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# Computing in Mathematics, Natural Science, Engineering and Medicine - Science topic

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I shared the picture of three parameters 1.Change in Temperature, 2. Change in Relative Humidity, 3. Change in Pressure and respective error value for that.
From the attached data(picture and excel file attached), I need to find the Error value for different input parameter.
If
1.Change in Temperature = 1°C
2. Change in Relative Humidity = 1%
3. Change in Pressure = 1mbar
What is the error value?
If
1.Change in Temperature = 2°C
2. Change in Relative Humidity = 2%
3. Change in Pressure = 2mbar
What is the error value?
If
1.Change in Temperature = 4°C
2. Change in Relative Humidity = 3%
3. Change in Pressure = 2mbar
What is the error value?
Is it possible to find the error value by mathematics. Please tell the way to calculate using calculator or python programming.
if you don’t have the original model that this error term come from then you can’t get the exact answer you’re after. Though you could approximate it by fitting a regression model. E.g. fit a least-squares model to find the best set of parameters a,b,c,d to the equation error = a*temp + b*humid + c*pressure +d.
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- Could you please point me out to some Computer science, and Computer Engineering applications modeled, described, or analyzed using partial differential equations?
- Preferably, involving heat, reaction-diffusion, Poisson, or Wave equation.
- If possible in fuzzy environment.
Best regards
I suggest that you read
"Modeling Information Diffusion in Online Social Networks with Partial Differential Equations".
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I have a function as follows:
y= a*x^b
a=7e-5
b=-0.755
I attached a simple graph of the function. As it is apparent from the graph the CURVATURE of the function increases from ZERO to a finite value (around x=0.1-0.2) and then it decreases to reach a value of ZERO. I did my best to draw the CURVATURE of this function using the following formula:
K=f"/(1+f'^2)^1.5
However, using this formula I could not reach the predictable trend of the curvature. Do you have any idea what is the problem?
I can work with MATLAB and Excel.
Kind regards,
Ebrahim
Check the power index in the denominator of your expression for the curvature. It should be 3/2 rather than 1/2. Good luck
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Given the presented scatter-plot, it is looking like that there is a relationship between X and Y in my data. Unfortunately, the simple nonlinear curves can not describe this relationship. However, I guessed some equations like Y= aX^b + c and Y= a*exp(b*lnX) that can describe the relationship but it seems that they are not the perfect ones.
I am able to do the analysis in MATLAB, SPSS and Excel if you have any suggestion to solve the problem.
kind regards,
Ebrahim
I decided to write a short piece, based on the questions and reasoning I saw here. I mean no offense of course, but I think this is an important point: https://medium.com/@dgoldman0/bad-science-and-modeling-data-c2c13c305c8e
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Dear all,
I'd be grateful if you provide me the solution of this ratio of double integration. I think, the solution will be approximately by using Lindley approximation. Thanks in advance
Regards,
Huda
Dear Amir,
As I mentioned previously, I need the mth moment for reliability function of Erlank distribution when the shape and scale parameters are unknown, which is the solution of the ratio of double integration. I 'll try to use different values of Alpha.
Regards
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Do you think that the iThenticate/CrossCheck/Similarity Index would cause heavy and serious confusion in mathematics? Even destroy, ruin, damage Mathematics? Our mathematics and mathematicians should follow and inherite symbols, phrases, terminology, notions, notations in previous papers, but now we have to change these to avoid, to escape, to hide, to decrease the iThenticate/CrossCheck/Similarity Index! It’s very ridiculous for mathematics and mathematicians! Mathematics is disappearing! being damaged!
Yes! Even standard mathematical symbols and notations are captured in similarity index. The habit of using unconventional symbols and notations just to reduce similarity index is destroying the beauty and taste of mathematics.
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First a large size matrix requires sufficient memory to inverse the matrix. Secondly, there are several mathematical techniques are available to solve the inverse of a matrix. But in handling a large matrix, still I couldn't find any faster and accurate method which can solve this problem with less memory consumption as well.
It depends on the matrix and no universally fast method exists!
