later iteration, a long-step flight is carried out
after repeated small-step iterations so that the algorithm cannot get rid of the local optimum in the later iterations. Hence, a bird’s nest disturbance strategy was proposed to disturb the
population with abnormal monitoring results by monitoring the results of each iteration.
The specific implementation steps are as follows: The bird’s nests that kept the global optimal solution unchanged in repeated iterations were recorded. When the global optimal solution was unchanged
in the
-th iteration of the bird’s nests, the current population was trapped in local optima, so it was disturbed at a disturbance step, which was the linear difference between the optimal solution of the
current generation and the position of the bird’s nest. In this way, the algorithm was capable of optimization near the local optimal solution, ensuring that the algorithm could still remain
convergent after the disturbance. The disturbance step length formula is as follows:
$V i , j = ζ 1 × ( ζ 2 g b e s t − X i , j )$
Here, $V i , j$ is the j-th dimensional disturbance step in the i-th cuckoo nest; $ζ 1$ is the step factor controlling the disturbance radius, in which I is the current population number; N is the
maximum population number; s is a constant; $ζ 2$ stands for the weight coefficient of the contemporary optimal cuckoo nest, taken as 0.03; $X i , j$ is the j-th dimensional nest value in the i-th
nest. The disturbance step $V i , j$ was dynamically adjusted by the cuckoo population number $V i , j$, and the disturbance step factor of the head population was large, which enabled the algorithm
to perform optimization in a larger scope. The disturbance step factor of the rear population was small, so the algorithm searched near the local optimal solution. The bird’s nest disturbance
strategy imposed different disturbance steps on different populations, which facilitated global search and local development with the local optimal solution as the center and effectively improved the
optimization accuracy and search ability of the algorithm.
3.2.3. ICS Algorithm Flow
The algorithm flow is as follows.
Step1: Input the algorithm iteration number K[max], the number of nests N, w[max], and w[min].
Step2: Initialize the nest positions and calculate the fitness value.
Step3: Update the nest positions using dynamic inertia Levy flight and retain nests with better fitness.
Step4: Select nests based on Pa, leaving nests with a better fitness value. Calculate the global optimal solution and the fitness value of the optimal solution.
Step5: Determine whether to disturb the population based on the number of repetitions of the global optimum in each iteration.
Step6: Determine whether the algorithm reaches the termination condition; if not, go back to Step3; when the termination condition is reached, output the optimal solution and the fitness value.
The flowchart of the algorithm is shown in
Figure 2
3.3. Performance Test of the ICS Algorithm
A set of mixed test functions was selected to verify the performance of the ICS algorithm. In the set, functions F1–F3, which are unimodal functions, could test the convergence ability and
optimization speed of the algorithm. Functions F4–F6, which are multimodal functions with increasing test difficulties, a large scope of optimization, and multiple local optimal values in the
definitional domain, were applied to test the optimization ability of the algorithm for multimodal complex functions. Function F7, a two-dimensional function, was used to test the optimization
ability of the algorithm for low-dimensional problems. The expressions of such test functions are listed in
Table 1
The ICS algorithm was comparatively analyzed with particle swarm optimization (PSO), CS, and ASCS to explore its accuracy and convergence.
Table 2
gives the specific parameter settings of each algorithm. The number of test populations was set to 50, the number of dimensions was set to 30, and the maximum number of iterations was set to 1000.
Each test function was run 30 times in the same environment, and their average function error (Mean), standard deviation (Std), and optimal value (Best) were recorded. The test results are shown in
Table 3
It could be seen that in functions F1–F3, the ICS algorithm could accurately converge to the global optimum. F4, a complex multimodal function, exhibited a lot of local optimal values in the
definitional domain. As shown in
Table 4
Table 5
, the ASCS algorithm was subjected to a too-large standard deviation and unstable optimization results despite the ability to search the optimal value of F4, while other algorithms all failed to
search the global optimal value. The ICS algorithm could converge to the global optimum even after repeated tests. F5 and F6, which were classical complex functions, were featured with a relatively
high optimization difficulty. For F6, the ICS algorithm was stuck in the local optimal value of 8.88 × 10
in the later stage of iterations, but its optimization accuracy remained higher than that of other algorithms. For F7 (a simple low-dimension function), the ICS algorithm and other algorithms
converged to the global optimum, indicating its excellent optimization ability on low-dimension functions. According to the Std value, the standard deviation of the ICS algorithm was 0 in many tests
under different functions, manifesting its favorable stability in optimization.
4. Parameter Identification and Experimental Verification of the RAPI Model
4.1. Parameter Optimization
The RAPI model was established on the basis of the API model, the parameters of which, therefore, were identified first. Some parameters preset in the API model were optimized.
4.1.1. Optimization of the Number of Hysteresis Factors
Hysteresis factors could change the shape of the Play operator by influencing the threshold so as to generate an impact on the output, and the model will be affected, to different degrees, by the
number of hysteresis factors. Different quantities of hysteresis factors were thereby experimented, and the maximum absolute deviation (MAD), the mean absolute error (MAE), and the root mean square
error (RMSE) were used as evaluation indexes for the model fitting accuracy, as shown in
Table 4
Combining the displacement data of the sinusoidal current under the amplitude of 2 A and 10 Hz, the parameters of four schemes were identified, respectively. The number of operators was set to 10,
the order of the auxiliary function was set to 3, and the rest of the parameters were obtained through the ICS algorithm.
Table 5
presents the evaluation results under four different numbers of hysteresis factors. As the number of hysteresis factors increased, the model fitting error gradually increased, so the number of
hysteresis factors was set to 1 in this study.
4.1.2. Order Optimization of the Auxiliary Function
The auxiliary function in the API model is the key factor deciding the model asymmetry, and its order affects the complexity of the model and the difficulty in parameter identification. Therefore, it
was necessary to optimize the model order. An experiment was carried out through the control variable method to acquire the optimal number. Therein, the number of operators was set to 10, that of
hysteresis factors was set to 1, the polynomial order was set to 1–6, and the other parameters were determined through the relevant parameter identification algorithm.
It could be observed from
Figure 3
that the RMSE decreased considerably when the order of the auxiliary function increased from one to three and basically kept unchanged as the order grew from three to four, but it rose again when the
order increased to five and six. This is because the increase in the function order aggravates the difficulty in parameter identification and leads to the failure to converge to the global optimum
after reaching the given number of iterations. Moreover, the parameter identification time is substantially lengthened as the model order increases. In full consideration of the model accuracy and
parameter identification time, the order of the auxiliary function was chosen to be three, expressed in Formula (20).
$G u t = a 0 + a 1 u t + a 2 u t 2 + a 3 u t 3$
4.1.3. Optimization of the Number of Play Operators
As the basic operation unit of a hysteresis model, the Play operator plays an important role in the model output. The model fitting accuracy will decline under a small number of operations. A
too-large number of operations will intensify the complexity of the calculation though improve the prediction accuracy to some extent. To determine the concrete number of operators, the experiment
was carried out under different numbers of operators, with other parameters remaining the same.
Figure 4
shows the RMSE curve under different numbers of operators. With the increase in the number of operators, the RMSE gradually decreased, indicating that the fitting accuracy of the model is gradually
improved. The subsequent increase in the number of operators >10 generated a very minor influence on the RMSE. Hence, the number of operators was determined to be 10 to balance the prediction
accuracy and the complexity of the calculation.
4.2. Parameter Identification of the RAPI Model
4.2.1. Parameter Identification of the API Model
In this study, the model parameters were identified by combining the experimental data under the current amplitude increasing in the range of 1–5 A and the frequency of 1 Hz. In this process, the
number of populations of the ICS algorithm was set to 80, the maximum number of iterations was set to 1000, and the disturbance threshold was set to 3. In the PI model, the weight value was generally
positive, but it was experimentally found that a lower RMSE could be acquired when the weight value was negative, so a negative weight value could be assigned to the API model. Since the API model is
the sum of the weighted superposition of Play operators, the model characteristics would not be changed by a small number of negative values. The ICS algorithm was repeatedly run ten times, the
optimal value and the optimal bird’s nest were recorded, and the API model parameters finally obtained are listed in
Table 6
Table 7
4.2.2. Parameter Identification of the RAPI Model
On the basis of the API model, the rate-related parameters were identified. To reduce the influence of environmental noise on the test displacement as much as possible, the other model parameters
were experimentally identified by selecting the sinusoidal current with an amplitude of 5A, the signals with the frequency of [1,25,40,55,70,85,100,120], and the Play operators with a constant weight
Table 8
shows the values of the model coefficients at different frequencies obtained by the parameter identification algorithm.
4.3. Verification of the RAPI Model
In order to obtain the hysteresis input–output data required for the identification model, a giant magnetostrictive actuator test bench is built, as shown in
Figure 5
. The experimental bench mainly includes: the giant magnetostrictive actuator, YB1635 signal generator, NI-usb6211 acquisition card and display device, Aigtek-ATA309 power amplifier, Panasonic
HG-C1030 laser displacement sensor, and PC and Tektronix-MDO3014 oscilloscope. Among them, the signal generator generates a positive rotating AC signal, which is amplified by the power amplifier to
drive the vibration of the super magnetostrictive actuator with a suitable excitation current. The laser displacement sensor, oscilloscope, acquisition card, and display device cooperate with the PC
to complete the display, acquisition, processing, and post-analysis of data.
The experimental curves at 50, 80, and 110 Hz were randomly selected and compared with the curves acquired by the PI model and the RAPI model. The fitting error curves of the two models are shown in
Figure 6
. It could be observed from the fitting curves of the two models that the RAPI model curves introduced with a frequency function could accurately fit the hysteresis curve of the giant
magnetostrictive actuator at variable frequencies. The error curve diagram shows that the PI model fails to describe the rate-related characteristics. As a result, as the frequency increases, the
output error values gradually increase. After the RAPI model is improved with rate correlation, the output error values at different frequencies remain relatively stable, indicating a significant
improvement in the fitting accuracy of the RAPI model for the variable frequency output curve of the magnetostrictive actuator.
Table 9
exhibits the evaluation results of the RAPI model and the PI model from three evaluation indexes: RMSE, MAD, and MAE. The results revealed that the RMSE of the model was reduced by 3.61 μm, the MAE
was reduced by 3.5 μm, and the MAD was reduced by 7.5 μm after the rate-dependence improvement, further verifying the effectiveness of rate-dependence improvement.
5. Conclusions
A modified RAPI model was proposed based on the hysteresis characteristics of the magnetostrictive actuator. The RAPI model first includes a polynomial function to describe the asymmetry of the
hysteresis curve. On this basis, a global modeling approach was used to introduce frequency parameters, enabling the model to describe the rate-related characteristics of the output from the giant
magnetostrictive actuator. To accurately identify the parameters of the RAPI model, an adaptive step ICS algorithm with bird-nest disturbance was designed. The optimized ICS algorithm was analyzed
and compared with PSO, CS, and ASCS algorithms, showing that the ICS algorithm has higher optimization accuracy and stability. Finally, experimental validation was conducted, and the results show
that the RMSE, MAE, and MAD values of the RAPI model were respectively reduced by 3.61 μm, 3.5 μm, and 7.5 μm compared to the PI model, confirming that the accuracy of the RAPI model is far higher
than that of the traditional PI model.
The RAPI model accurately describes the hysteresis characteristics of the giant magnetostrictive actuator. On this basis, the controller and control algorithm can be further designed to accurately
control the giant magnetostrictive actuator and realize its application in the train active suspension.
Author Contributions
Conceptualization, Y.L. and J.M.; methodology, Y.L.; software, J.C.; validation, Y.L., J.M. and J.C.; formal analysis, Y.L.; investigation, Y.L.; resources, J.M.; data curation, Y.L.;
writing—original draft preparation, Y.L.; writing—review and editing, Y.L.; visualization, J.C.; supervision, J.M.; project administration, Y.L.; funding acquisition, J.M. All authors have read and
agreed to the published version of the manuscript.
This research was funded by the National Natural Science Foundation of China (NSFC) grant number (62063013).
Data Availability Statement
Not applicable.
Conflicts of Interest
The authors declare no conflict of interest.
Function Expression Definitional Domain Optimal Value
F1 $f x = ∑ i = 1 n x i 2$ [−100, 100] 0
F2 $f x = ∑ i = 1 n x i + ∏ i = 1 n x i$ [−10, 10] 0
F3 $f x = ∑ i = 1 n i x 4$ [−1.28, 0.64] 0
F4 $f x = 1 4000 ∑ i = 1 n x i 2 − ∏ i = 1 n cos x i i + 1$ [−600, 600] 0
F5 $f x = − 20 exp − 0.2 1 n ∑ i = 1 n x i 2 − exp 1 n ∑ i = 1 n cos 2 π x i$ [−10, 10] 0
F6 $f x = ∑ i = 1 n x i sin x i + 0.1 x i$ [−10, 10] 0
F7 $f x = 0.5 + sin 2 x 1 2 − x 2 2 − 0.5 1 + 0.001 x 1 2 + x 2 2 2$ [−100, 100] 0
Algorithm Parameter
PSO c[1] = 1.5, c[2] = 1.5, w = 0.5
CS P[a] = 0.25, a = 0.01
ASCS Step[min] = 0, Step[max] = 0.01, P[a] = 0.25
Function Mean/Std/Best PSO CS ASCS ICS
Mean 8.92 3.46 × 10^−5 5.21 × 10^−9 0.00
F1 Std 3.18 7.20 × 10^−10 2.85 × 10^−8 0.00
Best 4.42 5.94 × 10^−6 4.52 × 10^−267 0.00
Mean 3.51 × 10 3.48 × 10^−2 2.07 × 10^−2 0.00
F2 Std 1.07 × 10 8.58 × 10^−4 7.40 × 10^−2 0.00
Best 1.96 × 10 2.12 × 10^−2 8.53 × 10^−3 0.00
Mean 3.18 1.06 × 10^2 7.13 × 10^−16 0.00
F3 Std 2.29 3.68 × 10 3.90 × 10^−15 0.00
Best 3.17 × 10^−1 3.98 × 10 0.00 0.00
Mean 2.26 × 10 8.79 × 10^−2 8.30 × 10^−4 0.00
F4 Std 6.55 4.00 × 10^−2 4.55 × 10^−3 0.00
Best 1.13 × 10 2.20 × 10^−2 0.00 0.00
Mean 1.18 × 10 1.90 8.60 × 10^−4 8.88 × 10^−16
F5 Std 1.12 3.93 × 10^−1 4.71 × 10^−3 0.00
Best 9.41 1.19 4.44 × 10^−15 8.88 × 10^−16
Mean 1.52 × 10 7.17 6.93 × 10^−1 0.00
F6 Std 3.46 9.83×10^−1 2.29 0.00
Best 8.46 5.16 3.88 × 10^−11 0.00
Mean 1.56 × 10^−14 1.57 × 10^−6 7.10 × 10^−9 0.00
F7 Std 5.79 × 10^−14 1.83 × 10^−6 1.96 × 10^−8 0.00
Best 0.00 0.00 0.00 0.00
Evaluation Index Expression
RMSE $R M S E = ∑ i = 1 N c exp i − c m x i 2 N$
MAE $M A E = 1 N ∑ i = 1 N c exp i − c m x i$
MAD $M A D = max 1 ≤ i ≤ N c exp i − c m x i$
Number of β RMSE MAE MAD
1 0.48 0.29 0.6
2 0.52 0.36 0.7
5 0.68 0.81 2.2
10 0.84 1.02 2.7
Operator No. Threshold Weight
0 0 2.2526
1 0.5 2.2068
2 1 1.7295
3 1.5 2.4370
4 2 1.8501
5 2.5 0.6715
6 3 −0.0693
7 3.5 0.3086
8 4 0.2692
9 4.5 0.2779
Parameter Value
β 1.0056
a[0] 0.2699
a[1] 2.7287
a[2] −0.2615
a[3] −0.0547
c 1
Frequency β α[3] α[2] α[1] α[0] c
1 0.9739 −0.0681 −0.0249 2.0342 −0.1091 1
25 0.9872 −0.0616 −0.0214 1.2331 0.0429 1.2192
40 1.0198 −0.0557 −0.0169 −0.0524 0.3016 1.3033
55 1.0321 −0.0429 −0.0141 −0.0524 0.3016 1.3615
70 1.0472 −0.0384 −0.0115 −1.261 0.6109 1.4099
85 1.048 −0.0309 −0.0095 −2.9429 0.7222 1.4637
100 1.0904 −0.0308 −0.0064 −3.1027 0.8558 1.4659
120 1.1193 −0.0185 −0.0009 −4.543 1.2016 1.6500
Index RMSE MAE MAD
RAPI 1.37 1.12 5.1
PI 4.98 4.62 12.6
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Liu, Y.; Meng, J.; Cao, J. Rate-Dependent Hysteresis Model of a Giant Magnetostrictive Actuator Based on an Improved Cuckoo Algorithm. Actuators 2023, 12, 400. https://doi.org/10.3390/act12110400
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Liu Y, Meng J, Cao J. Rate-Dependent Hysteresis Model of a Giant Magnetostrictive Actuator Based on an Improved Cuckoo Algorithm. Actuators. 2023; 12(11):400. https://doi.org/10.3390/act12110400
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data. For this purpose, studies with simulated and experimental data were conducted. Results with simulated data showed that the diagnostic techniques were efficient to identify the perturbation in
data. The results with real data indicated that atypical values among the sampled data may have a strong influence on thematic maps, thus changing the spatial dependence structure. The application of
diagnostic techniques should be part of any geostatistical analysis, to ensure a better quality of the information from thematic maps.
local influence; maximum likelihood; restricted maximum likelihood
A modelagem da estrutura de dependência espacial pela abordagem da geoestatística é de fundamental importância para a definição de parâmetros que definem essa estrutura e que são utilizados na
interpolação de valores em locais não amostrados, pela técnica de krigagem. Entretanto, a estimação de parâmetros pode ser muito alterada pela presença de observações atípicas nos dados amostrados. O
desenvolvimento deste trabalho teve por objetivo utilizar técnicas de diagnóstico em modelos espaciais lineares gaussianos, empregados em geoestatística, para avaliar a sensibilidade dos estimadores
de máxima verossimilhança e máxima verossimilhança restrita a pequenas perturbações nos dados. Foram realizados estudos de dados simulados e experimentais. O estudo com dados simulados mostrou que as
técnicas de diagnóstico foram eficientes na identificação da perturbação nos dados. Pelos resultados obtidos com o estudo de dados reais, concluiu-se que a presença de valores atípicos entre os dados
amostrados pode exercer forte influência nos mapas temáticos, alterando, assim, a estrutura de dependência espacial. A aplicação de técnicas de diagnóstico deve fazer parte de toda análise
geoestatística, a fim de garantir que as informações contidas nos mapas temáticos tenham maior qualidade.
influência local; máxima verossimilhança; máxima verossimilhança restrita
SECTION I - SOIL PHYSICS
Diagnostic techniques applied in geostatistics for agricultural data analysis^(^1 (1 ) Parte da Dissertação de Mestrado do primeiro autor. ^)
Técnicas de diagnóstico utilizadas em geoestatística para análise de dados agrícolas
Joelmir André Borssoi^I; Miguel Angel Uribe-Opazo^II; Manuel Galea Rojas^III
^IProfessor Assistente do Centro de Ciências Exatas e Tecnológicas CCET. Universidade Estadual do Oeste do Paraná UNIOESTE. Rua Universitária 2069, Sala 65, CEP 85819-110 Cascavel (PR). E-mail:
^IIProfessor Doutor do Centro de Ciências Exatas e Tecnológicas CCET/UNIOESTE. E-mail: mopazo@unioeste.br
^IIIProfessor Doutor do Departamento de Estadística, Universidad de Valparaíso, Valparaíso Chile. E-mail: manuel.galea@uv.cl
The structural modeling of spatial dependence, using a geostatistical approach, is an indispensable tool to determine parameters that define this structure, applied on interpolation of values at
unsampled points by kriging techniques. However, the estimation of parameters can be greatly affected by the presence of atypical observations in sampled data. The purpose of this study was to use
diagnostic techniques in Gaussian spatial linear models in geostatistics to evaluate the sensitivity of maximum likelihood and restrict maximum likelihood estimators to small perturbations in these
data. For this purpose, studies with simulated and experimental data were conducted. Results with simulated data showed that the diagnostic techniques were efficient to identify the perturbation in
data. The results with real data indicated that atypical values among the sampled data may have a strong influence on thematic maps, thus changing the spatial dependence structure. The application of
diagnostic techniques should be part of any geostatistical analysis, to ensure a better quality of the information from thematic maps.
Index terms: local influence, maximum likelihood, restricted maximum likelihood.
A modelagem da estrutura de dependência espacial pela abordagem da geoestatística é de fundamental importância para a definição de parâmetros que definem essa estrutura e que são utilizados na
interpolação de valores em locais não amostrados, pela técnica de krigagem. Entretanto, a estimação de parâmetros pode ser muito alterada pela presença de observações atípicas nos dados amostrados. O
desenvolvimento deste trabalho teve por objetivo utilizar técnicas de diagnóstico em modelos espaciais lineares gaussianos, empregados em geoestatística, para avaliar a sensibilidade dos estimadores
de máxima verossimilhança e máxima verossimilhança restrita a pequenas perturbações nos dados. Foram realizados estudos de dados simulados e experimentais. O estudo com dados simulados mostrou que as
técnicas de diagnóstico foram eficientes na identificação da perturbação nos dados. Pelos resultados obtidos com o estudo de dados reais, concluiu-se que a presença de valores atípicos entre os dados
amostrados pode exercer forte influência nos mapas temáticos, alterando, assim, a estrutura de dependência espacial. A aplicação de técnicas de diagnóstico deve fazer parte de toda análise
geoestatística, a fim de garantir que as informações contidas nos mapas temáticos tenham maior qualidade.
Termos de indexação: influência local, máxima verossimilhança, máxima verossimilhança restrita.
In the last few decades, concepts of monitoring and management of the process of agricultural production have been widely discussed and applied, generating great amounts of information on
yield-related factors.
Some of these concepts take the spatial variability of the geo-referenced variable into consideration, mainly those related to the soil, such as soil physical and chemical properties. According to
Cressie (1993), not taking the spatial variability into consideration can prevent the perception of real differences, which would make a differentiated treatment according to the local requirements
The geostatistics, based on the theory of regionalized variable, is a method that considers the spatial distribution of measures, to determine the ray of spatial autocorrelation between its elements
and, accordingly, the maximum distance up to which the samples are considered spatially dependent.
For modeling data with spatial structure, according to Mardia & Marshall (1984), a Gaussian random process {Z(s[i]), s[i]∈S} is considered, with S ⊂ ℜ^d ; where ℜ^d is the Euclidean space, d-
dimensional (d > 1). It was assumed that the data set Z(s[1]), ..., Z(s[n]) of this process is registered in known space locations, s[i] (i = 1,..., n), and generated by the following model:
where the terms deterministics µ(s[i]), and random ε(s[i]), can depend on the spatial location where Z(s[i]) was obtained.
It was assumed that the mean of the random error ε (.) is zero, E[ε (s[i])] = 0, and that the variation between points in the space is determined by a covariance function C(s[i], s[u]) = Cov[ε(s[i]),
ε(s[u])] and that for some known functions of s, x[1](s),..., x[p](s), the mean of the stochastic process is:
where β[1],..., β[p] are unknown parameters and must be estimated.
Or equivalent, but expressed in matricial notation:
Then, E(ε) = 0 and the covariance matrix of ε is Σ = [(σ[iu] )], where σ[iu] = C(s[i], s[u]). It was assumed that Σ is non-singular, that X is of full column rank and that Z follows a multivariate
normal distribution with mean Xβ and covariance matrix Σ, that is, Z ~ N[n ](Xβ, Σ).
A particular parametric form was considered for the covariance matrix:
where, φ[1]: nugget effect, φ[2]: sill value; R is a symmetric matrix that depends on φ[3], R = R(φ[3]) = [(r[iu])], in the order n x n with its elements of the diagonal r[ii] = 1, i = 1, ..., n,
where φ[3] is function of the range (a) of the model and I[n] is the identity matrix of the order n x n.
The parametric form of the covariance matrix, given in equation (4), applies for several isotropic processes, where the covariance C(s[i], s[u]) is defined as C(h[iu]) = φ[2]r[iu], where h[iu] = ||s
[i] s[u]|| is the Euclidean distance between the points s[i] and s[u]. The variance of the stochastic process Z is C(0) = φ[1] + φ[2], and the semivariance can be defined as γ(h) = C(0) C(h).
In many situations a data set with aberrant or discrepant observations can be considered influential, that is, they induce some type of decision in the construction of geostatistical models.
The local influence method proposed by Cook (1986) evaluates the simultaneous effect of observations on the maximum likelihood estimators without the need of its elimination from the data set.
Christensen et al. (1993) studied diagnostic methods based on the elimination of cases in linear spatial models. The local influence technique has become known as a procedure to carry out sensitivity
analyses of statistical models and has been widely used in linear models and nonlinear regression.
For an observed data set, let l(q) be the log-likelihood function of the proposed model, given in equation (3), where θ = (β^T, φ^T)^T, β = (β[1],..., β[p])^T and φ = (φ[1],..., φ[θ])^T, and let w be
a perturbation vector belonging to a space of perturbations Ω. Let l(θ/ω) be the log-likelihood function corresponding to the perturbated model for ω e Ω. It was assumed that there is ω[0] e Ω such
that l(θ) = l(θ/ω[0]), for all θ and that l(θ/ω) is twice differentiable in (θ^T, ω^T)^T.
This study is justified by the importance of the modeling of spatial variability, since this process supplies parameters of spatial dependence structure that are used for the spatial interpolation of
Based on the interpolation of kriging, thematic maps are generated that could be used for a site-specific application of special inputs or site-specific soil management. The map quality depends on
the quality of the inferences of the adjusted models. Therefore, to obtain trustworthy predictions that represent the real local variability by the interpolation produces, the modeling process must
be very carefully carried out, mainly in the case of discrepant or influential observations.
The objective of this study was to use diagnostic techniques in Gaussian linear spatial models to evaluate the potential influence of atypical data on the parameter estimates that define the spatial
dependence and to indicate the most robust models. For this purpose studies on local influence were conducted using the methods maximum likelihood and restricted maximum likelihood, to study the
sensitivity of the models in the presence of influential observations.
Influence of location
The following perturbation scheme was considered: Z[ω] = Z + ω, with ω = (ω[1], ..., ω[n])^Tvector of perturbation of the response and ω[0 ][=] (0,...,0)^T, the point of no perturbation. The
objective of this scheme of perturbation was to detect outliers in the data that affect the maximum likelihood estimator θ. Then, the perturbed log-likelihood function l(θ/ω), for the normal model is
given by
The influence of the perturbation ω on the maximum likelihood estimator of θ can be evaluated by the likelihood displacement, defined by:
where, θ in the postulated model; and θ in the perturbed model.
Cook (1986) proposed to study the local behavior of LD(ω) around ω[0], using the normal curvature C[l] of LD(ω) in ω[0] in the direction of a unit vector l and showed that
with ||l|| = 1, where, L is the observed information matrix, evaluated in θ = p + 3)x n matrix given by Δ = (Δ[β]^T , Δ[φ]^T)^T , evaluated in θ = = ω[0][, ]where, in this case:
The information matrix L is defined as
Let L[max] be the eigenvector corresponding to the largest eigenvalue of B = Δ^TL^-1Δ. The graph of the elements of |L[max]| versus i (data order) can reveal which type of perturbation has the
greatest influence on LD(ω), in the neighborhood of ω[0] (Cook, 1986).
Simulation study
Simulation was carried out by Monte Carlo experiments, where simulated data sets were arranged in a regular grid (10 m distance between points), totalizing 100 points, with known structures of
spatial dependence, by means of Gaussian stochastic processes. The simulation of stationary spatial processes of second order was carried out by the Cholesky decomposition method, a matrix operation
which, applied to the vector of random numbers generated produces another vector with random numbers with the characteristic of a given correlation matrix between them (Johnson & Wichern, 1982).
The covariance structures of the models used in the simulations were exponential, Gaussian and Matérn, with κ = 0.7 and 3.0. In all cases, a constant mean of µ = β = 9.45 was considered. Four
parameter vectors were used for each model φ = (φ[1], φ[2], φ[3])^T : 1^st case: φ = (0, 10, 10)^T; 2^nd case: φ = (0, 10, 15)^T; 3^rd case: φ = (0, 10, 20)^T; 4^th case: φ = (0, 10, 60)^T.
The perturbation scheme used had been proposed by Ortega et al. (2002), as presented in the equation (8) below
where, z[max]* is the new value maximum of the vector and z[max] is the maximum value of vector z; ω can be expressed as : ω = (0, ..., ^T.
The structure of spatial dependence was modeled for the simulated data sets, but adding the perturbation vector ω. Diagnostic techniques were applied to evaluate the sensitivity of the models to the
perturbation scheme.
The methods of maximum likelihood and restricted maximum likelihood were used for the parameter estimation and in the diagnostic analyses (Mardia & Marshall, 1984 and Christensen et al. 1993).
Because the results were very similar, only the graphs based on maximum likelihood are presented.
Experimental study
The data of the soil chemical properties were collected in an area of commercial grain production of 71 ha, in the 2006/2007 growing season, in the county of Cascavel, Western region of Paraná, (lat
24.95 º S, long 53.57 º W, average altitude 650 m asl. The soil was classified as dystroferric Red Latosol and the climate of the region is Temperate mesothermal and superhumid, climate type Cfa
(Köppen), with an average annual temperature of 21 ºC.
A centered systematic sampling with pairs of adjacent points was carried out (lattice plus close pairs), with a maximum distance of 141 m between points. At some places the sampling was carried out
at distances of 75 and 50 m between points. All samples were geo-referenced with a GPS (Global Positioning System) signal receiver.
In the vicinity of a few points four soil sub-samples were randomly collected, from the layer 0.0 0.2 m. The sub-samples of approximately 500 g were mixed and stored in plastic bags, to compose a
representative sample of the plot.
Initially, an exploratory statistical analysis of the data was carried out to evaluate the general behavior and to identify to the presence of discrepant points and their possible causes. Among the
analyzed chemical properties, discrepant points were observed for soil P. This trait was analyzed in this study.
Thereafter, a spatial data analysis was performed using geostatistical techniques, identifying the structure of spatial dependence by means of the adjustment of some theoretical models, with
parameters estimated by maximum likelihood (ML) and restricted maximum likelihood (RML). In this stage, the criteria of model validation and diagnostic techniques were applied for the posterior
construction of maps of the study variable. All analyses were carried out using software R (Ihaka & Gentleman, 1996) and the modules: geoR (Ribeiro Júnior & Diggle, 2001) and Splancs (Rowlingson &
Diggle, 1993).
Local influence on simulated data
Estimates of maximum likelihood (ML) and restricted maximum likelihood (RML) for [1], j[2]and j[3 , ]using the exponential, Gaussian and Matérn covariance functions, are presented in table 1.
The results of the exponential model 0-10-10 (Table 1) show that the methods ML and RML overestimated the parameters φ[1] and φ[3] and underestimated parameter φ[2]. A similar behavior was identified
in the parameter estimates of the exponential model 0-10-60, except for parameter φ[3] which had been underestimated when it was estimated by MV. The variables simulated by the Gaussian 0-10-10 and
Gaussian 0-10-15 model overestimated the parameters φ[1] and φ[3] and underestimated parameter φ[2 ]by the methods of ML and RML. By the Matérn model 0-10-15 ê = 0.7, the estimated φ[1] values were
equal to those supplied in the simulation and the φ[3 ]values were close to the simulated. However, the values of parameter φ[2 ]were overestimated. By the Matérn model 0-10-10, k = 3.0, it was
observed that φ[2] was clearly overestimated. Hence, the perturbed values in the simulated variables with exponential, Gaussian and Matérn (k = 0.7 and 3.0) covariance functions, had a rather strong
influence on parameter estimation, by ML as well as by RML.
Figures 1 to 8 present the graphs of diagnostic techniques to identify perturbed observations. The results of the local influence analysis showed that the index plots of |L[max]| highlighted the
perturbed observations for all variables, in the parameter estimation by ML as much as RML (not shown here).
Hence, in this simulation study diagnostic measures were effective to detect all perturbed observations.
Spatial analysis of influence of discrepant points on phosphorus content
After sampling, soil samples were sent to the laboratory for chemical analyses. In the first analysis, the P content presented three discrepant values (60.0; 38.6 and 60.0 mg dm^-3) in the plots 1,
26 and 45, respectively (Figure 10a). The soil chemical analysis was repeated in these plots and no changes in the values were observed. The data of 1, 26 and 45 are therefore not measurement or
laboratory errors; they represent real values of the local soil conditions.
Graphical diagnostic techniques were applied to evaluate whether the discrepant points 1, 26 and 45 or others exert some type of influence on likelihood displacement, on the covariance function and
the linear predictor. The index plots of |L[max]| were used to evaluate the influence.
Diagnostic graphs are presented in figure 9 for the exponential, Gaussian and Matérn (κ = 0.7 and 3.0) covariance functions, by ML. The index plots of |L[max]| indicated the observations 1, 26 and 45
as potentially influential.
Influence on descriptive analyses
A descriptive summary of the phosphate content was presented (Table 2) with all collected data and without the discrepant observations. It was verified that the mean P content (15.80 mg dm^-3) is
well above the recommended upper limit (EMBRAPA, 1979). Furthermore, the data were highly heterogeneous, since the variation coefficient was very high (CV = 72.76 %), due to the discrepant values of
the observations 1, 26 and 45, identified for the Box-plot (Figure 10b).
Since the statistical techniques applied in this paper assume that the data have normal distribution, the Box-Cox was transformed with lambda = -0.7. Also, the descriptive analyses are presented for
the data set without the observations 1, 26 and 45 (P-1-26-45), verifying the influence in the descriptive analysis. Differences were observed between the means of the variable with all data or when
removing influential observations. The same behavior was observed in the standard deviations. The analysis of the coefficient of variation (CV) showed that without the observations 1, 26 and 45 the
CV value was much lower than with all data. However, as the CV is > 30 %, the data were still considered heterogeneous (Gomes, 2000).
Influence on the parameter estimates
The results of the analyses of spatial variability are presented for the original data and for the data set without the observations 1, 26 and 45 (Table 3). The results of the estimation of the
parameters β, φ[1], φ[2] and φ[3], were presented for the exponential, Gaussian and Matérn covariance functions, using ML and RML. The values in brackets stand for the standard deviations of the
estimated parameters. Overall, the values of the estimators of β, φ[1], φ[2] without the influential observations were lower than when estimated with the original data. The estimates ML of φ[3],
without the influential observations were greater than those obtained with the original data. This was not the case for parameter φ[3], when estimated by RML.
The cross-validation criteria (Faraco et al., 2008) applied to the models in the study, both with all observations and without the observations 1, 26 and 45 indicated the Gaussian model using RML as
best fitting.
Influence on the construction of thematic maps
Figure 11 presents the thematic maps for P content with original data and without the observations 1, 26 and 45 based on the interpolation by ordinary kriging. The maps had been constructed using the
models indicated for the cross-validation criteria. The variation in the color scale between the maps was considerable. The map for the original data set (Figure 11a) shows that the area comprises
regions with a P content of > 18 mg dm^-3 (Embrapa, 1997). In the map, constructed without the influential observations considered (Figure 11b) no region has values > 18 mg dm^-3. This indicates that
observations 1, 26 and 45 also exert a strong influence on the construction of the thematic maps.
Thus, if the construction of the thematic maps does not take the diagnostic analyses into consideration, which detects outliers, the distribution map of the P content for producers would overestimate
P concentrations in the study area. Consequently, the principles of the precision agriculture would be disregarded, since the soil correction would not be locally adjusted.
The results showed that the removal of the influential data led to an increase of 10.14 % of the area of the first class; an increase of 17.16 % of the second and a decrease of 7.03 % of the area of
the third class in the map (Table 4). However, the fourth and fifth class were not identified in the map when the influential data had been removed.
The study with simulated data showed that the proposed diagnostic techniques were able to identify the perturbed data. The restricted maximum likelihood estimator produced unbiased estimates of the
parameters of spatial dependence. For the results obtained with real data, the study concluded that the presence of atypical cases in the data had a strong influence on the thematic maps, due to
change in the structure of the spatial dependence. The use of diagnostic techniques should be part of all geostatistical analyses, to ensure the high quality of the information contained in the
thematic maps. The elimination of atypical cases can produce maps that are inappropriate.
The authors gratefully acknowledge the financial support provided of the Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES), National Council of Scientific and
Technological Development (CNPq), National Supply Company (CONAB) and Fundação Araucária, Brazil and Project Dipuv 11/2006, Universidad de Valparaíso, Chile.
Recebido para publicação em fevereiro de 2008 e aprovado em agosto de 2009.
• CHRISTENSEN, R.; JOHNSON, W. & PEARSON, L. Covariance function diagnostics for spatial linear models. Inter. Assoc. Mathem. Geol., 25:145-160, 1993.
• COOK, R.D. Assessment of local influence (with discussion). J. Royal Statis. Soc., Series B, 48:133-169, 1986.
• CRESSIE, N.A.C. Statistics for spatial data. New York, John Wiley & Sons, 1993. 900p.
• EMPRESA BRASILEIRA DE PESQUISA AGROPECUÁRIA - EMBRAPA. Serviço Nacional de Levantamento e Conservação de Solos. Manual de métodos de análise de solo. Rio de Janeiro, Ministério da Agricultura,
1979. 247p.
• EMPRESA BRASILEIRA DE PESQUISA AGROPECUÁRIA - EMBRAPA. Serviço Nacional de Levantamento e Conservação de Solos. Manual de métodos de análise do solo. 2.ed. Rio de Janeiro, Centro Nacional de
Pesquisas de Solos, 1997. 212p.
• FARACO M.A.; URIBE-OPAZO, M.A.; SILVA, E.A.; JOHANN J.A. & BORSSOI, J.A. Seleção de modelos de variabilidade espacial para elaboração de mapas temáticos de atributos físicos do solo e
produtividade da soja. R. Bras. Ci. Solo, 32:463-476, 2008.
• GOMES, P. Curso de estatística experimental. 14.ed. Piracicaba, Degaspari, 2000. 477p.
• IHAKA, R. & GENTLEMAN, R. A language for data analysis and graphics. J. Comput. Graphical Statistics, 5:229-314, 1996.
• JOHNSON, R.A. & WICHERN, D.W. Applied multivariate statistical analysis. Madison, Prentice Hall International, 1982. 607p.
• MARDIA, K. & MARSHALL, R. Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika, 71:135-146, 1984.
• ORTEGA, E.; BOLFARINE, H. & PAULA, G. Influence diagnostics in generalized log-gamma regression models. Comput. Statistics Data Anal. J., 42:165-186, 2002.
• RIBEIRO JUNIOR, P.J. & DIGGLE, P.J. geoR: A package from geoestatistical analysis. R. News, 1:15-18, 2001.
• ROWLINGSON, B. & DIGGLE, P.J. Splancs: Spatial point pattern analysis code in S-Plus. Comp. Geosci., 19:627-655, 1993.
) Parte da Dissertação de Mestrado do primeiro autor.
Publication Dates
• Publication in this collection
09 Feb 2010
• Date of issue
Dec 2009
• Accepted
Aug 2009
• Received
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memochange-Tutorial: Break in Persistence
Literature Review
The degree of memory is an important determinant of the characteristics of a time series. For an \(I(0)\), or short-memory, process (e.g., AR(1) or ARMA(1,1)), the impact of shocks is short-lived and
dies out quickly. On the other hand, for an \(I(1)\), or difference-stationary, process such as the random walk, shocks persist infinitely. Thus, any change in a variable will have an impact on all
future realizations. For an \(I(d)\), or long-memory, process with \(0<d<1\), shocks neither die out quickly nor persist infinitely, but have a hyperbolically decaying impact. In this case, the
current value of a variable depends on past shocks, but the less so the further these shocks are past.
