Science topics: Mathematical Computing
Science topic

# Mathematical Computing - Science topic

Computer-assisted interpretation and analysis of various mathematical functions related to a particular problem.
Questions related to Mathematical Computing
Question
I want to check whether the ( Journal of Advances in Mathematics and Computer Science ISSN: 2456-9968 ) is a fake one or not? I could not find it in the Clarivate Analytics list.
Thanks for ur help!
Fakes are everywhere these days.
Question
Hi everyone. recently I designed a customized semantic segmentation network with 31 layers and SGDM optimation to segment plant leaf regions from complicated backgrounds. can anyone help me how to explain this with mathematical expressions using image processing. thank you
I think the best way is to use the results of the semantic segmentation and samples of leaves from fieldwork to create your mathematical expression using any curve fitting mathematical tool.
Question
If we have three different domain of data (e.g. security, AI and sport) and we did 3 different case study or experiments (1 for each domain) and we estimate the Precision, Recall and F-measure for each experiment. How we can estimate the overall Precision, Recall, F-measure for the model. Is use normal mean average is suitable or F1 or p-value? Which one is better?
Question
Suppose we have a signal as x(t) = exp(i(omega*t + phi)), after a simple calculation as y(t) = 1/x(t). We can clearly see that there is a phase shift of Pi=180deg. However, using directly calculation as y(t) = 1/x(t) = exp(-i(omega*t + phi)), the phase shift shall be:
delta phi = angle(x(t)*conj(y(t))) = angle(exp(i(omega*t + phi)*exp(i(omega*t + phi)))) = 2*omega*t + 2*phi, which does not equal to Pi.
This problem occur for a general combination of calculations for a signal. Suppose the calculations can be treated as an operator upon the signal function as L(f). Then after these operation, what phase shift will we get?
phase shift = angle(x(t)*conj(y(t))) = angle(x(t)*conj(L(x(t)))) = ?
Where conj() means to get the conjugate of the a complex value.
The phase shift we wish to get here can be defined in this example, where two signals x(t) and y(t) are generated using real valued functions, and the phase shift between the two signals are calculated using Fast Fourier Transformation (FFT) method.
eg. A minimal coding example to get phase shift:
x = 2 + cos(2*Pi*f*t) + noise, y = 1/x
X = FFT(x), Y = FFT(y)
delta phi = angle(X*conj(Y))
Where f is the signal oscillation frequency, t is time axis. Function angle() to get the argument (phase) of complex value. Function conj() to get the conjecture of complex value.
Question
The Riemann zeta function or Euler–Riemann zeta hypothesis is the more challenging and unsolved problem in mathematics. What's the applications in physics and science engineering ? Some research advances to solve it ?
The Zeta function is a very important function in mathematics. While it was not created by Riemann, it is named after him because he was able to prove an important relationship between its zeros and the distribution of the prime numbers. His result is critical to the proof of the prime number theorem.
For more details see
Question
Does someone know how to get an empirical equation from three variable data?
The data is listed in the attached file
without sin, sinh and tanh
y = 22.1343029549693 + 10.8292764965611*x + 0.296189687976693*x*z^2 + 27*z/x^2 - 2.11016161227361*x*z - 0.270179597887278*x^2
Question
I'm currently working on an optimization problem (please see attached file).
Any tipps to linearize the objective function? Please note that a,b and c are real constants.
Thanks!
This
also provide a lot of information for how to convert a convex problem to conic form e.g. second order cone form. This should be your best option as mentioned by Adam Letchford. Mosek is of course one among several optimizers for SOCPs.
Question
I have a set of straight lines with an specific order which I can use to form a polygon, what I need is to configure the internal angles of the (almost certainly irregular) polygon in order to get the biggest posible circle inside it (it's posible that the circle doesn't touch many of the lines).
-how can I guarantee the constructed polygon gives the largest circle? (maximizing angles?)
-I plan to apply numerical methods for the solution but I need "rules" for the code.
thanks in advance to all of you.
Hi, I forgot to write here that I solved it: for the first part, I found the configurarion that made it a cyclic polygon (which means Its area was maximized), then with a defined shape (edges and angles), using Voronoi diagrams I found the center of the inner circle and with it I computed its diameter, sorry for writting after so much time, another project took all my atention for the last months
Question
Are there simulations that...
- simulate changes in the tRNA pool?
- simulate flexizymes?
- simulate aaRS?
I did a lot of research but didn't find practical approachs on the role of these three components in genetic code evolution (either mathematical or computer simulations or laboratory experiments).
I'd appreciate any information in this direction.
Hi Hanna!
If you are interested about more theoretical aspects of genetic code emergence, especially about a coevolving nucleic acid/protein world and gene-replicase-translatase systems, I suggest to take at look at the work of Peter R Wills. Good papers to start with are:
(about a theoretical model of self-organization of the coding system)
Question
I would like to publish SCI -INDEXED journal ? is the above mentioned is SCI-indexed or not? pls. suggest
International Journal of Applied Mathematics and Computer Science
Language English
Edited byJózef Korbicz
Publication details
Former name(s)Applied Mathematics and Computer Science
Publication history 1991-present
Publisher University of Zielona Góra and Lubuskie Scientific Society (Poland)
Frequency Quarterly
Open access Yes
Impact factor (2016)1.420 Standard abbreviations ISO 4 Int. J. Appl. Math. Comput. Sci.Math Sci Net Internat. J. Appl. Sci. Comput.
Indexing
ISSN 1641-876X (print) 2083-8492 (web) OCLC no.54678624 Links
• Journal homepage
• Online archive
Question
Using this PECE method, I have noticed that i get finite number of dependent variable(population) values with respect to finite number of independent variable(time) values. As far I know, this PECE method gives discrete values w.r.t discrete time. so I am unable to get full time series of the population. Is there any process to get full time series using PECE?
