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

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!

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

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?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 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 ?

Does someone know how to get an empirical equation from three variable data?

The data is listed in the attached file

Thanks in advance

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!

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.

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.

Thanks in advance.

I would like to publish SCI -INDEXED journal ? is the above mentioned is SCI-indexed or not? pls. suggest

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...

The combined theory of developing unbreakable codes includes complex mathematical and computational methods in conjunction with AI.

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.

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?

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.

I'm looking for optimizing multivalued vector valued function.

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.

Given a

_{1}, a_{2}, ..., a_{n}positive real numbers, and definedp

_{k }= a_{k }\prod { i = 1 to n, i <> k} [(a_{i})^{2 }- (a_{k})^{2}]how to prove that \sum \frac{1}{p

_{i}} 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.

Is BVPh mathematica package for HAM valid for initial value PDEs?

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 F

_{q}. Then how to count the number of solutions (a(x),c(x)) in F_{q.} 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

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..

matrix entries may be integer or real

matrices size any size(n)

For comparison of two homography transformation matrix, which cost function can use?

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

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.

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 = F

_{out}/F_{in}, or GA = u_{out}/u_{in}), 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

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.I am trying to learn Homotopy Method (HAM). Can you please suggest me a book or source to learn HAM with Mathematica..?

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?

Thanks in advance.

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?

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 ?

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.

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?

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

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.

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?

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!

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.

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?

Where can i find the complete Lagrangian of SQCD (in the WZ gauge)?

I have seen lot of papers on incomplete hypercube architecture on 1991-2000 Why there is no recent works on that?

bw1 = edge(I,'canny');

I need to use canny edge but it is not working as "sobel" and "prewitt"

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.

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 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!

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.

Article On Minimum Distance Problem

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?

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

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?

How about these coefficients are time-independent functions? Since the constant coefficients only lead to the convenience in the stability analysis.

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?

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 ?

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).

It might be helpful to think about this question another way:

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 + A

^{T}J=0And T being symplectic means T

^{T}JT=JI 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.

Suppose I want to find the orthogonal projection of (x

_{1},x_{2},y_{1},y_{2}) such that x_{1}=x_{2}, y_{1}=y_{2}. I have to calculate the A matrix whose columns are the basis vectors of given subspace. I choose A=[v_{1};v_{2}] 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(A^{T }A)^{-1}A.Now if I want to find the Projection matrix of (x

_{1},x_{2},x_{3},y_{1},y_{2},y_{3},z_{1},z_{2},z_{3}) such that(x

_{2}−x_{1})^{2}+(y_{2}−y_{1})^{2}+(z_{2}−z_{1})^{2}=64(x

_{2}−x_{3})^{2}+(y_{2}−y_{3})^{2}+(z_{2}−z_{3})^{2}=36(x

_{3}−x_{1})^{2}+(y_{3}−y_{2})^{2}+(z_{3}−z_{1})^{2}=100Do 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)?

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?

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.

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

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?

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(x^{2})+2A(x^{3})]/6Is there any mathematical or computational approach to verify the results obtained from DMA?

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?

is weka follows any default discretization technique or not?

Uni axial test data :

- Highly nonlinear behavior at very low strain.

- Includes strain hardening.

- Tangent modulus increases as pressure increases

Multilevel thresholding based on entropy and image processing

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)?

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.

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.

Is there anything faster than solving the dual simplex problem?

What is the recursive function to decide if a number (from domain R, set of real numbers) belongs to (or has an equivalent value in) the set of integers?

Start from 1 and keep incrementing till you hit the number is not really what I am looking for, since it does not reveal how exactly the next incremented number is being decided (or been assumed) to be part of the set of integers.

Explicitly stating 1, 2, 3... so on all belong to N is not really a characteristic function - is there any mathematical characteristic function that does not depend upon such enumeration, but rather on some inherent properties that differentiates between elements of N and R?