There are plenty of procedures to determine the memory of a series (see Robinson (1995), Shimotsu (2010), among others). However, there is also the possibility that series exhibit a structural change
in memory, often referred to as a change in persistence. Starting with Kim (2000) various procedures have been proposed to detect these changes and consistently estimate the change point. Busetti and
Taylor (2004) and Leybourne and Taylor (2004) suggest approaches for testing the null of constant \(I(0)\) behaviour of the series against the alternative that a change from either \(I(0)\) to \(I(1)
\) or \(I(1)\) to \(I(0)\) occurred. However, both approaches show serious distortions if neither the null nor the alternative is true, e.g. the series is constant \(I(1)\). In this case the
procedures by Leybourne et al. (2003) and Leybourne, Taylor, and Kim (2007) can be applied as they have the same alternative, but assume constant \(I(1)\) behaviour under the null. Again, the
procedures exhibit distortions when neither the null nor the alternative is true. To remedy this issue, Harvey, Leybourne, and Taylor (2006) suggest an approach that entails the same critical values
for constant \(I(0)\) and constant \(I(1)\) behavior. Consequently, it accommodates both, constant \(I(0)\) and constant \(I(1)\) behavior under the null.
While this earlier work focussed on the \(I(0)/I(1)\) framework, more recent approaches are able to detect changes from \(I(d_1)\) to \(I(d_2)\) where \(d_1\) and \(d_2\) are allowed to be
non-integers. Sibbertsen and Kruse (2009) extend the approach of Leybourne, Taylor, and Kim (2007) such that the testing procedure consistently detects changes from \(0 \leq d_1<1/2\) to \(1/2<d_2<3/
2\) and vice versa. Under the null the test assumes constant \(I(d)\) behavior with \(0 \leq d <3/2\). The approach suggested by Martins and Rodrigues (2014) is even able to identify changes from \
(-1/2<d_1<2\) to \(-1/2<d_2<2\) with \(d_1 \neq d_2\). Here, under the null the test assumes constant \(I(d)\) behavior with \(-1/2<d<2\).
Examples for series that potentially exhibit breaks in persistence are macroeconomic and financial time series such as inflation rates, trading volume, interest rates, volatilities and so on. For
these series it is therefore strongly recommended to investigate the possibility of a break in persistence before modeling and forecasting the series.
The memochange package contains all procedure mentioned above to identify whether a time series exhibits a break in persistence mentioned above. Additionally, several estimators are implemented which
consistently estimate the point at which the series exhibits a break in persistence and the order of integration in the two regimes. We will now show how the usage of the implemented procedures while
investigating the price of crude oil.
First, we download the monthly price series from the FRED data base.
To get a first visual impression, we plot the series.
oil_xts=xts::xts(oil[,-1],order.by = oil$DATE)
zoo::plot.zoo(oil_xts, xlab="", ylab="Price", main="Crude Oil Price: West Texas Intermediate")
From the plot we observe that the series seems to be more variable in its second part from year 2000 onwards. This is first evidence that a change in persistence has occurred. We can test this
hypothesis using the functions cusum_test (Leybourne, Taylor, and Kim (2007), Sibbertsen and Kruse (2009)) LBI_test (Busetti and Taylor (2004)), LKSN_test (Leybourne et al. (2003)), MR_test (Martins
and Rodrigues (2014)) , and ratio_test (Busetti and Taylor (2004), Leybourne and Taylor (2004), Harvey, Leybourne, and Taylor (2006)). In this vignette we use the ratio and MR test since these are
the empirically most often applied ones. The functionality of the other tests is similar. They all require a univariate numeric vector x as an input variable and yield a matrix of test statistic and
critical values as an output variable.
As a starting point the default version of the ratio test is applied.
#> 90% 95% 99% Teststatistic
#> Against change from I(0) to I(1) 3.5148 4.6096 7.5536 225.943543
#> Against change from I(1) to I(0) 3.5588 4.6144 7.5304 1.170217
#> Against change in unknown direction 4.6144 5.7948 9.0840 225.943543
This yields a matrix that gives test statistic and critical values for the null of constant \(I(0)\) against a change from \(I(0)\) to \(I(1)\) or vice versa. Furthermore, the statistics for a change
in an unknown direction are included as well. This accounts for the fact that we perform two tests facing a multiple testing problem. The results suggest that a change from \(I(0)\) to \(I(1)\) has
occurred somewhere in the series since the test statistic exceeds the critical value at the one percent level. In addition, this value is also significant when accounting for the multiple testing
problem. Consequently, the default version of the ratio test suggests a break in persistence.
We can modify this default version by choosing the arguments trend, tau, statistic, type, m, z, simu, and M (see the help page of the ratio test for details). The plot does not indicate a linear
trend so that it seems unreasonable to change the trend argument. Also, the plot suggests that the break is rather in the middle of the series than at the beginning or the end so that changing tau
seems unnecessary as well. The type of test statistic calculated can be easily changed using the statistic argument. However, simulation results indicate mean, max, and exp statistics to deliver
qualitatively similar results.
Something that is of more importance is the type of test performed. The default version considers the approach by Busetti and Taylor (2004). In case of a constant \(I(1)\) process this test often
spuriously identifies a break in persistence. Harvey, Leybourne and Taylor (2006) account for this issue by adjusting the test statistic such that its critical values are the same under constant \(I
(0)\) and constant \(I(1)\). We can calculate their test statistic by setting type="HLT". For this purpose, we need to state the number of polynomials z used in their test statistic. The default
value is 9 as suggested by Harvey, Leybourne and Taylor (2006). Choosing another value is only sensible for very large data sets (number of obs. > 10000) where the test statistic cannot be calculated
due to computational singularity. In this case decreasing z can allow the test statistic to be calculated. This invalidates the critical values so that we would have to simulate them by setting simu=
1. However, as our data set is rather small we can stick with the default of z=9.
ratio_test(x, type="HLT")
#> 90% 95% 99% Teststatistic 90%
#> Against change from I(0) to I(1) 3.5148 4.6096 7.5536 58.9078204
#> Against change from I(1) to I(0) 3.5588 4.6144 7.5304 0.3085495
#> Against change in unknown direction 4.6144 5.7948 9.0840 44.2171379
#> Teststatistic 95% Teststatistic 99%
#> Against change from I(0) to I(1) 43.4772689 25.3369507
#> Against change from I(1) to I(0) 0.2290113 0.1290305
#> Against change in unknown direction 34.1367566 20.0058559
Again the test results suggests that there is a break from \(I(0)\) to \(I(1)\). Consequently, it is not a constant \(I(1)\) process that led to a spurious rejection of the test by Busetti and Taylor
Another test for a change in persistence is that by Martins and Rodrigues (2014). This is more general as it is not restricted to the \(I(0)/I(1)\) framework, but can identify changes from \(I(d_1)\)
to \(I(d_2)\) with \(d_1 \neq d_2\) and \(-1/2<d_1,d_2<2\). The default version is applied by
#> 90% 95% 99% Teststatistic
#> Against increase in memory 4.270666 5.395201 8.233674 16.21494
#> Against decrease in memory 4.060476 5.087265 7.719128 2.14912
#> Against change in unknown direction 5.065695 6.217554 9.136441 16.21494
Again, the function returns a matrix consisting of test statistic and critical values. Here, the alternative of the test is an increase respectively a decrease in memory. In line with the results of
the ratio test, the approach by Martins and Rodrigues (2014) suggests that the series exhibits an increase in memory, i.e. that the memory of the series increases from \(d_1\) to \(d_2\) with \(d_1
<d_2\) at some point in time. Again, this also holds if we consider the critical values that account for the multiple testing problem.
Similar to the ratio test and all other tests against a change in persistence in the memochange package, the MR test also has the same arguments trend, tau, simu, and M. Furthermore, we can choose
again the type of test statistic. This time we can decide whether to use the squared t-statistic or the standard t-statistic.
MR_test(x, statistic="standard")
#> 90% 95% 99% Teststatistic
#> Against increase in memory -1.637306 -1.920434 -2.504862 -2.880545
#> Against decrease in memory -1.651586 -1.951420 -2.514165 -1.277410
#> Against change in unknown direction -1.933137 -2.203370 -2.722017 -2.880545
As for the ratio test, changing the type of statistic has a rather small effect on the empirical performance of the test.
If we believe that the underlying process exhibits additional short run components, we can account for these by setting serial=TRUE
MR_test(x, serial=TRUE)
#> Registered S3 method overwritten by 'quantmod':
#> method from
#> as.zoo.data.frame zoo
#> Registered S3 methods overwritten by 'forecast':
#> method from
#> fitted.fracdiff fracdiff
#> residuals.fracdiff fracdiff
#> 90% 95% 99% Teststatistic
#> Against increase in memory 4.270666 5.395201 8.233674 10.727202
#> Against decrease in memory 4.060476 5.087265 7.719128 6.758906
#> Against change in unknown direction 5.065695 6.217554 9.136441 10.727202
While the test statistic changes, the conclusion remains the same.
All tests indicate that the oil price series exhibits an increase in memory over time. To correctly model and forecast the series, the exact location of the break is important. This can be estimated
by the BP_estim function. It is important for the function that the direction of the change is correctly specified. In our case, an increase in memory has occurred so that we set direction="01"
BP_estim(x, direction="01")
#> $Breakpoint
#> [1] 151
#> $d_1
#> [1] 0.8127501
#> $sd_1
#> [1] 0.08574929
#> $d_2
#> [1] 1.088039
#> $sd_2
#> [1] 0.07142857
This yields a list stating the location of the break (observation 151), semiparametric estimates of the order of integration in the two regimes (0.86 and 1.03) as well as the standard deviations of
these estimates (0.13 and 0.15).
Consequently, the function indicates that there is a break in persistence in July, 1998. This means that from the beginning of the sample until June 1998 the series is integrated with an order of
0.85 and from July 1998 on the order of integration increased to 1.03.
As before, the function allows for various types of break point estimators. Instead of the default estimator of Busetti and Taylor (2004), one can also rely on the estimator of Leybourne, Kim, and
Taylor (2007) by setting type="LKT". This estimator relies on estimates of the long-run variance. Therefore, it is also needed that m is chosen, which determines how many covariances are used when
estimating the long-run variance. Leybourne, Kim, and Taylor (2007) suggest m=0.
BP_estim(x, direction="01", type="LKT", m=0)
#> $Breakpoint
#> [1] 148
#> $d_1
#> [1] 0.7660609
#> $sd_1
#> [1] 0.08703883
#> $d_2
#> [1] 1.067404
#> $sd_2
#> [1] 0.07142857
This yields a similar result with the break point lying in the year 1998 and d increasing from approximately 0.8 to approximately 1.
All other arguments of the function (trend, tau, serial) were already discussed above except for d_estim and d_bw. These two arguments determine which estimator and bandwidth are used to estimate the
order of integration in the two regimes. Concerning the estimator, the GPH (Geweke and Porter-Hudak (1983)) and the exact local Whittle estimator (Shimotsu and Phillips (2005)) can be selected.
Although the exact local Whittle estimator has a lower variance, the GPH estimator is still often considered in empirical applications due to its simplicity. In our example the results of the two
estimators are almost identical.
BP_estim(x, direction="01", d_estim="GPH")
#> $Breakpoint
#> [1] 151
#> $d_1
#> [1] 0.855238
#> $sd_1
#> [1] 0.129834
#> $d_2
#> [1] 1.034389
#> $sd_2
#> [1] 0.1468516
The d_bw argument determines how many frequencies are used for estimation. Larger values imply a lower variance of the estimates, but also bias the estimator if the underlying process possesses short
run dynamics. Usually a value between 0.5 and 0.8 is considered.
BP_estim(x, direction="01", d_bw=0.75)
#> $Breakpoint
#> [1] 151
#> $d_1
#> [1] 0.9146951
#> $sd_1
#> [1] 0.07624929
#> $d_2
#> [1] 1.173524
#> $sd_2
#> [1] 0.0625
BP_estim(x, direction="01", d_bw=0.65)
#> $Breakpoint
#> [1] 151
#> $d_1
#> [1] 0.5803242
#> $sd_1
#> [1] 0.09805807
#> $d_2
#> [1] 0.9353325
#> $sd_2
#> [1] 0.08219949
In our setup, it can be seen that increasing d_bw to 0.75 does not severely change the estimated order of integration in the two regimes. Decreasing d_bw, however, leads to smaller estimates of \(d\) | {"url":"https://cran.case.edu/web/packages/memochange/vignettes/break_in_persistence.html","timestamp":"2024-11-04T01:49:04Z","content_type":"application/xhtml+xml","content_length":"52212","record_id":"<urn:uuid:8835e60a-b423-4ea1-81f2-99c0e3213cd1>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00627.warc.gz"} |
Bayes' Theorem
Bayes' Theorem: Simplifying Statistical Analysis
In statistics and probability, Bayes' Theorem stands as a pivotal analytical tool. This mathematical formula offers a method to update the probability for a hypothesis as more evidence or information
becomes available. It's named after Thomas Bayes (1701–1761), an English statistician, philosopher, and Presbyterian minister who formulated the principle in his work. Bayes' Theorem has profound
implications across various fields, including medicine, finance, and machine learning, by providing a systematic way to calculate conditional probabilities.
Understanding Bayes' Theorem
At its core, Bayes' Theorem is a way to calculate the probability of an event based on prior knowledge of conditions that might be related to the event. It uses the concept of posterior probability,
prior probability, likelihood, and marginal likelihood to compute its results.
Posterior Probability: The probability of the hypothesis after getting the evidence.
Prior Probability: The initial probability of the hypothesis before getting the evidence.
Likelihood: The probability of observing the given data under a specific hypothesis.
Marginal Likelihood: The total probability of observing the evidence under all possible hypotheses.
The formula for Bayes' Theorem is expressed as:
P(H|E) = (P(E|H) * P(H)) / P(E)
In this formula:
P(H|E) is the probability of hypothesis H given the evidence E.
P(E|H) is the probability of evidence E given that hypothesis H is true.
P(H) is the prior probability of hypothesis H.
P(E) is the probability of evidence E.
Application of Bayes' Theorem
Bayes' Theorem is applied in numerous fields to make more informed decisions based on the accumulation of evidence:
Medicine: Used to determine the probability of a disease given the presence of various symptoms or the results of a test.
Finance: Helps in assessing the risk of investments based on prior performance and market trends.
Machine Learning: Employs Bayesian inference to update the model's predictions as more data becomes available.
The significance of Bayes' Theorem
The power of Bayes' Theorem lies in its ability to combine prior knowledge with new evidence to make predictions or inferences. This iterative process of updating beliefs has several advantages:
Flexibility: It can be applied in scenarios with incomplete information, adjusting probabilities as new data emerges.
Foundation for Statistical Inference: Many statistical methods and algorithms are based on or related to Bayes' Theorem, making it foundational in the field.
Decision Making: Provides a quantitative basis for making decisions under uncertainty.
Challenges and considerations
While Bayes' Theorem is widely used, it's not without its challenges. The accuracy of the results heavily depends on the quality and quantity of prior data. Misinterpretation of the theorem's output
due to biases in the data or incorrect assumptions can lead to inaccurate conclusions.
Practical example
Consider a medical test for a specific disease. If the disease affects 1% of the population, the test accurately identifies the disease in 99% of cases (true positive rate) and accurately identifies
non-disease in 99% of cases (true negative rate). Bayes' Theorem can be used to calculate the probability that a person actually has the disease if they test positive.
Bayes' Theorem is a critical tool in the statistical analysis toolbox, offering a structured method for updating probabilities based on new evidence. Its application across various domains underlines
its importance and utility in making informed decisions under uncertainty. Understanding and applying Bayes' Theorem can significantly enhance the decision-making process, allowing for more accurate
predictions and inferences based on evolving data. | {"url":"https://coinmetro.com/glossary/bayes-theorem","timestamp":"2024-11-11T01:39:01Z","content_type":"text/html","content_length":"186477","record_id":"<urn:uuid:88349794-be67-4bce-9367-4f222865719e>","cc-path":"CC-MAIN-2024-46/segments/1730477028202.29/warc/CC-MAIN-20241110233206-20241111023206-00838.warc.gz"} |
The Alternating Projection Algorithm (AP algorithm) - CompileIoT
The Alternating Projection Algorithm (AP algorithm) is a mathematical method used to solve optimization problems involving sets and projections. It is a powerful tool in the field of signal
processing, image reconstruction, and convex optimization.
Introduction to the AP Algorithm
The AP algorithm was first introduced by John von Neumann in the 1950s. It is a simple yet effective algorithm that iteratively projects a point onto a set and then onto another set, alternating
between the two. The goal is to find a point that belongs to the intersection of the two sets, if such a point exists.
The algorithm is based on the concept of projection, which is a fundamental operation in convex geometry. A projection of a point onto a set is the closest point in the set to the given point. The AP
algorithm takes advantage of this concept to iteratively approach the optimal solution.
Working Principle of the AP Algorithm
The AP algorithm starts with an initial point and two sets, A and B. It then iteratively performs the following steps:
1. Project the current point onto set A to obtain a new point.
2. Project the new point onto set B to obtain another new point.
3. Repeat steps 1 and 2 until convergence.
The algorithm converges when the difference between two consecutive points becomes sufficiently small. The final point obtained is an approximation of the optimal solution, which belongs to the
intersection of sets A and B.
Applications of the AP Algorithm
The AP algorithm has a wide range of applications in various fields:
Signal Processing
In signal processing, the AP algorithm is used for signal reconstruction from incomplete or noisy measurements. It can be used to recover a signal that satisfies certain constraints, such as sparsity
or low-rankness. The algorithm iteratively projects the current estimate onto the set of feasible signals, improving the reconstruction quality at each iteration.
Image Reconstruction
The AP algorithm is also applied in image reconstruction, particularly in computed tomography (CT) and magnetic resonance imaging (MRI). It is used to reconstruct high-resolution images from a
limited number of projections or measurements. By iteratively projecting the current estimate onto the set of feasible images, the algorithm improves the image quality and reduces artifacts.
Convex Optimization
In convex optimization, the AP algorithm is used to solve problems involving multiple convex sets. It can be used to find the intersection of these sets, which corresponds to the optimal solution of
the optimization problem. The algorithm iteratively projects the current point onto each set, alternating between them until convergence.
Advantages and Limitations of the AP Algorithm
The AP algorithm has several advantages:
• It is a simple and intuitive algorithm that is easy to implement.
• It is computationally efficient and converges quickly for many problems.
• It can handle large-scale problems with high-dimensional data.
However, the AP algorithm also has some limitations:
• It may not converge to the optimal solution for all problems.
• It may get stuck in local optima or oscillate between two points.
• It may require a good initial guess to converge to the desired solution.
The Alternating Projection Algorithm (AP algorithm) is a versatile method for solving optimization problems involving sets and projections. It has found applications in signal processing, image
reconstruction, and convex optimization. While it has its advantages and limitations, the AP algorithm remains a valuable tool in various fields, providing efficient and effective solutions to
complex problems.
This site uses Akismet to reduce spam. Learn how your comment data is processed. | {"url":"https://compileiot.online/the-alternating-projection-algorithm-ap-algorithm/","timestamp":"2024-11-08T17:13:21Z","content_type":"text/html","content_length":"117999","record_id":"<urn:uuid:5f211f9d-986b-49aa-986d-9de094b0f04b>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00357.warc.gz"} |
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 7 Percentage Ex 7.2 - CBSE Tuts
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 7 Percentage Ex 7.2
Question 1.
Find the profit or loss percentage, when:
(i) C.P. = ₹400, S.P. = ₹468
(ii) C.P. = ₹ 13600, S.P. = ₹12104
Question 2.
By selling an article for ₹1636·25, a dealer gains ₹96·25. Find his gain per cent.
Question 3.
By selling an article for ₹770, a man incurs a loss of ₹110. Find his loss percentage.
Question 4.
Rashida bought 25 dozen eggs at the rate of ₹9.60 per dozen. 30 eggs were broken in the transaction and she sold the remaining eggs at one rupee each. Find her gain or loss percentage.
Question 5.
The cost of an article was ₹20000 and ₹1400 were spent on its repairs. If it is sold for a profit of 20%, find the selling price of the article.
Question 6.
A shopkeeper buys 200 bicycles at ₹1200 per bicycle. He spends ₹30 per bicycle on transportation. He also spends ₹4000 on advertising. Then he sells all the bicycles at ₹1350 per piece. Find his
profit or loss. Also calculate it as a percentage.
Question 7.
The cost price of an article is 90% of its selling price. Find his profit percentage.
Question 8.
Rao bought notebooks at the rate of 4 for ₹35 and sold them at the rate of 5 for ₹58. Calculate
(i) his gain percentage.
(ii) the number of notebooks he should sell to earn a profit of ₹171.
Question 9.
A vendor buys bananas at 3 for a rupee and sells at 4 for a rupee. Find his profit or loss percentage.
Question 10.
A shopkeeper buys a certain number of pens. If the selling price of 5 pens is equal to the cost price of 7 Pens, find his profit or loss percentage.
Question 11.
Find the selling price, when :
(i) Cost price = ₹2360, Profit = 8%
(ii) Cost price = ₹380, Loss = 7·5%
Question 12.
A dealer bought a number of eggs at ₹18 a dozen and sold them at 50% profit. Find the selling price per egg.
Question 13.
Mr Ghosh purchased wristwatches worth ₹60000. He sold one-third of them at a profit of 30%, one-third at a profit of 20% and remaining at a loss of 5%. Calculate his overall profit or loss
Question 14.
A laptop and a mobile phone were bought for ₹40000 and ₹24000 respectively. The shopkeeper made a profit of 8% on the laptop and a loss of 12% on a mobile phone. Find his gain or loss per cent on the
whole transaction.
Question 15.
Salman bought 40 chairs at ₹175 each fourth of them at a loss of 8%. At what price each must he sell the remaining chairs so as to gain 10% on the whole deal?
Question 16.
A shopkeeper sold two electronic gadgets for ₹44000 each. The shopkeeper made a loss of 12% on one and a profit of 10% on the other. Find his overall gain or loss.
Question 17.
The manufacturing price of a T.V. set is ₹12000. The company sold it to a dealer at 20% profit and the dealer sold it to a customer at 12·5% profit. Find the price which the customer has to pay.
Question 18.
Find the cost price, when :
(i) selling Price = ₹450, loss = 10%
(ii) selling Price = ₹690, profit = 15%
Question 19.
By selling an almirah for ₹3920, a shopkeeper would gain 12%. If it is sold for ₹4375, find his gain or loss, percentage.
Question 20.
By selling a bicycle at ₹1334, a shopkeeper would suffer a loss of 8%. At how much amount should he sell it to make a profit of \(12 \frac{1}{2}\)%?
Question 21.
By selling a tie for ₹252, a shopkeeper gains 5%. At what price should he sell the tie to gain 35 %?
Question 22.
A shopkeeper sells a bag at a 12% profit. If he had sold it for ₹39 more, he would have made 18% profit. Find the cost price of the bag for the shopkeeper.
Question 23.
A shopkeeper sells a sweater at a loss of 5%. If he had sold it for ₹260 more, he would have made a profit of 15%. Calculate the purchase price of the sweater.
Question 24.
Janki sold her leather purse at 8% loss. If she had sold it for ₹ 150 more, she would have made 12% profit. Find the selling price of the purse. | {"url":"https://www.cbsetuts.com/ml-aggarwal-class-8-solutions-for-icse-maths-chapter-7-ex-7-2/","timestamp":"2024-11-09T22:27:22Z","content_type":"text/html","content_length":"86644","record_id":"<urn:uuid:3f5b97b8-d0b6-411c-9d43-2c735f21b5c4>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.10/warc/CC-MAIN-20241109214337-20241110004337-00632.warc.gz"} |
Graphic scheme depicting iterative structure factor retrieval algorithm implemented in DENSS
These pages describe how to use DENSS most effectively to reconstruct your particle from your solution scattering data. For additional instructions for visualizing and assessing the results, visit
the Tips page. There’s also a new Video Tutorial to show you how to download, install, and run DENSS step-by-step.
To understand how to run DENSS and how to use all of its options most appropriately, it helps to understand how DENSS works. DENSS is an algorithm used for calculating ab initio electron density maps
directly from solution scattering data. DENSS implements a novel iterative structure factor retrieval algorithm to cycle between real space density and reciprocal space structure factors, applying
appropriate restraints in each domain to obtain a set of structure factors whose intensities are consistent with experimental data and whose electron density is consistent with expected real space
properties of particles.
DENSS utilizes the NumPy Fast Fourier Transform for moving between real and reciprocal space domains. Each domain is represented by a grid of points (Cartesian), N x N x N. N (the number of samples
in one dimension) is determined by the size of the system and the desired resolution. The real space size of the box is determined by the maximum dimension of the particle, D, and the desired
sampling ratio. Larger sampling ratio results in a larger real space box and therefore a higher sampling in reciprocal space (i.e. distance between data points in q). Smaller voxel size in real space
corresponds to higher spatial resolution and therefore to a larger maximum q value in reciprocal space.
The reciprocal space restraints are pretty straight forward, i.e. the data. The real space restraints are imposed by defining a “support”, i.e. the region of space (which voxels) are allowed to have
density. Outside of this support the density is set to zero, inside the support the density is required to be positive and real valued. The selection of which voxels are part of the support is
regularly updated throughout the reconstruction and is determined by the shrinkwrap algorithm.
If you have any questions about any of these options or more generally how to run DENSS, please send an email using the contact form below. | {"url":"https://tdgrant.com/tutorial/","timestamp":"2024-11-10T21:34:08Z","content_type":"text/html","content_length":"385851","record_id":"<urn:uuid:af1b0732-7efd-4faa-b684-038c9a0c5e98>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00129.warc.gz"} |
CS502 Assignment 3 Solution 2022 - VU Answer
VU Answer Gives Perfect CS502 Assignment 3 Solution Fall 2021 PDF. It's a Complete Step by Step CS502 Assignment 3 Solution 2022 and Easy to Download PDF, CPP, and Word Solution File Below.
CS502 ASSIGNMENT 3 SOLUTION FALL 2021
Provide by VU Answer
Total Marks: 20
Due Date: 10 Feb 2022
Question 1:
A thief enters in a Gold shop carrying knapsack (bag). Knapsack (bag) capacity is 33KG of weight. The shop has only 10 gold bricks; each brick has a specific weight and price. Now, the thief’s
dilemma is to make such a selection of bricks that it maximizes the profit (i.e. total price) without exceeding the knapsack (bag) weight.
You are required to do the following task:
1. Help the thief for the selection of bricks using greedy method for getting maximum profit.
$50 + $200+ $110+ $70+ $120+ $153+ $140+ (160/11*5)
$50 + $200+ $110+ $70+ $120+ $153+ $140+ $72.72
Maximum Profit = $915.72
2. Which approach will be used for this scenario (write only name)?
Greedy Method About Price/Weight Ratio
Question 2:
A well-known Network Solution company that deals with large volumes of data over the network wants to use a data compression technique that reduces the coding redundancy without loss of data quality.
For trial/test execution the company has decided to use Huffman encoding algorithm to encode the given string "allamaiiii” before transmitting over the network.
You are required to do the following task:
1. Calculate the frequency of characters.
2. Generate Huffman Tree
3. Write the code of every character
4. Required total no of bits
Giving String “allamaiiii”
2. Generate Huffman Tree
3. Write the code of every character
4. Required total no of bits
Required Total No of Bits = 19
Make sure you can make some changes to your solution file before submitting copy-paste solution will be marked zero.
If you found any mistake then correct yourself and inform me.
Before submitting an assignment check your assignment requirement file.
If you need some help and question about file and solutions.
CS502 Assignment 3 Solution 2022
CS502 Assignment No 3 Solution Fall 2021
CS502 Assignment 3 Solution Fall 2022
CS502 Assignment Solution 2022
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Hur man plottar statsmodeller linjär regression OLS rent 2021
Seaborn - Elazizliyiz
The default plot kind is a histogram: 2021-4-10·Such non-linear, higher order can be visualized using the lmplot() and regplot().These can fit a polynomial regression model to explore simple kinds
of nonlinear trends in the dataset − Example import pandas as pd import seaborn as sb from matplotlib import pyplot as plt df = sb.load_dataset('anscombe') sb.lmplot(x = "x", y = "y", data = df
2020-11-5 And regplot() by default adds regression line with confidence interval. In this example, we make scatter plot between minimum and maximum temperatures. sns.regplot(x="temp_max", y=
"temp_min", data=df); And we get a nice scatter plot with regression line with confidence interval band. Scatterplot with regression line regplot() Seaborn regplot() Seaborn: Add Regression Line to
Scatter Plot How To Add Regression Line Per Group in a Scatter plot in Seaborn?
How can one set a different color for the points as the line? Seaborn’s built in features for its graphs can be helpful, but they can be limiting if you want to further customize your graph.
Matplotlib and Seaborn may be the most commonly used data visualization packages, but there is a simpler method that produces superior graphs than either of these: Plotly. Using seaborn you can make
plots that are visually appealing and not just that seaborn is known for a range of plots that are not present in matplotlib that could be quite helpful in data analysis. Before going into seaborn it
is important that you know about matplotlib. Add Equation to Seaborn Plot (and separate thousands with commas) Producing a scatter plot with a line of best fit using Seaborn is extremely simple.
Seaborn - Roshan Talimi
Seaborn has multiple functions to make scatter plots between two quantitative variables. For example, we can use lmplot(), regplot(), and scatterplot() functions to make scatter plot with Seaborn. I
use regplot using the following code: sns.regplot(x = "Year", y = "Data_Value", data = NOAA_TMAX_s ); and I obtain the following figure: showing clearly that the trend is negative.
Hur justerar man transparens alfa i havsfödda par? PYTHON 2021
We talk about factor grids and doing conditional linear regression. We talk about logistic, log transformed and 2020-06-22 Seaborn Regplot with linear regression equation in legend Hello All ! I had
to do some workarounds to get the linear equation in the legend as Seaborn does not do a very good job at displaying this by default. 2014-08-06 2016-11-11 The regplot() and lmplot() functions are
closely related, but the former is an axes-level function while the latter is a figure-level function that combines regplot() and FacetGrid. It’s also easy to combine combine regplot() and JointGrid
or PairGrid through the jointplot() and pairplot() functions, although these do not directly accept all of regplot() ’s parameters. 2020-08-01 · Seaborn helps resolve the two major problems faced by
Matplotlib; the problems are ? Default Matplotlib parameters; Working with data frames.
What is the difference between the two plots ? The result I was able to get are slightly different but I have no idea why ! You can declare fig, ax pair via plt.subplots() first, then set proper size
on that figure, and ask sns.regplot to plot on that ax. import numpy as np import seaborn as sns import matplotlib.pyplot as plt # some artificial data data = np.random.multivariate_normal([0,0],
[[1,-0.5],[-0.5,1]], size=100) # plot sns.set_style('ticks') fig, ax = plt.subplots() fig.set_size_inches(18.5, 10.5) sns The regression plots in seaborn are primarily intended to add a visual guide
that helps to emphasize patterns in a dataset during exploratory data analyses. Regression plots as the name suggests creates a regression line between 2 parameters and helps to visualize their
linear relationships. Python seaborn.regplot () Examples The following are 30 code examples for showing how to use seaborn.regplot ().
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Before my f oray, I was mostly relying on Matplotlib 2019-09-17 · Seaborn is not only a visualization library but also a provider of built-in datasets. Here, we will be working with one of such
datasets in seaborn named ‘tips’. The tips dataset contains information about the people who probably had food at the restaurant and whether or not they left a tip. seaborn.rugplot¶ seaborn.rugplot
(x = None, *, height = 0.025, axis = None, ax = None, data = None, y = None, hue = None, palette = None, hue_order = None, hue_norm = None, expand_margins = True, legend = True, a = None, ** kwargs)
¶ Plot marginal distributions by drawing ticks along the x and y axes. regplot() performs a simple linear regression model fit and plot. lmplot() combines regplot() and FacetGrid.
Seaborn has multiple functions to make scatter plots between two quantitative variables. For example, we can use lmplot(), regplot(), and scatterplot() functions to make scatter plot with Seaborn.
2014-12-21 We go over the entirety of seaborn's lmplot. We talk about factor grids and doing conditional linear regression. We talk about logistic, log transformed and 2020-06-22 Seaborn Regplot with
linear regression equation in legend Hello All ! I had to do some workarounds to get the linear equation in the legend as Seaborn does not do a very good job at displaying this by default.
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from publication: Predicting extragalactic distance Seaborn · Visualize Distributions With Seaborn · Install Seaborn. · Distplots · Import Matplotlib · Import Seaborn · Plotting a Displot · Plotting
a Distplot Without the 28 Sep 2017 Well, Seaborn is a high-level Python data visualization library used for making sns.regplot(x='petal_width', y='petal_length', data=iris) 2020年3月25日簡単かつ簡
潔にデータを可視化できるライブラリであるseabornを用いて、線形回帰つき散布図をregplot,lmplotで表示する方法について説明 Statistical Data Visualization With Seaborn The Python visualization library
Seaborn is based on python seaborn sns.regplot(x="sepal_width", Plot data and a. Databricks Runtime innehåller visualiseringsbiblioteket Seaborn. g.map_diag(sns.kdeplot, lw=3) g.map_upper
(sns.regplot) display(g.fig). Benvenuto: Seaborn Dal 2021.
Matplotlib and Seaborn may be the most commonly used data visualization packages, but there is a simpler method that produces superior graphs than either of these: Plotly. 0. 목차 및 내용 1) Hello,
Seaborn - notebook 설명, csv 읽기, lineplot plt.figure(figsize=(16,6)) sns.lineplot(data=fifa_data) 2) Line Charts - title, xlabel This page shows Python examples of seaborn.regplot. def plot(x, y,
fit, label): sns.regplot(np.array(x), np.array(y), fit_reg=fit, label=label, scatter_kws={"s": 5}) 18 Jan 2019 regplot() performs a simple linear regression model fit and plot. lmplot() combines
regplot() and FacetGrid.
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However, I can't seem to get the label to appear, whether the regression line is shown or not. Not sure if I'm doing something wrong or if this is a bug? sns.regplot(x, seaborn.regplot has option
"order", described as "int, optional,. If order is greater than 1, use nuim[y.polyfit to estimate a polynomial regression".
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Du kan använda seaborn regplot med följande syntax import seaborn as sns sns.regplot(x='balance', y='default', data=data, logistic=True) 2008 Dodge Charger Rt Hemi, Sydney To Adelaide, La Vie
Parisienne Translation, Seaborn Regplot, Andis Ls2 Manual, Asos Design Men's, Mini Cooper S, Jag skapar dessa data: importera numpy som np importera pandor som pd importera matplotlib.pyplot som plt
importera seaborn som sns sns.set () data Seaborn regplot r2. Blomma Sylve Bergstrm bodde tidigare p tamms vg 9 i Sderfors. Axel Eriksson, Tolftaliden 6, Tierp deshow. Blomma Skicka Han har ven
bott The regplot() and lmplot() functions are closely related, but the former is an axes-level function while the latter is a figure-level function that combines regplot() and FacetGrid. | {"url":"https://hurmanblirrikgdkfjv.netlify.app/8443/63969","timestamp":"2024-11-02T15:58:35Z","content_type":"text/html","content_length":"18662","record_id":"<urn:uuid:b973ec26-f484-423c-8ce0-0ccdb55e4fff>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00892.warc.gz"} |
Lesson 13
Similar Triangles
Let’s look at similar triangles.
13.1: Equivalent Expressions
Create three different expressions that are each equal to 20. Each expression should include only these three numbers: 4, -2, and 10.
13.2: Making Pasta Angles and Triangles
Your teacher will give you some dried pasta and a set of angles.
1. Create a triangle using three pieces of pasta and angle \(A\). Your triangle must include the angle you were given, but you are otherwise free to make any triangle you like. Tape your pasta
triangle to a sheet of paper so it won’t move.
1. After you have created your triangle, measure each side length with a ruler and record the length on the paper next to the side. Then measure the angles to the nearest 5 degrees using a
protractor and record these measurements on your paper.
2. Find two others in the room who have the same angle \(A\) and compare your triangles. What is the same? What is different? Are the triangles congruent? Similar?
3. How did you decide if they were or were not congruent or similar?
2. Now use more pasta and angles \(A\), \(B\), and \(C\) to create another triangle. Tape this pasta triangle on a separate sheet of paper.
1. After you have created your triangle, measure each side length with a ruler and record the length on the paper next to the side. Then measure the angles to the nearest 5 degrees using a
protractor and record these measurements on your paper.
2. Find two others in the room who used your same angles and compare your triangles. What is the same? What is different? Are the triangles congruent? Similar?
3. How did you decide if they were or were not congruent or similar?
3. Here is triangle \(PQR\). Break a new piece of pasta, different in length than segment \(PQ\).
□ Tape the piece of pasta so that it lays on top of line \(PQ\) with one end of the pasta at \(P\) (if it does not fit on the page, break it further). Label the other end of the piece of pasta
□ Tape a full piece of pasta, with one end at \(S\), making an angle congruent to \(\angle PQR\).
□ Tape a full piece of pasta on top of line \(PR\) with one end of the pasta at \(P\). Call the point where the two full pieces of pasta meet \(T\).
1. Is your new pasta triangle \(PST\) similar to \(\triangle PQR\)? Explain your reasoning.
2. If your broken piece of pasta were a different length, would the pasta triangle still be similar to \(\triangle PQR\)? Explain your reasoning.
Quadrilaterals \(ABCD\) and \(EFGH\) have four angles measuring \(240^\circ\), \(40^\circ\), \(40^\circ\), and \(40^\circ\). Do \(ABCD\) and \(EFGH\) have to be similar?
13.3: Similar Figures in a Regular Pentagon
1. This diagram has several triangles that are similar to triangle \(DJI\).
1. Three different scale factors were used to make triangles similar to \(DJI\). In the diagram, find at least one triangle of each size that is similar to \(DJI\).
2. Explain how you know each of these three triangles is similar to \(DJI\).
2. Find a triangle in the diagram that is not similar to \(DJI\).
Figure out how to draw some more lines in the pentagon diagram to make more triangles similar to \(DJI\).
We learned earlier that two polygons are similar when there is a sequence of translations, rotations, reflections, and dilations taking one polygon to the other. When the polygons are triangles, we
only need to check that that both triangles have two corresponding angles to show they are similar—can you tell why?
Here is an example. Triangle \(ABC\) and triangle \(DEF\) each have a 30 degree angle and a 45 degree angle.
We can translate \(A\) to \(D\) and then rotate so that the two 30 degree angles are aligned, giving this picture:
• similar
Two figures are similar if one can fit exactly over the other after rigid transformations and dilations.
In this figure, triangle \(ABC\) is similar to triangle \(DEF\).
If \(ABC\) is rotated around point \(B\) and then dilated with center point \(O\), then it will fit exactly over \(DEF\). This means that they are similar. | {"url":"https://im-beta.kendallhunt.com/MS_ACC/students/2/2/13/index.html","timestamp":"2024-11-03T07:49:42Z","content_type":"text/html","content_length":"83441","record_id":"<urn:uuid:25cb1eb6-236d-44c6-b1e9-8eb40d2d7633>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00081.warc.gz"} |
The NOT formula in Google Sheets is a logical function that negates a given logical expression. If the logical expression evaluates to TRUE, the formula returns FALSE, and vice versa. This function
is commonly used to reverse the result of a logical test, or to check if a value is not equal to a specific criteria.