In particular its eigenvalue characteristics and rank of the matrix or the pattern of non-zero elements. For sparse and patterned matrix which are usually seen in numerical solutions of PDEs (like FEM and FDM) there are well established methods which are developed over years and some of them are very efficient:
In general, if you want to invert a full matrix of size N X N you have to do O(n3) arithmetic operations (without applying any numerical tricks).
But we have methods for inverting sparse matrix of size N X N which are as efficient as O(N log N) like Thomas Algorithm (see below)
If you want more in depth discussion on numerical method s for inverting a matrix, there numerical efficiency and palatalization see these three:
1- Yousef Saad web page:
2- Works by Roland Freund (UC Dvais Department of Math)
3- Book by Gene H. Golub of Stanford:
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Global search vs local search.
Dear Ang,
The answers provided against this question are right. If you are looking more, you may find some interesting answers through the link below.
Thanks,
Sobhan
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I'm trying to go through the data for JRA-55 but I can't even get into it. If possible, please name some packages for this job.
Hi Gabriel. I just saw your question:
library(stars) library(cptcity) met <- read_stars("ftp://nomads.ncdc.noaa.gov/GFS/analysis_only/201501/20150103/gfsanl_3_20150103_0000_000.grb") met2 <- filter(met, band == 2) plot(met2, col = cpt())
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Could you please point me out to some successful nanotechnology real life applications modeled by using partial differential equation? Preferably, involving heat, reaction-diffusion, Poisson, or Wave equation. If possible in fuzzy environment.
Best regards
1. Critical factors of the application of nanotechnology in construction industry by using ANP technique under fuzzy intuitionistic environment https://www.tandfonline.com/doi/abs/10.3846/13923730.2017.1343202?journalCode=tcem20
2. Fuzzy and Boolean logic gates based on DNA nanotechnology
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- Could anyone please help me to some Biochemistry, Genetics and Molecular Biology modeled, described, or analyzed using partial differential equations? "the model is very appriciated"
- Preferably, involving heat, reaction-diffusion, Poisson, or Wave equation, an If possible in fuzzy environment.
Best regards
Turing patterns in reaction diffusion equations.
SIR modelling
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- Could you please point me out to some successful Medical sciences applications using partial differential equations?
- Preferably, involving heat, reaction-diffusion, Poisson, or Wave equation.
- If possible in fuzzy environment.
Best regards
Dear Professor, In mathematical modelling for drug delivery we are using PDE.
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What is the fastest way to learn about neural networks? there types? how to use them? full solved examples? real life applications?
Many thanks
Coursera
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Could you please point me out to some successful Signal, image, or video processing real life applications using partial differential equation?
Preferably, involving heat, reaction-diffusion, Poisson, or Wave equation.
If possible in fuzzy environment.
Best regards
PDE are the basis of many "inpainting" image restoration techniques:
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Could you please point me to real life applications with complete model and description to its details? and if possible in fuzzy environment.
Best regards and many thanks.
The propagation of the electrical signal in the heart can be modelled by the monodomain equation, which is a simplification of the more accurate bidomain equations. This simplification is usually made for computational purposes. The monodomain equation is reaction-diffusion partial differential equation.
A derivation of the monodomain equation can be found on http://www.uio.no/studier/emner/matnat/ifi/INF5610/h07/undervisningsmateriale/review_part6.pdf . I have had a quick look and it seems this derivation is clear.
Best,
Max
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Dear All,
Can I transform a linear fractional Volterra integro-differential equation into a fractional differential equation? If yes, then how?
The equations are written in the attached file.
Thank you very much in advance for your help.
Sarah
Dear Sarah,
I think that you have to impose some extra conditions on f, k and even to the notion of the fractional derivative to obtain the corresponding fractional differential equation (FDE). Even in the simplest cases it is not clear what is the corresponding FDE. Let us consider a couple of examples.
First, take k(x,t)=1 and f is differentiable. Then differentiating
(1) D^\alpha y(x)=f(x)+\int_0^x k(x,t)y(t)dt
yields
(2) DD^\alpha y(x)=f'(x)+y(x).