Thanks a Lot...
Yes Roberto Ferretti , I have done that by using Matlab.
Question
I am doing M.Tech in Mathematics and Computing from IIT Patna and I want to go for Ph.D. after M.tech. I am from Mathematics background (M.Sc.). I want to know the research opportunities in the fields of network science and artificial intelligence.
Hey there,
You can find interesting topics, related to artificial intelligence, in "https://www.quora.com/What-are-the-hot-topics-in-artificial-intelligence-for-research". In general, neural networks (in particular, convolutional neural networks) have received many efforts of the research community, therefore, this is an important/relevant topic.
Question
The combined theory of developing unbreakable codes includes complex mathematical and computational methods in conjunction with AI.
There is no such methodology used in developing unbreakable codes, I guess.
Question
I think mesh-based methods can be completely replaced by mesh-free methods, but maybe mesh-based methods such as FEMs have some useful properties that mesh-free methods don't have them.
Its a trade off between matrix dimension and sparsity. Often, FEM methods have large but sparse matrices, whilst RBFs tend to involve smaller but less well conditioned metric matrices. Progress on ill-conditioning of RBF kernel matrices is partially overcome by Mercer expansion of the GRBF. See Fornberg & co, as well as Fasshauer and McCourt.
Question
The applied mathematics is essential tool in computer science and engineering. What is the best methodology to teach applied mathematics in computer science and engineering?
I believe that, we can use it the physics laboratory and engineering laboratory to make the data experiments and Mathematics equations after that solving mathematically, so you can use it ta the class for more interesting during the lecture.
regards
Question
GA and other Evolutionary Algorithms seems to be quite famous within the researchers from Computer Science and Management but researchers from Mathematics just don't like it. Is there any particular reason for that?
We know that with these algorithms we can't prove that our solution is optimal but still in most of the cases we end up with an optimal solution. Apart from that, these algorithms are very easy to implement and fast.
Actually, I don't think it is the case that mathematicians don't like evolutionary algorithms.  I think what mathematicians really don't like is the way that some researchers claim to come up with "new" meta-heuristics every month or two, based on things like bats, fireflies and water droplets.  Very good discussions of this phenomenon can be found in the following papers.
Question
We developed an application for Mathematical and Computational Modelling of the Tumor Growth Based on Evolutionary Aspects of Hypoxia and Acidosis on the Microenvironment of Cancer Cells.
This application has the potential to be used in the study the growth pattern of the different cancer phenotypes, the clonal evolution of tumor, the tumor heterogenicity, Multi Drug Resistance and interactions of cancer cells and their microenvironment.You can find more details about the project in the link below.
I would like to ask, how we can label and define each cell is this kind of models to understand to know the origin of each cell, lifetime, and similar cells which create clones and generally how we can define clones in the mathematical models?
We applied a great idea to this question but I didn't find any similar approaches. Therefore, I will thankful if there is anyone who can help us to get more info.
Question
Given a1, a2, ..., an positive real numbers, and defined
p= a\prod { i = 1 to n, i <> k} [(ai)- (ak)2]
how to prove that \sum \frac{1}{pi} is positive?
I had an idea of proof, but not sure it would work....
I have the idea written in the attached .png file.
EDIT: See the .png file here.
Thanks Viera answer I've got that the proof for even  n  is quite sufficient. Thank you Viera for keeping calm while giving interesting answers to interesting questions:)
Best regards, Joachim
PS. Meanwhile I have realized, that replacing   ak2  by  ck  and and assuming increasing ordering (without losses, as Viera has noticed) , we are getting for the sum S of the question the following expression with the use of divided difference of order  n-1:
(n-1)! (-1)n-1 S = (n-1)! [ c1, c2, . . . , cn :  f(c) ],
which equals the value   f(n-1)(b)  of the derivative  of  f  of  order  n-1  at some point  b  from [c1 ,  cn ],  where  in this case   f(c) = 1/\sqrt{c}.
For the calculus of divided differences and their reprepresentation see e.g.
Having this and the sign changes of the derivative of the inverse square root one gets positive value of   S, for any choice of   positive   ck -s .
Further conclusion is the  this holds for every negative power of  c  put in place of  f(c),  and also for every Laplace transform  of a positive measure on  R+  since then the derivatives of order  n  have  sign equal   (-1)n  (cf. the William Feller Bible on probability about the completely monotone functions)  JoD
Question
Is BVPh mathematica package for HAM valid for initial value PDEs?
I think yes. It provides a convenient analytic tool to solve many nonlinear ordinary differential equations  as well as some nonlinear partial differential equations.
Question
Here a(x) and b(x)  satisfy b(x)=a(1/x), c(x) and d(x) satisfy d(x)=c(1/x), where the coefficients of polynomials a(x),b(x),c(x),d(x) belong to Fq. Then how to count the number of solutions (a(x),c(x)) in Fq.
Dear Patrick, thank you. Apparently, I was concentrated on the first sentence of the question, and did not pay attention to the last one.
Question
I was wondering if someone knows whether Mathematica allows one to plot another 'probability function over the unit 2 simplex (it can be expressed as a function of two arguments subject to certain contrainsts function .
Where I am taking the domain to be of the function to be over vectors in  the 2- standard simplex  itself as it were,subject to certain contrain'ts.
Does it actually have a closed form expression as a function x,y coordinates. as a function of two arguments. I presume  mathematica can allows you plot it .and optimize certain functions over  tenary plot, ternary graph, triangle plot, simplex plot, G? Is that correct
If you plot is assigned to G, then type FullForm[G]. Pay attention to the head.If you see Graphics[stuff], then you can use the Show command to combine plots, Its you see Graph[stuff], it might still be possible, but is harder. If you code is not too long, I recommend attaching it to your question.
