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Hi Nursena Kayabasi ,

CpG's in islands located near promotors are usually methylated and play a role in gene regulation (as mentioned) while CpG's in gene regions like introns/exons tend to be unmethylated. Methylation at such sites is usually subject to persistent epigenetic remodeling as part of genome packaging and chromosome structure but tend to become globally hypomethylated with age. I would check if there is any literature on this gene having parental imprinting - a quick search I did found a few articles on the epigenetic silencing of this gene and its involvement in Friedreich's ataxia ( ) which might be relevant to what you're looking at.

It seems the linearization is accomplished by replacing x1, for x1^2. And separately by replacing x2, for x2^2 & x2^4.

In this way, the surface function is linearized about the origin (0,0), it means we can find f1(x1,x2)=a*x1+b*x2, whilst a and b are calculable in terms of the algebraic parameters, k and c.

But my question transforms to another level. How, we can find a compact algebraic expression for f1(x1,x2), and f2(x1,x2), close enough to the origin. This algebraic expression, need NOT be necessarily linear (it could be a nonlinear function).

1--How to find another compact analytical expression equivalent to f1(x1,x2), f2(x1,x2)? (with fair accuracy)

2-- Is it possible to find an approximation near the origin (0,0), for f1(x1,x2), f2(x1,x2), as a function of only one of the two variables (either x1, or x2)?

Regarding the second synopsis, I am to cite another ResearchGate question linked below:

However, the gist of the idea in this link is not clear to me.

I have attached the past 3 manual to this response; hopefully it its helpful

I put together a solution of the RH myself. While it can't be considered a complete proof while not vetted by experts, it presents various strong arguments and a real breakthrough, which is the inversion formula for Dirichlet series. Given any Dirichlet F(s), you know a(n) from F(s). Unfortunately, it's impossible to have an integral representation for a(n) usually, it's a Taylor power series. Please head to my page for the paper.

Bruno, did you get an answer to your question. I'm interested in the answer since I'm dealing with the same issue.

The solution of ODE is an Integral function, I think it always belongs to the space of continouse functions.

The probability density function p(x) is defined by the following relation:

P(x, x+dx)= p(x) dx,

x is the random variable, P(x,x+dx) is the probability to find x between x and x+dx,

dx is the interval over which one calculates the probability.

So, finally

p(x)=P(x, x+dx)/dx

As for the power spectral density it can be defined by the relation:

P(f, f+df) = p(f) df,

where p(f) is the spectral power density, P(f, f+df) is the power contained in the frequency interval df around the frequency f.

So, p(f)=P(f, f+df)/df,

So the spectral power density is the total power contained in a frequency interval df divide by the frequency interval df.

Best wishes

t = 20:0.1:40;

x = t.*cos(t);

y = t.*sin(t)

plot(x,y)

https://genome.cshlp.org/content/15/12/1777.full

https://en.wikipedia.org/wiki/Open_reading_frame

Thank you @Guillermo Valencia-Palomo

@ Fabio,

It seems very nice example. Did you mean the discriminant of the (Klein's J-function) ? In general, some of modular forms are Fractals.

But not all of them.

Best regards

Dear Ali,

I would like to suggest the following for your mentioned one:

1. Four orthogonal polynomials connected to a two parameter function of Mittag-Leffler type by R. Rangarajan and P. Shashikala

2. The Orthogonal Polynomials and the Pade Approximation by Ahmad F.

3. An Introduction to Orthogonal Polynomials by Chihara T. S.

4. Orthogonal Polynomials: Computation and Approximation by Gautchi W.

Unclear about the question. Although in the text is described that the locking is mechanical (due to loose bodies or meniscal and ACL tear) when usually the knee locks in flexion or the pseudo-locking, when the knee usually locks in extension, the logic of the question was demonstrated in a clear way. The common reason for pseudo-locking is patello-femoral pathology (degeneration of the articular surface of the patella or the trochlea or in rare conditions the existence of a thick plica, folding of the synovium). Nothing of all this is influenced by the diet, except if the amount of food that is consumed is excessive and is resulting to obesity. This is the only case that diet can influence the knee locking. Dietary habits can influence the uric acid and so the potential gouty synovial reaction and consequently arthritis, but this is another matter.

Hi Anass,

You can say it like that. My explanation would be that flc2hs simply is a heavyside funcition. Y(T). So y=0 for T<0 and y=1 for T>0. With your “x2“ you generate an T offset of step of the function.

In your example you substract Tm-T different from my example, so also the sign of the argument is changend. So You will get a function which is 1 for values smaler Tm and 0 for values higher Tm, which is what you wanted.

So normaly it should work. But if you are not sure about your function you can also plot the function to check if your syntax is ok.

Hope I was able to help you again. Seems like you are in the wright way.