But since the fractional integration and differentiation does not commute in general, DD^\alpha is not necessarily a fractional derivative of order \alpha+1. If D^\alpha denotes the Riemann-Liouville fractional derivative, then (2) corresponds to FDE:
(3) D^(\alpha+1) y(x)-y(x)=f'(x).
However, if D^\alpha denotes e.g. the Caputo fractional derivative, then DD^\alpha is not necessarily D^(1+\alpha).
Second, take k(x,t)=c(x-t)^(\beta-1) for some constant c. If c=1/\Gamma(\beta), then the integral term in (1) corresponds to the Riemann-Liouville fractional integral of order \beta, which is denoted as I^\beta y. If the fractional derivative D^\beta f exists and D^\beta is the left inverse of I^\beta, then (1) converts into
(4) D^\beta D^\alpha y(x)=D^\beta f(x)+y(x).
But for the same reason as in the first case, D^\beta D^\alpha is not D^(\alpha+\beta) in general.
Hopefully you will find this useful in your further considerations.
Best regards, Jukka
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Dear all,
I have developed a new technique which solves linear integro-differential equations of fractional type. This includes Fredholm and Volterra equations.
I am looking for an application which can be modeled into such equation so I can apply my method. It can be any kind of application.
I also solve mixed system of equations e.g.1. A system of multiple Fredholm equations of different order of fractional derivatives (0, 1/2, 1, 3/2, etc..) or e.g. 2. A system of same or different kinds of Volterra equations. So, if there is an application to this kind of equation, it would be great!
I would appreciate your help. Please refer me to an article.
P.S. Only linear equations please.
Thank you very much in advance.
Sarah
Dear Sara,
First of all, let me congratulate you for your achievement.
Do not bother about applications. Go on your research,
But if you want to have an application, you can see
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I need to find the column reduction form of a matrix.  Are there any easy methods, free online books or pdfs where I can get examples?
From a computational viewpoint there is not much difference between row reduction and column reduction.  Instead of doing the operations on rows you are doing the operations on columns.  In fact you can turn column reduction into row reduction.
Take the transpose of the matrix, do row reduction (this can be found in any linear algebra text) and at the end take the transpose again.
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I'm looking for an equation:
prob(death) = ...
Yes I can see where you go. Of course LD50 /IC50 is the best way because indeed a value of cytokine(s) is complex, more than one product can be involved from cells and their created environment with the culture or treatment milieu.
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I would like to know a good reference (text book and/or library c) of how to adjust/align 2D images.
I am using Dynamic Time Warping to align 2D images along one axis, but I would like to make a multi-dimensional adjustment. I also need the shift matrix associate to this alignment.
You might want to consider the cepstrum approach. Not sure if a ready library implementation exists, but it takes little more than a Fourier transform (and a reverse one), so you should be able to implement it with any math package. Cepstrum was first invented to detect time shift in sonar signals (1D), only later extended to 2D images.
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Dear all,
I am working in the prostate edema modeling where i want to simulate the interaction of swelling prostate with the neighbor organs using finite element analysis. In my development i use the FeBio software.
I set contacts between the prostate and the neighbor organs (bladder and rectum). Initialy they are separate and while the prostate swells interaction between the organs occur. My problem is that if i constrain the bladder and rectum the prostate penetrates and if I let some degrees of freedom the prostate pushes away the two other organs.
The desired response would be the prostate pushing the two other organs in some degree while all the three organs undergo shape deformation due to the contact pressure between them. For a reason I can't figure out why I can't produce this response. Has anyone an idea why this is happening?
ps. I consider uncompressible materials for the prostate and rectum and poroelastic material for the prostate.
Thank you in advance,
Konstantinos.
Hi Konstantinos,
at first sight, your model seems to be correct. I do hope it will not be too embarrassing: Did you perform some convergence tests with "your" organs? As I mentioned before contact is really nasty. Moreover, you have complex contact surfaces.