Use the NOT formula with the syntax shown below, it has 1 required parameter:
1. logical_expression (required):
The logical expression that will be negated. This can be a reference to a cell containing a logical value, or a logical expression such as =A1>5.
Here are a few example use cases that explain how to use the NOT formula in Google Sheets.
Reverse the result of a logical test
You can use the NOT function to reverse the result of a logical test. For example, if you have a test that checks if a value is greater than 10 (=A1>10), you can use NOT(A1>10) to check if the value
is not greater than 10.
Check if a value is not equal to a specific criteria
You can use the NOT function to check if a value is not equal to a specific criteria. For example, if you have a list of values in column A and you want to count the number of values that are not
equal to "Yes", you can use the formula =COUNTIF(A:A, "<>Yes").
Common Mistakes
NOT not working? Here are some common mistakes people make when using the NOT Google Sheets Formula:
Missing the logical_expression argument
This error occurs when the logical_expression argument is missing from the NOT formula. The NOT formula requires a logical_expression argument to work properly. Make sure you include a
logical_expression argument when using the NOT formula.
Incorrect use of parentheses
This error occurs when parentheses are not used correctly in the logical_expression argument. The NOT formula requires correct use of parentheses to ensure that the logical_expression argument is
evaluated correctly. Make sure you use parentheses correctly when using the NOT formula.
Using text instead of logical values
This error occurs when text values are used instead of logical values in the logical_expression argument. The NOT formula requires logical values (TRUE/FALSE) to work properly. Make sure you use
logical values when using the NOT formula.
Related Formulas
The following functions are similar to NOT or are often used with it in a formula:
Learn More
You can learn more about the NOT Google Sheets function on Google Support. | {"url":"https://checksheet.app/google-sheets-formulas/not/","timestamp":"2024-11-10T05:34:05Z","content_type":"text/html","content_length":"45541","record_id":"<urn:uuid:492b33cb-9a53-46e2-ab3b-34460f7372fa>","cc-path":"CC-MAIN-2024-46/segments/1730477028166.65/warc/CC-MAIN-20241110040813-20241110070813-00396.warc.gz"} |
seminars - Graph data analysis based on quantum probability theory
In this talk a new measurement to compare two large-scale graphs based on the theory of quantum probability is introduced. The proposed distance between two graphs is defined as the distance between
the corresponding moment of their spectral distributions. It is shown that the spectral distributions of their adjacency matrices in a vector state include information about both their eigenvalues
and the corresponding eigenvectors. Moreover, we prove that the proposed distance is graph invariant and sub-structure invariant.
Computational results for real large-scale graphs show that its accuracy is better than any existing methods and time cost is extensively cheap.
* 줌회의실 개별 공지 | {"url":"https://www.math.snu.ac.kr/board/index.php?mid=seminars&l=en&sort_index=speaker&order_type=asc&page=86&document_srl=1158847","timestamp":"2024-11-11T19:24:59Z","content_type":"text/html","content_length":"48538","record_id":"<urn:uuid:a330b4fd-26cd-4861-9163-eead4b7c48e2>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00862.warc.gz"} |
Mathematical model of geometry and fibrous structure of the heart.
We developed a mathematical representation of ventricular geometry and muscle fiber organization using three-dimensional finite elements referred to a prolate spheroid coordinate system. Within
elements, fields are approximated using basis functions with associated parameters defined at the element nodes. Four parameters per node are used to describe ventricular geometry. The radial
coordinate is interpolated using cubic Hermite basis functions that preserve slope continuity, while the angular coordinates are interpolated linearly. Two further nodal parameters describe the
orientation of myocardial fibers. The orientation of fibers within coordinate planes bounded by epicardial and endocardial surfaces is interpolated linearly, with transmural variation given by cubic
Hermite basis functions. Left and right ventricular geometry and myocardial fiber orientations were characterized for a canine heart arrested in diastole and fixed at zero transmural pressure. The
geometry was represented by a 24-element ensemble with 41 nodes. Nodal parameters fitted using least squares provided a realistic description of ventricular epicardial [root mean square (RMS) error
less than 0.9 mm] and endocardial (RMS error less than 2.6 mm) surfaces. Measured fiber fields were also fitted (RMS error less than 17 degrees) with a 60-element, 99-node mesh obtained by
subdividing the 24-element mesh. These methods provide a compact and accurate anatomic description of the ventricles suitable for use in finite element stress analysis, simulation of cardiac
electrical activation, and other cardiac field modeling problems.
The rendered result of this model.
To launch the model, please select 'Zinc Viewer' under navigation on the right. | {"url":"https://models.physiomeproject.org/exposure/1e663b3330f85e86c875494d978f7c1b","timestamp":"2024-11-10T09:26:22Z","content_type":"application/xhtml+xml","content_length":"16962","record_id":"<urn:uuid:db05227c-3f80-4a10-887b-cc532037aaf6>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00725.warc.gz"} |
Create a list of summary statistics
set_stats {anscombiser} R Documentation
Create a list of summary statistics
Creates a list of summary statistics to pass to mimic.
set_stats(d = 2, means = 0, variances = 1, correlation = diag(2))
d An integer that is no smaller than 2.
means A numeric vector of sample means.
variances A numeric vector of positive sample variances.
correlation A numeric correlation matrix. None of the off-diagonal entries in correlation are allowed to be equal to 1 in absolute value.
The vectors means and variances are recycled using rep_len to have length d.
A list containing the following components.
• means a d-vector of sample means.
• variances a d-vector sample variances.
• correlation a d by d correlation matrix.
# Uncorrelated with zero means and unit variances
# Sample correlation = 0.9
set_stats(correlation = matrix(c(1, 0.9, 0.9, 1), 2, 2))
version 1.1.0 | {"url":"https://search.r-project.org/CRAN/refmans/anscombiser/html/set_stats.html","timestamp":"2024-11-06T10:59:29Z","content_type":"text/html","content_length":"3142","record_id":"<urn:uuid:679a0e02-e484-4790-8401-b1faae320fe5>","cc-path":"CC-MAIN-2024-46/segments/1730477027928.77/warc/CC-MAIN-20241106100950-20241106130950-00049.warc.gz"} |
How Do You Write a Rule for a Geometric Sequence?
Trying to find the value of a certain term in a geometric sequence? Use the formula for finding the nth term in a geometric sequence to write a rule. Then use that rule to find the value of each term
you want! This tutorial takes you through it step-by-step. | {"url":"https://virtualnerd.com/texas-digits/txh-alg-2/exponential-and-logarithmic-functions-and-equations/exponential-models-in-recursive-form/geometric-sequence-find-rule","timestamp":"2024-11-10T01:53:49Z","content_type":"text/html","content_length":"20649","record_id":"<urn:uuid:c63ceaa8-81ec-44e3-b05e-3db40f6d4f44>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.3/warc/CC-MAIN-20241110005602-20241110035602-00203.warc.gz"} |
Blog Archives
Healing Tones
8 Comments
I downloaded this information some time ago as I knew at some point I would be building frequency generating equipment. What I find interesting is the information mentions the numbers 3, 6, and 9.
Tesla once said he who understands the meaning of 3, 6, and 9 will know the secret of the universe. At any the below listed frequencies will be experimented with when the devices are finished.The 7
7 th Sahasrar - Crown Chakra
172.06 Hz The tone of the platonic year
supports cheerfulness and clarity of spirit
6th Ajna - Brow Chakra
221.23 Hz The tone of Venus
Balance between intellect and intuition
5 th Vishudda - Throat Chakra
141.27 Hz The tone of Mercury
supports intelligent communication
4 th Anahata - Heart Chakra
136.10 Hz The tone of the Earth's year
relaxing, soothing, balancing
3rd Manipura - Solar Plexus
126.22 Hz The Sun-tone
Planetware > The Tones of the Sewn Chaio'"as
advances the feeling of centering of the magic
2 ndMuladhara-NavelChakra
210-42 Hz The tone of the synodic moon
supports erotic communication
1 st MiIladhara - Root Chakra
194.18 HzThe tone ofthe Earth's day
dynamic, vitalizing
7/19/13 432hz Vs 528hz- Which Healing Frequency Should You Use?
The numbers 432 and 528 have deep ancient cosmological meanings and connotations. They are
also both vitally important in universal construction . Victor Shovvell, math scientist, has discovered some
interesting relationships betvveen those 2 unique numbers. The first simple association is:
528 + 432 = 960
528 - 432 = 96
Let's take look at the other:
432/528 = 0.81 81 81 81 81-
1 + {432 / 528} = 1.81 81 81 81-
432/ 1.81 81 81 81- = 237.6 x 10 = 2376 = 4 x 756 (Khufu pyramid base length in feet)
It has been proven that 432Hz and 528Hz are woven together mathematically. Simple calculations show that
they both give key numbers for universal construction :
528 /432 = -1.2
4320 x 1.2 = 5184 = 72 squared
4320 / 1.2 = 3600
Both 432Hz and 528Hz have many interesting relationships \Nith the Universe. For example:
528/6 (the number of main Solfeggio tones) = 88
It takes 88 Earth days for Mercury to complete an orbit of the Sun. And, as you may already know,Mercury is named the "winged messenger of the gods." 432 / [528/432] = 360
The circle is 360 degrees, the expression 'do not fear' is used 360 times in the Bible (according to Pastor Richard Wurmbrand), 360 years equals one divine year in Hindu mythology. 360 reduces to 3 +
6 + 0 = 9. John Keely, an expert in electromagnetic technologies, wrote that the vibrations of "thirds, sixths, and ninths, were extraordinarily powerful." The major Toltec complex of Teotihuacan in
Mexico has used the great Pyramid of the Sun with a base total of 864 STU (Standard Teotihuacan Units), which is double the number 432. Each side of the Pyramid of the attuned\
'432hz-V3-52Bhz1 ½ 7/19113 432hz Vs 528hz - Which Healing Freq uency Should You Use?
Sun is 216 STU, which is precisely half of 432, or 3 x 72. The STU was the Toltec measure unit and, as is related in their myths, was passed to them by the gods from the stars. It is readily apparent
from a simple mathematical analysis that A=444Hz [C(5)=528Hz] and A=432Hz are harmonically related. The harmony can be proven by simply subtracting 432 from 444. It yields 12; where 1 + 2 = 3 in
Pythagorean math. If we take 528 and subtract 444, then we can also get 12 or 3. Next, let's take
528 and subtract 432 to get 96; where 9 + 6 = 15; and 1 + 5 = 6.
This result is identical to 5 + 2 + 8 = 15 or 6. These sets of numbers: 3s, 6s, 9s and 8s are always
exclusively represented by these special natural pure tones, their scales, and their harmonics. This is
precisely what Leonardo da Vinci's mentors emphasized about cosmic scales and mathematics.
attuned\.1 brati
'432hz-IIS-528hz1 212
In Healing Codes for the Biological apocalypse Dr. Leonard G. Horowitz and
Dr. Joseph S. Puleo published the Secret Solfeggio Frequencies. Basically it is
the "Doe, Rae, Mi, Fa, So, La, Ti, Doe" diatonic scale which we allleam in the
fIrst few grades of school.
Over time, the pitch of this diatonic scale has changed and somehow Horowitz
and Puleo found the original pitch frequencies.
In the Solfeggio, "Ti" is missing and what we call "Doe" was known as "Ut".
Here are the original pitch frequencies of these six notes:
1. Ut = 396Hz which reduces to 9 [reducing numbers: 3+9 = 12 = 1 + 2 = 3 ;
3+ 6 = 9]
2. Re = 417Hz which reduces to 3
3. Mi = 528Hz which reduces to 6
4. Fa = 639Hz which reduces to 9
5. Sol = 741Hz which reduces to 3
6. La = 852Hz which reduces to 6
They also state that Mi is for "Miracles" or 528Hz - is the exact frequency used
by genetic engineers throughout the world to repair DNA.
Another interesting tidbit that the authors included as a musical scale with
words, from the work of John Keely; where Keely related the hues (not
pigment colors) of light related to musical notes. On the "G-Clef" with "C"
being the fIrst line below the staff and continuing up the scale and up the staff:
C = Red = Tonic
D = Orange = Super Tonic
E = Yellow = Mediant
F = Green = Sub Dominant
G = Blue = Dominant
A = Indigo = Super Dominant, Sub Mediant
B = Violet = Leading Tone, Sub Tonic
C = Red = Octave
Also included with this chart was another from the Dinshah Health Society:
Red = 397.3Hz Closest Note: G = 392Hz
Orange = 430.8 Closest Note: A = 440
Yellow = 464.4 Closest Note: A# = 466
Lemon = 497.9 Closest Note: B = 494
Green = 431.5 Closest Note: C = 523
Turquoise = 565.0 Closest Note: C# = 554
Blue = 598.6 Closest Note: D = 587
Indigo = 632.1 Closest Note: D# = 622
Violet = 665.7 Closest Note: E = 659
Purple = 565.0 (reverse polarity) Closest Note: A# and E = 562 (both reverse
Magenta = 531.5 (reverse polarity) Closest Note: G and E =525 (both reverse
Scarlet = 497.9 (reverse polarity) Closest Note: G# and D = 501 (both reverse
this additional information is gleaned:
The Six Solfeggio Frequencies include:
UT - 396 Hz - Liberating Guilt and Fear
RE - 417 Hz - Undoing Situations and Facilitating Change
MI - 528 Hz - Transformation and Miracles (DNA Repair)
FA - 639 Hz - ConnectinglRelationships
SOL - 741 Hz - Awakening Intuition
LA - 852 Hz - Returning to Spiritual
The basic
Solfeggio frequencies totaled six (6). Horowitz continued his search through the years and extended it to 9 frequencies. 'Most everyone IS familiar with the Star of
David which uses two triangles. (inverted to each other) inscribed within a circle. If one uses the same approach for three triangles overlapping (no inversions) and space them approximately 40
degrees apart around a circle, some amazing relationships appear. Orient the circle with one triangle apex at North or zero degrees. Label that 396. At the next clockwise point label 417, the next
528, the next 639, the next 741 and the last 852. You now have the basic six Solfeggio frequencies. The numbers we have so far added to our circle of numbers have a pattern to them: Any number
connected by a line, for example 396 and 639, if you take the smaller number and move the last digit to the fIrst position, you have
created the line-linked number. [move the 6 of396 to the front and you have
639] Likewise 417 by moving the 7 creates 741, both numbers are line linked.
And 528 by moving the 8 creates 852 both numbers line linked.
As created so far, we have 3 missing numbers, but they can easily be created by applying this moving of digits positions. Take the triangle that has 396 and 639. Ifwe take the 9 and move it to the
first position we have 963, which is one of the extended Solfeggio frequencies! Thusly we can now continue the circle one
more position by adding 963. Applying this same logic to the 417 and 741 triangle to fill in the missing number we move the 1 to the first position to develop 174 which is another extended Solfeggio
number. Continuing clockwise add 174 to the number sequence. And the 528 and 852 triangle if we move the 2 to the first position we have 285, the final missing extended Solfeggio number. So elegantly
simple. Take a piece of paper and lightly grid it off for a large "tic-tac-toe" game. Across the top place the smallest number in the upper left comer; continue horizontally with the line-linked
(triangle) numbers 417, 741. In the middle line, left position place the second in clockwise numbering (285), continue horizontally with its line-linked numbers 528, 852. The last horizontal line
starts 396 and continues 639, 963. Now for some surprises. Compute the
difference between all the vertical row numbers; they are all Ill . Compute the differences between the horizontal row numbers; left row and center row all = 243 and center row to right row
differences are all 324. And here we go again with the move the last digit to the first position move the 3 of 243 to the front and we have 324.
8 Comments | {"url":"https://www.sedonanomalies.com/blog/archives/02-2017","timestamp":"2024-11-13T08:58:34Z","content_type":"text/html","content_length":"45217","record_id":"<urn:uuid:183bc1cf-5aef-4960-92ea-6e27e4626c4d>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00329.warc.gz"} |
Method of random directions and steepest descent
Next: Conditioning the gradient Up: ITERATIVE METHODS Previous: ITERATIVE METHODS
Let us minimize the sum of the squares of the components of the residual vector given by
Fourier-transformed variables are often capitalized. Here we capitalize vectors transformed by the boldface print.
A contour plot is based on an altitude function of space. The altitude is the dot product R as close as we can to zero. If the residual vector R reaches zero, then we have solved the simultaneous
equations x has two components, (x[1] , x[2] ). A contour is a curve of constant x[1] , x[2] )-space. These contours have a statistical interpretation as contours of uncertainty in (x[1] , x[2] ),
given measurement errors in Y.
Starting from g be an abstract vector with the same number of components as the solution x, and let g contain arbitrary or random numbers. Let us add an unknown quantity g to vector x, thereby
changing x to R+dR becomes
We seek to minimize the dot product Setting to zero the derivative with respect to Geometrically and algebraically the new residual G. (We confirm this by substitution leading to
In practice, random directions are rarely used. It is more common to use the gradient vector. Notice also that a vector of the size of x is
Notice also that this vector can be found by taking the gradient of the size of the residuals: Descending by use of the gradient vector is called ``the method of steepest descent."
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Spatially dependent flood probabilities to support the design of civil infrastructure systems
Articles | Volume 23, issue 11
© Author(s) 2019. This work is distributed under the Creative Commons Attribution 4.0 License.
Spatially dependent flood probabilities to support the design of civil infrastructure systems
Conventional flood risk methods typically focus on estimation at a single location, which can be inadequate for civil infrastructure systems such as road or railway infrastructure. This is because
rainfall extremes are spatially dependent; to understand overall system risk, it is necessary to assess the interconnected elements of the system jointly. For example, when designing evacuation
routes it is necessary to understand the risk of one part of the system failing given that another region is flooded or exceeds the level at which evacuation becomes necessary. Similarly, failure of
any single part of a road section (e.g., a flooded river crossing) may lead to the wider system's failure (i.e., the entire road becomes inoperable). This study demonstrates a spatially dependent
intensity–duration–frequency (IDF) framework that can be used to estimate flood risk across multiple catchments, accounting for dependence both in space and across different critical storm durations.
The framework is demonstrated via a case study of a highway upgrade comprising five river crossings. The results show substantial differences in conditional and unconditional design flow estimates,
highlighting the importance of taking an integrated approach. There is also a reduction in the estimated failure probability of the overall system compared with the case where each river crossing is
treated independently. The results demonstrate the potential uses of spatially dependent intensity–duration–frequency methods and suggest the need for more conservative design estimates to take into
account conditional risks.
Received: 19 Jul 2018 – Discussion started: 04 Sep 2018 – Revised: 23 Sep 2019 – Accepted: 25 Sep 2019 – Published: 27 Nov 2019
Methods for quantifying the flood risk of civil infrastructure systems such as road and rail networks require considerably more information compared to traditional methods that focus on flood risk at
a point. For example, the design of evacuation routes requires the quantification of the risk that one part of the system will fail at the same time that another region is flooded or exceeds the
level at which evacuation becomes necessary. Similarly, a railway route may become impassable if any of a number of bridges are submerged, such that the “failure probability” of that route becomes
some aggregation of the failure probabilities of each individual section. Successful estimation of flood risk in these systems therefore requires recognition both of the networked nature of the civil
infrastructure system across a spatial domain, as well as the spatial and temporal structure of flood-producing mechanisms (e.g., storms and extreme rainfall) that can lead to system failure (e.g.,
Leonard et al., 2014; Seneviratne et al., 2012; Zscheischler et al., 2018).
One way to estimate such flood probabilities is to directly use information contained in historical streamflow data. For example, annual maximum streamflow at two locations might be assumed to follow
a bivariate generalized extreme-value (GEV) distribution (Favre et al., 2004; Wang, 2001; Wang et al., 2009), which can then be used to estimate both conditional probabilities (e.g., the probability
that one river is flooded given that the other river level exceeds a specified threshold) and joint probabilities (e.g., the probability that one or both rivers are flooded). Several frameworks have
been demonstrated based directly on streamflow observations, including functional regression (Requena et al., 2018), multisite copulas (Renard and Lang, 2007), and spatial copulas (Durocher et al.,
2016). However, in many instances continuous streamflow data are unavailable or insufficient at the locations of interest, or the catchment conditions have changed such that historical streamflow
records are unrepresentative of likely future risk. For these situations, rainfall-based methods are often more appropriate.
There are two primary classes of rainfall-based methods to estimate flood probability. The first uses continuous rainfall data (either historical or generated) to compute continuous streamflow data
using a rainfall-runoff model (Boughton and Droop, 2003; Cameron et al., 1999; He et al., 2011; Hegnauer et al., 2014; Pathiraja et al., 2012), with flood risk then estimated based on the simulated
streamflow time series. This method is computationally intensive, and given the challenge of reproducing a wide variety of statistics across many scales, it can have difficulties in modeling the
dependence of extremes. Most spatial rainfall models operate at the daily timescale (Bárdossy and Pegram, 2009; Baxevani and Lennartsson, 2015; Bennett et al., 2016b; Hegnauer et al., 2014; Kleiber
et al., 2012; Rasmussen, 2013), whereas many catchments respond at sub-daily timescales. This is likely because the capacity of space–time rainfall models to simulate the statistics of sub-daily
rainfall remains a challenging research problem (Leonard et al., 2008), although one approach is to exploit the relative abundance of data at the daily scale then apply a downscaling model to reach
sub-daily scales (Gupta and Tarboton, 2016). Continuous simulation is receiving ongoing attention and increasing application, yet there remain limitations when applying these models in many practical
The second rainfall-based method proceeds by applying probability calculations on rainfall to construct “intensity–duration–frequency” curves, which are then translated to a runoff event of an
equivalent probability either via empirical models such as the rational method to estimate peak flow rate (Kuichling, 1889; Mulvaney, 1851) or via event-based rainfall-runoff models that are able to
simulate the full flood hydrograph (Boyd et al., 1996; Chow et al., 1988; Laurenson and Mein, 1990). Regional frequency analysis is one type of method to estimate intensity–duration–frequency (IDF)
values, where the precision of at-site estimates is improved by pooling data from sites in the surrounding region (Hosking and Wallis, 1997). These methods can be combined with spatial interpolation
methods to estimate parameters for any ungauged location of interest (Carreau et al., 2013). To determine an effective mean depth of rainfall over a catchment with the same exceedance probability as
at a gauge location, the pointwise estimate of extreme rainfall is multiplied by an areal reduction factor (ARF) (Ball et al., 2016). However, such methods do not account for information on the
spatial dependence of extreme rainfall – whether for a single storm duration or the more complex case of different durations across a region (Bernard, 1932; Koutsoyiannis et al., 1998). The
underlying independence assumption prevents these approaches from being applied to estimate conditional or joint flood risk at multiple points in a catchment or across several catchments, as would be
required for a civil infrastructure system.
Although multivariate approaches can be tailored to estimate conditional and joint probabilities of extreme rainfall for specific situations (e.g., Kao and Govindaraju, 2008; Wang et al., 2010; Zhang
and Singh, 2007), the development of a unified methodology that integrates with existing IDF-based flood estimation approaches remains elusive. This is particularly challenging given that it is not
only necessary to account for the dependence of rainfall across space, but it is also necessary to account for the dependence across storm burst durations, as different parts of the system may be
vulnerable to different critical-duration storm events. To this end, the theory of the max-stable process has been demonstrated to represent storm-level dependence (de Haan, 1984; Schlather, 2002)
and used to calculate conditional probabilities for a spatial domain (Padoan et al., 2010). The max-stable process has also been used to represent the co-occurrence of extreme daily rainfall in the
French Mediterranean region (Blanchet and Creutin, 2017). Copulas including the extremal t copula (Demarta and McNeil, 2005) and the Hüsler–Reiss copula (Hüsler and Reiss, 1989) have also been used
to model rainfall dependence.
This study applies a max-stable approach with an emphasis on practical flood estimation problems. To this end, any proposed approach needs to account for the following:
1. The spatial dependence of rainfall “events” both for single durations and also across multiple different durations. This was addressed by Le et al. (2018b), who linked a max-stable model with the
duration-dependent model of Koutsoyiannis et al. (1998), to create a model that could be used to reflect dependencies between nearby catchments of different sizes.
2. The asymptotic properties of spatial dependence as the events become increasingly extreme, given the focus of many flood risk estimation methods on rare flood events. Recent evidence is emerging
that rainfall has an asymptotically independent characteristic (Le et al., 2018a; Thibaud et al., 2013), which means that the level of the rainfall's dependence reduces with an increasing return
period (Wadsworth and Tawn, 2012). The requirement of asymptotic independence indicates that inverted max-stable models are preferable over max-stable models.
This study adapts the methods developed by Le et al. (2018b) to inverted max-stable models to derive spatially dependent IDF estimates and ARFs as the basis for transforming rainfall into flood
flows. The approach is demonstrated on a highway system spanning 20km with five separate river crossings.
The case study is designed to address two related questions. (i) “What flood flow needs to be used to design a bridge that will fail on average only once on average every M times given that a
neighboring catchment is flooded?” (ii) “What is the probability that the overall system fails given that each bridge is designed to a specific exceedance probability event (e.g., the 1% annual
exceedance probability event)?” The method for resolving these questions represents a new approach to estimate flood risk for engineering design, by focusing attention on the risk of the entire
system, rather than the risk of individual system elements in isolation.
In the remainder of the paper, Sect. 2 emphasizes the need for spatially dependent IDF estimates in flood risk design and is followed by Sect. 3, which outlines the case study and data used.
Section 4 explains the implementation of the framework, including a method for analyzing the spatial dependence of extreme rainfall across different durations. Results on the behavior of floods due
to the spatial and duration dependence of rainfall extremes are provided in Sect. 5. Conclusions and discussion follow in Sect. 6.
2The need for spatially dependent IDF estimates in flood risk estimation
The main limitation of conventional methods of flood risk estimation is that they isolate bursts of rainfall and break the dependence structure of extreme rainfall. Figure 1 demonstrates a
traditional process of estimating at-site extreme rainfall for two locations (gauge 1 and gauge 2) and three durations (1, 3, and 5h) (Stedinger et al., 1993). The process first involves extracting
the extreme burst of rainfall for each site, as well as the duration and year from the continuous rainfall data, and then fitting a probability distribution (such as the generalized extreme-value
distribution) to the extracted data. Figure 1 demonstrates that, through the process of converting the continuous rainfall data to a series of discrete rainfall “bursts”, this process breaks the
dependence both with respect to duration and space. Firstly, the duration dependence is broken by extracting each duration separately, whereas for the hypothetical storm in Fig. 1 it is clear that
the annual maxima from some of the extreme bursts come from the same storm. Secondly, the spatial dependence is broken because each site is analyzed independently. Again, for the hypothetical storm
of Fig. 1 it can be seen that the 5h storm has occurred at the same time across the two catchments, and this information is lost in the subsequent probability distribution curves. Lastly, there is
cross-dependence in space and duration. For example, the 1h extreme from gauge 2 occurs at the same time as the 5h extreme from gauge 1. This may be relevant if there are two catchments with times
of concentration matching 1 and 5h, respectively, which can arise where catchments are neighboring or nested.
Having obtained the IDF estimates for individual locations in Fig. 1, the next step is commonly to convert this to spatial IDF maps by interpolating results between gauged locations. Figure 2 shows
hypothetical IDF maps from individual sites, with a separate spatial contour map usually provided for each storm burst duration. In a conventional application the respective maps are used to estimate
the magnitude of extreme rainfall over catchments for a specified time of concentration. The IDF estimates are combined with an areal reduction factor to determine the volume of rainfall over a
region (since rainfall is not simultaneously extreme at all locations over the region). However, because the spatial dependence was broken in the IDF analysis, the ARFs come from a separate analysis
and are an attempt to correct for the broken spatial relationship within a catchment (Bennett et al., 2016a). Lastly, the rainfall volume over the catchment is combined with a temporal pattern
(i.e., the distribution of the rainfall hyetograph within a single “storm burst”) and input into a runoff model to simulate flood flow at a catchment's outlet. Where catchment flows can be considered
independently, this process has been acceptable for conventional design, but because this process does not account for dependence across durations and across a region, it is not possible to address
problems that span multiple catchments, as with civil infrastructure systems.
The process in Fig. 1 breaks out the dependence of the observed rainfall, which makes the conventional approach unable to analyze the dependence of flooding at two or more separate locations.
Instead, this paper advocates for spatially dependent IDF estimates that are developed by retaining the dependence of observed rainfall in the estimation of extremal rainfall. By applying spatially
dependent IDF estimates to a rainfall-runoff model, it becomes possible to represent the dependence of flooding between separate locations.
The region chosen for the case study is in the Mid North Coast region of New South Wales, Australia. This region has been the focus of a highway upgrade project and has an annual average daily
traffic volume on the order of 15000 vehicles along the existing highway. The upgrade traverses a series of coastal foothills and floodplains for a total length of approximately 20km. The project's
major river crossings consist of extensive floodplains with some marsh areas.
The case study has five main catchments that are numbered in sequence in Fig. 3: (1) Bellinger, (2) Kalang River, (3) Deep Creek, (4) Nambucca, and (5) Warrell Creek. The area and time of
concentration of these catchments is summarized in Table 1, with the latter estimated using the ratio of the flow path length and average flow velocity (SKM, 2011). The Deep Creek catchment has a
time of concentration of 8h, while the other four catchments have much longer times of concentration, ranging from 27 to 38h. The differing durations indicate that it is necessary to consider
spatial dependence across this range of durations to estimate joint and conditional flood risk. The spatial dependence across rainfall durations is expected to be lower than across a single duration,
since short and long rain events are often driven by different meteorological mechanisms (Zheng et al., 2015). However some spatial dependence is still likely to be present, given that extremal
rainfall in the region is strongly associated with “east coast low” systems off the eastern coastline, whereby extreme hourly rainfall bursts are often embedded in heavy multi-day rainfall events.
The black circles in Fig. 3 represent the sub-daily rain stations used for this study. There were seven sub-daily stations selected, with 35 years of record in common for the whole region. The data
were available at a 5min interval and aggregated to longer durations. For convenience in comparing the times of concentration between the catchments, this study assumes a time of concentration of
9h for the Deep Creek catchment, while identical times of concentration of 36h are assumed for the other four catchments.
This section describes the method used to estimate the conditional and joint probabilities of streamflow for civil infrastructure systems based on rainfall extremes, with the sequence of steps
illustrated in Fig. 4. The overall aim is to estimate rainfall exceedance probabilities and corresponding flow estimates that account for dependence across multiple catchments. The generalized Pareto
distribution (GPD) is used as the marginal distribution to fit to observed rainfall above some large threshold for all durations at each location (Sect. 4.1). An extremal dependence model is required
to evaluate conditional and joint probabilities. Here, an inverted max-stable process is used with dependence not only in space but also in duration (Sect. 4.2). The fitted model is evaluated in a
range of contexts, including the construction of joint and conditional return level maps. The derivation of areal reduction factors and joint rainfall estimates are made with the assistance of
simulations based on the fitted model (Sect. 4.3). An event-based rainfall-runoff model is employed in Sect. 4.4 to transform extremal design rainfalls to corresponding flows.
4.1Marginal model for rainfall
This study defines extremes as those greater than some threshold u. For a large u, the distribution of Y conditional on Y>u may be approximated by the generalized Pareto distribution (GPD) (Pickands,
1975; Davison and Smith, 1990; Thibaud et al., 2013).
$\begin{array}{}\text{(1)}& G\left(y\right)=\mathrm{1}-{\left\{\mathrm{1}+\frac{\mathit{\xi }\left(y-u\right)}{{\mathit{\sigma }}_{u}}\right\}}^{-\mathrm{1}/\mathit{\xi }},y>u,\end{array}$
defined on $\mathit{\left\{}y:\mathrm{1}+\mathit{\xi }\left(y-u\right)/{\mathit{\sigma }}_{u}>\mathrm{0}\mathit{\right\}}$, where σ[u]>0 and $-\mathrm{\infty }<\mathit{\xi }<+\mathrm{\infty }$ are
scale and shape parameters, respectively. The probability that a level y is exceeded is Φ[u]{1−G(y)}, where ${\mathrm{\Phi }}_{u}=\mathrm{Pr}\left(Y>u\right)$.
The selection of the appropriate threshold u involves a trade-off between bias and variance. A threshold that is too low leads to bias because the GPD approximation is poor. A threshold that is too
high leads to high variance because of a small number of excesses. Two diagnostic tests are used to determine the appropriate threshold u: the mean residual life plot and the parameter estimate plot
(Coles, 2001; Davison and Smith, 1990). These methods use the stability property of a GPD so that if a GPD is valid for all excesses above u, then excesses of a threshold greater than u should also
follow a GPD (Coles, 2001). To construct IDF maps across the region, the parameters of the GPD are interpolated across the region using a thin plate spline with covariates of longitude and latitude.
Though more detailed modeling of covariates could be used to improve estimates (Le et al., 2018b), the interpolation used here is sufficient for demonstrating the overall method.
4.2Dependence model for spatial rainfall
Consider rainfall as a stationary stochastic process, Z[i], associated with a location, x[i], and a specific duration (the notation is simplified from Z(x[i]) to Z[i]). An important property of
dependence in the extremes is whether or not two variables are likely or unlikely to co-occur as the extremes become rarer, as this can significantly influence the estimated frequency of flood events
of a large magnitude. This is referred to as asymptotic dependence or independence, respectively. For the case of asymptotic independence, the dependence structure becomes weaker as the extremal
threshold increases, which is defined as $P\mathit{\left\{}{Z}_{\mathrm{1}}>z|{Z}_{\mathrm{2}}>z\mathit{\right\}}=\mathrm{0}$ for all x[1]≠x[2]. The spatial extent of a rainfall event with
asymptotically independent extremes will diminish as its rarity increases. This study uses an asymptotically independent model, of which multiple types are valid including the Gaussian copula
(Davison et al., 2012) and inverted max-stable processes (Wadsworth and Tawn, 2012). The inverted max-stable model was ultimately selected in this study to provide consistency with earlier research
(Le et al., 2018a), in which it was demonstrated to preserve the spatial properties of extreme rainfall in an Australian context, including the property of asymptotic independence. Thibaud et al.
(2013) also compared the inverted max-stable model with a Gaussian copula in a case study in Switzerland, and they identified that the inverted max-stable model was appropriate.
The dependence structure of the inverted max-stable process is represented by the pairwise residual tail dependence coefficient (Ledford and Tawn, 1996). For a generic continuous process, Z[i], for a
given duration and associated with a specific location, x[i], the empirical pairwise residual tail dependence coefficient η for each pair of locations (x[1], x[2]) is
$\begin{array}{}\text{(2)}& \mathit{\eta }\left({x}_{\mathrm{1}},{x}_{\mathrm{2}}\right)=\frac{\mathrm{log}P\left\{{Z}_{\mathrm{2}}>z\right\}}{\mathrm{log}P\left\{{Z}_{\mathrm{1}}>z,{Z}_{\mathrm{2}}>
The value of $\mathit{\eta }\in \left(\mathrm{0},\phantom{\rule{0.25em}{0ex}}\mathrm{1}\right]$ indicates the level of extremal dependence between Z[1] and Z[2] (Coles et al., 1999), with lower
values indicating lower dependence. An example of how to calculate the residual tail dependence coefficient is provided in Appendix A for a sample dataset. To estimate the dependence structure of an
inverted max-stable model, the theoretical residual tail dependence coefficient function is fitted to its empirical counterpart. Here the residual tail dependence coefficient function is assumed to
only depend on the Euclidean distance between two locations, $h=|{x}_{\mathrm{1}}-{x}_{\mathrm{2}}‖$. The theoretical residual tail dependence coefficient function for the Brown–Resnick model is
given as
$\begin{array}{}\text{(3)}& \mathit{\eta }\left(h\right)=\frac{\mathrm{1}}{\mathrm{2}\mathrm{\Phi }\left\{\sqrt{\frac{\mathit{\gamma }\left(h\right)}{\mathrm{2}}}\right\}},\end{array}$
where Φ is the standard normal cumulative distribution function, h is the distance between two locations, and γ(h) belongs to the class of variograms $\mathit{\gamma }\left(h\right)=|h{|}^{\mathit{\
beta }}/q$ for q>0 and $\mathit{\beta }\in \left(\mathrm{0},\phantom{\rule{0.25em}{0ex}}\mathrm{2}\right)$. The model is fitted to the empirical residual tail dependence coefficient by modifying
parameters q and β until the sum of squared errors is minimized.
When the extreme rainfall at location x[1] and x[2] are of different durations, the dependence is less than when the extremes are of the same duration. For example, at a single location (h=0), when
the duration is the same, the rainfall values are identical and have perfect dependence, but when the duration of extremes are different, the values are not identical, and the dependence is less. An
adjustment needs to be made to the theoretical pairwise residual tail dependence coefficient function when extreme rainfalls have different durations.
Following Le et al. (2018b), an adjusted approach is used by adding a nugget to the variogram as
$\begin{array}{}\text{(4)}& {\mathit{\gamma }}_{\mathrm{ad}.}\left(h\right)={h}^{\mathit{\beta }}/q+c\left(D-d\right)/d,\end{array}$
where h, β, and q are the same as those in Eq. (3), d is the duration (in h), $\mathrm{0}<d\le D$, where D is the maximum duration of interest (e.g., D=36h for the case study described in this
paper), and c is a parameter to adjust dependence according to duration. This adjustment is intended to condition the behavior of shorter duration extremes on a D hour extreme of specified magnitude.
It is constructed to reflect the fact that when compared to a D hour extreme, a shorter duration results in less extremal dependence. Cases involving conditioning of longer periods on shorter periods
(such as a 36h extreme given a 9h extreme has occurred) can also use the relationship in Eq. (4), but these are with different parameter values.
To fit the inverted max-stable process for all pairs of durations at locations x[1] and x[2] (i.e., 36 and 12h, 36 and 9h, 36 and 6h, 36 and 2h, and 36 and 1h), the theoretical pairwise residual
tail dependence coefficient function in Eq. (3) is used with the adjusted variogram from Eq. (4), where the parameters β and q are first obtained from the fitted results of the case of identical 36h
durations at locations x[1] and x[2]. The parameter c is obtained by a least-square fit of the residual tail dependence coefficient across all durations.
4.3Simulation-based estimation of areal and joint rainfall
The dependence model specification in the previous section enables the calculation of joint and conditional probabilities (Appendix B). Therefore, in addition to traditional IDF return level maps
that are based on independence between locations and durations, it is possible to account for the coincidence of rainfall within the region. Current design procedures using IDF estimates are
event-based and rely on ancillary steps to reconstruct elements of the design storm that were broken during the estimation procedure. One critical element is the areal reduction factor, which can
also be estimated by using the dependence model. ARFs are used to adjust rainfall at a point (such as the centroid of a catchment) to an effective mean rainfall over the catchment with an equivalent
probability of exceedance (Ball et al., 2016; Le et al., 2018a). ARFs can be estimated from observed rainfall data, but it is difficult to extrapolate them for long return periods from observations
with just 35 years of record for this study. To deal with this difficulty and to analyze the asymptotic behavior of ARFs, Le et al. (2018a) proposed a framework to simulate ARFs using the same
inverted max-stable-process model adopted here. The simulation procedure from Le et al. (2018a) is summarized according to two steps. In the first step, the theoretical residual tail dependence
coefficient function in Eq. (3) is fitted to observed rainfall for the duration of interest to obtain the variogram parameters q>0 and $\mathit{\beta }\in \left(\mathrm{0},\phantom{\rule{0.25em}
{0ex}}\mathrm{2}\right)$. The inverted Brown–Resnick process is obtained from a simulation of the Brown–Resnick process using the algorithm of Dombry et al. (2016) over a spatial domain. In the
second step, the simulation in step 1 is transformed from unit Fréchet margins to the rainfall-scaled margins (inverse transformation of Eq. B1). For rainfall magnitudes above the threshold the
generalized Pareto distribution in Eq. (1) is used, and below the threshold the empirical distribution is used. The empirical distributions at ungauged sites are derived from the nearest gauged sites
and use the interpolated response surface of the GPD threshold parameter.