Question
In solution of non-linear algebraic equations, now researchers suggest Holomorphic Embedding solutions. These are supposed to give a non-iterative unique solution. And reliable at the same time.
Homotopy methods using a real number for embedding (say Lamda) are also suggested. It would be interesting to me to see a simple tutorial on the issue. Let us take say, three non-linear equations in x1, x2 and x3. and solve by both the methods so we can know how each one id different from the other. Thanks to research gate..
Right, Mr Ravi.Homotopy methods use a real valued embedding parameter on a convex trajectory and traverse from a easy solution to the real and more difficult solution.
The other similar method is holomorphic embedding with a complex parameter, also used foe loadflow studies.
My doubt is: Is the homotopy method a special case of holomorphic method. What special advantage, if any, does the holomorphic method has over homotopy method?
G K Rao
Question
matrix entries may be integer or real
matrices size any size(n)
Automatic code converter from matlab to verilog/hdl code is available. Choose: File ->New-> Code Generation Project and save the project it in the form of  hdl code generation format. Now perform the basic steps to obtain the final code in VHDL/Verilog code format.
Question
For comparison of two homography transformation matrix, which cost function can use?
@Latrache - In given PDE solution, we can consider x and y points are two matrix values?
Question
Mathematica 11.0.1 has a habit of expressing real valued functions in terms of combinations of functions of a complex variable. This makes it difficult to see exactly how the function depends on the real valued variable for which it is defined.
An example that I have in mind is the function f(T) which is defined below. f is a real valued function and T is a dimensionless time which is also real.
f(T) is defined as Ei[2(Eulergamma) - i(pi) + ln[1/(4T)]] + Ei[2(Eulergamma) + i(pi) + ln[1/(4T)]].
Eulergamma is Euler's second constant which is approximately 0.5772, i is the complex number i, ln is the natural logarithm, and Ei is the Exponential Integral Ei function which is defined by Mathematica 11.0.1 as
Ei(z) = - Integral from (-z) to infinity of (e^(-t))/t dt.
If it can be shown how the above function f(T) can be written only in terms of real valued variables, I would be very grateful.
Thanks very much for your generous help,
Ron Zamir
e^(-t+i*pi))=-e^(-t)
e^(-t-i*pi))=-e^(-t)
Ei(z) = - Integral from (-z) to infinity of (e^(-t+i*pi))/(t-i*pi) dt=
= Integral from (-z) to infinity of (e^(-t))*(t+i*pi)/(t^2+pi^2) dt=
=Integral from (-z) to infinity of (e^(-t))*t/(t^2+pi^2) dt+
+i*Integral from (-z) to infinity of (e^(-t))*pi/(t^2+pi^2) dt
Question
First, separable Hilbert space technology must be merged with non-separable Hilbert space technology. Next function theory must be merged with Hilbert space operator technology. The following step implies the usage of a multidimensional number system.
Okay Hans,
Kind regards, florian
Question
Hello,
I am currently trying to create a compliant mechanism by topology optimization in Abaqus 6.14-1, but I am already stuck at the standard examples from literature.
Take the compliant gripper for example. I understand the theory of maximizing the geometrical advantage (GA = Fout/Fin, or GA = uout/uin), while constraining the volume and input displacement.
My problem is implementing the geometrical advantage into Abaqus. How can I add the geometrical advantage to the design responses? Under "single-term" I can (obviously) not find the GA.
Under "combined-term" I could (in theory) combine the two single-term displacements or forces, but a division or multiplication is not possible. Just "substract", "absoulte difference" and "weighted combination".
Any help how to implement the GA would be really appreciated! :-)
Best regards
Rene Moitroux
Thank you very much for your answer!
Our library has this book, I will try to get it this afternoon. I read about the MatLAB codes, but tried to solve the problem solely with Abaqus to reduce complexity. As this does not work, I guess MatLAB should be the easiest solution then, I will check it out. Thank you again for your input!
Best regards
Rene Moitroux
Question
Please, what is the length of the square element used to discretize the design domain in "A 99 line topology optimization code written in Matlab" by O Sigmund? Thank you.
Thank you, Professor Michael.
Question
I am trying to learn Homotopy Method (HAM). Can you please suggest me a book or source to learn HAM with Mathematica..?
This is an excellent question wilth many possible answers.   In addition to the helpful answer given by @Richard Epenoy, there is a bit more to consider.
A very detailed introduction to the use of Mathematica to implement the homotopy method is given in
A very good example of Mathematica using the homotopy analysis method (complete with detailed Mathematica code) is given in
Question
I am confronted with a research problem in a field which is unfamiliar to me, and though I am a quick learner, I need to know where to start!
My problem concerns proving the existence of global solutions to a set of coupled integro-differential and partial differential equations. I do not need to find specific solutions. I have some scant experience with finite difference methods but I fear they will not cut it in this case, or at least they are slightly less-than-satisfactory here.
Can anyone please give me a) any texts/links they would recommend for this purpose, and/or b) any particular methods or theorems I should be googling?
An excellent book is:
Partial Differential Equations by Lawrence C. Evans, Graduate Studies in Mathematics, Volume 19, American Mathematical Society, Rhode Island (1998). This is a very readable textbook, that is also highly estimated by some of my colleagues in mathematics. Warning: Results on the existence of global (not only local) solutions are meagre.
Question
There is a multitude of well balanced schemes for the shallow water models with source terms.
Which five of them can you recommend? The hydrostatic reconstruction is actually top on my list. So what do you think?