I recommend a stepwise procedure. Perform a contact analysis rigid body with rigid body motion against the bladder, e.g., with a sphere as contactor. If you get realistic deformations, try the contact deformable sphere against the (deformable) bladder. The problem in your model is the multiple contact. You do not have very much control by mere intuition.
If you have already done such tests, please forget the previous paragraph.
Contact is lots of trial and error, mostly error.
Greetz, hp
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Dear All,
I am facing trouble handling convective flux in a scalar transport equation for two-phase flow along wall boundary. Some wall boundary cells have low density and viscosity while the rest of the cells have high density and viscosity.
Due to this boundary condition I am getting non-physical unbounded scalar values.
Kindly either suggest some way to handle this or please share some link to literature regarding it.
I am seeking some expert advice.
Thanks a lot in advance.
Dear Bharat
It would be helpful to know the type of the transport model and the scheme you are using, but generally I would recommend to consider the following points:
1. As the convection term is nonlinear, it should be noticed to use conservative form of the equations to handle the large gradients.
2. If the density variation along the boundary is large, instabilities may occur handling large gradients for the adjacent cells. To overcome this it would be helpful to know whether you are solving the convection-diffusion equation together or separately.
3. The variation of viscosity along the boundary will not affect the convection as it only appears in the diffusion part of the transport equation.
4. For the interface boundaries if you apply the kinematic boundary condition on the interface it might be ok. If the mesh is distorted along the boundary you may need to fulfil the kinematic boundary condition along the liquid column.
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I am trying to fit this kind of data plot. So far I came with a mix of 2 stretched exponential and one linear (Fitting1.jpg). But it's not that, as it cannot take the long convex curvature at the right of the plot (Fitting2.jpg). Also when I take the same set of function, it does not match other curves from the same experimental setup. This curve represents the current in function of time after starting the illumination of a solar cell. I am expecting super dispersive transport dictated by a complex netword of traps. Please let me know if you already saw such shape. Thank you.
While diffusion does usually apply to atoms and ions, electrons can be viewed as diffusing through a material, especially if it is some kind of hopping conductivity. Dispersive electron transport dictated by a complex network of traps should look similar to transport of a molecule through a material dominated by adsorption sites (which is where diffusion becomes dominant process). Therefore, similar mathematical description could apply.
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I have a problem with this - the image has more cells so that makes a problem when I enhance or segment.
Dear Shumoos Taha Hammadi,
If you want to get any serious reply or help with your matter I suggest you attach at least a .jpg or .bmp out of your recent analysis/analyses to this thread.
It makes no sense to discuss anything about not knowing what your problem really is (specimen: ok: we know about EYE (animal-human?) / Cornea epithelium.... but nothing about methods to get sections(?): paraffin-, cryo-, semithin plastic /resin sections, stain(s) used, method of image acquisition etc, etc.).
Sorry to bother you with my request,  but hopefully you'll answer some of my questions.
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We know that the monic Chebyshev polynomial of degree n,  T_n(x), has the least deviation from the origin among all polynomials of degree n. What about the polynomial of degree n that has the least deviation from the origin that also satisfies boundary conditions, continuity at both end points, for example?
The problem can be explained for a particular case as follows:
Suppose that we are interested in approximating a polynomial f of degree >n on [-1,1] by a polynomial p of degree n so that they meet at the endpoints.
Minimize Maximum |f(x)-p(x)|   on  [-1,1].
Dear Demetris,
Thanks for the link. Unfortunately, it didn't work for me.
Dear Dmitrii
"If you mean value at points, then you can use a classical polynomial interpolation, which will give you exactly that you want."
I am not sure what you mean. If constraints come under the form of n nodes imposed in the approximation interval, then the classical polynomial interpolation will not be the answer to the question. This case is considered in the following reference (in French)
S. Paszkowski, "Sur l'approximation uniforme avec des noeuds." Ann. Polon. Math. 2.1 (1955), 118-135
Dear Abdellah,
Perhaps you should add that the least-deviation property of the monic Chebyshev polynomial holds in the interval [-1; +1]
The following references could be interesting depending on which type of constraints you are considering.