Best regards

Thomas

Dear all,

I have checked the fits proposed by Joachim and also tries to see if weights according to the differences between subsequent values will improve the fit. I made a figure showing the results. Black: data from "values 1", red: data from "values 2". Upper row: data & fitted curve shown in a double-log plot (1 was added to incluse the value at (0|0). This is only for plotting. The fit was done using the original data. Lower row: the residuals, multiplied by 1000, the x-axis is scaled identically to the upper plots.

The fits are impressively good, I think. They follow the data closely. There is never a larger residual than 0.005. Using equal weights, the residuals at low x are the largest. This is improved using weights proportional to the change. I also tried weights proportional to the squared change, what further improved the residuals at low x but starts having a bad influence on the residuals of large x.

I think this result is pretty good, I am happy with it and I am grateful for all your help and interest. Hoewever, I you fell that you can further improve it or come up with an entierly different model that explains the data better, feel free to let us know.

PS: I did the fit and the plot in R. Fitting was done with optim() using all defaults (method = "Nelder-Mead"). The function that was optimized was the sum of squared residuals. Weights were included as factors on the squared residuals:

# the function to be fitted with 3 parameters:

f <- function(par) 1-1/(1+par[1]*x^par[2])^par[3]

# the loss function to be optimized; y: data, w: weights

optFn <- function(par, y, w=1) sum(w*(y - f(par))^2)

# get the fitted parameters

# par: resonable starting parameters

# y: data, w: weights

optim(par=c(0.25, 0.8, 0.2), fn=optFn, y=y, w=w)

you can use flipud in matlab, and you can get the opposite sequence.

for example:

clc

clear

cd('F:\PAPER CREAT\MK')

w=xlsread('.xls');

data=w;time=(1900:1990)';U=norminv(1-0.05/2,0,1);

N=size(data,1);n=2;nb=1;nB=2;ri=zeros(N,1);rbi=zeros(N,1);s=0;datac=flipud(data);

SFk=zeros(N,1);SBk=zeros(N,1);UFk=zeros(N,1);UBk=zeros(N,1);%data be limited in column

%in inverse order(RbI,UBK,SBK) & natural order(RI,UFK,SFK)

for n=2:N

ri(n)=sum(double(data(1:n-1)<=data(n)));

rbi(n)=sum(double(datac(1:n-1)<=datac(n)));

SFk(n)=SFk(n-1)+ri(n);

SBk(n)=SBk(n-1)+rbi(n);

UFk(n)=(SFk(n)-n*(n-1)/4)/sqrt(n*(n-1)*(2*n+5)/72);

UBk(N-n+1)=(-(SBk(n)-n*(n-1)/4)/sqrt(n*(n-1)*(2*n+5)/72));

end

To be effective in addictions treatment, outcomes need to be truly individualized; how deeply is the patient's addiction affectting his everyday functioning? Is he able to perform daily hygiene?

Does he need reminders? Is he able to shop and prepare meals? Does he eat 3 meals / day? measured by how much weight has been lost and is it gaining back? Is he able to maintain clean clothing, etc. Break the GAF down to parts that can be evaluated in this manner. You may want to put together a flow sheet that can be individualized. Good luck!! GBH

There exist primal and dual characterizations of roots.

In such a case, I personally prefer numerical integration of the function (using Laplace integral definition) instead of analytical methods. However, the result will be numeric but not a function. I am not sure it can be useful for your case or not.

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Sorry I am not a mathematician only a physician

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you are welcome for any suggestions

imresize3 means 3D image resize in all axis

Dear Bogdan,

Choosing activation functions for MLPs depend on a couple of things as discussed below.

1. The activation function for the output layer would depend on whether you are performing classification or regression. For binary classification (i.e. problems of two classes), the Logistic-Sigmoid function can be used with binomial cross-entropy as the cost function. For multiclass classification (i.e. problems with more than two classes), the softmax function is used with multinomial cross-entropy as the cost function. For regression problems (i.e. real-value outputs), the linear/identity function is used.

2. For hidden layer units, your options would depend on the depth of your model as follows:

(a) For shallow models (1 or 2 hidden layers), the Logistic-Sigmoid, Tangent-Sigmoid or rectified linear function can be used. Here, choosing the most appropriate activation function among the aforementioned would be via experiments.

(b) For deep models (i.e. more than 2 hidden layers), the rectified linear function would become more appropriate to alleviate the problem of vanishing gradients.

I hope this helps.

Oyebade

What is your purpose? First, you could test whether the antibody binds both targets, but further experiments depend on what you want to do with the antibody at the end.  

Thank you Riese, it's very helpful. 

I guess you are minimizing. My impression is, first of all, that you have dominated (inferior) solutions, so it is nor really a PAreto front, but a set of solutions. For a Pareto front, you should delete all dominated solutions.