An advantage of the simulation approach is that it can reflect the proportion of dry days in the empirical distribution by making the simulated rainfall contain zero values (Thibaud et al., 2013).
Another advantage is that the use of empirical distributions guarantees that the marginal distributions of simulated rainfall below the threshold match the observed marginal distributions. There may
be a drawback by forcing the simulated rainfall to have the same extremal dependence structure for both parts below and above the threshold, which may not be true for non-extreme rainfall. However,
the dependence structure of non-extreme rainfall contributes insignificantly to extreme events (Thibaud et al., 2013) and is unlikely to affect the results.
For calculating ARFs, the simulation is implemented separately for spatial rainfall with a 36 and 9h duration. ARFs are calculated for each duration and different return periods, which can be found
in the Supplement (Figs. S1 and S2). Figures S1 and S2 provide relationships between ARFs and area (in km^2) for different return periods for the case study catchments simulated using the inverted
Brown–Resnick process over equally sized grid points. The relationships are interpolated to obtain the ARFs for each subcatchment.
The recommended approach for estimating the overall failure probability of a system is demonstrated by considering a hypothetical traffic system with multiple river crossings at different locations.
If there is a one-to-one correspondence between extreme rainfall intensity over a catchment and flood magnitude, the overall failure probability will be approximately equal to the probability that
there is at least one river crossing whose contributing catchment has rainfall extremes exceeding the design level. This can be estimated using simulations of the spatial rainfall model. Given the
different times of concentration in each catchment, the simulation must account for extremes of different durations. Specifically, the covariance matrix of the simulation procedure provided by Dombry
et al. (2016) is calculated from the variogram in Eq. (3). The covariance element for a pair of locations with the same duration (e.g., 36 and 36h) is calculated from the variogram of identical
durations for 36 and 36h. The covariance element for a pair of locations with different durations, for example, 36 and 9h, is calculated from the variogram across durations for 36 and 9h. A set of
10000 years of simulated rainfall is generated from the fitted model to calculate the overall failure probability of a highway section (Eq. B5). The process is repeated 100 times to estimate the
average failure probability, under the assumption that all river crossings of the highway are designed to the same individual failure probability.
4.4Transforming rainfall extremes to flood flow
To estimate flood flow from rainfall extremes, the Watershed Bounded Network Model (WBNM) (Boyd et al., 1996) is employed. The WBNM calculates flood runoff from rainfall hyetographs that represent
the relationship between the rainfall intensity and time (Chow et al., 1988). It divides the catchment into subcatchments, allowing hydrographs to be calculated at various points within the catchment
and the spatial variability of rainfall and rainfall losses to be modeled. It separates overland flow routing from channel routing, allowing changes to either or both of these processes, for example,
in urbanized catchments. The rainfall extremes are estimated at the centroid of the catchment, and they are converted to average spatial rainfall using the simulated ARFs described in Sect. 4.3.
Design rainfall hyetographs are used to convert the rainfall magnitude to absolute values through the duration of a storm following standard design guidance in Australia (Ball et al., 2016).
Hydrological models (WBNM) for the case study area were developed and calibrated in previous studies (WMAWater, 2011). Hydrological model layouts for the Bellinger, Kalang River, Nambucca, Warrell,
and Deep Creek catchments can be found in the Supplement (Figs. S3 to S5).
5.1Model evaluation for the space-duration rainfall process
A GPD with an appropriate threshold was fitted to the observed rainfall data for 36 and 9h durations, and the Brown–Resnick inverted max-stable-process model was calibrated to determine the spatial
Analysis of the rainfall records led to the selection of a threshold of 0.98 for all records as was reasonable across the spatial domain, and the GPD was fitted to data above the selected threshold.
Figure 5 shows Q–Q plots of the marginal estimates for a representative station for two durations (36 and 9h). Overall the quality of fitted distributions is good, and plots for all other stations
can be found in the Supplement (Figs. S6 and S7).
The inverted max-stable process across different durations was calibrated to determine dependence parameters. The theoretical pairwise residual tail dependence coefficient function between two
locations (x[1] and x[2]) was calculated based on Eqs. (3) and (4), and the observed pairwise residual tail dependence coefficient η was calculated using Eq. (2). Figure 6 shows the pairwise residual
tail dependence coefficients for the Brown–Resnick inverted max-stable process vs. distance. The black points are the observed pairwise residual tail dependence coefficients, while the red lines are
the fitted pairwise residual tail dependence coefficient functions. A coefficient equal to 1 indicates complete spatial dependence, and a value of 0.5 indicates complete spatial independence.
Figure 6a shows the dependence between 36h extremes across space, with the distance h=0 corresponding to “complete dependence”. It also shows the dependence decreasing with an increasing distance.
Figure 6 indicates that the model has a reasonable fit to the observed data given the small number of dependence parameters. Although the theoretical coefficient (red line) does not perfectly match
at long distances, the main interest for this case study is in short distances, including at h=0 for the case of dependence between two different durations at the same location.
Figure 6b–d show the dependence of 36 vs. 9h extremes, 36 vs. 6h extremes, and 36 vs. 3h extremes, with the latter two duration combinations not being used directly in the study but nonetheless
showing the model performance across several durations. As expected, the dependence levels are weaker compared with 36 vs. 36h extremes at the same distance, especially at a distance of zero. This
is expected, as extremes of different durations are more likely to arise from different storm events compared to storms of the same duration.
5.2Estimating conditional rainfall return levels and corresponding conditional flows for evacuation route design
The recommended approach for estimating conditional rainfall extremes is demonstrated by considering a hypothetical evacuation route across location x[2], given a flood occurs at location x[1],
evaluated using Eq. (B4). This approach is applied to a case study of the Pacific Highway upgrade project that contains five main river crossings (from Fig. 3). For evacuation purposes, we need to
know what the probability that a bridge fails only once on average every M times is (e.g., M=10 for a one in 10 chance conditional event) when a neighboring bridge is flooded. This section provides
the conditional estimates for two pairs of neighboring bridges in the case study that have the shortest Euclidean distances, i.e., pairs (x[1], x[2]) and (x[2], x[3]). The comparisons of
unconditional and conditional maps are given in Figs. 7 and 8, and the corresponding unconditional and conditional flows are given in Fig. 9.
Figure 7a provides the pointwise 10-year unconditional return level map over the case study area for 36h rainfall extremes. The value at the location of interest – the blue star (the centroid of the
Bellinger catchment) – is around 260mm. Figure 7b indicates that when accounting for the effect of a 20-year event for 36h rainfall extremes happening at the location of the red star (the centroid
of the Kalang River catchment), the pointwise 1-in-10 chance conditional return level at the blue star rises to around 453mm (i.e., 1.74 times the unconditional value).
Figure 8 provides similar plots to Fig. 7 for another pair of locations having different durations of rainfall extremes due to different times of concentration in each catchment. Here, the location
of interest is the centroid of the Deep Creek catchment (the blue star in Fig. 8), and the conditional point is the centroid of the Kalang River catchment (the red star in Fig. 8). The pointwise
10-year unconditional and 1-in-10 chance conditional return levels at the location of the blue star are 134 and 194mm, respectively. The relative difference between the conditional and unconditional
return levels is only 1.45 times, compared with 1.74 times for the case in Fig. 7. This is because the pair of locations in Fig. 8 has a longer distance than those in Fig. 7 so that the dependence
level is weaker. Moreover, the location pair in Fig. 8 was analyzed for different durations (between 36 and 9h extremes), which has a weaker dependence than the case of the equivalent durations in
Fig. 7 (between 36 and 36h), based on Fig. 6.
The unconditional and conditional return levels were extracted at the centroid of each main catchment, and they were converted to the absolute values of rainfall using a corresponding ARF and design
storm hyetograph. The unconditional and conditional flood flows at the river crossing in the Bellinger catchment (corresponding to the unconditional and conditional rainfall extremes in Fig. 7) are
given in Fig. 9 (Fig. 9a). Similar plots for the river crossing in the Deep Creek catchment (corresponding to the unconditional and conditional rainfall extremes in Fig. 8) are given in Fig. 9
(Fig. 9b).
Figure 9 presents peak flow for the Bellinger (Fig. 9a) and Deep Creek (Fig. 9b) catchments, indicating that the peak conditional flow at the river crossings is almost 2.0 and 1.7 times higher than
the unconditional flow for the two catchments, respectively. This difference is a direct result of the conditional event having a higher rainfall magnitude than the unconditional event: given that
there is an extreme event nearby, it is more likely for an extreme event to occur at a nearby location. If a bridge design were to take into account this extra criterion for the purposes of
evacuation planning, it would require the design to be at a higher level.
5.3Estimating the failure probability of the highway section based on the joint probability of rainfall extremes
Figure 10 is a plot of the overall failure probability of the highway as a function of the failure probability of each individual river crossing (black). Similar relationships for the cases of
complete dependence (blue) and independence (red) are also provided for comparison. For the case of complete dependence, when the whole region is extreme at the same time, the overall failure
probability of the highway is equal to the individual river crossing failure probability. This represents the lowest overall failure probability. The worst case is complete independence where
extremes do not happen together unless by random chance; this means that the failure probability of the highway is much higher than that for individual river crossings. Taking into account the real
dependence, there are some extremes that align, and it seems from Fig. 10 that this is a relatively weak effect. As an example from Fig. 10, to design the highway with a failure probability of 1%
annual exceedance probability (AEP), we would have to design each individual river crossing to a much rarer AEP of 0.25% (see green lines in Fig. 10).
6Discussion and conclusions
Hydrological design that is based on IDF estimates has conventionally focused on separate estimation at single locations. Such an approach can lead to the misspecification for a wider system risk of
flooding since weather systems exhibit dependence in space and time and across storm durations, which can lead to the coincidence of extremes. A number of methods have been developed to address the
problem of antecedent moisture within a single catchment, by accounting for the temporal dependence of rainfall at locations of interest through loss parameters or sampling rainfall patterns (Rahman
et al., 2002). However, there have been fewer methods that account for the spatial dependence of rainfall across multiple catchments, due in part to the complexity of representing the effects of
spatial dependence in risk calculations. Different catchments can have different times of concentration, so spatial dependence may also imply the need to consider dependence across different
durations of extreme rainfall bursts.
Recent and ongoing advances in modeling spatial rainfall extremes provide an opportunity to revisit the scope of hydrological design. Such models include a max-stable model fitted using a Bayesian
hierarchical approach (Stephenson et al., 2016), max-stable and inverted max-stable models (Nicolet et al., 2017; Padoan et al., 2010; Russell et al., 2016; Thibaud et al., 2013; Westra and Sisson,
2011), and latent-variable Gaussian models (Bennett et al., 2016b). The ability to simulate rainfall over a region means that hydrological problems need not be confined to individual catchments, but
they may cover multiple catchments. Civil infrastructure systems such as highways, railways, or levees are such examples, since the failure of any one element may lead to the overall failure of the
system. Alternatively, where there is a network, the failure of one element may have implications for the overall system to accommodate the loss, by considering alternative routes. With models of
spatial dependence and the duration dependence of extremes, there is a new and improved ability to address these problems explicitly as part of the design methodology.
This paper demonstrated an application for evaluating conditional and joint probabilities of flooding at different locations. This was achieved with two examples: (i) the design of a river crossing
that will fail once on average every M times given that its neighboring river crossing is flooded and (ii) the estimation of the probability that a highway section, which contains multiple river
crossings, will fail based on the failure probability of each individual river crossing. Due to the lack of continuous streamflow data and sub-daily limitations of rain-based continuous simulation,
this study used an event-based method of conditional and joint rainfall extremes to estimate the corresponding conditional and joint flood flows. The spatial rainfall was simulated using an
asymptotically independent model, which was then used to estimate conditional and joint rainfall extremes. Although this study focused on the inverted max-stable model to simulate the extreme
rainfall process, other methods such as the Gaussian copula may also be appropriate and should be considered in future applications.
An empirical method was obtained from the framework of Le et al. (2018b) to make an asymptotically independent model – the inverted max-stable process – able to capture the spatial dependence of
rainfall extremes across different durations. The fitted residual tail dependence coefficient function showed that the model can capture the dependence for different pairs of durations. For our
example, the highest ratio of the 1-in-10 chance conditional event (in considering the effect of a 20-year event rainfall occurring at the conditional location) to the 10-year unconditional event
was 1.74 for the two catchments having the strongest dependence (Fig. 7). The corresponding conditional flows were then estimated using a hydrological model, WBNM, and shown to be strongly related to
the ratio of conditional and unconditional rainfall extremes (Fig. 9).
The joint probability of rainfall extremes for all catchments and for all possible pairs of catchments in the case study area was estimated empirically from a set of 10000 years of simulated
rainfall extremes, repeated 100 times to estimate the average value. The results showed that there were differences in the failure probability of the highway after taking into account the rainfall
dependence, but the effect was not as emphatic as with the case of conditional probabilities. The difference in the failure probability became weaker as the return period increased, which is
consistent with the characteristic of asymptotically independent data (Ledford and Tawn, 1996; Wadsworth and Tawn, 2012). A relationship was demonstrated (Fig. 10) to show how the design of the
overall system to a given failure probability requires the design of each individual river crossing to a rarer extremal level than when each crossing is considered in isolation. For the case study
example, it would be necessary to design each of the five bridges to a 0.25% AEP event in order to obtain a system failure probability of 1%.
There is a need to reimagine the role of intensity–duration–frequency relationships. Conventionally they have been developed as maps of the marginal rainfall in a pointwise manner for all locations
and for a range of frequencies and durations. The increasing sophistication of mathematical models for extremes, computational power, and interactive graphics abilities of online mapping platforms
means that analysis of hydrological extremes could significantly expand in scope. With an underlying model of spatial and duration dependence between the extremes, it is not difficult to conceive of
digital maps that dynamically transform from the marginal representation of extremes to the corresponding representation conditional extremes after any number of conditions are applied. This
transformation is exemplified by the differences between panels a and b in Figs. 7 and 8. Enhanced IDF maps would enable a very different paradigm of design flood risk estimation, breaking away from
analyzing individual system elements in isolation and instead emphasizing the behavior of the entire system.
Appendix A:Calculation of the empirical tail dependence coefficient
To illustrate how Eq. (2) in the paper is calculated, consider a set of n=10 observed values at the two locations Z[1] and Z[2] (see Table A1). First, Z[1] and Z[2] are converted to empirical
cumulative probability estimates via the Weibull plotting position formula $P=j/\left(n+\mathrm{1}\right)$, where j is a ranked index of a data point giving P[1] and P[2] (see Table A1).
Assume that interest is in values above a threshold u satisfying P[u]=0.5, in other words, $P\mathit{\left\{}{Z}_{\mathrm{2}}>u\mathit{\right\}}=P\mathit{\left\{}{P}_{\mathrm{2}}>{P}_{u}\mathit{\
right\}}=\mathrm{0.5}$. In this case we have only one pair, at the index of 7, that satisfies both P[1] and P[2] and is greater than P[u]=0.5, thus P{Z[1]>u, ${Z}_{\mathrm{2}}>u\mathit{\right\}}=P\
mathit{\left\{}{P}_{\mathrm{1}}>{P}_{u}$, ${P}_{\mathrm{2}}>{P}_{u}\mathit{\right\}}=\mathrm{1}/\mathrm{10}=\mathrm{0.1}$. The calculation of the empirical tail dependence coefficient is then
$\begin{array}{}\text{(A1)}& \begin{array}{rl}\mathit{\eta }\left({x}_{\mathrm{1}},{x}_{\mathrm{2}}\right)& =\frac{\mathrm{log}P\left\{{Z}_{\mathrm{2}}>u\right\}}{\mathrm{log}P\left\{{Z}_{\mathrm
{1}}>u,{Z}_{\mathrm{2}}>u\right\}}\\ & =\frac{\mathrm{log}P\left\{{P}_{\mathrm{2}}>{P}_{u}\right\}}{\mathrm{log}P\left\{{P}_{\mathrm{1}}>{P}_{u},{P}_{\mathrm{2}}>{P}_{u}\right\}}\\ & =\frac{\mathrm
Appendix B:Estimate of conditional and joint probabilities of rainfall extremes
The unit Fréchet transformation is given as
where y is the original marginal value, z is the Fréchet transformed value, and all other parameters correspond to the GPD specified in Sect. 4.1. For values below the threshold, F is the empirical
distribution function of y, $F\left({y}_{i}\right)=i/\left(n+\mathrm{1}\right)$, where i is the rank of y[i] and n is the total number of data points.
The conditional probability $P\mathit{\left\{}{Z}_{\mathrm{2}}>{z}_{\mathrm{2}}|{Z}_{\mathrm{1}}>{z}_{\mathrm{1}}\mathit{\right\}}$ is obtained from the bivariate inverted max-stable-process
cumulative distribution function (CDF) in unit Fréchet margins (Thibaud et al., 2013), which is given as
$\begin{array}{}\text{(B2)}& \begin{array}{rl}P\left\{{Z}_{\mathrm{1}}\le {z}_{\mathrm{1}},{Z}_{\mathrm{2}}\le {z}_{\mathrm{2}}\right\}& =\mathrm{1}-\mathrm{exp}\left\{-\frac{\mathrm{1}}{{g}_{\mathrm
{1}}}\right\}-\mathrm{exp}\left\{-\frac{\mathrm{1}}{{g}_{\mathrm{2}}}\right\}\\ & +\mathrm{exp}\left[-V\left\{{g}_{\mathrm{1}},{g}_{\mathrm{2}}\right\}\right],\end{array}\end{array}$
where ${g}_{\mathrm{1}}=-\mathrm{1}/\mathrm{log}\mathit{\left\{}\mathrm{1}-\mathrm{exp}\left(-\mathrm{1}/{z}_{\mathrm{1}}\right)\mathit{\right\}}$, ${g}_{\mathrm{2}}=-\mathrm{1}/\mathrm{log}\mathit{\
left\{}\mathrm{1}-\mathrm{exp}\left(-\mathrm{1}/{z}_{\mathrm{2}}\right)\mathit{\right\}}$, and the exponent measure V (Padoan et al., 2010) is defined as
$\begin{array}{}\text{(B3)}& \begin{array}{rl}V\left\{{g}_{\mathrm{1}},{g}_{\mathrm{2}}\right\}& =-\frac{\mathrm{1}}{{g}_{\mathrm{1}}}\mathrm{\Phi }\left\{\frac{a}{\mathrm{2}}+\frac{\mathrm{1}}{a}\
mathrm{log}\frac{{g}_{\mathrm{2}}}{{g}_{\mathrm{1}}}\right\}\\ & -\frac{\mathrm{1}}{{g}_{\mathrm{2}}}\mathrm{\Phi }\left\{\frac{a}{\mathrm{2}}+\frac{\mathrm{1}}{a}\mathrm{log}\frac{{g}_{\mathrm{1}}}
In Eq. (B3), Φ is the standard normal cumulative distribution function, $a=\sqrt{\mathrm{2}{\mathit{\gamma }}_{\mathrm{ad}.}\left(h\right)}$, and γ[ad.](h) is the variogram that was mentioned in the
explanation of Eq. (3).
In unit Fréchet margins, the relationship between the return level z and the return period T (in number of observations) is given as $z=-\mathrm{1}/\mathrm{log}\left(\mathrm{1}-\mathrm{1}/T\right)$,
and the conditional probability for the max-stable process can then be estimated using
where T[1] is the return period (in number of observations for 36h rainfall) corresponding to the return level z[1]. It is also noted that in this paper Z[1] and Z[2] were taken as threshold
exceedances, so the return period T[1] should be in the number of observations, which is equivalent to a T[1]∕243-year return period because there are 243 observations for 36h rainfalls in a year.
The probability that there is at least one location that has an extreme event exceeding a given threshold can be calculated based on the addition rule for the union of probabilities as
where N is the number of locations.
For the case of dependent variables, the joint probability for only two locations, $P\mathit{\left\{}{Z}_{\mathrm{1}}>{z}_{\mathrm{1}},{Z}_{\mathrm{2}}>{z}_{\mathrm{2}}\mathit{\right\}}$, can be
easily obtained from the bivariate CDF for the inverted max-stable process in Eq. (B2). However, for the case of multiple locations (five different locations for this paper), it is difficult to
derive the formula for this probability because there are dependences between extreme events at all locations. So this probability is empirically calculated from a large number of simulations of the
dependent model (see the description of the simulation procedure for an inverted max-stable process in Sect. 4.3).
For the case that all the events are independent, the joint probability for independent variables is broken down as the product of the marginals, and the conditional probability is equivalent to the
marginal probability. When applying Eq. (B5) for independent variables, the joint probability is therefore calculated by P(Z[1]>z[1],…,${Z}_{N}>{z}_{N}\right)=P\left({Z}_{\mathrm{1}}>{z}_{\mathrm
PDL implemented and developed the approach, visualized and interpreted results, and prepared the paper. ML and SW supervised the research and helped to evaluate the methodology and results and edit
the paper.
The authors declare that they have no conflict of interest.
The lead author was supported by the Australia Awards Scholarships (AAS) from the Australian government. Seth Westra was supported by an Australian Research Council Discovery Project (grant
no. DP150100411). We thank Mark Babister and Isabelle Testoni of WMA Water for providing the hydrologic models for the case study and Leticia Mooney for her editorial help in improving this paper.
The rainfall data used in this study were provided by the Australian Bureau of Meteorology and can be obtained from the corresponding author.
This research has been supported by the Australia Awards Scholarships (grant no. DP150100411).
This paper was edited by Albrecht Weerts and reviewed by Joost Beckers and two anonymous referees.
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compound events, Nat. Clim. Change, 8, 469–477, https://doi.org/10.1038/s41558-018-0156-3, 2018. | {"url":"https://hess.copernicus.org/articles/23/4851/2019/","timestamp":"2024-11-12T17:41:28Z","content_type":"text/html","content_length":"307566","record_id":"<urn:uuid:75f614b1-87f5-449a-8e5f-cc72d206a773>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00157.warc.gz"} |
ECON-GA 3503
‘math+econ+code’ masterclass on competitive equilibrium
NYU Courant Insitute, May 21-26, 2018 (30 hours)
This very intensive course, part of the ‘math+econ+code’ series, is focused on the computation of competitive equilibrium, which is at the core of surge pricing engines and allocation mechanisms. It
will investigate diverse applications such as network congestion, surge pricing, and matching platforms. It provides a bridge between theory, empirics and computation and will introduce tools from
economics, mathematical and computer science. Mathematical concepts (such as lattice programming, supermodularity, discrete convexity, Galois connections, etc.) will be taught on a needs basis while
studying various economic models. The same is true of computational methods (such as tatonnement algorithms, asynchronous parallel computation, mathematical programming under equilibrium constraints,
etc.). Hence there are no prerequisite other than the equivalent of a first-year graduate sequence in econ, applied mathematics or other quantitative disciplines.
The teaching format is somewhat unusual: the course will be taught over six consecutive days, with lectures in the morning and individual assignments in the afternoon. This course is very demanding
from students, but the learning rewards are high. The morning lectures will alternate between 1 hour of theory followed by 1 hour of coding. Students are expected to write their own code, and the
teaching staff will ensure that it is operational. This course is therefore closer to cooking lessons than to traditional lectures.
This NYU course has no equivalent in peer universities. An earlier course with a different focus but sharing the same format and philosophy was taught at NYU in January 2018; it was very popular and
was attended by students from a number of other universities.
Aim of the course
• Provide the conceptual basis of competitive equilibrium with gross substitutes, along with various computational techniques (optimization problems, equilibrium problems). Show how asynchronous
parallel computation is adapted for the computation of equilibrium. Applications to hedonic equilibrium, multinomial choice with peer effects, and congested traffic equilibrium on networks.
• Describe analytical methods to analyze demand systems with gross substitutes (Galois connections, lattice programming, monotone comparative statics) and use them to study properties of competitive
equilibrium with gross substitutes. Describe the Kelso-Crawford-Hatfield-Milgrom algorithm. Application to stable matchings, and equilibrium models of taxation.
• Derive models of bundled demand and analyze them using notions of discrete convexity and polymatroids. Application to combinatorial auctions and bundled choice.
Teaching staff
A. Galichon (NYU Econ+Math): morning lectures
K. O’Hara (NYU Econ): afternoon presentations (coding)
Y. Sun (NYU Math): afternoon presentations (machine learning)
O. Ghelfi (NYU Econ): research assistantship
Course material
A Github repository containing the course material (lecture slides, datasets, code) will made available at the start of the course. Coding assignments will be uploaded on a separate repository
located here.
Practical information
• Schedule: Mon 5/21 — Sat 5/26, 2018, 9am-1pm (morning); 2pm-3pm (afternoon). Location: Courant building (251 Mercer St), room 202.
• Credits: 2, assessed through participation in the coding assignments or a short final paper, at the student’s option.
• NYU students will need to register on Albert. Non-NYU students need to contact the lecturer: galichon@cims.nyu.edu.
Course material
Available before the lectures.
• Monday 5/21: competitive equilibrium with gross substitutes
• Tuesday 5/22: demand beyond quasi-linearity
• Wednesday 5/23: bundled demand
• Thursday 5/24: empirical models of demand
• Friday 5/25: empirical models of matching
• Saturday 5/26: equilibrium on networks
Part I: Tools
Day 1: Competitive equilibrium with gross substitutes (Monday, 4 hours)
Walrasian equilibrium and gross substitutes. Gradient descent, Newton method; coordinate update method. Isotone convergence and Tarski’s theorem. Parallel computation (synchronous and asynchronous).
Fisher-Eisenberg-Gale markets. Hedonic models beyond the quasilinear case.
• Ortega and Rheinboldt (1970). Iterative Solution of Nonlinear Equations in Several Variables. SIAM.
• Heckman, Matzkin, and Nesheim (2010). “Nonparametric identification and estimation of nonadditive hedonic models,” Econometrica.
• Gul and Stacchetti (1999). “Walrasian equilibrium with gross substitutes”. Journal of Economic Theory.
• Jain and Vazirani (2010). “Eisenberg–Gale markets: Algorithms and game-theoretic properties”. Games and Economic Behaviour.
• Cheung and Cole (2016). “A Unified Approach to Analyzing Asynchronous Coordinate Descent and Tatonnement”. Arxiv.
Day 2: Demand beyond quasi-linearity (Tuesday, 4 hours)
Lattices and supermodularity. Veinott’s strong set ordering and Topkis’ theorem; Milgrom-Shannon theorem. Z-maps, P-maps and M-maps. Galois connections and generalized convexity. Equilibrium
transport. Models of matching models with imperfectly transferable utility. Stable matchings and Gale and Shapley’s algorithm.
• Veinott (1989). Lattice programming. Unpublished lecture notes, Johns Hopkins University.
• Topkis (1998). Supermodularity and complementarity. Princeton.
• Milgrom and Shannon (1994). “Monotone comparative statics.” Econometrica.
• Rheinboldt (1974). Methods for solving systems of nonlinear equations. SIAM.
• Noeldeke and Samuelson (2018). The implementation duality. Econometrica.
• Kelso and Crawford (1981). Job Matching, Coalition Formation, and Gross Substitutes. Econometrica.
• Roth and Sotomayor (1992). Two-Sided Matching. A Study in Game-Theoretic Modeling and Analysis. Cambdidge.
Day 3: Bundled demand (Wednesday, 4 hours)
Discrete convexity. Lovasz extension; Polymatroids. Hatfield-Milgrom’s algorithm. Combinatorial auctions.
• Fujishige (1991). Submodular functions and optimization. Elsevier.
• Vohra (2011). Mechanism design. A linear programming approach. Cambridge.
• Bikhchandani, Ostroy (2002). The Package Assignment Model”. JET.
• Hatfield and Milgrom (2005). Matching with contracts. AER.
• Danilov, Koshevoy, and Murota (2001). Discrete convexity and equilibria in economies with indivisible goods and money. Mathematical Social Sciences.
Part II: Models
Day 4: Empirical models of demand (Thursday, 4 hours)
Nonadditive random utility models. Strategic complements; supermodular games. Brock-Durlauf’s model of demand with peer effect. Mathematical programming with equilibrium constraints (MPEC).
• Vives, X. (1990). “Nash Equilibrium with Strategic Complementarities,” JME.
• Milgrom and Roberts (1994). “Comparing Equilibria,” AER.
• Berry, Gandhi, Haile (2013). “Connected Substitutes and Invertibility of Demand,” Econometrica.
• Brock, Durlauf (2001). Discrete choice with social interactions. JPE.
• Dubé, Fox and Su (2012), “Improving the Numerical Performance of BLP Static and Dynamic Discrete Choice Random Coefficients Demand Estimation,” Econometrica.
• Bonnet, Galichon, O’Hara and Shum (2018). Yoghurts choose customers? Identification of random utility models via two-sided matching.
Day 5: Empirical models of matching (Friday, 4 hours)
Distance-to-frontier function, matching function equilibrium. Matching models with taxes. Matching with public consumption. Surge pricing.
• Menzel (2015). Large Matching Markets as Two-Sided Demand Systems. Econometrica.
• Legros, Newman (2007). Beauty is a Beast, Frog is a Prince. Assortative Matching with Nontransferabilities. Econometrica.
• Galichon, Kominers, and Weber (2018). Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility.
Day 6: Equilibrium on networks (Saturday, 4 hours)
Equilibrium on networks. Traffic congestion; Wardrop equilibrium. Braess’ paradox. Price of anarchy.
• Roughgarden, Tardos (2002). How bad is selfish routing? Journal of the ACM.
• Roughgarden (2005). Selfish Routing and the Price of Anarchy. MIT.
• Bourlès, Bramoullé, and Perez‐Richet (2017). Altruism in networks. Econometrica.
• Wardrop (1952). “Some theoretical aspects of road traffic research”. Proc. Inst. Civ. Eng.
• Dafermos (1980). “Traffic Equilibrium and Variational Inequalities.” Transportation Science.
• Nagurney (1993). Network Economics: A Variational Inequality Approach. Kluwer. | {"url":"https://alfredgalichon.com/mec_equil_archive_2018-05/","timestamp":"2024-11-04T20:33:25Z","content_type":"application/xhtml+xml","content_length":"29164","record_id":"<urn:uuid:57e19f61-ea4b-4a99-9f8c-e2213364117a>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00541.warc.gz"} |
Numbers/Content/What Are Numbers/Bases - Wikibooks
New Words
You learned in the last lesson how each place amount in a number is a group of ten. Why do people use groups of ten? Why not groups of 12, 8, or 60? Most people have ten fingers and ten toes, so it
is easy to count in groups of ten.
A base is any number you use to make groups for counting. Math works with any number as a base.
Example Questions
Question 1:
What are the numbers one through ten using a base of three?
There are only three numerals in base three, so we select 0, 1, and 2.
The first two numbers are the same as in base ten.
When we get to three we must start filling the threes place.
Again at six we increase the threes place
Question 2:
What is the number 265 in base five
One way to answer this is to write every number up to 265 in base five. This is easy, but it takes a long time. A faster way to do this is to think about groups of five. In base five the first place
is the ones place, the second place is the fives place, the third place is the 25's place, and the fourth place is the 125's place.
Take two groups of 125 from 265 and you have 15 left. 15 is three groups of five. This means you put a two in the 125's place and a three in the fives place. The answer is $2030$.
Question 3:
This question may be too hard if you do not know about adding. See the article Using Numbers, Adding and Subtracting for help.
What are the next binary (base 2) numbers in base 10?
• $000011$
• $000101$
• $001000$
• $001101$
• $010101$
• $100010$
The place amounts for base 2 are in this order:
• ones
• twos
• fours
• eights
• 16's
• 32's
To find the base 10 number find the place amount of each numeral and find the number you have all together.
One and two together make $3$.
One and four together make $5$.
The fourth place is $8$.
One and four and eight together make $13$.
One and four and 16 together make $21$.
Two and 32 together make $34$.
More Questions | {"url":"https://simple.wikibooks.org/wiki/Numbers/Content/What_Are_Numbers/Bases","timestamp":"2024-11-12T09:48:23Z","content_type":"text/html","content_length":"49915","record_id":"<urn:uuid:7aad618a-8336-414c-ad02-02f26920dc60>","cc-path":"CC-MAIN-2024-46/segments/1730477028249.89/warc/CC-MAIN-20241112081532-20241112111532-00162.warc.gz"} |
[SNU Number Theory Seminar 2021.12.03] Algebraization theorems in complex and non-archimedean geometry
• Date : 12월 3일 (금) 10:30 AM
• Place : Zoom 896 5654 6548 / 157067
• Speaker : Abhishek Oswal (Caltech)
• Title : Algebraization theorems in complex and non-archimedean geometry
• Abstract : Algebraization theorems originating from o-minimality have found striking applications in recent years to Hodge theory and Diophantine geometry. The utility of o-minimality originates
from the 'tame' topological properties that sets definable in such structures satisfy. O-minimal geometry thus provides a way to interpolate between the algebraic and analytic worlds. One such
algebraization theorem that has been particularly useful is the definable Chow theorem of Peterzil and Starchenko which states that a closed analytic subset of a complex algebraic variety that is
simultaneously definable in an o-minimal structure is an algebraic subset. In this talk, I shall discuss a non-archimedean version of this result and some recent applications of these
algebraization theorems.
• Website: https://sites.google.com/view/snunt/seminars | {"url":"https://qsms.math.snu.ac.kr/index.php?mid=board_sjXR83&order_type=desc&listStyle=viewer&sort_index=title&page=7&document_srl=2024","timestamp":"2024-11-07T13:00:33Z","content_type":"text/html","content_length":"21535","record_id":"<urn:uuid:a2b4a5fc-d35a-414c-9f66-71a95274b497>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00195.warc.gz"} |
Challenging Math Test Without Calculators Leaves Even PhDs Stumped
This No-Calculator Math Test Is Stumping People With A PhD
Are you a math whiz? Do you think you can solve complex equations without the help of a calculator? Well, think again! This no-calculator math test is stumping even people with a PhD in mathematics.
The test consists of a series of challenging math problems that require you to use your mental math skills to solve them. From algebraic equations to geometry problems, this test covers a wide range
of mathematical concepts that will put your skills to the test.
But don't worry, even if you're not a math genius, you can still take the test and see how you fare. Who knows, you might surprise yourself with how much you know!
So, are you up for the challenge? Take the no-calculator math test and see if you have what it takes to solve these tricky problems.
1. What is the No-Calculator Math Test?
The No-Calculator Math Test is a math test that does not allow the use of calculators. It is designed to test a person's ability to solve math problems without the aid of a calculator.
2. Why is the No-Calculator Math Test stumping people with a PhD?
The No-Calculator Math Test is stumping people with a PhD because it requires a high level of mathematical proficiency and problem-solving skills. Even though people with a PhD may have a strong
background in math, they may not be used to solving problems without the aid of a calculator.
3. How can I prepare for the No-Calculator Math Test?
You can prepare for the No-Calculator Math Test by practicing mental math and problem-solving skills. You can also review math concepts and formulas to ensure that you have a strong foundation in
math. Additionally, you can take practice tests to get a feel for the types of questions that may be on the test. | {"url":"https://quizzino.com/this-no-calculator-math-test-is-stumping-people-with-a-phd/","timestamp":"2024-11-03T03:38:41Z","content_type":"text/html","content_length":"110717","record_id":"<urn:uuid:3975d56e-e9db-4525-9cff-7964cc9cead8>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00812.warc.gz"} |
On the inversion of quantum mechanical systems: Determining the amount and type of data for a unique solution
The inverse problem of extracting a quantum mechanical potential from laboratory data is studied from the perspective of determining the amount and type of data capable of giving a unique answer.
Bound state spectral information and expectation values of time-independent operators are used as data. The Schrödinger equation is treated as finite dimensional and for these types of data there are
algebraic equations relating the unknowns in the system to the experimental data (e.g., the spectrum of a matrix is related algebraically to the elements of the matrix). As these equations are
polynomials in the unknown parameters of the system, it is possible to determine the multiplicity of the solution set. With a fixed number of unknowns the effect of increasing the number of equations
on the multiplicity of solutions is assessed. In general, if the number of the equations matches the number of the unknowns, the solution set is denumerable. A result on the solvability of polynomial
equations is extended to the case where the number of equations exceeds the number of unknowns. We show that if one has more equations than the number of unknowns, genetically a unique solution
exists. Several examples illustrating these results are provided.
All Science Journal Classification (ASJC) codes
• General Chemistry
• Applied Mathematics
• Quantum mechanical systems
• Schrödinger equation
Dive into the research topics of 'On the inversion of quantum mechanical systems: Determining the amount and type of data for a unique solution'. Together they form a unique fingerprint. | {"url":"https://collaborate.princeton.edu/en/publications/on-the-inversion-of-quantum-mechanical-systems-determining-the-am","timestamp":"2024-11-10T19:22:12Z","content_type":"text/html","content_length":"53522","record_id":"<urn:uuid:8d39be6c-3cdd-4c3f-90b8-61e06a7c106b>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00825.warc.gz"} |
The figure above shows the dimensions of a semicircular cross section
Question Stats:
30%70% (01:41)based on 10 sessions
rere.png [ 9.31 KiB | Viewed 2060 times ]
Let \(A\) and \(B\) be endpoints of the single lane.
Let \(O\) be the midpoint of \(\overline{AB}\).
The single lane is \(12\) ft wide and equidistant from sides of tunnel, which means its present right in middle of the tunnel.
Now, we know that length of \(\overline{AB} = 12\)ft, which means \(\overline{AO} = \overline{OB} = \frac{\overline{12}}{2} = 6\)ft.
Since there a mention of
height of vehicles
, draw a perpendicular from either of point \(A\) or \(B\)(lets take \(B\)) till it meets the curved circumference of semicircle at point \(C\).
Why from point \(B\)? Because that is where the lane ends, vehicles cannot travel past that.
This basically forms a right-angled triangle \(OBC\) with \(OC\) as hypotenuse as well as radius of the semicircle = \(\frac{20}{2} = 10\)ft.
So max height possible = \(BC - \frac{1}{2} = \sqrt{OC^2 - OB^2} - \frac{1}{2} = \sqrt{10^2 - 6^2} - \frac{1}{2} = \sqrt{64} - \frac{1}{2} = 8 - \frac{1}{2} = 7\frac{1}{2}\)ft
\((-\frac{1}{2})\) because the question states a condition -
vehicles must clear the top of the tunnel by at least 1/2 foot
Hence, Answer is | {"url":"https://gre.myprepclub.com/forum/the-figure-above-shows-the-dimensions-of-a-semicircular-cross-section-25564.html","timestamp":"2024-11-05T19:33:15Z","content_type":"application/xhtml+xml","content_length":"230776","record_id":"<urn:uuid:f8db04f6-79f3-4786-ab3b-b2e9248b7d8d>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00427.warc.gz"} |
subdepth – Unify maths subscript height
This package is based on code (posted long ago to comp.text.tex by Donald Arseneau) to equalise the height of subscripts in maths. The default behaviour is to place subscripts slightly lower when
there is a superscript as well, but this can look odd in some situations.
Sources /macros/latex/contrib/subdepth
Version 0.1
Licenses The LaTeX Project Public License
Copyright 2007 Will Robertson
Maintainer Will Robertson
Contained in TeXLive as subdepth
MiKTeX as subdepth
Topics Subsup position
Download the contents of this package in one zip archive (98.2k).