E Kimchi, N Richter-Dyn, "Properties of best approximation with interpolatory and restricted range side conditions", J. Approximation Theory, 15 (1975), 101–115
E Kimchi, N Richter-Dyn, "Best uniform approximation with Hermite-Birkhoff interpolatory side conditions",J. Approximation Theory, 15 (1975), 85–100
Hope this helps.
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I'm working in genetic fields and I need to improve some algorithm based on the Dirichlet process. Recommendation for books or articles are awaiting - will be cited if useful.
Are you trying to model the distribution or using the Dirichlet process on the parameters in order to fit a mixture model? Two articles that can be of use, for the latter (mixtures):
Escobar, M Estimating Normal Means With a Dirichlet Process Prior. JASA (1994). vOL 89, No. 425, p 268-277.
Escobar, M & West, Mike. Bayesian Density Estimation and Inference Using Mixtures. JASA, (1995). Vol 90, No. 430 p 577-588.
Also, there are some worked examples in Congdons textbook Bayesian Statistical Modelling, second edition", (2006).starting at p 201.
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Hi,
I've just started screening experiments to determine the molecular binding mode of four proteins, and unfortunatelly I still have problems determining which sidechains are in contact with the ligand, especially the hydrophobic interactions. Is there any rule of thumb on how to determine it? Of course I can use the software provided option, but reluctantly it's not enough to catch all interactions.
Thanks,
Tomek
Hello,
For in silico, and if you have the x-ray structures of the four protein-ligand complexes, we have two algorithms available: Gemini and SpectralPro. Gemini will give you  the minimum amino acid-ligand pairs of interactions while spectralpro will give you the most likely amino acid-ligand pairs of interactions. The two software are based on measuring the closest neighbors and not on cut off distances and as such the selections of the interactions are naturally based on the geometry of the ligand-protein surface. Moreover, the algorithms are based on graph theory and consider the ligand-protein contacts as a network of interactions. This allows to address question relative to dynamics of contacts.There is no user friendly version of our alogrithms, but if you tell us the PDB we can send you the result as graphs or text files. It takes about 2sec to produce the result, so do not hesitate if you think that can help.
if you want some publications let me know
best
claire
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1/a is the height of the capillary fringe above the water table, and d is the depth to the water table. Both of them decrease during rainfall period.
You can also use MATLAB to solve this problem (root-finder) by using the command 'fsolve'. After setting some values for 'a' and 'd', you may define a function 'f' and find the roots with 'fsolve'.
For example:
>> a=10;d=5;
>> f=@(x)[tan(a*x*d)+2*x]
If we give the initial condition 'x0' as 'x0=1', and use 'fsolve' in MATLAB, you get:
>> x0=1;
>> x=fsolve(f,x0)
Output:
x =
0.983302064820308
>> x0=2;
>> x=fsolve(f,x0)
x =
1.984140541948211
This goes on... With each initial guess as positive integer, you get a root
close to it..
The transcendental equation f(x) = 0 has infinitely many positive roots.
The 'OptimTool' in MATLAB is very handy for finding solutions (positive roots) for different values of the constants a and d.
Best wishes,
Sundar
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I am developping a library of mesh mover for FSI, but I got some problem to keep valid mesh for movement of high lift components of aircraft (from takeoff to cruise). I use an interpolation function (IDW) to move the mesh but when two bodies are close of each other the mesh in between get distorted to generate negative elements.
Lattice Boltzmann currently has acquired a lot of attention , because it overcomes the problems of the structure complexity . and can be used as long as you are working in the low mach number region.
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NCBI Genbank hosts enormous numbers of COI sequences. However, it is not explicit how many species have their COI being sequenced, since there is also so many multiple sequences from one single species. I followed the keywords provided by Kwong et al (2012) to pull out the metazoan COI sequences (link provided below), with which I can obtain ~900,000 sequences, but cannot get the number of species information.