There has been great emphasis in the literature on the derivation of well balanced schemes for the shallow water (SHW) and similar equations in the case in which both the continuity equation and the momentum equation are in full flux form. However, for many applications (especially in subcritical regimes), in my opinion,  there is no real necessity of employing the momentum equation in full flux form, since strict momentum conservation is often not really necessary (especially when dissipative terms are important and, as often happens, uncertain). In these cases the pressure gradient term is best written in non conservative form (see e.g. what is done in this paper
Rosatti, G., Bonaventura, L., Deponti, A., & Garegnani, G. (2011). An accurate and efficient semi‐implicit method for section‐averaged free‐surface flow modelling. International Journal for Numerical Methods in Fluids, 65(4), 448-473,
but there are many others also doing this). If you do that, the well balancing property is essentially automatic and granted for free and you do not need to worry about which approach to choose. Going deeper into well balancing issues is only really necessary when strict momentum conservation is essential (for example, when solving dam break problems). However, you can see from the previous paper that good solution for dam break problems can also be achieved for SHW equations formulated as suggested above.
Question
For calculating mean of x1, x2 and x3, instead of simply adding them and divide by 3, I have adopted another method similar to inverse distance weighing function.
μx = (x1 + x2 + x3)/3
wi = 1/(μx − xi)^2 = 1/(di)^2......i ∈ [1, 3]
μ(wx)=wi ∗xi/(w1+ w2+w3)....i∈[1,3]
where, wi is the weight of each observation and μ(wx) is the final mean which I have used in my research.
Is this method admissible ? Please give your comments and any references if you have ?
Dear Rajkamal Kumar,
I like your idea of diminishing the role of outstanding data, which is an especially important feature for measurements/observations exposed to extraordinary random perturbations. However, there are some places, where we cannot aply the term of the 'true' mean value, unless a particular model of the perturbation is assumed and then analysed. Seemingly, a simle and directly correponding to your idea example can be given as follows:
The statistical procedure measures a rv $X$ with pd being a convex combination of the PROPER pd (with pr. p) and the FALSE pd Q (with pr. q = 1- p), in symbols:
$P_X = p \cdot P + q \cdot Q$
Now, for being more specific, let both be normal
${\cal N}(m,v)$ and ${\cal N}(M,V)$, respectively,
where the expectations are different ( $m \ne M$ ) and with variances satisfying $0 < v << V$. I think, that simulations will show in this case better approximation of $m$ with your weighted mean that the usual arithmetic mean.
Best wishes and good luck in continuing the proposal.
PS. The following is a sketch of a reason to ASSUME, that Kumar's average $K(x)$ of $d$ entries
$x = ( x_1, . . . x_d)$
takes value zero, at points, where at least one coordinate equals the arithmetic average, denoted further by $A(x)$:
0.The average $K$ is defined only for sequences where none coordinate equals the average $A(x)$.
1. For these $x$-s, denoting
$y_j := 1 / (x_j - A(x))$ and $\sum$ for $\sum_{j=1}^d$
we have horeover,
$|K(x) - A(x)| \le |(\sum_{j=1}^d y_j ) / ( \sum y_j^2 ) | \le (\sum_{j=1}^d |y_j| ) / ( \sum y_j^2 ) \le ( \sum_{j=1}^d |y_j| ) / ( [ max{ |y_j| : over j} ]^2 ) \le ( d \cdot max{ |y_j| : over j} ) / ( [ max{ |y_j| : over j} ]^2 ) \le d \cdot [ min{ |x_j - A(x)| : over j} ]$
Joachim Domsta
Question
How do I prove that a nth order differential equation has n linearly independent solutions?
Also, how to prove that there is no possible solution other than those covered by the linear combination of these solutions?
Please suggest a text to find out these answers.
The textbooks  that I used when I was a student are in Russian, which I afraid make them of little use for you :).  I have made a google search with keyword existence and uniqueness of solution for linear differential equation'' and have found immediately the following text that contains the exact statement of the theorem and the reference  to a texbook:
It also contains the explanation, why in the homogeneous case there are n linearly independent solutions, that I sketched in my previous post, and what happens in the non- homogeneous case.
Another reference:
D. Willett.  The Existence-Uniqueness Theorem for an nth Order Linear Ordinary Differential Equation.  The American Mathematical Monthly
Vol. 75, No. 2 (Feb., 1968), pp. 174-178
Question
I am new to this field and would like to use this concept.I want to know what features decide the size of texton for an image.Please help me in calculation of texton of an image?
pls refere to the files
Question
Consider two system of nonlinear equations. In this case we will get F(x1, x2)=[c1 c2] ^T; Based on my problem, I need to calculate inverse of F. Also, I have try pinv(F), inv(F) but code gives
............................................
??? Error using ==> sym.svd
Too many input arguments.
Error in ==> pinv at 29
[U,S,V] = svd(A,0);
Error in ==> sys_4th_kt at 48
t=f(y)*pinv(f(x0));
............................
The following one:
ux = Df(x0)\f(x0); %System of linear equation Ax = b, x = inv(A)*b, but better way is x=A\b.
y = x0 - (1)*ux;
t=f(y)*pinv(f(x0));
p=Df(x0)*(I-t)^2;
ux1 = f(y)*pinv(p);
x1 = y-ux1; % 4th order Kung and Traub
You need to understand the meaning of inverse and where it exists.
Question
Hello all,
I would like to discuss a best possible method for consumer behavior modelling.
For example, if a consumer goes same super market all the time, i would like to model the purchasing behavior so that the model can  accurately predict the goods he may buy next time he visits the store.
The problem may be approached  from the patter recognition point of view also.
Dear Chittesh,
This is a good question with many possible answers and points-of-view.   It seems that it is often the case that we learn about human behaviour indirectly by considering how humans interact with other humans, the environment and machines.   In short, mathematical views of human behaviour often focus on stimulus-response modelling.