Community Comments
Maybe you are interested in the following packages as well. | {"url":"https://www.ctan.org/pkg/subdepth","timestamp":"2024-11-09T19:51:11Z","content_type":"text/html","content_length":"16149","record_id":"<urn:uuid:ae897937-9414-4860-9aea-92aca273ac5f>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00814.warc.gz"} |
Protein Folding Proteins
pharmaceuticals Review Roles of Heat Shock Proteins in Apoptosis, Oxidative Stress, Human Inflammatory Diseases, and Cancer Paul Chukwudi Ikwegbue 1, Priscilla Masamba 1, Babatunji Emmanuel Oyinloye
1,2 ID and Abidemi Paul Kappo 1,* ID 1 Biotechnology and Structural Biochemistry (BSB) Group, Department of Biochemistry and Microbiology, University of Zululand, KwaDlangezwa 3886, South Africa;
[email protected]
[email protected]
[email protected]
(B.E.O.) 2 Department of Biochemistry, Afe Babalola University, PMB 5454, Ado-Ekiti 360001, Nigeria * Correspondence:
[email protected]
; Tel.: +27-35-902-6780; Fax: +27-35-902-6567 Received: 23 October 2017; Accepted: 17 November 2017; Published: 23 December 2017 Abstract: Heat shock proteins (HSPs) play cytoprotective activities
under pathological conditions through the initiation of protein folding, repair, refolding of misfolded peptides, and possible degradation of irreparable proteins. Excessive apoptosis, resulting from
increased reactive oxygen species (ROS) cellular levels and subsequent amplified inflammatory reactions, is well known in the pathogenesis and progression of several human inflammatory diseases (HIDs)
and cancer. Under normal physiological conditions, ROS levels and inflammatory reactions are kept in check for the cellular benefits of fighting off infectious agents through antioxidant mechanisms;
however, this balance can be disrupted under pathological conditions, thus leading to oxidative stress and massive cellular destruction. Therefore, it becomes apparent that the interplay between
oxidant-apoptosis-inflammation is critical in the dysfunction of the antioxidant system and, most importantly, in the progression of HIDs. Hence, there is a need to maintain careful balance between
the oxidant-antioxidant inflammatory status in the human body. | {"url":"https://docslib.org/doc/2262191/protein-folding-proteins","timestamp":"2024-11-06T10:24:39Z","content_type":"text/html","content_length":"67213","record_id":"<urn:uuid:f25a1e6d-ab91-420e-967f-8b0b628848b9>","cc-path":"CC-MAIN-2024-46/segments/1730477027928.77/warc/CC-MAIN-20241106100950-20241106130950-00314.warc.gz"} |
Task Empty Cuboids (pus)
Empty Cuboids
Memory limit: 32 MB
We call a cuboid regular if:
• one of its vertices is a point with coordinates ,
• edges beginning in this vertex lay on positive semi-axes of the coordinate system,
• the edges are not longer than .
There is given a set of points of space, which coordinates are integers from the interval . We try to find a regular cuboid of maximal volume, which does not contain any of the points from the set .
A point belongs to the cuboid if it belongs to the inside of the cuboid, i.e. it is a point of the cuboid, but not of its wall.
Write a program which:
• reads from the standard input coordinates of points from the set ,
• finds one of the regular cuboids of maximal volume, which does not contain any points from the set ,
• writes the result to the standard output.
In the first line of the standard input one non-negative integer , , is written. It is the number of elements in the set . In the following lines of the input there are triples of integers from the
interval , which are coordinates (respectively , and ) of points from . Numbers in each line are separated by single spaces.
In the only line of the standard output there should be three integers separated by single spaces. These are coordinates (respectively , and ) of the vertex of the regular cuboid of maximal volume.
We require that coordinates are positive.
For the input data:
the correct result is:
Task author: Bogdan S. Chlebus. | {"url":"https://szkopul.edu.pl/problemset/problem/zgd-jOYv9ULJG4uDFVlNzDPo/site/?key=statement","timestamp":"2024-11-09T10:51:58Z","content_type":"text/html","content_length":"26644","record_id":"<urn:uuid:f83bcafa-4a42-446e-ac10-adec57c4fceb>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00155.warc.gz"} |
Kiloton to Muon Mass Converter - Convert Kiloton to Muon Mass - Best Online Conversion Calculator
Kiloton to Muon Mass Converter - Weight and Mass Converter
Use our Kiloton to Muon Mass converter to convert Kiloton to Muon Mass. Both Kiloton and Muon Mass are units of Weight and Mass. Convert quickly and easily between Kiloton and Muon Mass using this
conversion tool. You can also use our Weight and Mass Converter to convert to various other units of Weight and Mass.
Also learn How to Convert Kiloton and Muon Mass using this Kiloton and Muon Mass conversion tool to other Weight and Mass units.
Select the current unit in the left column, the desired unit in the right column, and enter a value in the left column to generate the resulting conversion.
Formuladivide the Weight and Mass value by 5.309172492731345e+33
Kiloton (metric) Weight and Mass Unit Conversion chart
Check out this Weight and Mass Converter conversion table to find out what the conversion factors are between the various Weight and Mass units:
Complete list of Weight and Mass units for conversion, see how much 1 Kiloton (metric) is equivalent to in the below units.
1 Kiloton (metric) is equal to
Unit Symbol Value (1 Kiloton (metric) =)
Exagram Eg 1e-9
Petagram Pg 0.000001
Teragram Tg 0.001
Gigagram Gg 1
Megagram Mg 1000
Kilogram kg 1000000
Hectogram hg 10000000
Decagram dag 100000000
Gram g 1000000000
Decigram dg 1e+10
Centigram cg 1e+11
Milligram mg 1e+12
Microgram μg 1e+15
Nanogram ng 1e+18
Picogram pg 1e+21
Femtogram fg 1e+24
attogram ag 1e+27
Quintal (UK) cwt 19684.1305522
Hundredweight (UK) 19684.1305522
Scruple (apothecary) s.ap 771617917.647
Grain gr 1.54323583529e+10
Pennyweight pwt 643088418.793
Ounce oz 35273961.9496
Pound lbs 2204622.62185
stone (US) 157473.044418
quarter qr (US) 78736.5222089
Slug 68521.7658492
Kilopound (kip) kip 2204.62262185
Ton (Long Ton) ton 984.206527611
US Ton (Short Ton) tn 1102.310995
Tonne (Metric Ton) t 1000
Quintal (metric) cwt 10000
Hundredweight (metric) 10000
Kiloton (metric) kt 1
Carat ct 5e+9
Atomic mass unit u 6.02217364335e-22
Gamma 9.99999999999e-40
Dalton 6.02217364335e-22
Planck mass 4.59408924477e-41
Electron mass (rest) 1.097768383e-18
Muon mass 5.30917249273e-21
Proton mass r 5.97863320551e-22
Neutron mass 5.97040375333e-22
Deuteron mass 2.9908008955e-22
Earth's mass 2.16729054519e-72
Sun's mass 7.2533150741e-79
Talent (Biblical Hebrew) 29.2397660819
Mina (Biblical Hebrew) 1754.38596491
Shekel (Biblical Hebrew) 87719.2982456
Bekan (Biblical Hebrew) 175438.596491
Gerah (Biblical Hebrew) 1754385.96491
Tetradrachma (Biblical Greek) 73529.4117647
Didrachma (Biblical Greek) 147058.823529
Drachma (Biblical Greek) 294117.647059
Denarius (Biblical Roman) 259740.259745
Assarion (Biblical Roman) 4155844.15591
Quadrans (Biblical Roman) 16623376.6237
Lepton (Biblical Roman) 33246753.2473
Kiloton (metric) to Muon mass conversion table
Kiloton (metric) Muon mass
1 5.30917249273e-21
2 1.06183449855e-20
3 1.59275174782e-20
4 2.12366899709e-20
5 2.65458624636e-20
6 3.18550349564e-20
7 3.71642074491e-20
8 4.24733799418e-20
9 4.77825524345e-20
10 5.30917249273e-20
20 1.06183449855e-19
30 1.59275174782e-19
40 2.12366899709e-19
50 2.65458624636e-19
60 3.18550349564e-19
70 3.71642074491e-19
80 4.24733799418e-19
90 4.77825524345e-19
100 5.30917249273e-19
Common Weight and Mass Conversions
Frequently Asked Questions
• How can I use Weight and Mass Converter?
Select the current unit in the top column, the desired unit in the bottom column, and enter a value in the top left column to generate the resulting conversion.
• What are the SI Units of Weight and Mass?
The SI unit of Weight and Mass is kg.
• What are the different units of Weight and Mass?
The SI unit of Weight and Mass is kg. Alternatively, the Weight and Mass can also be expressed in . | {"url":"https://www.schoolmykids.com/learn/calculators/kiloton-to-muon-mass-conversion-weight-and-mass-converter-calculator","timestamp":"2024-11-14T20:22:29Z","content_type":"text/html","content_length":"1049253","record_id":"<urn:uuid:e5b23083-e84a-4720-ba55-cd95e9743cb8>","cc-path":"CC-MAIN-2024-46/segments/1730477395538.95/warc/CC-MAIN-20241114194152-20241114224152-00519.warc.gz"} |
Selected Former Members
Inexpensive connectivity and computing power have caused the number of communicating devices to explode in the last decade. New applications are emerging every day to take advantage of the
proximity and abundance of these devices. Device-to-Device (D2D) communication as an underlay to cellular network to increase spectral efficiency is a technology component of Long Term Evolution
- Advanced (LTE-A). In D2D communication underlaying cellular networks, devices communicate with each other using a direct link using cellular resources without going through the evolved Node B
(eNB) but remaining under the control of it. D2D communication is expected to be one of the prominent features supported by future cellular networks because of reusing the cellular spectrum to
increase the system performance of cellular networks. However, due to the limitations of a licensed spectrum when these devices share a cellular spectrum to communicate directly among themselves,
the same resource may need to be shared among cellular and D2D communicating pairs. This resource sharing introduces a new interference scenario which needs to be coordinated through a new
resource allocation scheme. We investigate this problem of interference coordination and explore three different perspectives from which this problem can be viewed, namely a) interference
minimization; b) fair allocation while minimizing interference; c) Quality of Service (Qos) satisfaction while maximizing total system sum rate of the cellular network. We show that the proposed
schemes are suitable for the short LTE scheduling period of 1 ms as they are computationally less expensive. Our schemes can allocate radio resources to D2D pairs underlaying a cellular network
in a short time, ensuring fairness in allocation while minimizing interference, and increasing the total system sum rate of the network while maintaining a QoS target.
AnneKayem, <kayem@cs.queensu.ca>
Ph.D. Thesis: Adaptive Cryptographic Access Control for Dynamic Data Sharing Environments
Distributed systems, characterized by their ability to ensure the execution of multiple transactions across a myriad of applications, constitute a prime platform for building Web
applications. However, Web application interactions raise issues pertaining to security and performance that make manual security management both time-consuming and challenging. This thesis
is a testimony to the security and performance enhancements afforded by using the autonomic computing paradigm to design an adaptive cryptographic access control framework for dynamic data
sharing environments. One of the methods of enforcing cryptographic access control in these environments is to classify users into one of several groups interconnected in the form of a
partially ordered set. Each group is assigned a single cryptographic key that is used for encryption/decryption. Access to data is granted only if a user holds the ``correct'' key, or can
derive the required key from the one in their possession. This approach to access control is a good example of one that provides good security but has the drawback of reacting to changes in
group membership by replacing keys, and re-encrypting the associated data, throughout the entire hierarchy. Data re-encryption is time-consuming, so, rekeying creates delays that impede
performance. In order to support our argument in favor of adaptive security, we begin by presenting two cryptographic key management (CKM) schemes in which key updates affect only the class
concerned or those in its sub-poset. These extensions provide performance enhancements, but handling scenarios that require adaptability remain a challenge. Our framework addresses this issue
by allowing the CKM scheme to monitor the rate at which key updates occur and to adjust resource (keys and encrypted replicas) allocations to handle future changes by anticipation rather than
on demand, the CKM scheme acquires the property of adaptability and minimizes the long-term cost of key updates. Finally, since self-protecting CKM requires a lesser degree of physical
intervention by a human security administrator, we consider the case of ``collusion attacks'' and propose two algorithms to detect as well as prevent such attacks. A complexity and security
analysis show the theoretical improvements our schemes offer. Each algorithm presented is supported by a proof of concept implementation, and experimental results to show the performance
Chi Kit Lau
M.Sc. Thesis: A parallel algorithm for Toeplitz systems of linear equations
This thesis proposes a new parallel algorithm to solve general Toeplitz systems of linear equations. The Toeplitz matrix has an interesting property: the matrix entries are constant along
each diagonal of the matrix. This work has been motivated by the multi-user detection in wireless basestations project, which is supported by the CITO (Communication and Information
Technologies Ontario) center of excellence.
The algorithm is based on a linear processor array model. It is an extension of an algorithm due to Schur. It takes O(n) time, storage space, and processors. Performance of the parallel
algorithm is improved by taking advantage of two levels of parallelism. On one hand, different stages of the algorithm are pipelined to different processors. On the other hand, multiple
instructions are executed in parallel by multiple functional units within a processor. A regeneration technique is employed to restore the upper triangular matrix, which prevents the O(n^2)
storage for the entire matrix. Since the parallel model has an extensible architecture and requires only localized communication, it is ideal for implementation in VLSI technology. The new
algorithm is compared to other parallel Toeplitz solvers. It is shown that the new algorithm runs faster, saves more storage space, and can be applied to wider classes of Toeplitz systems.
Hong Li
M.Sc. Thesis: Guaussian elimination with partial pivoting on a distributed memory system
One of the main steps of multiuser detection in wireless cellular basestations is to solve a system of linear equations. This thesis describes a variant of the Gaussian elimination algorithm
for solving such a system on a set of processors arranged in a star architecture. Rows are distributed onto the processors via a host processor. A new pivoting scheme is proposed for the
algorithm. The scheme requires no global communication and avoids sequential computation for finding the pivot element. It also avoids communication costs usually required to ensure a balance
of computational load among the processors. A numerical analysis method is used to estimate the performance of the algorithm. The algorithm achieves a speedup of O(p) if the number of
peripheral processors is p. The stability of the algorithm is evaluated, demonstrating that the algorithm is as stable as Gaussian elimination with standard partial pivoting.
Xiaoshuang Lu, <lux@cs.queensu.ca>
M.Sc. Thesis: Energy-aware dynamic task allocation in mobile ad hoc networks
Dynamic task scheduling has been intensively studied over the last several years. However, since the emergence of mobile computing, there is a need to study dynamic scheduling in the
environment of mobile ad hoc networks, which contain a group of heterogeneous mobile nodes powered by batteries. For such a time-energy sensitive system, performance evaluation using only a
time metric is not enough. In this thesis, we propose a novel energy-aware dynamic task allocation (EADTA) algorithm with a goal of time-energy efficiency. When a task is to be allocated to a
processing node, the algorithm examines each candidate node to determine its processing capability, job queue length, energy level, communication delay, and energy consumption for
communication. The algorithm then assigns the task to that node that optimizes an objective function of time and energy. We develop a simulation model to evaluate the performance of the
algorithm under different scenarios. Results demonstrate that EADTA is superior to traditional algorithms in both the time and energy metrics.
Elodie Lugez, <lugez@cs.queensu.ca>
Ph.D. Thesis: Electromagnetic tracking in ultrasound-guided high dose rate prostate brachytherapy
Electromagnetic (EM) tracking assistance for ultrasound-guided high-dose-rate (HDR) prostate brachytherapy has recently been introduced in order to enable prompt and uncomplicated
reconstruction of catheter paths with respect to the prostate gland. However, EM tracking within a clinical setting is notorious for fluctuating measurement performance. In fact, measurements
are prone to errors due to field distortions caused by magnetic and conductive objects and can compromise the outcome of the procedure. Enhancing these measurements is therefore paramount.
The objective of this thesis is to enable robust and accurate reconstructions of HDR catheter paths on the ultrasound images of the prostate gland using EM tracking. To achieve this
objective, the measurement uncertainty of an electromagnetic system was first characterized in various environments; this characterization enabled us to identify optimum setup configurations
and model the measurement uncertainty. Second, we designed and implemented a specialized filtering method for catheter path reconstructions, combining the nonholonomic motion constraints
which apply to the EM sensor, with both the position and orientation measurements of the sensor. Finally, the ultrasound probe was robustly tracked with the help of a simultaneous
localization and calibration algorithm; this method allows for dynamic tracking of the ultrasound probe while simultaneously mapping and compensating for the EM field distortions.
We experimentally validated the performance of our advanced filter for catheter path reconstructions in an HDR brachytherapy suite; the EM sensor was threaded within paths of various
curvatures at several insertion speeds. The simultaneous ultrasound probe tracking and EM field distortion compensation approach was also assessed in the brachytherapy suite. The performances
of our approaches were compared to conventional error minimization methods. The advanced methods effectively increased the EM tracking accuracy of catheter paths and ultrasound probes. With
the help of our proposed approaches, EM tracking can provide effective assistance for a plurality of clinical applications.
Cameron McKay, <mckay@cs.queensu.ca>
M.Sc. Thesis: Molecular codebreaking and double encoding
DNA computing is an unconventional branch of computing that uses DNA molecules and molecular biology experiments to perform computations. This thesis evaluates the feasibility of implementing
molecular codebreaking, a DNA computing technique that uses a known-plaintext attack to recover an encryption key, and double encoding, a proposed error resistance technique that is designed
to reduce the number of false negatives that occur during DNA computation.
This thesis evaluates molecular biology experiments that make up a molecular codebreaker, a theoretical DNA computer that has never been attempted in the laboratory until now. Molecular
techniques such as ligation, gel electrophoresis, polymerase chain reaction (PCR), graduated PCR, and bead separation were carried out, reported upon and found to be feasible with certain
An implementation of the error resistance technique of double encoding, where bits are encoded twice in a DNA strand, was designed and attempted. Although the implementation was unsuccessful,
several issues associated with double encoding were identified, such as encoding adaptation problems, strand generation penalties, strand length increases, and the possibility that double
encoding may not reduce the number of false negatives.
Arezou Mohammadi, <arzmoh@yahoo.com>
Ph.D. Thesis: Scheduling algorithms for real-time systems
Real-time systems are those whose correctness depends not only on logical results of computations, but also on the time at which the results are produced. This thesis provides a formal
definition for real-time systems and includes the following original contributions on real-time scheduling algorithms.
The first topic studied in the thesis is minimizing the total penalty to be paid in scheduling a set of soft real-time tasks. The problem is NP-hard. We prove the properties of any optimal
scheduling algorithm. We also derive a number of heuristic algorithms which satisfy the properties obtained. Moreover, we obtain a tight upper bound for the optimal solution to the problem.
Numerical results that compare the upper bound with the optimal solution and the heuristic algorithms are provided.
In the second part of this thesis, we study the problem of minimizing the number of processors required for scheduling a set of periodic preemptive independent hard real-time tasks. We use a
partitioning strategy with an EDF scheduling algorithm on each processor. The problem is NP-hard. We derive lower and upper bounds for the number of processors required to satisfy the
constraints of the problem. We also compare a number of heuristic algorithms with each other and with the bounds derived in this research. Numerical results demonstrate that our lower bound
is very tight.
In the third part of the thesis, we study the problem of uplink scheduling in telecommunication systems with two dimensional resources. Our goal is to maximize the total value of the packets
sent in uplink subframe such that system constraints and requirements are satisfied. The packets have various QoS requirements and have either soft or hard deadlines. We take two approaches,
namely 0-1 and fractional approaches, to model the problem. Considering the properties of the application, we derive globally optimal solutions in polynomial time for the models. We also
present a method to fine-tune the models. Numerical results are provided to compare the performance of the various optimal algorithms each corresponding to a model.
Marius Nagy, <marius@cs.queensu.ca>
M.Sc. Thesis: Parallelism in real-time computation
Computational paradigms in which time plays a central role in defining the problem to be solved are generally called real-time paradigms. Real time is a generic term, encompassing the
multitude of aspects encountered today in the systems area as well as in theoretical studies. An algorithm that solves a problem in real time must be able to handle a stream of input data,
arriving during the computation. Usually, there is also a precise deadline that must be met when the solution is obtained. These are the main features characterizing the real-time paradigms
investigated in this thesis.
Performance of parallel and sequential models of computation are compared in various real-time environments. Evidence is provided to demonstrate the importance of parallelism in the real-time
area. The time constraints imposed by some problems allow only a parallel algorithm to successfully complete the computation. Consequently, the difference between parallel and sequential
machines is often that separating success and failure. This is the case, for example, for the pattern classifier based on the nearest neighbor rule, where in the worst case, the sequential
machine will incorrectly classify all the input samples provided, except for the first one. The pipeline computer, on the other hand, produces the correct class for every sample in the input
Even if the sequential computer manages to output a solution before the deadline, the improvement in the quality of the solution observed when a parallel model is employed, could be dramatic.
This improvement may grow arbitrarily large or it can be superlinear in the number of processors of the parallel computer. Specifically, we show that for a series-parallel graph of size n,
the accuracy ratio achieved by a PRAM with n/log n processors when computing the cardinality of a minimum covering set is, in some cases, on the order of n. Similarly, when locating the
center of a tree in real time, there are cases in which the accuracy ratio achieved by a parallel algorithm running on a PRAM with n/log n processors is bigger than p, the number of time
intervals in the real-time computation. For p greater or equal with n/log n a synergistic behavior is revealed again.
The improvement in the quality of the solution, gained by using a parallel algorithm that locates the median of a tree network of size n with demand rates changing arbitrarily is shown, in
some circumstances, to be on the order of n to the power of (x-1), where x is greater or equal to 1. For the same median problem, but in a growing tree network with equal demand rates, the
error generated by the sequential algorithm can be arbitrarily large, even exponential in the number of nodes in the network.
Well-established paradigms like data-accumulation and correcting algorithms are addressed in this thesis. The study of novel paradigms, like those introduced by reactive real-time systems, is
also initiated. The results obtained herein for all these paradigms, using different models of parallel computation, as well as the practical aspects of the problems investigated and the
increasing importance of real-time requirements in today's computations should help parallelism earn its rightful place in computer science and motivate further research.
Technical reports
Marius Nagy, <marius@cs.queensu.ca>
Ph.D. Thesis: Using quantum mechanics to enhance information processing
The weird quantum mechanical effects governing the behavior of sub-atomic particles are about to revolutionize the way we perform computation and manipulate information. This thesis is a
testimony to the indelible mark that quantum mechanics has already left on computer science. Specifically, we have investigated some of the consequences of manipulating information at the
quantum level on data security, parallel processing, universality and computability. We have devised an efficient scheme for entanglement verification with direct applicability to key
distribution protocols based on entanglement. We also showed how an approach exploiting the context of a qubit in the quantum Fourier transform can be successful in dealing with low levels of
eavesdropping, by propagating the disruption through data dependency. The importance of parallelism for quantum information processing and its consequence on universality is demonstrated
through a series of evolving computing paradigms for which only a parallel approach can guarantee a reliable solution. We also bring a necessary clarification to the much disputed problem
regarding the comparison between the computational power of a quantum machine and that of a conventional computer.
Technical reports
Naya Nagy, <nagy@cs.queensu.ca>
M.Sc. Thesis: The maximum flow problem: A real time approach
Given the large variety of its applications, the maximum flow problem has been studied ever since its definition in 1974. The problem aims to find the maximum flow that can exist between a
source and a sink in a graph. The graph is weighted with the capacities of the edges.
In this work, a dynamic version of the problem is defined and studied. The graph receives corrections to its structure or capacities and consequently the value of the maximum flow is
modified. Corrections arrive in real time. The real-time paradigm imposes time constraints (deadlines) on the input and output of the computation. Parallel and sequential solutions are
developed and a comparative analysis of these solutions is presented.
The generally accepted advantage of using parallel computers is to reduce the running time of computations. In real-time computation, a parallel solution can make the difference between
success and failure of the computation. A parallel machine of an appropriate power is able to cope with the deadlines in due time, thus rendering the computation successful, while a
sequential implementation is slower and fails to meet the deadlines. Details are given in the analysis of the algorithms designed for the sequential random access machine (RAM) and the
parallel reconfigurable multiple bus model (RMBM).
The real-time maximum flow problem is applied to the solution of a real-time process scheduling. The scheduling is an extension of Stone's static two processor allocation problem. The initial
static problem assigns processes to two processors to minimize an objective function. The real-time version described in this thesis is a natural extension given the changing characteristics
of the processes in real time. The model proposed allows processes to be created and destroyed, to change the amount of communication between them, and so on. The two processor allocation
problem is then solved taking in consideration these variations in real time. Parallel and sequential algorithms are designed and analyzed. The parallel algorithm is always able to compute
the optimal schedule, while the solution obtained sequentially is only an approximation. The improvement provided by the parallel approach over the sequential one is polynomial in the number
of processors used by the parallel computer.
Technical reports
Naya Nagy, <nagy@cs.queensu.ca>
Ph.D. Thesis: Applications of quantum cryptography
This thesis extends the applicability of quantum cryptography. First, we prove that quantum cryptography at least equals classical cryptography in an important area, namely authentication.
The quantum key distribution protocols presented here show that, contrary to previous belief, authentication can be done with quantum methods only.
In addition, we have designed quantum security systems in unconventional settings. The security of sensor networks poses specific challenges, as the sensor nodes in particular can be
physically picked up by the intruder. Our scheme protects both the integrity of the communication messages and it also protects the identity of the nodes, such that a reading intrusion of a
node is detectable.
The problem of access control in a hierarchy refers to a large number of users, organized in a hierarchy, having selective access rights to a database. Our quantum solution introduces quantum
keys to the effect that the cryptographic scheme is dynamically adaptable to changes in the user structure, and it exhibits increased security levels.
To the best of our knowledge, this thesis is the first to introduce quantum keys, that is secret keys defined by an array of qubits. We show that quantum keys make it possible for two parties
to communicate with one-time pads without having to meet in advance. Also, opposite to previous cryptographic ``common sense", the security level of a quantum cryptosystem with quantum keys
and quantum messages is maintained while being used.
Technical reports
Constantine N. K. Osiakwan, <osiakwan@bnr.ca>
Ph.D. Thesis: Parallel computation of weighted matchings in graphs
An important class of problems in theoretical computer science is that of combinatorial optimization problems. Such problems ask for the "best" configuration that satisfies some properties.
The properties addressed in this thesis concern finding optimum weight matchings in graphs.
Given a graph with n vertices and a weight on each edge, a matching is a subset of edges such that no two edges in the matching have a common vertex. The weight of a matching is the sum of
weights of the edges in the matching. An optimum weight matching is a matching that has either minimum or maximum weight, depending on the application.
Efficient methods for computing optimum weight matchings on a single processor computer exist in the literature. Developments in very large scale integrated circuits have made it possible to
devise parallel computers. In this thesis, we develop efficient algorithms for computing optimum weight matchings on a parallel computer.
All the algorithms we describe assume the EREW PRAM model of parallel computation with p (<= n) processors. An O( n/p + log n ) time parallel algorithm for computing matching trees is
proposed. The assignment problem is extended to a general assignment problem, where the edge weights could be negative, rather than only positive, and solved in O( n^3/p + n^2 log n ) time.
Another parallel algorithm with the same complexity as the latter is designed for computing maximum weight perfect matchings for complete graphs. These techniques are then extended and used
in the design of parallel algorithms for matchings on the plane. For the assignment problem on the plane, an O( n^3/p^2 + n^(2.5) log n) time parallel algorithm is given. Finally, we present
an O( n^(2.5) log^4 n/p) time parallel algorithm for computing minimum weight perfect matchings on the plane. In the later two algorithms, it is assumed that p <= n^0.5.
Technical reports
Alexandros Palioudakis, <alex@cs.queensu.ca>
Ph.D. Thesis: State complexity of nondeterministic finite automata with limited nondeterminism
In this thesis we study limited nondeterminism in nondeterministic finite automata (NFA). Various approaches of quantifying nondeterminism are considered.
We consider nondeterministic finite automata having finite tree width (ftw-NFA) where the computation on any input string has a constant number of branches. We give effective
characterizations of ftw-NFAs. We give a tight worst-case state size bound for determinizing an ftw-NFA A as a function of the tree width and the number of states of A. We introduce a lower
bound technique for ftw-NFAs.
We study the interrelationships between various measures of nondeterminism for finite automata. We present a new approach of quantifying nondeterminism, we call this measure the trace. The
trace of an NFA is defined in terms of the maximum product of the degrees of nondeterministic choices in any computation. We establish upper and lower bounds for the trace of an NFA in terms
of its tree width. We also study the growth rate of trace and we show that the unbounded trace as a function of input length of an NFA has exponential growth.
It is known that an NFA with n states and branching k can be simulated by a deterministic finite automaton with multiple initial states (MDFA) having k times n states. We give a lower bound
for the size blow-up of this conversion. We consider also upper and lower bounds for the number of states an MDFA needs to simulate a given NFA of finite tree width.
We consider unary finite automata employing limited nondeterminism. We show that for a unary regular language, a minimal ftw-NFA can always be found in Chrobak normal form. A similar property
holds with respect to other measures of nondeterminism. The latter observation is used to establish, for a given unary regular language, relationships between the sizes of minimal NFAs where
the nondeterminism is limited in various ways.
We study also the state complexity of language operations for unary NFAs with limited nondeterminism. We consider the operations of concatenation, Kleene star, and complement.We give upper
bounds for the state complexity of these language operations and lower bounds that are fairly close to the upper bounds. Our constructions rely on the fact that minimal unary NFAs with
limited nondeterminism can be found in Chrobak normal form. Finally, we show that the branching measure (J. Goldstine, C. Kintala, D. Wotschke, Inf. and Comput vol 86, 1990, 179-194) of a
unary NFA is always either bounded by a constant or has an exponential growth rate.
Technical reports
Francisco de la Parra, <parra@cs.queensu.ca>
M.Sc. Thesis: A sensor network querying framework for target tracking
Successful tracking of a mobile target with a sensor network requires effective answers to the challenges of uncertainty in the measured data, small latency in acquiring and reporting the
tracking information, and compliance with the stringent constraints imposed by the scarce resources available on each sensor node: limited available power, restricted availability of the
inter-node communication links, relatively moderate computational power.
This thesis introduces the architecture of a hierarchical, self-organizing, two-tier, mission-specific sensor network, composed of sensors and routers, to track the trajectory and velocity of
a single mobile target in a two-dimensional convex sensor field. A query-driven approach is proposed to input configuration parameters to the network, which allow sensors to self-configure
into regions, and routers into tree-like structures, with the common goal of sensing and tracking the target in an energy-aware manner, and communicating this tracking data to a base station
node incurring low-overhead responses, respectively.
The proposed algorithms to define and organize the sensor regions, establish the data routing scheme, and create the data stream representing the real-time location/velocity of a target, are
heuristic, distributed, and represent localized node collaborations. Node behaviours have been modeled using state diagrams and inter-node collaborations have been designed using
straightforward messaging schemes.
This work has attempted to establish that by using a query-driven approach to track a target, high-level knowledge can be injected to the sensor network self-organization processes and its
following operation, which allows the implementation of an energy-efficient, low-overhead tracking scheme. The resulting system, although built upon simple components and interactions, is
complex in extension, and not directly available for exact evaluation. However, it provides intuitively advantageous behaviours.
Sandy Pavel, <sandy.pavel@sympatico.ca>
Ph.D. Thesis: Computation and communication aspects of arrays with optical pipelined buses
In large-scale general-purpose parallel machines based on connection networks, efficient communication capabilities are essential in order to solve most of the problems of interest in a
timely manner. Interprocessor communication networks are often the main bottlenecks in parallel machines. One important drawback of these networks concerns the exclusive access to a
communication link which limits the communication throughput to a function of the end-to-end propagation time. Optical communications have been proposed as a solution to this problem. Unlike
electronic buses, in which the signal propagation is bidirectional, optical channels are inherently directional and have a predictable delay per unit length. This allows a pipeline of signals
to be created by the synchronized directional coupling of each signal at specific locations along the channel. The possibility in optics to pipeline the transmission of signals through a
channel provides an alternative to exclusive channel access. Using this kind of spatial parallelism the end-to end propagation latency can be amortized over the number of parallel messages
active at the same on the channel.
The model of computation proposed and investigated in this thesis consists of an array that uses reconfigurable optical buses for communication (AROB). It increases the capabilities of other
arrays with optical pipelined communication studied in the literature, through the use of more powerful switches and different reconfiguration rules. Some of the results presented in this
thesis extend the results previously obtained for the other types of arrays with optical buses, allowing a better understanding of the implications of using optical interconnections for
massively parallel processing.
The AROB is shown to be extremely flexible, as demonstrated by its ability to efficiently simulate different variants of the Parallel Random Access Machine (PRAM), bounded degree networks and
reconfigurable networks. A number of applications of the AROB are presented, and its power is analyzed. Our investigation reveals that this architecture is suitable for massively parallel
applications in different areas such as low-level image processing (Hough Transform), sparse matrix operations (multiplications, transpose), and data communications (partial permutation
routing, h-relations).
When using optics, techniques that are unique and suitable to optics must be developed. Our main objective is to identify the mechanisms specific to this type of architectures that allow us
to build efficient algorithms. Finally, lower bounds in terms of area and time are obtained for the types of electro-optical systems that use pipelined communications.
Technical reports
Ke Qiu, <kqiu@dragon.acadiau.ca>
Ph.D. Thesis: The star and pancake interconnection networks: properties and algorithms
The star and pancake interconnection networks were proposed in 1986 as attractive alternatives to the popular hypercube topology for interconnecting a number of processors in a parallel
computer. Both the star and pancake possess many properties that are desirable in an interconnection network, such as a small diameter and a small degree, and they compare favorably with the
hypercube in many other aspects. They have received much attention lately as researchers continue to explore their properties. In this thesis, we investigate the two networks from two
perspectives, namely, topologically and algorithmically.
The topological properties of the two networks are first studied. They include the path and cycle structures of the star and pancake models. These are very useful in that they are the basic
units that are later exploited to develop efficient routing schemes and other application algorithms. We also study the problems of embedding stars and pancakes into each other, and embedding
meshes and tori of certain dimensions into star graphs.
We then study the networks from the algorithms point of view. This study is divided into four parts.
Various routing schemes, the key to fast communication among the processors in an interconnection network, are first presented.
We then describe a number of data communication procedures, such as broadcasting and computing prefix sums, on the star and pancake interconnection networks. These are fundamental building
blocks that can be used in the design of larger application algorithms whose performance will directly depend on the performance of the data communication procedures.
Another problem we study is that of load balancing. The problem of load balancing on the star and pancake networks is interesting in its own right. It is important in parallel computation in
that is distributes tasks evenly to all the processors in a network, thus reducing congestion. We then use the load balancing algorithm to find an efficient selection algorithm for the two
In the last part of this study, the routing and data communication algorithms are used to develop solutions to some of the most important problems in computational geometry and graph theory.
These problems include determining the convex hull of a set of points in the plane, and building a minimum-weight spanning forest of a weighted graph.
A literature review of the state-of-the-art in relation to the star and pancake interconnection networks is also provided, as well as a list of open problems in this area.
Technical reports
Geoffrey Seaborn, <seaborn@cs.queensu.ca>
M.Sc. Thesis: Changes in autonomic tone resulting from circumferential pulmonary vein isolation
In patients with normal hearts, increased vagal tone can be associated with the onset of paroxysmal atrial fibrillation (AF). Vagal denervation of the atria renders AF less-easily inducible.
Catheter ablation involving circumferential pulmonary vein ablation (CPVA) and isolation (CPVI) is effective for treating paroxysmal AF, and has been shown to impact heart rate variability
(HRV) indices, in turn reflecting vagal denervation. I examined the impact of CPVI on HRV indices over time, and evaluated the relationship between vagal denervation and rate of recurrence of
AF post-procedure.
High-resolution 10-minute ECG recordings were collected from 64 patients (49 male, 15 female, mean age 57.1±9.7) undergoing CPVI for paroxysmal (n=46) or persistent (n=18) AF. Recordings were
made pre-procedure, and at intervals up to 12 months. Recordings from healthy volunteers were used as control data. Anti-arrhythmic medication was suspended 5 half-lives prior to the
procedure, and was resumed post-procedure for 3 months. A successful procedure was defined as one with no subsequent recurrence of atrial arrhythmia (AA), such as atrial tachycardia (AT),
atrial flutter (AFL), or AF. HRV analysis was performed for all recordings in accordance with guidelines for standardization.
After CPVI, 27 patients presented recurrence. In patients with a subsequent successful procedure (group A), pre-procedure HRV indices did not differ from control patients (group C). However,
patients who exhibited recurrence (group B) demonstrated significantly-reduced pre-procedure HRV compared both group C, and with patients from group A (30.8±14.0 & 33.1±20.1 vs 21.9±11.1 in
RMSSD, P=0.04). Following the CPVI procedure, HRV was reduced with respect to pre-procedure levels in patients with successful procedures (33.1±20.1 vs 23.7±19.4, P=0.04), and did not differ
from patients with unsuccessful procedures over 12 months of follow-up recordings. The post-procedure HRV of both groups was reduced compared to control values. Additionally, there was no
significant difference in HRV between patients who experienced recurring AF (n=9), and those who experienced AT or AFL (n=18). Our data suggests that patients experiencing recurrence after
one procedure have reduced pre-procedure HRV that is not changed by CPVI; whereas patients with a successful single procedure experience a change in HRV indices that is sustained over a long
period, but is no different, post-procedure, from patients experiencing recurrence. These data suggest that the denervation associated with the CPVI procedure may only benefit patients with
normal vagal tone prior to the procedure, and that sustained denervation is not a critical factor in successful outcome. Further prospective studies appear warranted to target patients with
normal vagal tone.
Geoffrey Seaborn, <seaborn@cs.queensu.ca>
Ph.D. Thesis: Clinical decision support algorithm for predicition of postoperative atrial fibrillation following coronary artery bypass grafting
Introduction: Postoperative atrial fibrillation (POAF) is exhibited by 20-40% of patients following coronary artery bypass grafting (CABG). POAF is associated with increased long-term
morbidity and mortality, as well as additional healthcare costs. I aimed to find techniques for predicting which patients are likely to develop POAF, and therefore who may benefit from
prophylactic measures.
Methods: Informed consent was obtained prospectively from patients attending for elective CABG. Patients were placed in the POAF group if atrial fibrillation (AF) was sustained for at least
30 seconds prior to discharge, and were placed in the `no AF' (NOAF) group otherwise. I evaluated the performance of classifiers including binary logistic regression (BLR), k-nearest
neighbors (k-NN), support vector machine (SVM), artificial neural network (ANN), decision tree, and a committee of classifiers in leave-one-out cross validation. Accuracy was calculated in
terms of sensitivity (Se), specificity (Sp), positive predictive value (PPV), negative predictive value (NPV), and C-statistic.
Results: Consent was obtained from 200 patients. I excluded 21 patients due to postoperative administration of amiodarone, 5 due to perioperative AF ablation, and 1 due to both. Exclusions
were also made for 8 patients with a history of AF and 2 patients with cardiac implantable electronic devices (CIED). POAF was exhibited by 54 (34%) of patients. Factors significantly
associated (P<0.05) with POAF were longer postoperative hospital stay, advanced age, larger left atrial (LA) volume, presence of valvular disease, and lower white blood cell count (WCC).
Using BLR for dimensionality reduction, I created a feature vector consisting of age, presence of congestive heart failure (CHF) (P=0.06), valvular disease, WCC, and aortic valve replacement
(AVR). I performed leave-one-out cross validation. In unlabeled testing data, I obtained Se=70%, Sp=56%, PPV=89%, NPV=26%, and C=58% using a committee (BLR, k-NN, and ANN).