"You will never be certain the obtained number is 100% correct "
agreed, thats why is wrote: "roughly"
- To retrieve sequences, I use my own programs (or via the eutils), not entrez which is not precise enough most of the time.
- then I filter on clade and minimal length.
- then I cluster sequences at some given % of similarity (needleman-wunsch, not blast).
knowing a number of manually confirmed sequences :
=>
- identify proper cluster(s), extract sequences & other infos from the genbank or embl entry.
- if new searches required in the future => try to estimate the best % of similarity to try to get every proper sequence but no non-target sequence in a single cluster (not always feasible).
Of course, this will need writing some lines in ... python of course
Best
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I want to do a comprehensive study on the hydrological regime of the Danube in the Small Wetlands of Braila and its role in the dynamics of ecosystems. Could you recommend me ways of computing and / or software for the hydrological's cyclicity and seasonality?
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A FORTRAN 77 based OpenMPI code, I need to execute. After certain iterations I am getting the error (please check the attachment). I am accessing the server from my machine with SSH Secure Shell Client. After checking every possible cause of failure (SSH connection problem, memory allotted for my work on server, OpenMPI packages, input data for code etc.) in running the program, I come to a conclusion (at my end) that the problem is related MPI looping. I don't have much experience with MPI mechanism and seek a help for this. Any possible related solutions will be a great help for me and heartily respected.
Thanks Mr. Tobias. :)
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By grey system theory I mean the one defined by Deng Julong in 1982. 'As far as
information is concerned, the systems which lack information, such as structure message, operation mechanism and behaviour document, are referred to as Grey Systems.', Deong Julong.
A lot of research in grey system theory has been done since 1982. There are books and articles, but performing all the calculations manually is not effective, especially when some changes have to be introduced repeatedly.
Thank you, Clyde!
Sylvia
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I work with electrophysiology on neuronal cells. I apply to each cell a series of currents, in 20 pA steps, ranging from 0 to 200 pA. At each step the cell produces a number of action potential (AP). I’d like to see if the application of certain drugs (treatments) changes the excitability (number of APs for each current) of the cells. One option would be to use multi-level models, but I'm not totally sure how to do this.
A good explanation of the problem, and with my attempts to solve it, is available in the link.
Is there any way we could compare these curves, between control and different treatments?
You can also compare the exact timing of the spikes before and after drug application. In addition, you can look at the height of the spikes and how that changes during the spikes. For example, a fast decrease in height may indicate that there is more sodium channel inactivation in the presence of drugs.
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Here is the problem:
There are 100 doors and 100 people. The doors have two states (open/closed). All the doors are closed at first. Then the first person opens all the doors, the second person toggles the doors in multiples of 2 (e.g. door 2,4,6..). The third person toggles the doors in multiples of 3 (3,6,9...). This continues until person 100 toggles the door 100. So how many doors are open and how many are closed. Please give an equation for any number of doors as well. Thank you.
The problem as described by you will cause the following pattern (assuming I understood correctly):
TRUE 2xFALSE TRUE 4xFALSE TRUE 6xFALSE TRUE 8xFALSE ...
This puts open doors at exact square positions:
1, 4, 9, 16, 25, 36, etc....
The total number of open doors is the sum of squares below the total door number N, and includes this one if it is an exact square:
For the 100 door problem, then it is:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100 = 10 open doors
In other words, your equation is:
open doors = floor( sqrt(N) )
, where floor() is the round-down operator.
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Data set of an image.
Thank you somuch. I will try to do it.....
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Let's say you have string (e.g. guitar), which is fixed on both ends; and you want to place a discrete number of actuators to damp natural frequencies of it.
How can I find the best position to damp for example the first five modes?
Or the other way around: There is an actuator on a fixed position and you want to know the damping characteristic on an specific mode?
In addition, you can use dampers too. Again, it is an optimisation problem where you place them to deal with multiple modes simultaneously.
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Solve for B, t1, t2
A1 =B.e^pt1
A2=B.e^pt2 .
t2 - t1 = c ; known constant.
p also another known constant.
Any method is acceptable.