Mathematical models of human behaviour have been recently been studied in the context of epidemics in
P. Poletti, Human behaviour in epidemic modelling, Ph.D. thesis, University of Trento, 2010:
Human behaviour is modelled by Poletti in terms of two mutually influencing phenomena: epidemic transitions and behavioural changes in the population of susceptible individuals (see Section 2.2, starting on page 16).
Modelling human-computer (device) interaction is the focus of
P. Eslambolchilar, Making sense of interaction using a model-based approach, Ph.D. thesis, National University of Ireland, Maynooth, 2006:
See, for example, the probabilistic framework of a model-based behaviour system in Fig. 6.13, starting on page 182.
A bit less mathematical but still very interesting model of human behaviour in terms of human-made music is given in
A. Tidemann, A groovy virtual drummer: Learning by imitation using a self-organizing connectionist architecture, Ph.D. thesis, Norwegian University of Science and Technology, 209:
For an overview of the Tidemann's approach to model and imitate human musical expressiveness, see Fig. 1.1, p. 5.
This thesis introduces the SHEILA architecture in terms of human drum-playing patterns with an accompanying melody (see Section 3, Architectuure, page 106 in the pdf file but unnumbered in the thesis).
(by James F Peters)
Question
I am exploring the performance of a measure that can be computed using different values of its parameters, so I have about 20 variables. I want to find out which of these variables are able to differentiate two groups. So, I want to know about the performance of the variables, rather than finding differences between the groups. Therefore, I don't really think that I am given myself multiple chances to find a difference between the two groups and so I am inflating the chances of getting significant differences by chance. Actually, I am considering from the begining that the groups are different. So, do I really need some correction if I compare the 20 variables between the groups?
Consider also using a stepwise logistic regression in which you use 0=group 1 and 1=group 2, with twenty independent variables. If there is multicollinearity among the independent variables, it may be better to remove some variables before running the logistic regression. The odds ratio will tell you which variables are most important.
Question
Hello dear colleagues!
Does any of you know how an effective algorithm to generate a graph with a given degree distribution with fixed number of elements? I developed a couple of them by myself, but they are not efficient enough. I realized that it is not a trivial problem if there are some geometric constrains (graph on cylinder) and fixed number of elements.
Any ideas or relevant references?
Thanks a lot in advance!
Likewise have a look at the igraph package, in particular the graph.*.game  constructors for a graph.  In R you can just do install.packages("igraph")  library(igraph) and then ??graph to see various ways to construct graphs.
Question
Let's say I'm developing a method for parameter estimations. I want it to be fast and accurate. What other characteristics would it need to make it the go to method, or the first attempted method for solving these kinds of problems? What are current methods lacking? If you can reference papers that would be great if not it's okay as well.
See, for instance,
- Bard, Y. "Nonlinear Parameter Estimation". Academic Press, 1974
- Seber, G. A. F. & Wild, C. J. "Nonlinear Regression". Wiley-Interscience, 2003,  Section 7.5
Question
I have an open-shell calculation, selective dynamics with >120 atoms. The frequency calculation uses NFREE=2 and apparently it still failed even with 6 days of walltime. I have optimized the parallel parameters, but is there really any way to resume the calculation? For geometry optimization, we could just take the contcar file and submit the calculation rightaway, but what about frequency calculation?
Generally to get the frequencies VASP calculates the total energy after moving all atoms in space by a small step +-dx in 3D. From this VASP generates the hessian second derivative matrix of total energy with respect to atomic coordinates (with a finite difference scheme, but depending on the option you used in the INCAR), at the wanted configuration, and the eigenvalues are the frequencies. Since you have 120 atoms in the cell, at NFREE=2, this is 120*2*3=720 DFT calculations, which should converge separately, each with 120 atoms, which is what is taking so long.
You can try to make this go faster by various ways, like reducing the convergence criteria, the kgrid density, and also by using selective dynamics on only part of the atoms if you don't need them all (say only near the surface if this is the case). There are many other ways of course.
If you want to salvage some of the data that was lost, you should check the OUTCAR, VASP should write there the energies at each configuration before the calculations was killed(depending on your INCAR input for NWRITE). You can then set selective dynamics off for the atoms that the calculation finished previously, and do the next calculation with only the missing atoms with seelctive dynamics turned on. From there you could construct your own hessian by a similar finite difference scheme and diagonalize it, instead of letting VASP do this.
Hope this helps,
Ofer.
Question
Where can i find the complete Lagrangian of SQCD (in the WZ gauge)?
In any textbook or lecture notes on the subject, e.g. http://www-fp.usc.es/~edels/SUSY/ (suffices to search for sqcd wz gauge and sort out the relevant entries).
Question
I have seen lot of papers on incomplete hypercube architecture on 1991-2000 Why there is no recent works on that?
This is an interesting question.
For very  recent consideration of incomplete hypercubes, see Section 4 in
and Section 3 in
Question
bw1 = edge(I,'canny');
I need to use canny edge but it is not working as "sobel" and "prewitt"
@Abdelrahiem Ahmed Hashem: I too agree to all ..there is absolutely no reason for canny to not work if sobel and prewitt work in your system (I mean by chance if the edge code is not corrupt or overwritten in your system).. Would u mind sharing the error plz?
Question
Hi all, I have a problem with regard to ill-conditioned linear system of solving sets of simultaneous equations using Mathematica program. I have tried my best to find a way to solve this problem but none was successful. I got results from m =1 and n =1 until m = 7 and n = 7, i,e. the systems are well-conditioned noting that I am dealing with exponential matrix. However, the problem started from m = 9 and n = 9 due to ill-conditioned systems. Note that m = n = 1,3,5,6,7,9,.........99. I am trying to find a treatment so that the matrix would not become a singular.
Thank you all for your replies.