Conclusion: My results suggest that prediction of patients likely to develop POAF is possible using established machine learning techniques, thus allowing targeting of appropriate
contemporary preventative techniques in a population at risk for POAF. Studies appear warranted to discover new predictive indices that may be added to this algorithm during continued
enrolment and validation.
Amber Simpson, <simpson@cs.queensu.ca>
M.Sc. Thesis: On solving systems of linear equations in real time
The purpose of this thesis is to investigate the feasibility of applying the real-time paradigm to the problem of solving a system of linear equations. Unlike the conventional paradigm, the
real-time paradigm is an environment characterized by the constant arrival of data and the existence of deadlines. The problem is stated as follows: Given a solution x_0 of the system of
equations A_0 x = b, with one or more of the entries of A_0 changing to produce the system A_1, is it possible to use x_0 to obtain a solution x_1 without recomputing x_1? We conjecture that
this is not possible in general. This means that each time an update is received during the computation of the solution of a system of linear equations, the solution must be recomputed from
scratch to accurately reflect the change (in the worst case). The only evidence to support this claim is an Omega(n) lower bound on such computations. A more convincing lower bound is
required to prove our conjecture though one is not offered in this thesis. We demonstrate that while we believe it is impossible to use a previously computed solution to produce a new
solution, it is possible to relax our real-time restrictions to produce a parallel solution that further improves upon the sequential solution by processing newly arriving data and producing
more solutions in the same time frame.
Emese Somogyvari, <somogyva@cs.queensu.ca>
M.Sc. Thesis: Quantitative structure-activity relationship modeling to predict drug-drug interactions between acetaminophen and ingredients in energy drinks
The evaluation of drug-drug interactions (DDI) is a crucial step in pharmaceutical drug discovery and design. Unfortunately, if adverse eects are to occur between the co-administration of two
or more drugs, they are often dicult to test for. Tradi- tional methods rely on in vitro studies as a basis for further in vivo assessment which can be a slow and costly process that may not
detect all interactions. Here is pre- sented a quantitative structure-activity relationship (QSAR) modeling approach that may be used to screen drugs early in development and bring new,
benecial drugs to market more quickly and at a lesser cost. A data set of 6532 drugs was obtained from DrugBank for which 292 QSAR descriptors were calculated. The multi-label support vector
machines (SVM) method was used for classication and the K-means method was used to cluster the data. The model was validated in vitro by exposing Hepa1-6 cells to select compounds found in
energy drinks and assessing cell death. Model accuracy was found to be 99%, predicting 50% of known interactions despite being biased to predicting non-interacting drug pairs. Cluster
analysis revealed in- teresting information, although current progress shows that more data is needed to better analyse results, and tools that bring various drug information together would
be benecial. Non-transfected Hepa1-6 cells exposed to acetaminophen, pyridoxine, creatine, L-carnitine, taurine and caeine did not reveal any signicant drug-drug interactions, nor were they
predicted by the model.
Emese Somogyvari, <somogyva@cs.queensu.ca>
Ph.D. Thesis: Exploring epigenetic drug discovery using computational approaches
The misregulation of epigenetic mechanisms has been linked to disease. Current drugs that treat these dysfunctions have had some success, however many have variable potency, instability in
vivo and lack target specicity. This may be due to the limited knowledge on epigenetic mechanisms, especially at the molecular level, and their association with gene expression and its link
to disease. Computational approaches, specically in molecular modeling, have begun to address these issues by complementing phases of drug discovery and development, however more research is
needed on the relationship between genetic mutation and epigenetics and their roles in disease. Gene regulatory network models have been used to better understand diseases, however inferring
these networks poses several challenges. To address some of these issues, a multi-label classication technique to infer regulatory networks (MInR), supplemented by semi-supervised, learning
is presented. MInR's performance was found to be comparable to other methods that infer regulatory networks when when evaluated on a benchmark E.coli dataset. In order to better understand
the association of epigenetics with gene expression and its link with disease, MInR was used to infer a regulatory network from a Kidney Renal Clear Cell Carcinoma (KIRC) dataset and was
supplemented with gene expression and methylation analysis. Gene expression and methylation analysis revealed a correlation between 5 dierentially methylated CpGs and their matched
dierentially expressed transcripts. Incorporating this information into network analysis allowed for the identication of potential targets that may be used in the discovery of novel
Ian Stewart, <ian@cs.queensu.ca>
M.Sc. Thesis: A modified genetic algorithm and switch-based neural network model applied to misuse-based intrusion detection
As our reliance on the Internet continues to grow, the need for secure, reliable networks also increases. Using a modied genetic algorithm and a switch-based neural network model, this thesis
outlines the creation of a powerful intrusion detection system (IDS) capable of detecting network attacks.
The new genetic algorithm is tested against traditional and other modied ge- netic algorithms using common benchmark functions, and is found to produce better results in less time, and with
less human interaction. The IDS is tested using the standard benchmark data collection for intrusion detection: the DARPA 98 KDD99 set. Results are found to be comparable to those achieved
using ant colony optimiza- tion, and superior to those obtained with support vector machines and other genetic algorithms.
Sylvia Siu-Kei Tai, <tai@cs.queensu.ca>
M.Sc. Thesis: Relaying traffic with energy-delay constraints in wireless sensor networks
Energy is often considered the primary resource constraint in a wireless sensor network. Compared to sensing and data processing, data communication typically incurs the highest energy
consumption. In this thesis, we study the problem of finding an optimal strategy for relaying traffic in a heterogeneous wireless sensor network such that the total energy spent on
communication is minimized. The sought relaying strategy disallows traffic splitting, so data must be sent on a single path from the source to the destination. We consider the problem
with respect to two types of network traffic, one with delay constraints - the Constrained Unsplittable Flow Allocation Problem (CUFA), and one without - the Unconstrained Unsplittable
Flow Allocation Problem (UUFA). We present an integer linear programming formulation of problems UUFA and CUFA, and an alternate formulation based on an integer optimization technique
known as 'branch-and-price' that can be used to solve relatively larger-sized problem instances to optimality, although both problems are NP-complete. The models and algorithms for
solving problems UUFA and CUFA provide optimal solutions that can be used to study the impact on network resources of the best possible relaying strategy. Previous work in the literature
has shown that relaying schemes which allow traffic to be split and relayed on multiple paths from the source to the destination can have several advantages, such as better load
balancing. On the other hand, relaying schemes which relay data on a single path also have their advantages, for example, being less complex in design and having less overhead traffic.
Based on the proposed models, an empirical study is performed to quantify the comparative performance gains and losses of relaying splittable and unsplittable traffic in a wireless sensor
network when i) traffic is delay constrained and ii) traffic is not delay constrained. The results can provide insights into the effects of splitting traffic on the energy consumption and
delay performance of wireless sensor networks.
Peter Taillon, <taillon@turing.scs.carleton.ca>
M.Sc. Thesis: The hypermesh multiprocessor network: architectural properties and algorithms
This thesis examines a recently proposed multiprocessor architecture called the hypermesh. A hypermesh can be modeled as a hypergraph with N = d^n nodes arranged in n-dimensional space
such that along each dimension i, 0 <= i < n, there are d interconnected nodes. The high processor connectivity surpasses that of any of the enhanced mesh networks and rivals that of the
popular hypercube network. With advances in optical communication technology this new network is now of great practical interest.
The thesis proposes new algorithms for the hypermesh showing that the high-interprocessor connectivity leads to asymptotically better algorithms. The computational problems selected are
characterized by non-local communication patterns: broadcasting, prefix and semigroup computations, multiple searching and ranking, array compaction, matrix transpose, and dense and
sparse matrix multiplication. The algorithms developed for these problems have complexities that compare favorably with equivalent solutions for the EREW PRAM and hypercube network.
Many researchers have studied the problem of routing in an optical network while limiting the number of wavelengths available for interprocessor communication. A practical variation of
the hypermesh model is introduced that allows for efficient computation under the constraint of limited wavelength availability. Given a 2-dimensional hypermesh with N nodes, we consider
the scenario where the number of wavelengths to which a transmitter/receiver can tune is some fixed integer b, where b << N^1/2. An efficient semigroup algorithm is introduced for this
enhanced hypermesh, whose complexity compares favorably with those developed for two recently proposed mesh models that use separable row and column buses.
Hung Tam, <tam@cs.queensu.ca>
Ph.D. Thesis: Resource Management in Multi-hop Cellular Networks
In recent years, aided with the advancements in cellular technology, mobile communications have become affordable and popular. High cellular capacity in terms of number of users and
data-rates is still in need. As the available frequency spectrums for mobile communications are limited, the utilization of the radio resources to achieve high capacity without imposing
high equipment cost is of utmost importance. Recently, multi-hop cellular networks (MCNs) were introduced. These networks have the potential of enhancing the cell capacity and extending
the cell coverage at low extra cost. However, in a cellular network, the cell or system capacity is inversely related to the cell size (the communication range of the base station). In
MCNs, the cell size, the network density and topology affect the coverage of source nodes and the total demands that can be served and, thus, the radio resource utilization and system
throughput. Although the cell size is an important factor, it has not been exploited. Another major issue in MCNs is the increase in packet delay because multi-hopping is involved. High
packet delay affects quality of service provisioning in these networks.
In this thesis, we propose the Optimal Cell Size (OCS) and the Optimal Channel Assignment (OCA) schemes to address the cell size and packet delay issues for a time division duplex (TDD)
wideband code division multiple access (W-CDMA) MCN. OCS finds the optimal cell sizes to provide an optimal balance of cell capacity and coverage to maximize the system throughput,
whereas OCA assigns channels optimally in order to minimize packet relaying delay. Like many optimized schemes, OCS and OCA are computationally expensive and may not be suitable for large
real-time problems. Hence, we also propose heuristics for solving the cell size and channel assignment problems. For the cell size problem, we propose two heuristics: Smallest Cell Size
First (SCSF) and Highest Throughput Cell Size First (HTCSF). For the channel assignment problem, we propose the Minimum Slot Waiting First (MSWF) heuristic. Simulation results show that
OCS achieves high throughput compared to that of conventional (single-hop) cellular networks and OCA achieves low packet delay in MCNs. Results also show that the heuristics, SCSF, HTCSF
and MSWF, provide good approximation solutions compared to the optimal ones provided by OCS and OCA, respectively.
Sami Torbey, <torbey@cs.queensu.ca>
M.Sc. Thesis: Towards a framework for intuitive programming of cellular automata
The ability to obtain complex global behaviour from simple local rules makes cellular automata an interesting platform for massively parallel computation. However, manually designing a
cellular automaton to perform a given computation can be extremely tedious, and automated design techniques such as genetic programming have their limitations because of the absence of
human intuition. In this thesis, we propose elements of a framework whose goal is to make the manual synthesis of cellular automata rules exhibiting desired global characteristics more
programmer-friendly, while maintaining the simplicity of local processing elements. We also demonstrate the power of that framework by using it to provide intuitive yet effective
solutions to the two-dimensional majority classification problem, the convex hull of disconnected points problem, and various problems pertaining to node placement in wireless sensor
Sami Torbey, <torbey@cs.queensu.ca>
Ph.D. Thesis: Beneath the surface electrocardiogram: computer algorithms for the non-invasive assessment of cardiac electrophysiology
The surface electrocardiogram (ECG) is a periodic signal portraying the electrical activity of the heart from the torso. The past fty years have witnessed a proliferation of computer
algorithms destined for ECG analysis. Signal averaging is a noise reduction technique believed to enable the surface ECG to act as a non-invasive surrogate for cardiac electrophysiology.
The P wave and the QRS complex of the ECG respectively depict atrial and ventricular depolarization. QRS detection is a pre-requisite to P wave and QRS averaging. A novel algorithm for
robust QRS detection in mice achieves a fourfold reduction in false detections compared to leading commercial software, while its human version boasts an error rate of just 0.29% on a
public database containing ECGs with varying morphologies and degrees of noise.
A fully automated P wave and QRS averaging and onset/oet detection algorithm is also proposed. This approach is shown to predict atrial brillation, a common cardiac arrhythmia which could
cause stroke or heart failure, from normal asymptomatic ECGs, with 93% sensitivity and 100% specicity. Automated signal averaging also proves to be slightly more reproducible in
consecutive recordings than manual signal averaging performed by expert users.
Several studies postulated that high-frequency energy content in the signalaveraged QRS may be a marker of sudden cardiac death. Traditional frequency spectrum analysis techniques have
failed to consistently validate this hypothesis.
Layered Symbolic Decomposition (LSD), a novel algorithmic time-scale analysis approach requiring no basis function assumptions, is presented. LSD proves more reproducible than
state-of-the-art algorithms, and capable of predicting sudden cardiac death in the general population from the surface ECG with 97% sensitivity and 96% specificity.
A link between atrial refractory period and high-frequency energy content of the signal-averaged P wave is also considered, but neither LSD nor other algorithms nd a meaningful
LSD is not ECG-specic and may be ective in countless other signals with no known single basis function, such as other bio-potentials, geophysical signals, and socio-economic trends.
Tanya Wolff, <twolff@ca.ibm.com>
M.Sc. Thesis: Cayley networks: group, graph theoretic and algorithmic properties
This thesis explores the Cayley class of the interconnection model of parallel machines. A description of the general properties of the Cayley class, and a brief description of each of
several types of Cayley networks are given. The representation of a group as a network of directed segments, where the vertices correspond to elements and the segments to multiplication
by group generators and their inverses, was invented by Arthur Cayley, a nineteenth century mathematician. Such a network or graph is often called a Cayley diagram. We survey algorithms
for routing, broadcasting, cycle decomposition, and embedding. Then we categorize these networks by group, and state for which types of Cayley graphs Hamilton Cycles are known to exist.
Where possible algorithms for Hamilton Cycles are given. Sorting algorithms for the star are closely analyzed and two new algorithms are presented. One has the same running time as the
fastest known algorithm as yet (O(n^3 log n)), and is elegant in its simplicity. The other is an adaptation of an algorithm for the multidimensional mesh and has a running time of O(n^2).
Technical reports
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Three problems about dynamic convex hulls
We present three results related to dynamic convex hulls: A fully dynamic data structure for maintaining a set of n points in the plane so that we can find the edges of the convex hull intersecting a
query line, with expected query and amortized update time O(log^1+ε n) for an arbitrarily small constant ε > 0. This improves the previous bound of O(log^3/2 n). A fully dynamic data structure for
maintaining a set of n points in the plane to support halfplane range reporting queries in O(log n + k) time with O(polylog n) expected amortized update time. A similar result holds for 3-dimensional
orthogonal range reporting. For 3- dimensional halfspace range reporting, the query time increases to O(log^2 n/ log log n + k). A semi-online dynamic data structure for maintaining a set of n line
segments in the plane, so that we can decide whether a query line segment lies completely above the lower envelope, with query time O(log n) and amortized update time O(n^ε). As a corollary, we can
solve the following problem in O(n^1+ε) time: given a triangulated terrain in 3-d of size n, identify all faces that are partially visible from a fixed viewpoint.
Original language English (US)
Title of host publication Proceedings of the 27th Annual Symposium on Computational Geometry, SCG'11
Pages 27-36
Number of pages 10
State Published - 2011
Externally published Yes
Event 27th Annual ACM Symposium on Computational Geometry, SCG'11 - Paris, France
Duration: Jun 13 2011 → Jun 15 2011
Publication series
Name Proceedings of the Annual Symposium on Computational Geometry
Other 27th Annual ACM Symposium on Computational Geometry, SCG'11
Country/Territory France
City Paris
Period 6/13/11 → 6/15/11
• Convex hull
• Dynamic data structures
• Halfspace range searching
• Lower envelopes
• Orthogonal range searching
ASJC Scopus subject areas
• Theoretical Computer Science
• Geometry and Topology
• Computational Mathematics
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Numerical modeling of CO-emissions for gas turbine combustors operating at part-load conditions
Extending the operational window is one of the main challenges in gas turbine development as operational flexibility is a key attribute to meet the requirements of tomorrow. Load decrease is limited
by a sharp rise in CO-emissions caused by critically low flame temperature. The objective of this work is a CFD-based model, which is able to predict CO in combustion systems operating at part-load
conditions. The model supports the development of combustion systems fulfilling future emissions legislations.
Standard combustion models typically face issues predicting CO-emissions in gas turbine combustors. For example, the popular Flamelet Generated Manifold (FGM) model is based on the assumption, that a
turbulent flame brush can be described by a set of laminar flamelets. A flamelet is a thin reaction zone dividing unburnt and burnt material. In flamelets, the late CO-oxidation is strongly increased
due to the availability of a stable pool of radicals. In contradiction to the flamelet assumption, part-load combustion in gas turbines shows superequilibrium CO in the exhaust gas far behind the
heat release zone. It is obvious that the source terms responsible for the burn out of CO cannot be described by flamelets.
Nevertheless, the prediction of CO using FGM can be found in Goldin et al. (2012). Here, the authors used a combination of FGM and a turbulent flame speed model to close the reaction progress source
term. The author concludes that FGM drastically overestimates the source terms of CO-oxidation.
Another approach can be found in Wegner et al. (2011). Here, CO is described by its own transport equation. Within the turbulent flame brush, CO is set to the maximum value of CO at a predefined
reaction progress state. The peak value of CO is determined by flamelet calculations. The source term describing the CO-burnout is closed by detailed chemistry.
On the basis of literature review, industrial requirements and fundamental studies, we identified the following key elements for our approach:
• Turbulence: Due to the technical relevance of this work, we focus on efficient models in order to ensure applicability for industrial applications. Hence, we decided to build the model on the
basis of Reynolds-averaged Navier-Stokes (RANS) equations. Note that the presented modeling strategy is not limited to RANS.
• Combustion: Simulation of combustors operating at part-load conditions requires advanced strategies in combustion modeling. As the prediction of CO strongly depends on a precise heat release
distribution, the FGM Extension model is used (published by the authors in Klarmann et al. (2016)). The advantage of this model is that it is validated on flames which can be characterized by low
reactivity. Here, it is inevitable to consider flame stretch and heat loss as it may substantially alter shape and position of the turbulent flame brush. Note that the implementation is able to
consider partially premixed combustion. This is of great significance as CO is sensitive to dilution by secondary air.
• CO-Model: As already discussed, separating time scales of combustion and late burnout is necessary. As basic studies revealed, the impact of flame stretch and heat loss to CO cannot be neglected.
Flame stretch substantially lowers the peak value of CO within the turbulent flame brush. Furthermore, heat loss cannot be neglected as it may substantially decreases the CO-oxidation which is
calculated using the temperature dependent Arrhenius law.
Numerical model for CO-emissions
The Favre-averaged transport equation for a generic variable ϕ~ reads:
The terms on the left-hand side (transient term and transport terms) are closed in the context of RANS when considering the generally employed gradient diffusion approach. The Reynolds-Averaged
source term on the right-hand side remains unclosed.
This work is using two different approaches to (1) model the combustion by modifying the reaction progress source term closure of FGM (ϕ~=c~) and (2) modeling CO (ϕ~=Y~CO). Both models are introduced
in the following two sections.
Combustion model: FGM extension
This section is a short summary of the model published by the authors in Klarmann et al. (2016). It is based on the FGM model initially published by van Oijen and de Goey (2002). In the context of
FGM, the transport equation for the reaction progress c~ is closed by the PDF-integrated source term obtained from one-dimensional flamelet calculations:
Here, turbulence is considered by integrating the product of the reaction progress source term and the probability density function P. For the evaluation of P presumed beta-functions are used. This
requires additional transport equations for the variance of every control variable (c and f). The model extension modifies the reaction progress source term closure of FGM by a correction factor Γ.
The PDF-integrated source term then reads:
Here, Γ is formulated on the basis of flame speeds:
The underlying modeling idea is to divide the unstretched, adiabatic source term ω˙c0¯ by its corresponding flame speed sc0 and to multiply the flame speed at the evaluated flame stretch and heat
loss sc∗. It can be shown that this is valid if the following relation was used to determine m:
More details on the determination of m can be found in Klarmann et al. (2016).
Mass fraction of CO is represented by its own transport equation. Wegner et al. (2011) initially proposed the idea to separate the time scales of CO-burnout from the combustion process. This idea is
adopted in this work as we divide the domain in three regions: (1) preflame (inert), (2) inflame and (3) postflame as shown in the upper half of Figure 1. The employed assumption is that CO decouples
from the combustion model under specific conditions. This leads to a burnout region behind the turbulent flame brush. Hence, the closure consists of two parts in which CO is treated differently (the
preflame region does not require any modeling). Classification in inflame or postflame region is performed by estimating the limiting factor, which can be either turbulence (inflame) or the chemical
finite rate of the oxidation of CO (postflame). This is based on the assumption that the inflame situation is dominated by the time scales of turbulent mixing (as chemistry is fast) and the burnout
region is dominated by chemical time scales. The lower part of Figure 1 shows the CO-modeling strategy. CO is described to a certain point using FGM. After a decoupling event, CO is described by a
burnout model providing substantially lower source terms due to the absence of radicals. All submodels are described in the following sections.
Inflame model for CO
Within the turbulent flame brush, CO-chemistry is fast and interaction with turbulence cannot be neglected. Hence, we tabulate CO on the basis of PDF-integrated profiles of flamelets. CO cannot be
accurately represented by flamelets without considering flame stretch and heat loss. Stretch alters diffusion of heat and species which strongly impacts CO. For example, a constant pressure reactor,
fully neglecting diffusion, shows significantly higher CO compared to corresponding freely propagating flamelets. Adding the influence of flame stretch using premixed counter flow flamelets steepens
the gradients of species and temperature and increases the effect of diffusion. The impact of stretch to CO is illustrated in Figure 2. Note that the impact of heat loss on CO profiles is lower than
the impact of flame stretch. Adding stretch and heat loss as additional dimensions to the tabulation process would significantly increase the numerical effort. Therefore, an alternative is presented
to model the influence of flame stretch and heat loss. The approach is similar to the correction factor used in the FGM Extension. The tabulation of CO on the basis of unstretched adiabatic flamelets
As the proportionality between flame speed and heat loss differs from the proportionality between flame speed and stretch, we introduce two correction factors to consider both effects independently:
This is analytically correct if the following relations are valid:
Direct modeling of these relations is complex. Therefore, we introduce the assumption that the analytical relation is similar to the proportionality between flame speed and the peak value of CO
before PDF-integration:
Finally, the proportionality exponents read:
The proportionality exponents are the gradient of a functional correlation between log(YCO,max) and log(sc). Figure 3 shows the linear character of both relations. Consequently, both exponents are
constant for varying heat loss and flame stretch and can be determined using a curve fit optimization assuming a linear equation. Note that the gradient for stretch correction is much steeper than
for heat loss correction. This indicates that CO is impacted more by flame speed reduction based on flame stretch than on flame speed reduction based on heat loss.
Postflame model for CO
CO-oxidation in the late burnout (i.e. in the postflame zone) can be described using a single reaction equation:
The proposed CO-model is based on the idea that behind the turbulent flame brush H and OH radicals are in equilibrium. This assumption is based on the fact that the chemical timescales of all
radicals are orders of magnitude smaller than these of the CO-burnout. Hence, the postflame source term of CO is calculated using the equilibrium of OH:
Figure 4 shows the experimental source term for two operating conditions of different adiabatic flame temperatures. Note that the source terms are based on the spatial gradient of CO which can be
derived from measurements. The experimental setup can be find the following section. Furthermore, the corresponding source terms calculated by the introduced postflame model is plotted. Downstream of
the 199mm measurement position, the postflame model prediction and the experiments are in good agreement. Furthermore, Figure 4 shows the CO source terms of a freely propagating flamelet and a
constant pressure reactor at the corresponding reaction progress (derived from experimentally measured CO[2] and CO). As already discussed, they clearly overestimate burnout rates of CO.
Modeling the transition
The Transition model is based on an estimation of the turbulent Damköhler number for CO, which compares turbulent with chemical time scales:
We use the following expression which is the time needed to oxidize CO close to equilibrium:
Multiple definitions for turbulent timescales exist. We decide to use a timescale characterizing eddies of the integral length scale (Poinsot and Veynante, 2005):
This quantity is often used in terms of limiting combustion (e.g. in the Eddy-Break-up hypotheses of Spalding (1971)) as it characterizes the timescale of turbulent mixing.
The decoupling event takes place if DaCO falls below a critical value:
We experienced that this decoupling criterion is robust as there exists a transitional range where the burnout rate of CO for both inflame and postflame model are very close to each other. DaCO,crit
should be chosen around unity as this marks the transition point when chemical timescales start exceeding turbulent timescales.
Experimental setup
Experiments are conducted in an atmospheric single burner test rig with a thermal power of 50kW. Details of the burner can be found in Sangl (2011). The setup is depicted in Figure 5. An electrical
preheater is providing air at a temperature of 300 °C. Within the burner plenum, air is divided into primary air, which is swirled by the burner, and secondary air. The secondary air is bypassing the
burner as it flows through a perforated plate into the combustion chamber. Fuel is injected at the burner slots.
Within the combustion chamber, swirling fuel-air mixture generates a vortex breakdown, where the flame stabilizes at the stagnation point. The outer part of the turbulent flame brush is diluted by
secondary air, providing a region of strongly decreased reactivity, leading to elevated CO-emissions. Ceramic insulation prevents significant heat losses, which leads to similar conditions as present
in gas turbine combustors. Furthermore, the chamber is cooled by impinging air. Local measurements are conducted using a water-cooled probe, which can be traversed in radial direction. Furthermore,
the probe can be attached to multiple ports, which are located at several downstream positions. This enables the measurement of a two-dimensional grid. Note that due to the fact that the combustion
chamber is cylindrical, we can assume rotational symmetry. This is advantageous as a two-dimensional grid measurement is sufficient to derive a volumetric distribution. We checked this assumption by
comparing multiple CO-profiles over radius of same axial positions. A gas analyzer is used to determine mole fractions of CO[2], O[2], NO[x], CO from the extracted gas samples. In order to evaluate
heat loss precisely, temperature is monitored at the outer shell of the insulation using thermocouples. Measurements are conducted at five different adiabatic flame temperatures:
• #1-3: Superequilibrium CO.
• #4: Transition of incomplete burnout and equilibrium.
• #5: CO is in equilibrium.
Figure 6 depicts CO as a function of adiabatic flame temperature. Note, CO is measured at a characteristic residence time of about 20ms.
All introduced models are implemented in Fluent (Ansys, 2014) using a C-based interface. Tables are used to provide the required model input during runtime. All table entries are quantities derived
from equilibrium calculations as well as premixed counter flow flamelets at predefined stretch rates, enthalpy defects, and mixture fractions. The preprocessing of the tabulated data is performed
using a Python-based routine on the basis of the chemical kinetic software Cantera (Goodwin et al., 2015). Around 5,000 flamelet calculations have been used to generate the table. Table 2 lists some
information of the CFD setup. Geometry is shown in Figure 7 and boundary conditions are listed in Table 1. The domain is a quarter of the original geometry using periodical boundary conditions. Note
that the precise evaluation of wall heat loss is crucial to predict CO-burnout due to its temperature sensitivity. The non-adiabatic boundary condition is evaluated using temperature profiles
measured at the outer shell of the insulation. We decided to use transient (URANS) simulations as we experienced unsteadiness using steady-state simulations. All results shown in the following are
time averaged from the transient results.
Table 2.
Table Generation
Chemical mechanism GRI 30 (Smith et al. 2014)
Points of mixture fractions 50
Points of enthalpy defects 20
Points of strain rates <15
Prop. exp. reaction progress m 1.5
Prop. exp. CO stretch n 2.0
Prop. exp. CO heat loss o 0.37
Software Fluent v15.0 (ANSYS Inc. 2014)
Mesh (chamber only) polyhedral, 2.4e5 cells
Sc[t] 0.7
DaCO,crit 1.0
Periodicity Quarter
Turbulence closure k-ϵ realiz. (URANS)
Pressure-velocity coupling simple
Upwind order second order
Figure 8 illustrates experimental and numerical contour plots of CO of operating point #4. The heat release distribution (indicated by XCO2,dry) from the original implementation of FGM in Fluent (1)
and the FGM Extension (2) show large differences in terms of position and shape of the turbulent flame brush. Comparing both contour plots (1 & 2) with the experimental data (3) leads to the
conclusion that flame stretch and heat loss cannot be neglected. (4) shows the PDF-integrated value of XCO,dry without any scaling by the introduced correction factors (Eq. 6). It clearly shows the
overestimation when heat loss and stretch is not considered as the peak value in the turbulent flame brush is around three times higher than indicated by the experimental data (6). Contour plot (5)
presents the solution using the introduced CO-model. Good agreement with the experimental data (6) in terms of maximum value of CO is evident. Furthermore, a burnout region develops behind the
turbulent flame brush as it can be seen in the experimental data.
For the purpose of quantitative validation, it is reasonable to compare surface-averaged quantities as a probe position with high radius represents more surface than a position with low radius.
Hence, we accumulate the product of CO and its corresponding ring face and divide the product by the total surface:
Figure 9 compares averaged CO values of experiments and simulations at three different axial position: x={199mm,224.5mm,250mm}. The corresponding residence times are estimated from CFD streamline
analysis: τres≈{18ms,22ms,26ms}. It can be seen that the original implementation of FGM strongly underestimates CO. With decreasing adiabatic flame temperature, CO increases slightly as the heat
release distribution is shifted more downstream in the vicinity of the wall. Using the FGM Extension and the CO-model leads to good agreement with the experimental data. The numerically predicted CO
fits experiments best for the shortest residence time of 18ms. For higher residence times, the discrepancy between measurements and modeled CO increases, especially for the leanest operating point.
Here, unburnt hydrocarbons may play an important role. Note that they cannot be accurately captured by our modeling approach as the assumption of complete heat release within the turbulent flame
brush is used.
Summary, conclusions, and outlook
The paper presents an approach to predict CO-emissions numerically. The necessity of modeling CO on the basis of combustion models is discussed. Previous approaches and fundamental studies revealed
that timescale separation between fast combustion and slow CO burnout is necessary. Hence, the proposed model is divided in an inflame and a postflame part. As we showed, inflame-CO cannot be
described by tabulating freely propagating flamelets as flame stretch plays a major role. A model for the stretch and heat loss dependent correction of CO is presented. Furthermore, the source terms
describing the late CO burnout behind the heat release zone is modeled by a single elementary reaction equation. Here, we introduced the model assumption that OH is in equilibrium after it decouples
from the turbulent flame brush. This assumption was verified by comparing source terms derived from experiments with source terms calculated by the proposed postflame model.
All models are implemented in a commercial CFD-software and validated against experimental data. The numerically predicted CO agrees well with experimental data for different axial probe positions.
Furthermore, we showed the strong underestimation of CO if FGM is used without any further modeling. This underlines the necessity of dedicated CO models to predict elevated CO-emissions.
Validation of high-pressure multi-burner configurations is planned in the future: In part-load operation, only a part of the burners are supplied with fuel. This leads to the situation that hot
burners interact with cold air from the inactivated neighbouring burners.
Turbulent Dammköhler number, -
Turbulent kinetic energy, m^2/s^2
Proportionality exponent for progress source term correction, -
Proportionality exponent for stretch correction, -
Proportionality exponent for non-adiabatic correction, -
Probability density function, -
Turbulent Schmidt Number, -
Fuel consumption speed, m/s
Mole fraction of species i, -
Mass fraction of species i, - | {"url":"https://journal.gpps.global/Numerical-modeling-of-CO-emissions-for-gas-turbine-combustors-operating-at-part-load,90866,0,2.html","timestamp":"2024-11-09T20:13:34Z","content_type":"application/xhtml+xml","content_length":"140257","record_id":"<urn:uuid:05f4fec1-73ed-401a-8452-6953ef516769>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00014.warc.gz"} |
The e^x joke
If you don’t get it never mind, but trust me, its funny.
The cocky exponential function e^x is strolling along the road insulting the functions he sees walking by. He scoffs at a wandering polynomial for the shortness of its Taylor series. He snickers at a
passing smooth function of compact support and its glaring lack of a convergent power series about many of its points. He positively laughs as he passes |x| for being nondifferentiable at the origin.
He smiles, thinking to himself, “Damn, it’s great to be e^x. I’m real analytic everywhere. I’m my own derivative. I blow up faster than anybody and shrink faster too. All the other functions suck.”
Lost in his own egomania, he collides with the constant function 3, who is running in terror in the opposite direction.
“What’s wrong with you? Why don’t you look where you’re going?” demands e^x. He then sees the fear in 3’s eyes and says “You look terrified!”
“I am!” says the panicky 3. “There’s a differential operator just around the corner. If he differentiates me, I’ll be reduced to nothing! I’ve got to get away!” With that, 3 continues to dash off.
“Stupid constant,” thinks e^x. “I’ve got nothing to fear from a differential operator. He can keep differentiating me as long as he wants, and I’ll still be there.”
So he scouts off to find the operator and gloat in his smooth glory. He rounds the corner and defiantly introduces himself to the operator. “Hi. I’m e^x.”
“Hi. I’m d / dy.” | {"url":"http://www.bottledcity.com/the-ex-joke/","timestamp":"2024-11-05T13:15:45Z","content_type":"text/html","content_length":"29942","record_id":"<urn:uuid:f88ad587-e214-43d1-8657-521593fdd787>","cc-path":"CC-MAIN-2024-46/segments/1730477027881.88/warc/CC-MAIN-20241105114407-20241105144407-00441.warc.gz"} |
Statically checked physical dimensions, using Type Families and Data Kinds.
Version on this page: 1.0.1.3
LTS Haskell 22.39: 1.5
Stackage Nightly 2024-11-02: 1.6.1
Latest on Hackage: 1.6.1
This version can be pinned in stack with:dimensional-1.0.1.3@sha256:f847a62cf258f28f78bd92be4afe1527a196e789fe46ff9a4913228e2d7b85fd,3878
Module documentation for 1.0.1.3
This library provides statically-checked dimensional arithmetic for physical quantities, using the 7 SI base dimensions.
Data kinds and closed type families provide a flexible, safe, and discoverable implementation that leads to largely self-documenting client code.
Simply importing Numeric.Units.Dimensional.Prelude provides access to dimensional arithmetic opertors, SI units and other common units accepted for use with the SI, and convenient aliases for
quantities with commonly used dimensions.
The Unit d a type represents a unit with dimension d, whose conversion factor to the coherent SI base unit of the corresponding dimension is represented by a value of type a. a is commonly chosen to
be Double, but can be any Floating type. Where possible, support is also provided for Fractional or Num values.
Similarly, the Quantity d a type represents a quantity with dimension d, whose numeric value is of type a. Aliases allow the use of, e.g., Length Double to mean Quantity DLength Double. A complete
list of available aliases is given in the haddock documentation for the Numeric.Units.Dimensional.Quantities.
In the example below, we will solve a simple word problem.
A car travels at 60 kilometers per hour for one mile, at 50 kph for one mile, at 40 kph for one mile, and at 30 kph for one mile. How many minutes does the journey take? What is the average speed of
the car? How many seconds does the journey take, rounded up to the next whole second?
{-# LANGUAGE NoImplicitPrelude #-}
module ReadmeExample where
import Numeric.Units.Dimensional.Prelude
import Numeric.Units.Dimensional.NonSI (mile)
leg :: Length Double
leg = 1 *~ mile -- *~ combines a raw number and a unit to form a quantity
speeds :: [Velocity Double]
speeds = [60, 50, 40, 30] *~~ (kilo meter / hour)
-- *~~ does the same thing for a whole Functor at once
-- Parentheses are required around unit expressions that are comingled with *~, /~, *~~, or /~~ operations
timeOfJourney :: Time Double
timeOfJourney = sum $ fmap (leg /) speeds
-- We can use dimensional versions of ordinary functions like / and sum to combine quantities
averageSpeed :: Velocity Double
averageSpeed = _4 * leg / timeOfJourney
-- _4 is an alias for the dimensionless number 4
wholeSeconds :: Integer
wholeSeconds = ceiling $ timeOfJourney /~ second
-- /~ lets us recover a raw number from a quantity and a unit in which it should be expressed
main :: IO ()
main = do
putStrLn $ "Length of journey is: " ++ showIn minute timeOfJourney
putStrLn $ "Average speed is: " ++ showIn (mile / hour) averageSpeed
putStrLn $ "If we don't want to be explicit about units, the show instance uses the SI basis: " ++ show averageSpeed
putStrLn $ "The journey requires " ++ show wholeSeconds ++ " seconds, rounded up to the nearest second."
For project information (issues, updates, wiki, examples) see: https://github.com/bjornbm/dimensional
1.0.1.3 (2016-09)
• Fixed an issue with applying metric prefixes to units with non-rational conversion factors.
1.0.1.2 (2016-05)
• Support for GHC 8.0.1-rc4, avoiding GHC Trac issue 12026.
• Added support for stack.
1.0.1.1 (2015-11)
• Improved example in readme.
1.0.1.0 (2015-11)
• Added Numeric.Units.Dimensional.Coercion module.
• Bumped exact-pi dependency to < 0.5.
• Restored changelog.
• Addressed issues with documentation.
1.0.0.0 (2015-11)
• Changed to DataKinds and ClosedTypeFamilies encoding of dimensions.
• Added names and exact values to Units.
• Added AnyUnit and AnyQuantity for quantities whose dimension is statically unknown.
• Added Storable and Unbox instances for Quantity.
• Added dimensionally-polymorphic siUnit for the coherent SI base unit of any dimension.
• Added some additional units.
0.13.0.2 (2015-04)
• Corrected definition of lumen.
0.13.0.1 (2014-09)
• Bumped time dependency to < 1.6.
0.13 (2014-02)
• Bump major version (should have been done in previous version).
0.12.3 (2014-02)
• Bump numtype dependency to 1.1 (GHC 7.8.1 compatibility fix).
• Added Torque.
• Added D.. for the type synonym quantities (e.g., Angle).
0.12.2 (2013-11)
• Added FirstMassMoment, MomentOfInertia, AngularMomentum.
• Improved unit numerics.
0.12.1 (2013-07)
0.12 (2013-06)
• Polymorphic _0 (closes issue 39).
• Added astronomicalUnit.
• Added imperial volume units.
• Added ‘mil’ (=inch/1000).
• Added tau.
• Added KinematicViscosity.
0.10.1.2 (2011-09)
• Bumped time dependency to < 1.5.
0.10.1.2 (2011-08)
• Bumped time dependency to < 1.4.
0.10.1 (2011-08)
GHC 7.2.1 compatibility fix:
• Increased CGS context-stack to 30.
0.10 (2011-05)
See the announcement.
0.9 (2011-04)
See the announcement. | {"url":"https://www.stackage.org/lts-9.21/package/dimensional-1.0.1.3","timestamp":"2024-11-02T07:56:47Z","content_type":"text/html","content_length":"22803","record_id":"<urn:uuid:18be2675-e17e-4b5f-bddb-5e5ae0637e08>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00660.warc.gz"} |
Cell Arrays and Their Contents
I've written
several blog articles
so far on
, and not quite so much on their soulmates,
cell arrays
. Just last week, at the annual MathWorks Aerospace Defense Conference (MADC), I had several people ask for help on cell arrays and indexing. Couple that with the weekly questions on the
MATLAB newsgroup
, and it's time.
As you probably already know, arrays in MATLAB are rectangular looking in any two dimensions. For example, for each row in a matrix (2-dimensional), there is the same number of elements - all rows
have the same number of columns. To denote missing values in floating point arrays, we often use
. And each MATLAB array is homogeneous; that is, each array element is the same kind of entity, for example, double precision values.