If A1=A2/(e^p.c) then the system has infinity number of solution, as
B=u, t1=ln(A1/u)/p, t2=t1+c.
If A1<>A2/(e^p.c) then the system has not a soluton.
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"Cloud models are effective tools for uncertain transition between a linguistic term of a qualitative concept and its quantitative description. In short, it is a model of the uncertain transition between qualitatives and quantitatives."
Sure someone does. Just see how many papers cite the original papers by Li Deyi. Google scholar finds over 200 such papers, though coming mostly from China and a few papers from Eastern Europe and, well, Iran. Since many papers that use cloud theory are written in a variety of the English language that is very difficult to understand, the concept is not widely known in Europe and the US. I myself struggle to understand it. Once I had to refuse to review a paper that used cloud theory precisely because it was close to totally incomprehensible.
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I am still looking for simulation models or submodels that combine plant/vegetation growth with herbivore grazing on these plants. I aim at using it for an MSc course on the use of models in ecology.
Yes i am interested, in fact if you have something related to transportation
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when I clicked the run button, the system shows
The matrix is not strictly diagonally dominant at row 1
The matrix is not strictly diagonally dominant at row 2
The matrix is not strictly diagonally dominant at row 3
The matrix is not strictly diagonally dominant at row 4
What dose this mean?? what's the matter with my input??
clear;clc
format compact
%% Read or Input any square Matrix
A = [-8.7673 9.4736 0 0 0;
4.7368 -8.4736 4.7368 0 0;
0 4.7368 -8.4736 4.7368 0;
0 0 4.7368 -8.4736 4.7368;
0 0 0 -9.4736 10.4736];% coefficients matrix
C = [20;20;20;20;20];% constants vector
n = length(C);
X = zeros(n,1);
Error_eval = ones(n,1);
%% Check if the matrix A is diagonally dominant
for i = 1:n
j = 1:n;
j(i) = [];
B = abs(A(i,j));
Check(i) = abs(A(i,i)) - sum(B); % Is the diagonal value greater than the remaining row values combined?
if Check(i) < 0
fprintf('The matrix is not strictly diagonally dominant at row %2i\n\n',i)
end
end
%% Start the Iterative method
iteration = 0;
while max(Error_eval) > 0.001
iteration = iteration + 1;
Z = X; % save current values to calculate error later
for i = 1:n
j = 1:n; % define an array of the coefficients' elements
j(i) = []; % eliminate the unknow's coefficient from the remaining coefficients
Xtemp = X; % copy the unknows to a new variable
Xtemp(i) = []; % eliminate the unknown under question from the set of values
X(i) = (C(i) - sum(A(i,j) * Xtemp)) / A(i,i);
end
Xsolution(:,iteration) = X;
Error_eval = sqrt((X - Z).^2);
end
%% Display Results
GaussSeidelTable = [1:iteration;Xsolution]'
MaTrIx = [A X C]
Hi Maria. As far as I got it without running the code, there is one error at
Check(i) = abs(A(i,i)) - sum(B);
which should rather read
for i=1:n
Check(i) = abs(A(i,i)) - sum(abs(A(i,:)));
if Check(i) < 0
fprintf('The matrix is not strictly diagonally dominant at row %2i\n\n',i)
end
or something like that, since diagonal dominance states that absolute values of diagonal elements are always greater or equal to the absolute values of the other remaining (absolute) row elements.
Moreover, it seems to me that the input matrix A in your example is not diagonal dominant, as e.g. |A(1,1)|<|A(2,1)|.
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So, to emphasize what I mean, consider the following example: You want to enter a chemical sum formula (or an whole equation) into a text, spreadsheet, whatever. Of course, you can abuse some of the already existing tools such as superscript/subscript in a word processor or math mode to get the symbols and format you need.
But, one could think of a more natural way to enter such information and I am sure there are already approaches to do so. Also approaches for data file formats to save this information, ...
Now, are there journals dealing with developing of such methods and approaches?