Question
i have studied the interaction between two reactants using SIESTA code . now i want to check whether my product is stable or not . How can i do this in SIESTA. ? i have heard about Minimum energy path models but i have got no idea from that . Can any body explain precisely ?
i also want to know , is it always necessary to calculate dissociation energy using various models like NEB or Drag and drop in Finding minimum energy path ?
Question
I am currently planning a longitudinal study looking at changes in inflammatory markers as a result of Mind Body Exercises. Is there any way to account for NFKB's oscillatory tendencies? I know modeling programs are under development to predict oscillatory frequencies and amplitudes, but I have no idea if a human model exists yet. I would love to be able to account for the variability in inflammatory profiles on both ends of the oscillation, thus being able to see an effect (if it exists) regardless of where in the phase I come in. Thanks!
Question
Do you usually use the long procedures given in the standard textbooks in calculus or have you tried using some derived formulas like the one given in the link below? Perhaps, you can also try deriving other formulas for solving some other optimization problems and if you have already, may be you can also share your formulas with us.
In the particular case when the distance is attained, mentioned above, the hyperplanes H_1, H_2 are tangent  respectively to the boundaries of A, B at the points where the distance d(A,B) is attained.
Question
I use usually Mathematica in my scientific work. It possesses two interesting functions Series[f,{x,x0,n}] and InverseSeries[s]. The first one generates a power series expansion for a given function f(x) about the point x=x0 to order (x-x0)^n, and the second takes the series s, and gives a series for the inverse of the function represented by s.
Of course we can implement appropriate algorithm in any mathematical software but I am looking for such programs which have a built in one as standard library (package).
I tried to find this feature in Matlab but I did not find any information on this subject in manuals?
I write for you example I expand the function sin(x+y) in taylor about (0,0) and I find the coefficient of x, y ,x^2y, xy^2,
restart:
f:=(x,y)-> sin(x+y);
e:=mtaylor(f(x,y), [x, y], 8);
coeftayl(e, [x, y] = [0, 0], [1, 0]);
coeftayl(e, [x, y] = [0, 0], [0, 1]);
coeftayl(e, [x, y] = [0, 0], [1, 1]);
coeftayl(e, [x, y] = [0, 0], [2, 1]);
coeftayl(e, [x, y] = [0, 0], [1, 2]);
coeftayl(e, [x, y] = [0, 0], [2, 2]);
Question
Hello dear all,
Here is my problem.Could you give me some suggestion? I want to solve a linear system Ax=B, and original A is 3000*3000 matrix, which is square, sparse and banded, having both the lower and upper bandwidths equal to 4. what is the best method for solving using Matlab?
Thank you
Generate the matrix A as a sparse matrix in Matlab. If it's banded, you only need to generate the diagonals as vectors in order to create the matrix using the spdiags  command.
Then generate the right-hand side B, and solve by the usual x = A\B.
A 3000x3000 system is not particularly large, and the problem should be solved literally within seconds.
Question
If the eigenvalues of my 6 x 6 stiffness matrix are 100, 1200, 1250, 1300, 1320, 1330, what do these values mean? How can I locate the points of applications of each of these eigenvalues on my model? What would be there influence on my model?
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How about these coefficients are time-independent functions? Since the constant coefficients only lead to the convenience in the stability analysis.
Alternating direction implicit is a splitting method based on treating terms coming from the discretization of spatial derivatives one at the time. It does not matter whether the coefficients are constant or functions of space and time as well. The main issue, from a modern perspective, is that the computational gains which made ADI popular 30 years ago are nowadays considered to be insufficient to justify the introduction of directional splitting error that results from using this method. I do not recall any relevant paper in CFD using ADI in the last 10 or 15 years. Conclusion: use any implicit method you want for time discretization, but solve the resulting linear/nonlinear system as it is, without introducing directional splitting by trying to reduce it to one dimensional problems.
Question
I am trying to code a system of reaction diffusion system with non-linear coupling terms (such as schnakenberg reaction). I am unable to code the numerical integration using area of each triangular element. Is there a step-by-step source of information that I can adopt to complete my script?
Question
Thanks!
For periodic functions integrated over a period (as when computing the coefficients of a Fourier series) the midpoint and the trapezoidal rule coincide. These formulas can be proven to be superconvergent in this specific case, which means that for this special kind of definite integral, rather than being just second order accurate they are convergent of arbitrarily high order for functions that are C^infinity. Also for this reason, the discrete Fourier coefficients are defined by the application of the trapezoidal rule to the definite integral that defines the Fourier coefficient: there is no need of more accurate integration formulae, and on top of that Fast Fourier Transform algorithm apply for this definition of the discrete Fourier coefficients.
You can find more details in several books, see e.g.
Question
Suggest me How i solve given problem with cubic spline or finete difference method or finite difference method with cubic spline.
f"'+f'f"=0
B.C. f(0)=constant , f'(0)=0  and f'(infinity)=1 ?
Your problem is solved in more general case in the attached file by using "Shooting method". It might have useful to solve your problem by "Difference method".
Question
Given a linear ODE, x'=Ax, where A is a Hamiltonian matrix, I transform via x=Ty s.t. T^(-1)AT is in Jordan canonical form. Is T a symplectic matrix?
Essentially, I want to know if the transformation to the eigenbasis of a linear Hamiltonian system is a symplectic transformation (also called a canonical transformation). I suspect that in general it will not be, unless one is careful with the scaling of the eigenvectors before placing in the columns of T, but I haven't found any obvious answers to this question in texts on Hamiltonian Dynamics (Meyer & Hall, Marsden & Ratiu, Arnold).
For a linear Hamiltonian system, it is possible to find a symplectic transformation which puts the system in Jordan canonical form?