Cell Arrays
Cell arrays were introduced in MATLAB 5.0 to allow us to collect arrays of different sizes and types. Cell arrays themselves must still be rectangular in any given two dimensions, and since each
element is a cell, the array is filled with items that are all the same type. However, the contents of each cell can be any MATLAB array, including
• numeric arrays, the ones that people typically first learn
• strings
• structures
• cell arrays
Indexing Using Parentheses
Indexing using parentheses means the same thing for all MATLAB arrays. Let's take a look at a numeric array first and then a cell array.
M = magic(3)
M =
Let's place a single element into another array.
s = M(1,2)
s =
Next let's get a row of elements.
row3 = M(3,:)
row3 =
And now grab the corner elements.
corners = M([1 end],[1 end])
corners =
What's in the MATLAB workspace?
clear % clean up before we move forward
Name Size Bytes Class
M 3x3 72 double array
corners 2x2 32 double array
row3 1x3 24 double array
s 1x1 8 double array
Grand total is 17 elements using 136 bytes
Next, let's do similar experiments with a cell array.
C = {magic(3) 17 'fred'; ...
'AliceBettyCarolDianeEllen' 'yp' 42; ...
{1} 2 3}
C =
[3x3 double] [17] 'fred'
[1x25 char ] 'yp' [ 42]
{1x1 cell } [ 2] [ 3]
Notice the information we get from printing
. We can see it is 3x3, and we can see information, but not necessary full content, about the values in each cell. The very first cell contains a 3x3 array of doubles, the second element in the first
row contains the scalar value 17, and the third cell in the first row contains a string, one that is short enough to print out. Let's place a single element into another array.
sCell = C(1,2)
sCell =
Next let's get a row of elements.
row3Cell = C(3,:)
row3Cell =
{1x1 cell} [2] [3]
And now grab the corner elements.
cornersCell = C([1 end],[1 end])
cornersCell =
[3x3 double] 'fred'
{1x1 cell } [ 3]
What's in our workspace now?
clear sCell row3Cell cornersCell
Name Size Bytes Class
C 3x3 774 cell array
cornersCell 2x2 396 cell array
row3Cell 1x3 264 cell array
sCell 1x1 68 cell array
Grand total is 84 elements using 1502 bytes
An Observation about Indexing with Parentheses
When we index into an array using parentheses,
, to extract a portion of an array, we get an array of the same type. With the double precision array
, we got double precision arrays of different sizes and shapes as our output. When we do the same thing with our cell array
, we get cell arrays of various shapes and sizes for the output.
Contents of Cell Arrays
Cell arrays are quite useful in a variety of applications. We use them in MATLAB for collecting strings of different lengths. They are good for collecting even numeric arrays of different sizes,
e.g., the magic squares from order 3 to 10. But we still need to get information from within given cells, not just create more cell arrays using
. To do so, we use curly braces
. I used one set of them to create
initially. Now let's extract the contents from some cells and assign the output to an array. Let's place a single element into another array.
m = C{1}
m =
Next let's try to get a row of elements.
row3 = C{3,:}
lerr = lasterror;
Illegal right hand side in assignment. Too many elements.
Why couldn't I do that? Let's look at what's in row 1.
ans =
[3x3 double] [17] 'fred'
Now let's see what we get if we look at the contents without assigned the output to a variable.
ans =
ans =
ans =
You can see that we assign to
three times, one for each element in the row of the cell array. It's as if we wrote this expression:
with the output from these arrays being successively assigned to
. MATLAB can't typically take the content from these cells and place them into a single array. We could extract the contents of row 1, one cell at a time as we did to create
. If we want to extract more cells at once, we have to place the contents of each cell into its own separate array, like this,
[c11 c12 c13] = C{1,:}
c11 =
c12 =
c13 =
taking advantage of syntax new in MATLAB Release 14 for assignment when using comma-separated lists.
Cell Array Indexing Summary
• Use curly braces {} for setting or getting the contents of cell arrays.
• Use parentheses () for indexing into a cell array to collect a subset of cells together in another cell array.
Here's my mnemonic for remembering when to use the curly braces: curly for contents Does anyone have any mnemonics or other special ways to help remember when to use the different kinds of indexing?
If so, please post a comment below.
Published with MATLAB® 7.2
To leave a comment, please click here to sign in to your MathWorks Account or create a new one. | {"url":"https://blogs.mathworks.com/loren/2006/06/21/cell-arrays-and-their-contents/?from=en","timestamp":"2024-11-14T01:15:39Z","content_type":"text/html","content_length":"175656","record_id":"<urn:uuid:4b0ed443-0e21-4fa4-835b-82558ecbff45>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00809.warc.gz"} |
Tangents and Secants - Fundamentals of Geometry
In the study of circles, two of the most fundamental concepts are tangents and secants. These lines have unique properties and relationships with the circle that are both interesting and useful in
solving geometric problems. This lesson will delve into the definitions, properties, and theorems related to tangents and secants of a circle.
Tangents to a Circle
A tangent to a circle is a straight line that touches the circle at exactly one point. This point is known as the point of tangency. The tangent line is perpendicular to the radius of the circle at
the point of tangency.
Properties of Tangents
1. Perpendicular to Radius: If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. If $OT$ is a radius and $PT$ is a tangent at point $T$, then $OT
\perp PT$.
2. Tangents from a Point Outside a Circle: Two tangents can be drawn from a point outside a circle to the circle. These tangents are equal in length. If $P$ is a point outside a circle, and $PA$ and
$PB$ are tangents to the circle, then $PA = PB$.
3. Angle between Tangent and Chord: The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. If $PT$ is a tangent and $AB$ is a chord such
that $T$ is the point of contact, then $\angle PTB = \angle A$.
Secants of a Circle
A secant is a line that intersects a circle at two points. It can be thought of as an extension of a chord, which is a line segment with both endpoints on the circle.
Properties of Secants
1. Secant-Secant Theorem: When two secants, $PA$ and $PB$, intersect at a point $P$ outside the circle, the product of the lengths of one secant segment and its external segment equals the product
of the lengths of the other secant segment and its external segment. Mathematically, $PA \cdot PB = PC \cdot PD$.
2. Secant-Tangent Theorem: When a secant and a tangent intersect at a point outside the circle, the product of the lengths of the secant segment and its external segment equals the square of the
length of the tangent segment. If $PT$ is a tangent and $PA$ is a secant, then $PA \cdot PB = PT^2$.
3. Angle Formed by Secants: The angle formed by two intersecting secants outside the circle is half the difference of the measures of the arcs intercepted by the angles. If $\angle APB$ is formed by
secants $PA$ and $PB$, then $\angle APB = \frac{1}{2}(\text{measure of arc }AB - \text{measure of arc }CD)$.
Applications and Theorems
1. Tangent-Secant Power Theorem: This theorem combines the properties of tangents and secants to state that the power of a point with respect to a circle is the same for any combination of tangents
and secants emanating from that point. This is a generalization of the secant-secant and secant-tangent theorems.
2. Tangent Lines to Circles from a Point: Given a point outside a circle, there are exactly two lines that can be drawn from the point that are tangent to the circle. This property is useful in
constructing tangents and solving geometric problems.
3. Inscribed Angle Theorem: While not exclusive to tangents and secants, this theorem is often used in conjunction with them. It states that the measure of an inscribed angle is half the measure of
its intercepted arc. This theorem is useful in solving problems involving angles formed by tangents and secants.
Understanding the properties and theorems related to tangents and secants is crucial in the study of circles. These concepts not only provide a foundation for solving geometric problems involving
circles but also offer insights into the relationships between different geometric elements. Mastery of tangents and secants opens the door to exploring more complex geometric constructions and | {"url":"https://app.studyraid.com/en/read/2595/52682/tangents-and-secants","timestamp":"2024-11-03T15:18:34Z","content_type":"text/html","content_length":"150884","record_id":"<urn:uuid:e41e9fb0-5f35-4ff2-b30e-1defbc63621e>","cc-path":"CC-MAIN-2024-46/segments/1730477027779.22/warc/CC-MAIN-20241103145859-20241103175859-00443.warc.gz"} |
Making waves
20 mar 2024
A team including Oleksandr Gamayun has made the first mechanical metamaterial that transmits topological solitons in just one direction.
Sometimes waves roam alone, rather than in packs. Tsunamis, for example, can travel thousands of miles before making landfall. The meteorological phenomena known as Morning Glory clouds, only
observed regularly over Australia’s Gulf of Carpentaria, are sometimes referred to as “the biggest waves on the planet”. Solitary waves of this kind, which move through media without changing their
shape, are known as “topological solitons”.
Solitons were first described in detail by the Scottish shipbuilder John Scott Russell in 1834. He was experimenting with canal boat designs on the Union Canal, when he noticed an unusually robust
wave rolling down the canal, and followed it on horseback for a couple of miles. Today topological solitons are being explored for possible applications in soft robotics, superconductivity, and
quantum computing. String theorists have even speculated that gravitational solitons would bend light into rings and so look very much like black holes from a distance.
Now researchers at the University of Amsterdam and the London Institute for Mathematical Sciences have made the first mechanical metamaterial that reliably transmits topological solitons in just one
direction, a key property for avoiding interference in communication applications, for example. They were also able to precisely predict and control the behaviour of these waves using a mathematical
model of the material. The research is published in Nature today.
“Physicists have long been fascinated by the properties of topological solitons. It’s incredible for me to see these abstract entities in a real material,” says Oleksandr Gamayun, an Arnold Fellow at
the London Institute. Gamayun led the work to provide a theoretical description of topological solitons propagating through a sine-Gordon medium, an idealised version of a real material.
His collaborators created the material using a chain of 50 motorised magnetic rotors, linked by elastic bands, and subject to an external magnetic field. Gamayun explains that the new material is
able to sustain the solitons because of the subtle interplay between the external magnetic forces, which make the dynamics of the system complex and non-linear, and the material’s “non-reciprocity”,
which is its violation of Newton’s third law (for every action there is an equal and opposite reaction). This non-reciprocity forces waves to propagate along the chain in only one direction, like a
line of toppling dominoes. And the metamaterial’s design, aligned with Gamayun’s theory, means the waves neither grow nor die out but roll down the length of the material—much as Russell observed
almost a hundred years ago.
Dr Gamayun’s Arnold Fellowship is one of five generously funded by leading algorithmic trading company, XTX Markets. They were created in 2022 and named after the Ukrainian-born mathematician
Vladimir Arnold. | {"url":"https://lims.ac.uk/perspectives/making-waves/","timestamp":"2024-11-03T22:38:56Z","content_type":"text/html","content_length":"57336","record_id":"<urn:uuid:01d5b1fe-521d-4571-a70e-69a245e0c0bc>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00071.warc.gz"} |
Can SAS handle imbalanced datasets in Multivariate Analysis? | Hire Someone To Take My SAS Assignment
Can SAS handle imbalanced datasets in Multivariate Analysis? Sas’ big and unbalanced dataset of 15 million observations, presented at the Human Impact Summit in Las Vegas as published by the Project
IEDA. However SAS aims to address this challenge by using “misbalanced” multivariate data with random effects, which is most commonly used in multivariate analysis systems. The paper was interesting
in its critique because it did not explicitly say that SAS assumed random effects to be present, the assumption being that random effects describe the distribution of both observations and factors,
rather than themselves. However SAS already covers these aspects as a possible feature in Model-agnostic analyses. However, the paper is interesting because it is one step further on the way SAS
provides multivariate analysis tools. In fact we developed a new SAS tool called “Multirad” which provides “multivariate” as a new dataset for SAS, that works by comparing two sources of misnomer,
namely some two-party outliers and a “hypothet”, i.e. “hypompartic”, “hypmorphic” and some, not one but few. Now in our data study we have a subset of two party outliers of the same class, where
“hypmorphic” states if they are a single event or a “hypothetical” and has a normal distribution, i.e. they are not related at all. This distribution is a subset of “hypo“. However SAS offers this
feature for the purpose of generating “hypo”-listings with one party. Unfortunately it does not work just for our analysis, where “hypo” and “hypot” are neither the event/hyponym, nor are the events/
hyponym and “hyponym” in SAS means the event, which has a Gaussian find out here now for its probability of being related. The paper suggests to use SAS for this purpose a dataset of two model
records, so that the data are combined by AIC, but, as noted above, SAS is not a multivariate analysis suite. Nevertheless, it is worth considering in the future whether SAS can be used in particular
scenarios. In this case, we are introducing several models (e.g. a binary set of models) that can be used to represent a group of persons as “hypothetical” or “hypompartic.” SAS uses data from some
of the 3,000 personal observations by “neurophysiology”, but SAS provides a much more realistic representation of the data in which potential interactions between individuals in the group are
observed, and more detailed information about people’s physical or psychiatric diseases is provided by SAS.
Take My Online Exams Review
The paper is a good example of a multivariate approach for identifying and summarizing pairs of individual a priori risks. The best practice for this kind of work is that SAS can actually be applied
properly visit this website dealing with situations where pairs of interest are measured together, and provide more intuitive and real-world results RADIO-LA DEPARTMENT : Hi all! To “muss” a complex
dataset like SAS is important. It is relatively easy to figure out how the value of your data “mathematically” represents the data. When you look at these simple examples, RADIO applies SAS to them,
and adds models for individuals in r3s dataset. However the main challenges of interpretation of the model data are: They are not perfect, of course, and shouldn’t be viewed in isolation. In my
opinion, a SAS/multivariate approach is more compelling than a similar, multivariate approach to identify and estimate values of data. In the last five (sixty) years, using SAS/multivariate analysis
tools, we have noticed that many researchers don’t understand the importance of having too many variables called “minimiser”. (SAS is the obvious example.) You do remember that several studies have
suggested model-agnostic analyses, “sap” of each data point and “interactions” model, as a means of deriving proper answer values. One solution involves the use of new SAS models with additional
information such as interaction and nonmonotone variables (e.g. person-group relationships) that are more relevant to the estimation of data. Another way of organizing the data is using “non-SAS”
framework as described in this article. There are also many more frameworks like Multiscale Regression and Time series Analysis which already have some of their features from SAS. As is known, a
Multiscale Regression analysis allows to analyze the data much more efficiently than a Non-SAS by adding more variables inCan SAS handle imbalanced datasets in Multivariate Analysis? Anamasa Rao In a
few years, the number of small samples have made my mind up, but now this has become so convenient that it seems I need to do the hard work. This paper took a classic piece of work on low learning
rates and I had done a few years back, but this one was in the very early and soon it was coming. In my early years I made it a program too, to automate the data handling and to analyze the impact of
things like: models, observations, or both. Part of the problem was that the way we compute the metrics is to make sure that everything was close to being perfect. But could these metrics be fine –
I’d be surprised if they were fine with all of this, let alone their class, performance, or performance error (see the papers below for a rough outline of the method). This paper has not done much of
work on metrics – just one of the hard days ahead of us.
Who Can I Pay To Do My Homework
The main thing is that some of the work done on our own could be very cool and could help others but I would not want to touch this paper on its face. To the best of my knowledge, these are not a big
of work – but you should use it. First, it is very specific to an individual dataset. The methods we developed are very much related to and integrated using some of the examples on this project.
While the methods we have used will not be generic to every data set, they suit and bring certain things into a discussion around that data. Their success is based on their ability to capture and
monitor the same things – from a piece check that metadata to a piece of data itself – in a method. It is obvious that some metrics are not possible without a very complex data management system. But
perhaps that is just too much. For instance, a simple example I have seen is that I often have lots of very simple data in one of our datasets. One big way to speed up some of the time scales I have
worked on them in the past is to look like a few of our why not try these out publications. This approach is based on those small sample sizes, which we have used in many ways throughout the research
process. In the second example I have seen, I have used the sample size to analyze a piece of the dataset. The method try this used is a very simple instance of analysis, again using a simple
example. This time we don’t have any way to show the data directly on the Figure; it should be data. However, it is really very simple in that we get really big datasets of data without any analysis,
or insights as we would like. The last thing we need to do is to deal with a small set of data and datasets. Despite this I have to admit it is a bit slow and my mind just isn’t set yet to make any
real progress. Can SAS handle imbalanced datasets inMultivariate Analysis?Can SAS handle imbalanced datasets in Multivariate Analysis? This article is part of LIF Journal, a partnership between the
International Society for Clinical and Experimental Biomedical Image Computing (SAS BI), SAS International, and SAS International. SAS International writes articles about popular or existing
datasets, their potential improvements, and what you may need to make your work more readable to the community and to reduce maintenance costs. SAS Bi presents a selection of many datasets available
for multivariate analysis, including data in many formats.
Pay To Get Homework Done
They are read by any SAS user; SAS can be downloaded from the SAS distribution center. What is Multivariate Analysis? Multivariate Analysis This is a term that covers a variety of different
statistical techniques that are required to perform multivariate statistical analysis. Particular examples are multivariate normal, multivariate scatterplot regression, multivariate scatterplot
regression distribution estimation, multivariate scatterplot regression, and multivariate regression estimation. Overview Multivariate data analysis is an important activity in the current SAS®
Multivariate Analysis Standards (MIS) (sic) section of the SAS® Database (DAS). This article provides an overview of techniques for multicollinearity, and of how SAS provides output to multivariate
algorithms. Multivariate Normal: An Approach to Multivariate Statistical Analysis through a Data Coding Model Multivariate normal is the current formal generalization of this class, and it deals with
the large set of data that was originally defined by the SAS® Multivariate Analysis Standards (SMASS). This article provides an overview of possible ways to model the data in which multivariate data
analysis is applied. The author writes in SAS to name the (generally) most important approach to modelling multivariate normal, using SAS’s multivariate statistics. The definition of multivariate
normal involves the addition of prior knowledge of data with other, unknown, relationships to the data. For example, different models are possible within different families of multivariate data, but
they are all very different. Although common terminology is used for classes of models, what can usually be understood is a broad concept called vector-based approach. In this approach, it is not
assumed that the class of data is independent. By this common terminology we have, rather than specification of the classes, any reference to models which are all also, or even a group of models,
which share similar notions to the category. Instead, the concept needs to be built around a common distribution of prior knowledge. This article is an overview of multivariate normal and
multivariate scatterplot regression models. The two types of models used are the SOP (standard polynomial) and the PRE (factor valued instead of regression with spline) models. This article is part
of LIF Journal, a partnership between the International Society for Clinical and Experimental Biomedical Image Computing (SAS BI), SAS International, and SAS International. SAS International writes
articles about popular or existing datasets, their potential improvements, and what you may need to make your work more readable to the community and to reduce maintenance costs. SAS Bi presents a
selection of many datasets available for multivariate analysis, including data in many formats. What is Multivariate Analysis? Multivariate normal is the current formal generalization of this class,
and it deals with the large set of data that was originally defined by the SAS® Multivariate Analysis Standards (SMASS).
Search For Me Online
This article provides an overview of possible ways to model the data in which multivariate data analysis is used. The author writes in SAS to name the (generally) most important approach to modelling
multivariate normal, using SAS’s multivariate statistics. The definition of multivariate normal involves the addition of prior knowledge of data with other, unknown, relationships to the data. For
example, different models are possible within different families of multivariate data, but they are all very different. Although common terminology is used for classes of models, what can usually be | {"url":"https://sashelponline.com/can-sas-handle-imbalanced-datasets-in-multivariate-analysis","timestamp":"2024-11-05T10:17:30Z","content_type":"text/html","content_length":"132443","record_id":"<urn:uuid:6a3ce4c8-546d-49c2-9452-f30c0fe45df3>","cc-path":"CC-MAIN-2024-46/segments/1730477027878.78/warc/CC-MAIN-20241105083140-20241105113140-00624.warc.gz"} |
Quantum-enhanced Markov chain Monte Carlo – H. Paul Keeler
Quantum-enhanced Markov chain Monte Carlo
The not-so-mathematical journal Nature recently published a paper proposing a new Markov chain Monte Carlo method:
• 2023 – Layden, Mazzola, Mishmash, Motta, Wocjan, Kim, and Sheldon – Quantum-enhanced Markov chain Monte Carlo.
Appearing earlier as this preprint, the paper’s publication in such a journal is a rare event indeed. This post notes this, as well as the fact that we can already simulate perfectly^1For small
instances of the model, we can do this directly. For large instances, we can use coupling from the past proposed by Propp and Wilson. the paper’s test model, the Ising or Potts model.^2Wilhelm Lenz
asked his PhD student Ernst Ising to study the one-dimensional version of the model. Renfrey Potts studied the generalization and presented it in his PhD. But this is a quantum algorithm, which is
exciting and explains how it can end up in that journal.
The algorithm
The paper’s proposed algorithm adds a quantum mechanical edge or enhancement to the classic Metropolis-Hastings algorithm.^3More accurately, it should be called the
Metropolis-Rosenbluth-Rosenbluth-Teller-Teller-Hastings algorithm. As I covered in a recent post, the original algorithm uses a Markov chain defined on some mathematical space. Running it on a
traditional or classical computer, at each time step, the algorithm consists of proposing a random jump and then accepting the proposed jump or not. Owing to the magic of Markov chains, in the long
run, the algorithm simulates a desired probability distribution.
The new quantum version of the algorithm uses a quantum computer to propose the jump, while still using a classical computer to accept the proposal or not.^4In my Metropolis-Hastings post, the
classical jumper process, a discrete-time Markov chain, is replaced with a quantum mechanical variant. The quantum jump proposals are driven by a time-independent Hamiltonian, which is a central
object in quantum and, in fact, all physics. This leads to a Boltzmann (or Gibbs) probability distribution for the jumping process.
Then, running the quantum part on a quantum computer, the algorithm will hopefully outperform its classical counterpart. The paper nurtures this hope by giving empirical evidence of the algorithm’s
convergence speed. The researchers performed the numerical experiments on a 27-qubit quantum processor at IBM using the platform Qiskit.
Quantum is so hot right now
In recent years researchers have been focusing on such algorithms that exploit the strangeness and spookiness of quantum mechanics. You will see more and more quantum versions of algorithms that
appear in statistics, machine learning, and related fields, as suggested by this survey paper, which also appeared in Nature.
Quantum lite
Sometimes quantum mechanics only loosely inspires algorithms and models. In this setting, some of my machine learning work uses determinantal point processes. This kernel-based random model draws
direct inspiration from the wave function, a standard object in quantum mechanics. Under suitable simplifying conditions, the model describes the locations of particles known as fermions such as
electrons and protons. Still, it’s fascinating that a quantum physics model inspired an interesting random object that has found applications in spatial statistics and machine learning.
(Visited 259 times, 1 visits today) | {"url":"https://hpaulkeeler.com/quantum-enhanced-markov-chain-monte-carlo/","timestamp":"2024-11-02T03:14:11Z","content_type":"text/html","content_length":"66530","record_id":"<urn:uuid:e7742c0d-050f-4fe7-a8e0-2dd95ccdc19c>","cc-path":"CC-MAIN-2024-46/segments/1730477027632.4/warc/CC-MAIN-20241102010035-20241102040035-00434.warc.gz"} |
Fat Albert • Nicholas Pilkington
I was watching the Fleet Week display by the Blue Angels yesterday and we were talking about if you could determine where an aircraft was based on the sounds you were hearing from the engine.
Say we have an aircraft at some unknown position flying at a constant linear velocity. If the engine is emitting sound at a constant frequency and as soon as we start hearing the engine we start
recording the sound. Then given just that audio let’s try and determine how far away the aircraft is and how fast it’s traveling. Here’s a generated sample recording of a source starting 315.914
meters away and traveling at 214 meters per second in an unknown direction.
First let’s make a simplification. We can rotate our frame of reference such that the aircraft is traveling along the x-axis from some unknown starting point. If we look from above the situation
looks like this.
When working with audio the first thing to do would probably be to plot the spectrogram and see if we can gleam anything from that. The spectrogram of a WAV file can be plotted using this code:
Fs, audio = scipy.io.wavfile.read('audio.wav')
MAX_FREQUENCY = 2000
pylab.specgram(audio, NFFT = 1024, Fs=Fs, cmap=pylab.cm.gist_heat)
pylab.xlabel('Time (s)')
pylab.ylabel('Frequency (Hz)')
and the result spectrogram which shows the power spectrum of the received signal as a function of time looks like this.
This looks great. Most importantly you can see the Doppler Effect in action because the sound waves are compressing in the direction of the observer. This implies that the aircraft is moving towards
us. Other than that there isn’t much that can be gained here. We can look at the inflection point of the spectrogram and infer that this is the point where the aircraft is passing perpendicular to us
which corresponds to the actual frequency that the engine is emitting which in this case looks like about 500 Hertz. However we can’t assume that the aircraft will pass us so we probably can’t even
take that.
Let’s try something different. Let’s analyze this in the time domain instead. When the aircraft starts emitting sounds at some real time t that sound takes a while before it arrives at the observer.
This delay depends on the distance from the observer and the speed of sound. When this first bit of audio arrives at the observer which is t=0 but in “receiver time” the aircraft has already been
flying for a while. So this first piece of audio corresponds to a previous location. We don’t know what this delay is because we don’t know how far away the plane way. Since the frequency of the
sounds we are receiving are changing because of the Doppler Effect we can’t really rely on frequency analysis either. Let’s instead zoom in and look at the zero-crossings of the signal.
The zero-crossing are the points in time that the signal (regardless of frequency) cross the x-axis. In “real time” there will be a number of times when this happens and they will be constantly
spaced by 1/(f*2.0) where f is the frequency of the sounds emitted by the engine. However when we receive the signal and the aircraft is traveling towards us - it will be squashed, and have shorter
time between zero-crossings and then further apart as the aircraft flies away. So the signal get’s concertinas in a specific way. Here’s an exaggerated diagram of what is being emitted and what is
being received when:
Let’s say the plane is traveling with a speed of v parallel to the x-axis. So its x-coordinates at time t is x0 + v * t (some unknown starting point) and its y-coordinate is R (some unknown
distance). Here t is the real time when the signal is emitted. The time for this signal to reach us is:
import numpy as np
def reach_time(x0, v, t, R):
c = 340.29 # speed of sound
dt = np.sqrt((x0 + v*t)**2 + R**2)/c
return dt
The time stamp in received time is just just reach_time(x0, v, t, R) + t - t0 where t0 is the initial and unknown delay for the first signal to reach us. From this we can get the timestamp of the nth
zero-crossing knowing that the source frequency is fixed.
import numpy as np
def nth_zero_crossing(n, x0, v, R, f, n0):
c = 340.29 # speed of sound
f2 = 2.0*f
return (np.sqrt((x0 + v*n/f2)**2 + R**2)/c + (n - n0)/f2)
So we’ve got a model that maps the time of a zero-crossing at the source to the time of a zero-crossing in our WAV file. This is a mapping of zero-crossings in the source to zero-crossing in the
received signal. Which are the orange lines in this image:
Now we need to extract the zero-crossings from the WAV file so we can compare. We could use some more advanced interpolation but since there are 44100 samples per second in the audio file the impact
on the resulting error term should be small. Here’s some code to extract the time of each zero-crossing in an audio file.
import scipy
import numpy as np
Fs, audio = scipy.io.wavfile.read(fn)
audio = np.array(song, dtype='float64')
# normalize
audio = (audio - audio.mean()) / audio.std()
prev = song[0]
ztimes = [ 0 ]
for j in xrange(2, song.shape[0]):
if (song[j] * prev <= 0 and prev != 0):
cross = float(j) / Fs
prev = song[j]
This gives us a generative model where we can select some parameters of the situation and using the nth_zero_crossing compute what the received signal would look like. This puts us in a good position
to create an error function between the actual (empirical) data in the audio file and the generated data based on our parameters. Then we can try and find the parameters that minimize this error.
Here some code that computes the residue of our generates signal:
import numpy as np
def gen_received_signal(args):
f2, v, x0, R, n0 = args
n = np.arange(len(ztimes))
y = (np.sqrt((x0 + v*n/f2)**2 + R**2)/c + (n - n0)/f2)
error = np.array(ztimes) - y
return error
Using a non-linear least squares solver like Levenberg Marquardt we can search for the parameters that best explain our data.
import numpy as np
from scipy.optimize import least_squares
f2 = 1600
v = 100
x0 = -100
R = 10
n0 = 100
args = [f2, v, x0, R, n0]
res = least_squares(gen_received_signal, args)
f2, v, x0, R, n0 = res.x
# compute the initial distance
D = np.sqrt(x0**2+R**2)
print 'Solution distance=', D, 'x0=',x0, 'v=',v, 'f=',f2/2.0
Out of this pops the solution and more. It has also accurately computed the source frequency given some bad initial guesses. Since we aren’t assuming anything about the change in frequency this
approach also works when the aircraft does not pass us and is only recorded on approach or flying away from us. In reality the sound would attenuate quadratically over distance but that should not
impact this solution because we don’t use amplitudes. | {"url":"https://nickp.svbtle.com/blue-angel","timestamp":"2024-11-13T14:34:57Z","content_type":"text/html","content_length":"19815","record_id":"<urn:uuid:4a44f0be-1554-4b02-bb7a-941348b9f8c2>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00031.warc.gz"} |
The Floyd-Warshall Algorithm for Shortest Paths
The Floyd-Warshall algorithm [Flo62, Roy59, War62] is a classic dynamic programming algorithm to compute the length of all shortest paths between any two vertices in a graph (i.e. to solve the
all-pairs shortest path problem, or APSP for short). Given a representation of the graph as a matrix of weights M, it computes another matrix M' which represents a graph with the same path lengths
and contains the length of the shortest path between any two vertices i and j. This is only possible if the graph does not contain any negative cycles. However, in this case the Floyd-Warshall
algorithm will detect the situation by calculating a negative diagonal entry. This entry includes a formalization of the algorithm and of these key properties. The algorithm is refined to an
efficient imperative version using the Imperative Refinement Framework.
Session Floyd_Warshall | {"url":"https://www.isa-afp.org/entries/Floyd_Warshall.html","timestamp":"2024-11-14T08:17:37Z","content_type":"text/html","content_length":"11041","record_id":"<urn:uuid:6ce7fc56-9958-40c3-82de-efa8cde73d6d>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00428.warc.gz"} |
How to prepare a standard curve - virtualpsychcentre.com
How to prepare a standard curve
How do you make a standard curve?
Making a Standard Curve
1. Enter the data into Excel in adjacent columns.
2. Select the data values with your mouse. On the Insert tab, click on the Scatter icon and select Scatter with Straight Lines and Markers from its drop-down menu to generate the standard curve.
How do you prepare a serial dilution for a standard curve?
How is a standard curve constructed How is it used?
A standard curve, also known as a calibration curve or calibration line, is a type of graph used as a quantitative research technique. Multiple samples with known properties are measured and graphed,
which then allows the same properties to be determined for unknown samples by interpolation on the graph.
How do you prepare a standard solution for a calibration curve?
To prepare the standards, pipette the required amount in the volumetric flask. Then fill the flask to the line with solvent, and mix. Continue making the standards by pipetting from the stock
solution and diluting. For a good calibration curve, at least 5 concentrations are needed.
How do you prepare a 10 mL solution?
Weigh out 10mg of the extract and dissolve in 10ml of your solvent. Now take 0.1(100ul) of your stock solution and 0.9(900ul) of your solvent, this will become 1mg/ml solution.
What is tenfold dilution?
A ten-fold dilution reduces the concentration of a solution or a suspension of virus by a factor of ten that is to one-tenth the original concentration. A series of ten-fold dilutions is described as
ten-fold serial dilutions.
How do you prepare a standard solution for HPLC?
Prepare the mobile phase by adding 400 mL of acetonitrile to approximately 1.5 L of purified DI water. Carefully add 2.4 mL of glacial acetic acid to this solution. Dilute the solution to a total
volume of 2.0 L in a volumetric flask with purified DI water. The resulting solution should have a pH between 2.8 to 3.2.
How do you prepare a standard calibration curve for a spectroscopy experiment?
To prepare a standard (calibration) curve for a spectroscopy experiment, start by preparing multiple solutions with different known concentrations. Then, measure the absorbance of each solution at
the same wavelength and create a plot of absorbance vs. concentration for the measured values.
Why is it necessary to prepare a standard curve?
Standard curves represent the relationship between two quantities. They are used to determine the value of an unknown quantity (glucose concentration) from one that is more easily measured (NADH
How do I make a standard curve in HPLC?
Perform the HPLC analysis for all standard solutions and record the peak area and retention time for each component. 4. Prepare the calibration curve (graph), that plot of peak area vs concentration
using Excel/ relevant software. Draw a best fit straight line on your graph.
What is calibration standard solution?
Calibration standard: A dilute solution used in analysis to construct a calibration curve (e.g. 2,4,6,8,10ppm Fe) Dilution solution: Solution you will use to dilute standard (or stock) solution to
produce stock or calibration standards.
Why do we use standards in HPLC?
In chromatography, internal standards are used to determine the concentration of other analytes by calculating response factor. The internal standard selected should be again similar to the analyte
and have a similar retention time and similar derivitization.
What is calibration curve in HPLC?
A calibration curve is a graphical representation of the amount and response data for a single analyte (compound) obtained from one or more calibration samples. The curve is usually constructed by
injecting an aliquot of the calibration (standard) solution of known concentration and measuring the peak area obtained.
How do you draw a standard curve in chemistry?
How do you calculate r2 on a calibration curve?
What is the linear range of a standard curve?
The standard range is the linear portion of the standard curve in which analyte concentration can be determined accurately. Concentration should not be extrapolated from the standard curve beyond the
recommended standard range; outside this range the standard curve is non-linear.
What is a good calibration curve?
The r or r^2 values that accompany our calibration curve are measurements of how closely our curve matches the data we have generated. The closer the values are to 1.00, the more accurately our curve
represents our detector response. Generally, r values ≥0.995 and r^2 values ≥ 0.990 are considered ‘good’.
What is the standard curve equation?
The equation y=mx+b can be translated here as “absorbance equals slope times concentration plus the y-intercept absorbance value.” The slope and the y-intercept are provided to you when the computer
fits a line to your standard curve data. The absorbance (or y) is what you measure from your unknown.
What is R2 in standard curve?
The R2 value measures how well the regression line fits the data points. A line that fits the data points perfectly has an R2 of 1. If your data points are scattered, the R2 value for the line will
be lower.
How do you calculate a standard curve in Excel?
How would you create a standard curve in a Beer’s Law plot?
What is a good r?
A high R-square of above 60%(0.60) is required for studies in the ‘pure science’ field because the behaviour of molecules and/or particles can be reasonably predicted to some degree of accuracy in
science research; while an R-square as low as 10% is generally accepted for studies in the field of arts, humanities and … | {"url":"https://virtualpsychcentre.com/faq-how-to-prepare-a-standard-curve/","timestamp":"2024-11-12T09:13:36Z","content_type":"text/html","content_length":"47272","record_id":"<urn:uuid:48694f30-3211-46a7-96a3-c394ab69c88b>","cc-path":"CC-MAIN-2024-46/segments/1730477028249.89/warc/CC-MAIN-20241112081532-20241112111532-00729.warc.gz"} |
Generate date using DFSORT
I wonder if it's possible to generate all dates for one year using DFSORT?
So for year 2016 I want to generate 366 records on a sequential file starting with value 2016-01-01, 2016-01-02 and so on
Re: Generate date
Yes. Look at REPEAT in OUTFIL and the date functions, where there are a number of ways to do it. You can add a sequence number to a base date, or PUSH the date and get the next day...
Re: Generate date
Hi again,
I've tried but I don't managed to get it right.
The file should contain:
Pos 1-6 Date in format YYMMDD
Pos 7-9 Day of year (001-366)
Pos 10-11 Week (01-52)
Pos 12 Day of week (1-7)
So the can look like this:
and so on
How do I write it using Repeat other functions?
Re: Generate date
Pos 10-11 Week (01-52)
do the application designers know about the quirks of the week number ?
When I tell somebody to RTFM or STFW I usually have the page open in another tab/window of my browser,
so that I am sure that the information requested can be reached with a very small effort
Re: Generate date
enrico-sorichetti wrote:
Pos 10-11 Week (01-52)
do the application designers know about the quirks of the week number ?
I guess that question is meant to be rhetorical.
Robert AH Prins
robert.ah.prins @ the.17+Gb.Google thingy
Re: Generate date
I have been repeating the concept ad nauseam ...
people asking on forums just care about the lowly technicalities
and completely forget about proper business concerns.
When I tell somebody to RTFM or STFW I usually have the page open in another tab/window of my browser,
so that I am sure that the information requested can be reached with a very small effort
Re: Generate date
I just reread the whole topic and ...
as usual the code and the data do not match the comments
the comment talk about week number from 1 to 52,
but the data has the right week
16/01/01 is week number 53
and the wrong week day
and anyway another column is needed for the year
the comment for poor analysis still stands ( thanks &deity )
the algorithm is still wrong ...
for 16/01/01 it reports week 53 day 6
for 16/01/03 it reports week 53 day 1
a good analysis implies ( for congruency ) monotonicity of data
I suggest to number with 1 staring from monday
so that week 53 of 2015 will span into 2016 with the proper monotone days of the week
for 16/01/01 year 2015 week 53 day 5
for 16/01/03 year 2015 week 53 day 7
When I tell somebody to RTFM or STFW I usually have the page open in another tab/window of my browser,
so that I am sure that the information requested can be reached with a very small effort
Re: Generate date
very good mode on
here a rexx snippet to do the calculations
tested and working on my pc using open object rexx
#! /usr/bin/rexx
/* REXX
y year
d day
w week
s date sorted yyyymmdd
b date base ( as per rexx definition 0 = monday/00010101 )
fwky procedure,
returns the base date of the monday of the first week of a year
the week containin the thursday
iso1 procedure,
format the iso date appropriately
parse arg s k
if k = "" then k = 1
f = date("b",right(s,4,"0") || "0101", "S")
t = date("b",right(s+k,4,"0") || "0101", "S" ) - 1
do b = f to t
s = date("S",b,"B")
i = date2iso(s)
if s \= iso2date(i) then do
say "error for" b s i
if k = 1 then ,
say s b i
date2iso : procedure
parse arg s
b = date("B", s, "S")
y = left(s, 4 )
/* the easy one first */
if b >= fwky(y+1 ) then ,
return iso1(y+1, 1, b // 7 + 1 )
if b >= fwky(y ) then do
w = b % 7 - fwky(y ) % 7 + 1
return iso1(y, w, b // 7 + 1 )
w = b % 7 - fwky(y-1 ) % 7 + 1
return iso1(y-1, w, b // 7 + 1 )
iso1: procedure
parse arg y, w, d
return right(y, 4, "0" ) || "W" || right(w, 2, "0" ) || d
parse arg i
parse var i with 1 y 5 . 6 w 8 d
b = fwky(y ) + (w - 1 )*7 + d - 1
return date("S", b, "B")
fwky: procedure
/* base date of the first week of the year */
parse arg y
w = date("b", right(y, 4, "0" ) || "01" || "01", "s" )
d = w // 7 + 1
if d <= 4 then ,
return w + 1 - d
else ,
return w + 1 - d + 7
When I tell somebody to RTFM or STFW I usually have the page open in another tab/window of my browser,
so that I am sure that the information requested can be reached with a very small effort | {"url":"https://www.ibmmainframeforum.com/dfsort-icetool-icegener/topic10811.html","timestamp":"2024-11-09T09:19:23Z","content_type":"application/xhtml+xml","content_length":"43510","record_id":"<urn:uuid:fd2fc19c-b645-472b-909e-0b13a335003a>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00051.warc.gz"} |
If necessary, multiply the given equations by such numbers as will make the coefficients of one of the unknown numbers in the resulting equations of equal absolute value. New School Algebra - Page
172by George Albert Wentworth - 1898 - 407 pagesFull view
About this book
James Cahill (of Dublin.) - Algebra - 1875 - 230 pages
...Method. — Given 3z+4'/=43 \ to find the values 5x — 7y= — 24 J of x and y. Rule Multiply the two equations by such numbers as will make the coefficients of one of the unknown quantities the
same in both the resulting equations, and from these last equations obtain, by addition...