If you're talking about equation and text formatting, have you considered using LaTeX? It was specifically designed for that. And more and more journals actually have templates for this format (good examples are Bioinformatics and all the IEEE journals and conferences)
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Simple robots, including LEGO based ones, are an engaging and physical tool for students can investigate and develop problem-solving skills in a fairly unthreatening ways. The question then comes to mind though where-else, if any where, could they be used for supporting teaching? Control is one but what about networking concepts?
Scott, depends a lot on what grade level you are talking about... teaching teachers to use robotics somewhere in K-12? using robotics in K-12? or for specific certain grades? or as a platform for engineering or science concepts in undergrad or grad? I just completed a chapter on STEM and robotics through a filter of gender and did a review of a large number of robotics programs at all age levels.
Also, a professor at Ohio State is using robotics in his curriculum, an introductory class to engage students in mechanical engineering. If I remember correctly, he is using an Arduino based robot challenge. For college, I think Arduino is more apropos than LEGO MINDSTORMS. You might check out information at hbrobotics.org for ideas on a variety of small robots and challenges suitable for a classroom environment university level.
If you want more info on K-12, let me know.
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I need a function f(x) such that when f(x) is applied to any function's sub-functions, the result is the same as if f(x) is applied over the entire function. For example: f((a^2)b + ln(c)/d - 2^e) = f( f( f( a^2 )b ) + f( f( f( ln(c) )/d ) - f( 2^e ) ) ). Another requirement is that f(x) cannot be linear. Does such a function exist?
EDIT: I've come up with another acceptable scenario: f((a^2)b + ln(c)/d - 2^e) = g( h( i(a^2)b ) + j( k( l( ln(c) )/d ) - m( 2^e ) ) ), where g(x) is always applied to addition operations, h(x) to multiplication, i(x) to powers, j(x) to subtraction, k(x) to division, and l(x) to logarithms, and m(x) to exponentiation, etc.. With this scenario, f(x) can be linear, but the g(x), h(x), etc. cannot be linear.
I don't know wether this will help but :
- if you look at the properties your function f must have, for example f(a+b)=f(a)+f(b) and f(a*b)=f(a)*f(b), then, for a such that f(a) is not 0, you must have f(a)=f(a*1)=f(a)*f(1), hence f(1)=1. In the same way, f(2)*f(a)=f(2*a)=f(a+a)=f(a)+f(a)=2*f(a), hence f(2)=2. To generalize, for any integer k, f(k)*f(a)=f(k*a)=f(a+...+a)=f(a)+...+f(a)=k*f(a), hence, for all integer k, f(k)=k. Of course, this works for positive or negative integers (and for 0 as well).
- Now, if you look at numbers in Q*, f(p/q)=f(p)/f(q)=p/q (as p and q are integers)...
- As all real number is the limit of a sequence of decimal numbers, we can extrapolate that for any real number r, we must have f(r)=r. (I guess it can further be extrapolated to complex numbers...)
Then, except for the identity function, I really don't see any function that can fulfill these properties. But of course, this is not what you are looking for... I'm probably missing something here ! (Or maybe I have misunderstood your search...)
By the way, why are you searching such a function ?
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Three light emitters are placed in a room and one detector in each corner (-1;1), (-1;-1), (1;-1) and (1,1). Also the positions of emitters are given. This system should be represented by a matrix. Source values should be found by LSQR. After that, SVD incl. gaussian 0.1 standard deviation noise has to be performed. Finally, Tikhonov regularization and the L-curve are needed. Anyone know how these two work mathematically and what their results represent?
To contribute a bit here. (mainly on the introductory question)
Tikhonov reguarization is, as already mentioned, a way to constrain the solution to small values. You do this by taking the 2nd norm of the solution vector, multiplying with a parameter λ and adding to the LSQ error. Then you try to minimize the whole sum.
The L-curve is a graphical indication of how the solution norm (y-axis) changes to the LSQ error (x-axis) for different values of λ. The curve has an L-shape and thus the name.
Maybe my contribution seems a bit confusing but you can check the attached file for further explanation. There are a couple of great paper on the subject by P.C.Hansen (he has them online on his webpage).
Good luck!
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