In practice, I am considering x in R^n where n is 4 or higher (n even). Let J be the canonical symplectic matrix (sometimes called the Poisson matrix). A Hamiltonian matrix (also called an infinitesimally symplectic matrix) is one such that
JA + ATJ=0
And T being symplectic means TTJT=J
There is an authorative answer to your question.  The paper
Wen-Wei Lin, Volker Mehrmann, and Hongguo Xu, Canonical forms for Hamiltonian and symplectic matrices and pencils. Linear Algebra and its Applications, Volume 302-303, pages 469--533, 199, doi:  http://dx.doi.org/10.1016/S0024-3795(99)00191-3
provides the sufficient and necessary conditions under which the Hamiltonian Jordan form exists.  There is a vast literature on related questions in the (Numerical) Linear Algebra and Matrix Theory literature.
NOTE: the transformation to diagonal or Jordan form should only be used for theoretical purposes, never, never do it on a computer!  The transformation will be - unlike for symmetric matrices - be very ill-conditioned and will destroy the numerical accuracy of any computations!  For numerical purposes, there are other symplectic (orthogonal) transformations that should be used to simplify linear Hamiltonian systems! There is a recent survey on these, see
Angelika Bunse-Gerstner, Heike Faßbender, Breaking Van Loan’s Curse: A Quest for Structure-Preserving Algorithms for Dense Structured Eigenvalue Problems, In P. Benner, M. Bollhöfer, D. Kressner, Ch. Mehl, and T. Stykel (Eds.), Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, Part I, pp. 3-23, Springer International Publishing, 2015.
DOI: 10.1007/978-3-319-15260-8_1
Question
I am working on verifying bandwidth consumption for my proposed method with the existing related work. I have verified the same with simulation results and would now also like to verify the results analytically. How can i proceed ahead. Should i have to derive a mathematical expression and then simulate it and compare with the simulation set of results. I lack the understanding of theoretical analysis.
Both analytical and simulation methods are modelling approaches which aim at providing an idea of system performance, in different conditions.
An analytic model is a mathematical abstraction that can be extended to address various working conditions, thanks to some assumptions about the way a process is evolving. In some cases, an exact solution can be derived and a result can be obtained in various conditions. The beauty of the analytical model is that it provides a generic way to get performance results in various conditions through a mathematical formulation. The accuracy of the model is to be considered through the alidity of the assumption to derive the mathematical formulation. Some uncertainties can be handled through a stochastic model to account for modelling and measurement model.
A simulation model such as a monte-carlo also make assumption of a model and some assumption about the behaviour of the process. It is used when an analytical formulation cannot be derived (for example when the size of the model is too large,or when no exact solution can be derived). Simulation models provide results for a specific use case and should be run many times to counterbalance the effect of numerical calculations. For a different functioning use case, the simulation should be run over again. A simulation model can be accepted when results are validated in  a number of working conditions under various input assumptions.
When the two approaches can be used, preference should be given to the analytical approach and simultation can be used to validate the assumptions and the models. For better analysis, the simultaion model could be used with assumptions slightly different from the analytical model, since simultation is not aimed at validating the model but the reality of the modelled process.
Question
Suppose I want to find the orthogonal projection of (x1,x2,y1,y2) such that x1=x2, y1=y2. I have to calculate the A matrix whose columns are the basis vectors of given subspace. I choose A=[v1;v2] as basis vector combination, where v1=[1 0 1 0] and v2=[0 1 0 1]. Then I calculated the Projection matrix as P=A(AT A)-1A.
Now if I want to find the Projection matrix of (x1,x2,x3,y1,y2,y3,z1,z2,z3) such that
(x2−x1)2+(y2−y1)2+(z2−z1)2=64
(x2−x3)2+(y2−y3)2+(z2−z3)2=36
(x3−x1)2+(y3−y2)2+(z3−z1)2=100
Do I have to find the basis vector for calculating Projection matrix? If yes, how?
Is there any other way to find its Projection matrix (P)?
For curved surface there is no projection. But there is a point (points) at the surface at the small distance from the initial poyint. It is the standard variational problem (conditional minimum)
Question
I often use Mathematica software in my scientific work. Sometimes computations are very complex and spend a lot of time on standard PC (4-6 physical cores or 8-12 logical cores). I try to use parallel calculations but they accelerate a few times.  Generally I solve numerically single or double integrals with nonlinear equations which can also contain integrals. One mentioned operation is calculated in non parallel mode but I need series of results which I can calculate parallel (for example ParalellTable[]).
I have question with CUDA in Mathematica. Theoretically very efficient graphic card should  give significant acceleration. After reading Mathematica manual we can state that it is easy to calculate matrix operations with CUDA but integrals and nonlinear equations are rather difficult to obtain. I have question if somebody has good experience in solving said issues using GPU computing and could give me clear tips, literature, etc?
Cuda processors are SIMD (single instruction multiple data) architectures. Cuda processors are extremely efficient at computation on data that is not dependent on one another. Depending on the algorithm several dependencies may arise that give way to a break in parallelism.This break in parallelism usually takes place through conditionals.
You would need to be specific on the algorithm to get a more specific answer, since integration could benefit from reduction operations in CUDA, but again it depends on the algorithm.
Question
Rational Legendre?
Dear A. H. Bhrawy,
I think you may better know about it . But if we implement Laguerre polynomials together with operational matrices of integration and differentiation we will easily convert the problem to system of algebric equations.
Question
Numerical solutions to differential equations are obtainable with various methods if the parameters in the equations are known. When such parameters are not determined, they could be determined if the solution of the equation is known at a given (presumably abundant) number of points.
I'm interested to know, according to experts, what are the most reliable and most commonly used techniques used to handle this problem.
If you are also interested in the theoretical point of view, you may want to look at this paper DOI: 10.1002/cpa.21453. This work was mainly motivated by the so called hybrid inverse problems. You can find similar problems and techniques from my contribution page.