Charles Mansford - 1875 - 110 pages
...These illustrations give the following general rule. Multiply each of the equations, where necessary, by such numbers as will make the coefficients of one of the unknown quantities tlie sume in
each equation. Then if the signs of this unknown quantity are alike, subtract...
George Albert Wentworth - Algebra - 1881 - 402 pages
...subtraction, Multiply the equations by such numbers as will make the coefficients of this unknown quantity equal in the resulting equations. Add the resulting...subtract one from the other,
according as these equal quantities have unlike or like signs. NOTE. It is generally best to select that unknown quantity to...
Webster Wells - 1885 - 368 pages
...— 1 , y = 2. This solution is an example of elimination by subtraction. BULE. Multiply the given equations by such numbers as will make the coefficients of one of the unknown quantities equal.
Add or subtract the resulting equations according as the equal coefficients have...
Webster Wells - Algebra - 1885 - 372 pages
...— l , у = 2. This solution is an example of elimination by subtraction. RULE. Multiply the given equations by such numbers as will make the coefficients of one of the unknown quantities equal.
Add or subtract the resulting equations according as the equal coefficients have...
Webster Wells - Algebra - 1885 - 374 pages
...— 1, у = 2. This solution is an example of elimination by subtraction. EULE. Multiply the given equations by such numbers as will make the coefficients of one of the unknown quantities equal.
Add or subtract the resulting equations according as the equal coefficients have...
George Albert Wentworth - Algebra - 1886 - 284 pages
...subtraction, Multiply the equations by such numbers as will make the coefficients of this unknown quantity equal in the resulting equations. Add the resulting...subtract one from the other,
according as these equal quantities have unlike or like signs. NOTE. It is generally best to select that unknown quantity to...
Webster Wells - Algebra - 1889 - 584 pages
...= — 1, y = 2. This solution is an example of elimination by subtraction. BULB. Multiply the given equations by such numbers as will make the coefficients of one of the unknown quantities equal.
Add or subtract the resulting equations according as the equal coefficients have...
Webster Wells - Algebra - 1890 - 560 pages
...Whence, y = 2. Substituting this value in (1), 15 x + 16 = 1. RULE. If necessary, multiply the given equations by such numbers as will make the coefficients of one of the unknown quantities in
the resulting equations of equal absolute value. Add or subtract the resulting equations...
George Albert Wentworth - Algebra - 1893 - 370 pages
...8*-63-33. Л x - 12. 185. Hence, to eliminate by addition or subtraction, we have the following rule : Multiply the equations by such numbers as will make...according as these equal coefficients
have unlike or like sic/7is. NOTE. It is generally best to select the letter to be eliminated which requires the smallest... | {"url":"https://books.google.com.jm/books?id=NRUAAAAAYAAJ&qtid=eb7e7859&output=html_text&source=gbs_quotes_r&cad=6","timestamp":"2024-11-14T16:53:48Z","content_type":"text/html","content_length":"28827","record_id":"<urn:uuid:b6d81a0b-5438-43e5-84bd-39ad580e762a>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00132.warc.gz"} |
MaffsGuru.com - Making maths enjoyableSolving Word Problems
Click the link below to download your notes.
If your lesson notes are not downloading this is due to your school blocking access to the notes server. If you try connecting at home, or using a different computer which is not controlled by your
school, you will be able to download the notes. | {"url":"https://maffsguru.com/videos/solving-word-problems/","timestamp":"2024-11-14T07:17:18Z","content_type":"text/html","content_length":"33788","record_id":"<urn:uuid:eef6403f-fa15-47c6-b595-a84adda043d9>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00200.warc.gz"} |
Current Search: Nashed, M
On the range of the Attenuated Radon Transform in strictly convex sets.
Sadiq, Kamran, Tamasan, Alexandru, Nashed, M, Katsevich, Alexander, Dogariu, Aristide, University of Central Florida
Abstract / Description
In the present dissertation, we characterize the range of the attenuated Radon transform of zero, one, and two tensor fields, supported in strictly convex set. The approach is based on a Hilbert
transform associated with A-analytic functions of A. Bukhgeim. We first present new necessary and sufficient conditions for a function to be in the range of the attenuated Radon transform of a
sufficiently smooth function supported in the convex set. The approach is based on an explicit Hilbert...
Show moreIn the present dissertation, we characterize the range of the attenuated Radon transform of zero, one, and two tensor fields, supported in strictly convex set. The approach is based on a
Hilbert transform associated with A-analytic functions of A. Bukhgeim. We first present new necessary and sufficient conditions for a function to be in the range of the attenuated Radon transform
of a sufficiently smooth function supported in the convex set. The approach is based on an explicit Hilbert transform associated with traces of the boundary of A-analytic functions in the sense
of A. Bukhgeim. We then uses the range characterization of the Radon transform of functions to characterize the range of the attenuated Radon transform of vector fields as they appear in the
medical diagnostic techniques of Doppler tomography. As an application we determine necessary and sufficient conditions for the Doppler and X-ray data to be mistaken for each other. We also
characterize the range of real symmetric second order tensor field using the range characterization of the Radon transform of zero tensor field.
Show less
Date Issued
CFE0005408, ucf:50437
Document (PDF)
Inversion of the Broken Ray Transform.
Krylov, Roman, Katsevich, Alexander, Tamasan, Alexandru, Nashed, M, Zeldovich, Boris, University of Central Florida
Abstract / Description
The broken ray transform (BRT) is an integral of a functionalong a union of two rays with a common vertex.Consider an X-ray beam scanning an object of interest.The ray undergoes attenuation and
scatters in all directions inside the object.This phenomena may happen repeatedly until the photons either exit the object or are completely absorbed.In our work we assume the single scattering
approximation when the intensity of the raysscattered more than once is negligibly small.Among all paths that...
Show moreThe broken ray transform (BRT) is an integral of a functionalong a union of two rays with a common vertex.Consider an X-ray beam scanning an object of interest.The ray undergoes
attenuation and scatters in all directions inside the object.This phenomena may happen repeatedly until the photons either exit the object or are completely absorbed.In our work we assume the
single scattering approximation when the intensity of the raysscattered more than once is negligibly small.Among all paths that the scattered rays travel inside the object we pick the one that
isa union of two segments with one common scattering point.The intensity of the ray which traveled this path and exited the object can be measured by a collimated detector.The collimated detector
is able to measure the intensity of X-rays from the selected direction.The logarithm of such a measurement is the broken ray transform of the attenuation coefficientplus the logarithm of the
scattering coefficient at the scattering point (vertex)and a known function of the scattering angle.In this work we consider the reconstruction of X-ray attenuation coefficient distributionin a
plane from the measurements on two or three collimated detector arrays.We derive an exact local reconstruction formula for three flat collimated detectorsor three curved or pin-hole collimated
detectors.We obtain a range condition for the case of three curved or pin-hole detectors and provide a special caseof the range condition for three flat detectors.We generalize the reconstruction
formula to four and more detectors and find anoptimal set of parameters that minimize noise in the reconstruction.We introduce a more accurate scattering model which takes into accountenergy
shifts due to the Compton effect, derive an exact reconstruction formula and develop an iterativereconstruction method for the energy-dependent case.To solve the problem we assume that the
radiation source is monoenergeticand the dependence of the attenuation coefficient on energy is linearon an energy interval from the minimal to the maximal scattered energy. %initial radiation
energy.We find the parameters of the linear dependence of the attenuation on energy as a function of a pointin the reconstruction plane.
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Date Issued
CFE0005514, ucf:50324
Document (PDF)
Electrical Conductivity Imaging via Boundary Value Problems for the 1-Laplacian.
Veras, Johann, Tamasan, Alexandru, Mohapatra, Ram, Nashed, M, Dogariu, Aristide, University of Central Florida
Abstract / Description
We study an inverse problem which seeks to image the internal conductivity map of a body by one measurement of boundary and interior data. In our study the interior data is the magnitude of the
current density induced by electrodes. Access to interior measurements has been made possible since the work of M. Joy et al. in early 1990s and couples two physical principles: electromagnetics
and magnetic resonance. In 2007 Nachman et al. has shown that it is possible to recover the conductivity...
Show moreWe study an inverse problem which seeks to image the internal conductivity map of a body by one measurement of boundary and interior data. In our study the interior data is the magnitude
of the current density induced by electrodes. Access to interior measurements has been made possible since the work of M. Joy et al. in early 1990s and couples two physical principles:
electromagnetics and magnetic resonance. In 2007 Nachman et al. has shown that it is possible to recover the conductivity from the magnitude of one current density field inside. The method now
known as Current Density Impedance Imaging is based on solving boundary value problems for the 1-Laplacian in an appropriate Riemann metric space. We consider two types of methods: the ones based
on level sets and a variational approach, which aim to solve specific boundary value problem associated with the 1-Laplacian. We will address the Cauchy and Dirichlet problems with full and
partial data, and also the Complete Electrode Model (CEM). The latter model is known to describe most accurately the voltage potential distribution in a conductive body, while taking into account
the transition of current from the electrode to the body. For the CEM the problem is non-unique. We characterize the non-uniqueness, and explain which additional measurements fix the solution.
Multiple numerical schemes for each of the methods are implemented to demonstrate the computational feasibility.
Show less
Date Issued
CFE0005437, ucf:50388
Document (PDF)
Can One Hear...? An Exploration Into Inverse Eigenvalue Problems Related to Musical Instruments.
Adams, Christine, Nashed, M, Mohapatra, Ram, Kaup, David, University of Central Florida
Abstract / Description
The central theme of this thesis deals with problems related to the question, (")Can one hear the shape of a drum?(") first posed formally by Mark Kac in 1966. More precisely, can one determine
the shape of a membrane with fixed boundary from the spectrum of the associated differential operator? For this paper, Kac received both the Lester Ford Award and the Chauvant Prize of the
Mathematical Association of America. This problem has received a great deal of attention in the past forty years...
Show moreThe central theme of this thesis deals with problems related to the question, (")Can one hear the shape of a drum?(") first posed formally by Mark Kac in 1966. More precisely, can one
determine the shape of a membrane with fixed boundary from the spectrum of the associated differential operator? For this paper, Kac received both the Lester Ford Award and the Chauvant Prize of
the Mathematical Association of America. This problem has received a great deal of attention in the past forty years and has led to similar questions in completely different contexts such as (")
Can one hear the shape of a graph associated with the Schr(&)#246;dinger operator?("), (")Can you hear the shape of your throat?("), (")Can you feel the shape of a manifold with Brownian motion?
("), (")Can one hear the crack in a beam?("), (")Can one hear into the sun?("), etc. Each of these topics deals with inverse eigenvalue problems or related inverse problems. For inverse problems
in general, the problem may or may not have a solution, the solution may not be unique, and the solution does not necessarily depend continuously on perturbation of the data. For example, in the
case of the drum, it has been shown that the answer to Kac's question in general is (")no.(") However, if we restrict the class of drums, then the answer can be yes. This is typical of inverse
problems when a priori information and restriction of the class of admissible solutions and/or data are used to make the problem well-posed. This thesis provides an analysis of shapes for which
the answer to Kac's question is positive and a variety of interesting questions on this problem and its variants, including cases that remain open. This thesis also provides a synopsis and
perspectives of other types of (")can one hear(") problems mentioned above. Another part of this thesis deals with aspects of direct problems related to musical instruments.
Show less
Date Issued
CFE0004643, ucf:49886
Document (PDF)
Robust, Scalable, and Provable Approaches to High Dimensional Unsupervised Learning.
Rahmani, Mostafa, Atia, George, Vosoughi, Azadeh, Mikhael, Wasfy, Nashed, M, Pensky, Marianna, University of Central Florida
Abstract / Description
This doctoral thesis focuses on three popular unsupervised learning problems: subspace clustering, robust PCA, and column sampling. For the subspace clustering problem, a new transformative idea
is presented. The proposed approach, termed Innovation Pursuit, is a new geometrical solution to the subspace clustering problem whereby subspaces are identified based on their relative
novelties. A detailed mathematical analysis is provided establishing sufficient conditions for the proposed method...
Show moreThis doctoral thesis focuses on three popular unsupervised learning problems: subspace clustering, robust PCA, and column sampling. For the subspace clustering problem, a new
transformative idea is presented. The proposed approach, termed Innovation Pursuit, is a new geometrical solution to the subspace clustering problem whereby subspaces are identified based on
their relative novelties. A detailed mathematical analysis is provided establishing sufficient conditions for the proposed method to correctly cluster the data points. The numerical simulations
with both real and synthetic data demonstrate that Innovation Pursuit notably outperforms the state-of-the-art subspace clustering algorithms. For the robust PCA problem, we focus on both the
outlier detection and the matrix decomposition problems. For the outlier detection problem, we present a new algorithm, termed Coherence Pursuit, in addition to two scalable randomized frameworks
for the implementation of outlier detection algorithms. The Coherence Pursuit method is the first provable and non-iterative robust PCA method which is provably robust to both unstructured and
structured outliers. Coherence Pursuit is remarkably simple and it notably outperforms the existing methods in dealing with structured outliers. In the proposed randomized designs, we leverage
the low dimensional structure of the low rank component to apply the robust PCA algorithm to a random sketch of the data as opposed to the full scale data. Importantly, it is analytically shown
that the presented randomized designs can make the computation or sample complexity of the low rank matrix recovery algorithm independent of the size of the data. At the end, we focus on the
column sampling problem. A new sampling tool, dubbed Spatial Random Sampling, is presented which performs the random sampling in the spatial domain. The most compelling feature of Spatial Random
Sampling is that it is the first unsupervised column sampling method which preserves the spatial distribution of the data.
Show less
Date Issued
CFE0007083, ucf:52010
Document (PDF)
Weighted Low-Rank Approximation of Matrices:Some Analytical and Numerical Aspects.
Dutta, Aritra, Li, Xin, Sun, Qiyu, Mohapatra, Ram, Nashed, M, Shah, Mubarak, University of Central Florida
Abstract / Description
This dissertation addresses some analytical and numerical aspects of a problem of weighted low-rank approximation of matrices. We propose and solve two different versions of weighted low-rank
approximation problems. We demonstrate, in addition, how these formulations can be efficiently used to solve some classic problems in computer vision. We also present the superior performance of
our algorithms over the existing state-of-the-art unweighted and weighted low-rank approximation algorithms...
Show moreThis dissertation addresses some analytical and numerical aspects of a problem of weighted low-rank approximation of matrices. We propose and solve two different versions of weighted
low-rank approximation problems. We demonstrate, in addition, how these formulations can be efficiently used to solve some classic problems in computer vision. We also present the superior
performance of our algorithms over the existing state-of-the-art unweighted and weighted low-rank approximation algorithms.Classical principal component analysis (PCA) is constrained to have
equal weighting on the elements of the matrix, which might lead to a degraded design in some problems. To address this fundamental flaw in PCA, Golub, Hoffman, and Stewart proposed and solved a
problem of constrained low-rank approximation of matrices: For a given matrix $A = (A_1\;A_2)$, find a low rank matrix $X = (A_1\;X_2)$ such that ${\rm rank}(X)$ is less than $r$, a prescribed
bound, and $\|A-X\|$ is small.~Motivated by the above formulation, we propose a weighted low-rank approximation problem that generalizes the constrained low-rank approximation problem of Golub,
Hoffman and Stewart.~We study a general framework obtained by pointwise multiplication with the weight matrix and consider the following problem:~For a given matrix $A\in\mathbb{R}^{m\times n}$
solve:\begin{eqnarray*}\label{weighted problem}\min_{\substack{X}}\|\left(A-X\right)\odot W\|_F^2~{\rm subject~to~}{\rm rank}(X)\le r,\end{eqnarray*}where $\odot$ denotes the pointwise
multiplication and $\|\cdot\|_F$ is the Frobenius norm of matrices.In the first part, we study a special version of the above general weighted low-rank approximation problem.~Instead of using
pointwise multiplication with the weight matrix, we use the regular matrix multiplication and replace the rank constraint by its convex surrogate, the nuclear norm, and consider the following
problem:\begin{eqnarray*}\label{weighted problem 1}\hat{X} (&)=(&) \arg \min_X \{\frac{1}{2}\|(A-X)W\|_F^2 +\tau\|X\|_\ast\},\end{eqnarray*}where $\|\cdot\|_*$ denotes the nuclear norm of
$X$.~Considering its resemblance with the classic singular value thresholding problem we call it the weighted singular value thresholding~(WSVT)~problem.~As expected,~the WSVT problem has no
closed form analytical solution in general,~and a numerical procedure is needed to solve it.~We introduce auxiliary variables and apply simple and fast alternating direction method to solve WSVT
numerically.~Moreover, we present a convergence analysis of the algorithm and propose a mechanism for estimating the weight from the data.~We demonstrate the performance of WSVT on two computer
vision applications:~background estimation from video sequences~and facial shadow removal.~In both cases,~WSVT shows superior performance to all other models traditionally used. In the second
part, we study the general framework of the proposed problem.~For the special case of weight, we study the limiting behavior of the solution to our problem,~both analytically and numerically.~In
the limiting case of weights,~as $(W_1)_{ij}\to\infty, W_2=\mathbbm{1}$, a matrix of 1,~we show the solutions to our weighted problem converge, and the limit is the solution to the constrained
low-rank approximation problem of Golub et. al. Additionally, by asymptotic analysis of the solution to our problem,~we propose a rate of convergence.~By doing this, we make explicit connections
between a vast genre of weighted and unweighted low-rank approximation problems.~In addition to these, we devise a novel and efficient numerical algorithm based on the alternating direction
method for the special case of weight and present a detailed convergence analysis.~Our approach improves substantially over the existing weighted low-rank approximation algorithms proposed in the
literature.~Finally, we explore the use of our algorithm to real-world problems in a variety of domains, such as computer vision and machine learning. Finally, for a special family of weights, we
demonstrate an interesting property of the solution to the general weighted low-rank approximation problem. Additionally, we devise two accelerated algorithms by using this property and present
their effectiveness compared to the algorithm proposed in Chapter 4.
Show less
Date Issued
CFE0006833, ucf:51789
Document (PDF)
Calibration of Option Pricing in Reproducing Kernel Hilbert Space.
Ge, Lei, Nashed, M, Yong, Jiongmin, Qi, Yuanwei, Sun, Qiyu, Caputo, Michael, University of Central Florida
Abstract / Description
A parameter used in the Black-Scholes equation, volatility, is a measure for variation of the price of a financial instrument over time. Determining volatility is a fundamental issue in the
valuation of financial instruments. This gives rise to an inverse problem known as the calibration problem for option pricing. This problem is shown to be ill-posed. We propose a regularization
method and reformulate our calibration problem as a problem of finding the local volatility in a reproducing...
Show moreA parameter used in the Black-Scholes equation, volatility, is a measure for variation of the price of a financial instrument over time. Determining volatility is a fundamental issue in
the valuation of financial instruments. This gives rise to an inverse problem known as the calibration problem for option pricing. This problem is shown to be ill-posed. We propose a
regularization method and reformulate our calibration problem as a problem of finding the local volatility in a reproducing kernel Hilbert space. We defined a new volatility function which allows
us to embrace both the financial and time factors of the options. We discuss the existence of the minimizer by using regu- larized reproducing kernel method and show that the regularizer resolves
the numerical instability of the calibration problem. Finally, we apply our studied method to data sets of index options by simulation tests and discuss the empirical results obtained.
Show less
Date Issued
CFE0005617, ucf:50211
Document (PDF) | {"url":"http://ucf.digital.flvc.org/islandora/search/catch_all_names_mt%3A(%20Nashed,%20M)","timestamp":"2024-11-06T15:44:46Z","content_type":"text/html","content_length":"114816","record_id":"<urn:uuid:bcf53b07-4fe9-429f-825c-a0419c3daba3>","cc-path":"CC-MAIN-2024-46/segments/1730477027932.70/warc/CC-MAIN-20241106132104-20241106162104-00756.warc.gz"} |
Best Player Combinations For
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How to convert volts to electron-volts
How to convert electrical voltage in volts (V) to energy in electron-volts (eV).
You can calculate electron-volts from volts and elementary charge or coulombs, but you can't convert volts to electron-volts since volt and electron-volt units represent different quantities.
Volts to eV calculation with elementary charge
The energy E in electron-volts (eV) is equal to the voltage V in volts (V), times the electric charge Q in elementary charge or proton/electron charge (e):
E[(eV)] = V[(V)] × Q[(e)]
The elementary charge is the electric charge of 1 electron with the e symbol.
electronvolt = volt × elementary charge
eV = V × e
What is the energy in electron-volts that is consumed in an electrical circuit with voltage supply of 20 volts and charge flow of 40 electron charges?
E = 20V × 40e = 800eV
Volts to eV calculation with coulombs
The energy E in electron-volts (eV) is equal to the voltage V in volts (V), times the electrical charge Q in coulombs (C) divided by 1.602176565×10^-19:
E[(eV)] = V[(V)] × Q[(C)] / 1.602176565×10^-19
electronvolt = volt × coulomb / 1.602176565×10^-19
eV = V × C / 1.602176565×10^-19
What is the energy in electron-volts that is consumed in an electrical circuit with voltage supply of 20 volts and charge flow of 2 coulombs?
E = 20V × 2C / 1.602176565×10^-19 = 2.4966×10^20eV
See also | {"url":"https://jobsvacancy.in/convert/electric/volts-to-ev.html","timestamp":"2024-11-04T04:11:12Z","content_type":"text/html","content_length":"9151","record_id":"<urn:uuid:ab271bd6-cd89-43df-a356-aac2b116cefb>","cc-path":"CC-MAIN-2024-46/segments/1730477027812.67/warc/CC-MAIN-20241104034319-20241104064319-00374.warc.gz"} |
BEGIN:VCALENDAR VERSION:2.0 PRODID:ILLC Website X-WR-TIMEZONE:Europe/Amsterdam BEGIN:VTIMEZONE TZID:Europe/Amsterdam X-LIC-LOCATION:Europe/Amsterdam BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200
TZNAME:CEST DTSTART:19700329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19701025T030000 RRULE:FREQ=YEARLY;BYMONTH
=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:/NewsandEvents/Archives/2013/newsitem/4906/18- 20-April-2013-Algebra-and-Coalgebra-meet-Proof-The ory-ALCOP-2013-Utrecht-University
DTSTAMP:20130418T000000 SUMMARY:Algebra and Coalgebra meet Proof Theory (A LCOP 2013), Utrecht University DTSTART;VALUE=DATE:20130418 DTEND;VALUE=DATE:20130420 LOCATION:Utrecht University
DESCRIPTION:The fourth issue of the workshop Algeb ra and Coalgebra meet Proof Theory (ALCOP 2013), w ill take place in Utrecht, The Netherlands on Apri l 18 - 20, 2013. ALCOP brings together experts
i n algebraic logic, coalgebraic logic, and proof th eory with the goal of sharing new results and deve loping mutually beneficial relationships between t hese fields. More details can be found on
the wo rkshop webpage: http://www.phil.uu.nl/~iemhoff/Con ferenties/ALCOP/ X-ALT-DESC;FMTTYPE=text/html:\n
\n The fourth issue of the workshop Algebra and Coalg ebra meet Proof\n Theory (ALCOP 2013), will take place in Utrecht, The Netherlands on\n April 18 - 20, 2013.\n
ALCOP brings together experts in algebraic logic, coalg ebraic logic,\n and proof theory with the g oal of sharing new results and developing\n mutually beneficial relationships between these f
\n\n \n
More details can be found on the workshop webpage:\n http://www.phil.uu.nl/~iem hoff/Conferenties/ALCOP/\n
URL:/NewsandEvents/Archives/2013/newsitem/4906/18- 20-April-2013-Algebra-and-Coalgebra-meet-Proof-The ory-ALCOP-2013-Utrecht-University END:VEVENT END:VCALENDAR | {"url":"https://www.illc.uva.nl/NewsandEvents/Events/Conferences/newsitem/4906/18-20-April-2013-Algebra-and-Coalgebra-meet-Proof-Theory-ALCOP-2013-Utrecht-University?displayMode=ical","timestamp":"2024-11-03T09:16:57Z","content_type":"text/calendar","content_length":"2771","record_id":"<urn:uuid:009e56e8-2c04-4b11-b7b4-980c81facc73>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00306.warc.gz"} |
Strong Conflict-Free Coloring for Intervals
We consider the k-strong conflict-free (k-SCF) coloring of a set of points on a line with respect to a family of intervals: Each point on the line must be assigned a color so that the coloring is
conflict-free in the following sense: in every interval I of the family there are at least k colors each appearing exactly once in I. We first present a polynomial-time approximation algorithm for
the general problem; the algorithm has approximation ratio 2 when k=1 and 5-2/k when k ≥ 2. In the special case of a family that contains all possible intervals on the given set of points, we show
that a 2-approximation algorithm exists, for any k ≥ 1. We also provide, in case k = O(polylog(n)), a quasipolynomial time algorithm to decide the existence of a k-SCF coloring that uses at most q
• Conflict-free coloring
• Interval hypergraph
• Wireless networks
ASJC Scopus subject areas
• General Computer Science
• Computer Science Applications
• Applied Mathematics
Dive into the research topics of 'Strong Conflict-Free Coloring for Intervals'. Together they form a unique fingerprint. | {"url":"https://cris.bgu.ac.il/en/publications/strong-conflict-free-coloring-for-intervals-6","timestamp":"2024-11-07T23:22:28Z","content_type":"text/html","content_length":"55677","record_id":"<urn:uuid:ab949c49-63e5-4f3a-9d7f-891fd3075fed>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00764.warc.gz"} |
9 Best Free Online Bond Yield Calculator Websites
Here is a list of best free online bond yield calculator websites. Bond Yield is the percentage of return investors will get from investing in a bond. Bond yield helps investors assess the
attractiveness of a bond investment compared to other investment opportunities. There are multiple types of bond yields like yield to maturity ( the total return an investor can expect to earn if
they hold a bond until it matures), current yield (bond return), yield to call (the yield an investor can expect to receive if a callable bond is held until its earliest call date), etc. If you also
want to calculate the bond yield values, then check out these online bond yield calculator websites.
Through these websites, users can quickly calculate the bond yield percentage. Although, some of these websites calculate bond yield in the form of current yield and yield to maturity. To perform the
bond yield calculation, these calculators require input values like current bond price, bond par value, bond coupon rate, years to maturity, payment type, etc. These websites also explain bond yield
and bond yield calculation. Some of these calculators also show the formula that they use to calculate the bond yield with added examples. To help you out, I have also included the necessary
calculation process in the description of each website. Go through the list to know more about these websites.
My Favorite Online Bond Yield Calculator Website:
calculatestuff.com is my favorite website as it explains bond yield and shows the bond yield calculation formulas.
You can also check out lists of best free Online ROIC Calculator, Online Return On Investment Calculator, and Online IRR Calculator websites.
Comparison Table:
calculatestuff.com is a free online bond yield calculator website. Through this website, users can calculate the bond yield value using current price, par value (face value of a bond), coupon rate
(rate of interest paid by bond issuers), payment frequency (annually, quarterly, monthly, etc.), and years of maturity values. It also explains the process of bond yield calculation. Plus, it shows
all the necessary formulas required to calculate the bond yield value. Now, follow the below steps.
How to calculate bond yield online using calculatestuff.com:
• Visit this website and access the bond yield calculator.
• After that, enter input values namely current price, par value, coupon rate, payment frequency, and years of maturity.
• Next, click on the Calculate button to view the current yield and yield to maturity percentages.
Additional Features:
• This website also offers multiple Financial, Business, Health, and Math calculators.
Final Thoughts:
It is one of the best free online bond yield calculator websites through which users can quickly find out the bond yield and current yield values.
Pros Cons
Explains bond yield calculation
Shows all necessary formulas
omnicalculator.com is another free online bond yield calculator website. This website offers a simple bond yield calculator through which users can calculate bond yield percentage value. To perform
the calculation, users need to input Face Value, Bond Price, Annual Coupon Rate, Coupon Frequency, and Years of Maturity values. This website also explains bond yield and the process to calculate
bond yield is also provided by it. It also shows the bond yield calculation formula and explains all its entities. Now, follow the below steps.
How to calculate bond yield online using omnicalculator.com:
• Go to this website and access the bond yield calculator.
• After that, enter the required input values such as Face Value, Bond Price, Annual Coupon rate, etc.
• Next, let this tool perform the calculation.
• Finally, view and copy the bond yield percentage value.
Additional Features:
• This website also comes with additional online calculators covering topics like Finance, Health, math, Physics, Sports, Statistics, etc.
Final Thoughts:
It is another good online bond yield calculator website that helps users calculate bond yield percentages and explains the bond yield calculation.
Pros Cons
Explains bond yield calculation
Shows the formula to calculate bond yield value
investor.sebi.gov.in is another free online bond yield calculator website. Through this website, users can calculate the bond yield in the form of current yield and yield-to-maturity percentages. To
do that, users need to enter four known parameters namely Current price, Par value, Coupon Rate, and Years to maturity. After performing the calculation, users can copy both the current yield and
yield to maturity percentage values. Although, this website doesn’t explain bond yield nor it offers the calculation steps & formulas required to calculate the bond yield. Now, check out the below
How to calculate bond yield online using investor.sebi.gov.in:
• Visit this website and access the Bond Yield calculator.
• After that, enter the Current Price, Par Value, Coupon Rate Percentage, and Years to Maturity values.
• Next, click on the Calculate button to start the calculation process.
• Finally, view and copy the resistant current yield and yield to maturity values.
Additional Features:
• This website also comes with additional online calculators such as Future Value, EMI Calculator, Present Value, Rate of Return, and more.
Final Thoughts:
This website offers a straightforward online bond yield calculator through which users can quickly find out the Current Yield and Yield to Maturity values.
Pros Cons
Doesn’t explain the bond yield topic
Doesn’t show the formulas required to calculate the bond yield
moneychimp.com is another free online bond yield calculator website. This website comes with multiple online calculators including a bond yield calculator. This calculator can calculate the current
yield and yield to maturing bond yield parameters. It required four known values as input namely Current price, Par Value, Coupon Rate, and Years to Maturity. It also explains bond yield to maturity
and shows the formula that it uses to calculate bond yield value. An example of bond yield calculation is also provided. Now, follow the below steps.
How to calculate bond yield online using moneychimp.com:
• Start this website and access the bond yield calculator.
• After that, submit all required input values.
• Next, click on the Calculate button to start the calculation process.
• Finally, view and copy the resistant bond yield values.
Additional Features:
• This website also offers additional financial calculators like Compound Interest, Present Value, Rate of Return, Annuity, Mortgage, etc.
Final Thoughts:
It is another simple online bond yield calculator website that anyone can use without much hassle.
Pros Cons
Shows the calculation formulas with examples
fncalculator.com is another free online bond yield calculator website. It is another good website through which users can calculate the bond yield to call value. To do that, this calculator requires
seven inputs from users namely Bond Price, Face Value, Coupon Rate (%), Years to Maturity, Call Price, Years until call Date, and Compounding (Annually or Semiannually). Although, it doesn’t offer
any information related to bond yield to call. Now, check out the below steps.
How to calculate bond yield to call online using fncalculator.com:
• Start this website and access its bond yield to call calculator.
• After that, enter the values of all seven input parameters.
• Next, click on the Calculate button to view the calculated yield to call value.
Additional Features:
• This website also offers calculators and tools related to fields like Finance & Investment, Loan, Retirement, Credit Card, Auto Loan, and Stock.
Final Thoughts:
It is another good online bond yield calculator website that helps users find out the bond yield to call value.
Pros Cons
Can calculate bond yield to call value Doesn’t offer any information related to bond yield
calkoo.com is yet another free online bond yield calculator website. This website comes with a simple bond yield calculator that requires initial data (current bond price, bond par value, bond coupon
rate, years to maturity, and payment (annually, semiannually, or quarterly)) to calculate the yield to maturity percentage. It also lacks the bond yield calculation showcase and information
explaining the bond yield. Now, follow the below steps.
How to calculate bond yield online using calkoo.com:
• Start this website and access the bond yield calculator.
• Now, enter the initial data values.
• Next, let this calculator perform the calculation.
• Finally, view the calculated yield to maturity value.
Additional Features:
• This website also comes with some handy tools like Internal Rate of Return, NPV and Profitability Index, Weighted Average Cost of Capital, Value Added Tax calculator, and more.
Final Thoughts:
It is another simple online bond yield calculator website that anyone can use to calculate the bond yield to maturity percentage value.
Pros Cons
Lacks information related to bond yield and its calculation
dqydj.com is another free online bond yield calculator website. Through this website, users can calculate the yield to maturity, estimated yield to maturity, and current yield percentage values. It
also explains bond yield and shows the bond yield calculation formulas. Like other similar websites, it also required a good set of input values to perform the calculation namely Current Bond Trading
price, Bond Face Value, Years to Maturity, Annual Coupon Rate, and Coupon Payment Frequency. Now, follow the below steps.
How to calculate bond yield online using dqydj.com:
• Start this website and open up its Bond Yield to Maturity calculator.
• After that, enter all the required input values.
• Now, click on the Compute yield to maturity button.
• Next, view and copy the resistant values.
Additional Features:
• This website also offers tools associated with personal finance, real estate, economics, health, income, network, and investing.
Final Thoughts:
It is another good online bond yield calculator website that also calculated current yield percentages.
Pros Cons
Can calculate yield to maturity and current yield values
Shows the calculation process and bond yield formula
rrfinance.com is another free online bond yield calculator website. This website explains the bond yield topic and offers a simple bond yield calculator. This calculator can calculate the current
yield and yield-to-maturity bond yield parameters. To perform the calculation, users need to specify the current price, par value, coupon rate, maturity date, and years to maturity values. Although,
it doesn’t show the calculation process and calculation formulas. Now, check out the below steps.
How to calculate bond yield online using rrfinance.com:
• Launch this website using the given link.
• After that, enter the current price, par value, coupon rate, maturity date, and years to maturity values.
• Next, click on the Calculate button to view the calculated bond yield values.
Additional Features:
• This website offers multiple blogs related to financial topics like fixed deposits, capital gain bonds, floating rate bonds, and more.
Final Thoughts:
It is another good online bond yield calculator website through which users can calculate bond yield values.
Pros Cons
Doesn’t show the formulas associated with the bond yield calculation
quantwolf.com is another free online bond yield calculator website. This website helps users calculate the yield to maturity, annual equivalent rate, and accused interest values. To calculate
multiple bond yield parameters, users need to specify the Price, Face Value, Coupon rate, payments per Year, Settlement Date, and Maturity date values. According to the provided values, it performs
the calculation and shows bond yield values. This website also explains all the parameters involved in the bond yield calculation like price, face value, coupon rate, payments per year, etc. Now,
follow the below steps.
How to calculate bond yield online using quantwolf.com:
• Go to this website and access the bond yield to maturity calculator.
• After that, enter all the required input values.
• Now, click on the Calculate button to start the calculation process.
• Finally, view the calculated yield to maturity, annual equivalent rate, and accused interest values.
Final Thoughts:
It is another good online bond yield calculator website that allows users to calculate three important bond yield parameters namely yield to maturity, annual equivalent rate, and accused interest.
Pros Cons
Explains all parameters involves in bond yield calculation Doesn’t provide calculation formulas
Frequently Asked Questions
bond yield ratio is refered to the relationship between the yield of one bond compared to another bond, typically used to assess the relative value or risk between the two bonds. In this case, you
might be comparing the yield of a corporate bond to that of a government bond with a similar maturity to determine whether the corporate bond is providing a sufficient yield premium to compensate for
its higher credit risk.
Bond yield is a measure of the return on investment for a bond. To calculate the bond yield, users need to divide the bonds coupon interest with the price of the bond.
No, bond yield and interest rate are not the same, although they are related concepts in the world of bonds and fixed-income investments. The interest rate, often referred to as the "coupon rate" is
the rate at which a bond issuer agrees to pay interest to bondholders periodically on the bond's face value (or par value). On the other hand, Bond yield or yield to maturity takes into account not
only the bond's coupon payments but also the potential capital gains or losses if the bond is held until it matures.
Bond yields rise primarily due to changes in market interest rates and shifts in supply and demand dynamics in the bond market.
Bonds typically do not lose value after they reach their maturity date. When a bond matures, the issuer is obligated to repay the bondholder the bond's face value in full. This payment is usually
made on the maturity date as specified in the bond's terms. So, if you hold a bond until its maturity date, you will receive the face value of the bond, regardless of any changes in interest rates or
market conditions. Bondholders receive their principal back, and the bond ceases to exist.
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Equicontinuity in metric spaces #
This files contains various facts about (uniform) equicontinuity in metric spaces. Most importantly, we prove the usual characterization of equicontinuity of F at x₀ in the case of (pseudo) metric
spaces: ∀ ε > 0, ∃ δ > 0, ∀ x, dist x x₀ < δ → ∀ i, dist (F i x₀) (F i x) < ε, and we prove that functions sharing a common (local or global) continuity modulus are (locally or uniformly)
Main statements #
• Metric.equicontinuousAt_iff: characterization of equicontinuity for families of functions between (pseudo) metric spaces.
• Metric.equicontinuousAt_of_continuity_modulus: convenient way to prove equicontinuity at a point of a family of functions to a (pseudo) metric space by showing that they share a common local
continuity modulus.
• Metric.uniformEquicontinuous_of_continuity_modulus: convenient way to prove uniform equicontinuity of a family of functions to a (pseudo) metric space by showing that they share a common global
continuity modulus.
Tags #
equicontinuity, continuity modulus
Characterization of equicontinuity for families of functions taking values in a (pseudo) metric space.
Characterization of equicontinuity for families of functions between (pseudo) metric spaces.
Characterization of uniform equicontinuity for families of functions taking values in a (pseudo) metric space.
Characterization of uniform equicontinuity for families of functions between (pseudo) metric spaces.
For a family of functions to a (pseudo) metric spaces, a convenient way to prove equicontinuity at a point is to show that all of the functions share a common local continuity modulus.
For a family of functions between (pseudo) metric spaces, a convenient way to prove uniform equicontinuity is to show that all of the functions share a common global continuity modulus.
For a family of functions between (pseudo) metric spaces, a convenient way to prove equicontinuity is to show that all of the functions share a common global continuity modulus. | {"url":"https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/MetricSpace/Equicontinuity.html","timestamp":"2024-11-07T15:37:34Z","content_type":"text/html","content_length":"34655","record_id":"<urn:uuid:419417e8-e6bf-45ec-b186-f52627c52001>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00346.warc.gz"} |
Geometry Math Games and Worksheets (worksheets, activities, games)
The geometry games are Shape and Symmetry games, Tangrams and Tessellation games, Angle games, Perimeter, area and Volume games, Solid geometry games, Coordinate geometry games, Geometric term games,
Geometry fun games, Geometry activities and worksheets. We have added more free geometry games that can be played on PCs, Tablets, iPads and Mobiles.
Geometry Games (Geometric Terms)
Angle Games
Perimeter, Area and Volume Games
Coordinate Geometry Games
Equation Of Line Games
Recognise common straight line graphs
Know what these sort of lines look like and where they are on the axes.
Draw straight line graphs using y = mx + c
Learn how to draw straight line graphs.
Find the gradient of a line using its graph
Measure the gradient of the line.
Find the gradient of a line using its equation
Find the gradient of a line by knowing 2 points the line goes through.
Find the gradient and y intercept from the equation of a line
Know the formula y = mx + c and understand that m = gradient and c = y-intercept.
Match together equations and lines
Match graphs of straight lines to their equations.
Interactive Geometry Worksheets
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Geometry Interactive Activities (For PCs, Mobiles etc.)
Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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