Question
I chose the GA for optimization by writing the program using ga code in matlab. This program is ok if I put the terms of fitness function as equations; for example:
y1=1/(s+10)(s+2)
y2=1(s+par)(s+2)
f=sum(y1-y2)^2
When I run the program the ga graphs and results is fine, and par=10.
However, when I put these equations as a model in simulation, the ga graphs (best value) is constant (line) which is incorrect.
My issue is that I need to import y1 from the simulation and y2 from data results to estimate par.
Really I got stuck in this point which is how can I use ga with simulation.
Moreover, I can share the knowledge with who is interested in.
Thanks
It generally can do that. There may be a limitation due to the specific implementation that you are using, but there should be no reason that the GA cannot do this.
Question
Is there a computationally effective method to solve overdetermined equations of the following form:
b=exp(A*x),
where b is a n*1 vector of data, A is a given n*m real matrix (m<n), x is a m*1 vector to be found? exp(.) here is an element-wise exponent of a vector.
If the system is not overdetermined (m=n) and b>0 then the solution is simple: the equation may be rewritten as log(b)=A*x and solved using standard methods for linear systems.
If the system is overdetermined (m<n) and b>0, it still can be solved with log(b)=A*x transformation and QR-decomposition method to solve an overdetermined linear system in the ordinary least squares sense, although there is a pitfall that the least squares are applied to log(b) instead of b.
In my case, I have some zero elements in b, and so the log-transformation does not work. And I'd like to define the "best fit" in the "natural" metrics of b instead of log(b). Of course, it is easy to use purely numerical residual-norm minimization methods, but they are too slow (I have to solve lots of such systems, although m and n are not that that big - on the order of 10).
I think, because the problem looks so simple, there should be a finalized/published solution to it. But I fail to google it. Could you point me in the right direction?
Rather than an answer, I have a few questions which are relevant to finding efficiencies  for solving your problems.  You say that one of the complications is that you have many such systems.  So my first question is:  Does the coefficient matrix A vary from problem to problem?  Secondly, is the known matrix A of full column rank?  And finally, is there any additional information you have about the data  b such as error estimates or distribution?  This would be useful information in designing an algorithm.
Question
In Maple 16,  how can we with the software combstruct,  to give the sentence about the recurrence formula,
A(x)=1+x[A(x)3+3A(x)A(x2)+2A(x3)]/6
Very strange, first the gf then the object to count!
Question
Is there any mathematical or computational approach to verify the results obtained from DMA?
That is straightforward. A finite element model is needed.
Afterwards you can compare the load deflection curve of your experimental setup with your numerical simulation.
Question
Hi, I am looking for literature tackling nondimensionalization of variables in a given system of differential equations. I have only seen up to four. Are there rules for nondimensionalizing a system with larger number of ODEs?
In principle it is possible to nondimensionalise any number of ordinary differential equations, but this rapidly becomes less useful as the number of equations becomes larger.
For the (linear) equation of a damped pendulum with displacement, time and (say) three physical coefficients, time and displacement can be scaled  to get an equation with one dimensionless parameter, say gamma, which determines whether the equation is under-, over- or critically damped.
If you had three or four equations for three or four coupled pendulums, in principle you still have a lot of dimensionless parameters after you scale  time and the displacements. This still gives you a large parameter space and very complicated, possibly chaotic behaviour, unless you are able to make simplifying assumptions and set some parameters to zero.
Question
is weka follows any default discretization technique or not?
not all data attributes  require discretization
so many classifiers can be used on such raw data
decision tree algorithms very often use a built-in default discretization  alg. not visible to the user
Question
See above.
I did
SetPrecision[Log10[Pi], 1000000]
in Mathematica10 and 4 seconds later I had many screens full of digits, the last three of them being 435.
Question
Uni axial test data :
- Highly nonlinear behavior at very low strain.
- Includes strain hardening.
- Tangent modulus increases as pressure increases
Does this have some relation with elasto-plasticity?
Question
Multilevel thresholding based on entropy and image processing
Tsallis is still in use , Shanon is used for comparison. Many papers show work on Renyi and Kernel entropy based methods.
Question
In one of my problems I tried to numerically integrate the following function, F(t) = Exp(-0.5 * t).
Can we use Simpon's rule to integrate it? Or are any other methods used to numerically integrate F(t)?
I guess that you are aware that you can compute the integral analytically, so the first numerical method would be a difference of function evaluations at the endpoints.
Apart from that:
If you want to do it in a purely numerical way, you might want to start with a composite trapezoidal integration just for a start to get a feeling what numerical integration is about.
You can also try higher Newton-Côtes formulas to see what differences in error order mean, and the Newton-Côtes formulae are still easy to implement.
As the final method, you should use Gauß-Laguerre integration, since it will compute the exact result of your integral, already with a 1st order formula.
Question
How i can use T-tecto to compute the Mohr Diagram? I used inverse analysis but there is some method or parameter i could not understand, or how i to used with my parameter.
Dear Milorad i used T-Tecto software to calculate the paleo stress but i still confused how to used the parameter in the paleo stress, i have only thrust fault (Azmuthe , dip, lineation , direction of the fault (scene) when i try to compute it i found difficulty to used the parameter in the inverse analysis i mean the best parameter for my data like (Parameter s ,Parameter d , Parameter q1 , Parameter q2, Stress parameter, Supposed dispersions, Inversion methods,) and other parameter i try with different input and in everytime i get result so i will appreciate your helpfull
thank
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I want to use a 3rd order WENO scheme to solve a transport equation. But for the outflow boundary, there are no boundary conditions. Therefore I don't know how to deal with the outflow boundary since the wide stencil is set to keep the 3rd order.