Second, although the fron looks straight, my guess is that it is not, and, as usual, it is convex. You are just finding the vertices of the feasible region in the objective space.  

If is were straight, there would be no way to find so many solutions...

I hope it helps.

Cheers,

Vlad

Logically, If the solutions are the same, orthogonality property would still be  valid irrespective of the methods that yielded the solution. However, you can subject each of the equivalent solutions to orthogonality test to be certain.

Caro Paolo,

Thank you for rapid answer, I am very happy with your answers.

Best regards,

Antonio Ronaldo.

I have to maximize hvdc transmission power. 

Dear Junichiro Ono

a specific paper does not exist on this topic but hope those papers you find above will be useful to you!

Cheers

The generalised skewed t distribution is a family of distributions: they will all be different based on the parameters (beta, mu and sigma) that you use. The student t distribution (not 'skewed' student t) is a special case (and also a family in itself) of the skewed t distribution that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.

I hope this helps :) 

 thanks all for your guidance

The autocorrelation gives you an idea of the duration of the pulse but you cannot determine the exact shape of your pulse (several pulse shapes can give you the same autocorrelation trace). Often it is assumed that the pulse coming from a laser has a sech² shape, and the autocorrelation is fitted based on this assumption. To better determine the temporal shape of the pulse, you need information on its phase. This can be achieved by measuring the FROG trace (Frequency Resolved Optical Gating, which is basically a spectrally resolved autocorrelation with a pulse retrieval algorithm). Other methods such as SPIDER and MIIPS can also provide this information.

"Might one inteptret the course of time as that irreversible computer heathing the present moment only in virtue of the course of time?" is an optional problem to demonstrate whether this is profound or not. ;)   

If I have a function of the type v=,v0 tang (t/tao). What will be the value of tao for v0=2000, 3000, is there any relation between them

Hello Salameh,

We have the most popular test is a Ashworth Scale / Modified Ashworth Scale.

See the link for description of this test.

Raimondas

Hi Stellamaris,

You can get a grid file by use of /usr/local/dock6/tutorials/solvent_scoring_demo/3_grid/solvent_grid.in.

Then add Zou GB/SA Score Parameters into a dock.in file, modify it, and dock.

Hi Ali Mahmoudpour

Happy New Year and thanks for your warm answer .

The first letter  -- a --  is a misprint and should be removed.

If you know the formula, it is not hard to implement it on excel or similar. Do you need to draw ROC curve? or sensitivity specificity pairs? FPR and TPR?

By the way, your very question has no clues that you are looking for an app. Rather it is understood that you are looking for the formula or the method. You said "ROC at each point" which did not remind me anything.

DearSatnam,

If functions are increasing as powers when x tends to infinity, you can use in the space of tempered distributions (generalized functions). See: Zemanian, A.H. - Generalized Integral Transformation. Interscience, New York. 

You also can instead of the Hankel tranform use the Meijer transform that holds even for functions of exponential growth.

The zero limit has no effect on the derivative. Take f(t):= \sin(t^2).t^{-1}. Then f'(t)=2\cos(t^2} - sin(t^2}.t^{-2} and the value of f' is 1 at any point t={2\Pi n}^{1/2} with a natural n.

Hello Naira.

a) Constraint satisfaction problems (CSPs) are mathematical problems defined as a set of objects whose state must satisfy a number of constraints or limitations.

b) FCSP represent an extension of CSPs by allowing a constraint to have a satisfaction degree from the unit interval, (a continuous variable). 

You can represent constraints with fuzzy sets over a particular domain and the amount  of satisfaction of a constraint is the membership degree of its domain value on the fuzzy set that represents it.

c) CSOP are CSP which incorporate some optimization algorithm...

See for instance:

I hope this helps. Best, RICARDO

The distribution of the "min" function (as well as the "max" function) acting over random variables is modeled to follow an "extreme value" distribution. With the use of this model, I have estimated means and variances in practical problems. I recommend you to read [Coles, S. (2001). "An Introduction to Statistical Modeling of Extreme Values". Springer Series in Statistics.] where you will find several examples and applications of this distribution, and you will find also the mathematical description of the extreme value distribution.

You can find this book here: (http://bookzz.org/dl/2296330/200a44) and here: (http://bookzz.org/ireader/2296330).

Best regards,

LM Gato.

Hint 1: show that if t₁ >t₂ , then {|f|>t₁ }*⊆{|f|>t₂ }*.

Hint 2: use this to show that if y is in {|f|>t}*

, then yis in {|f|>s}* for every 0<=s<=t. Notice that this implies that f*(y)>=t by the definition.

Hint 3: use hint 1 again to show that if y is not in {|f|>t}*

,sup{s≥0  |  y is in{|f|>s}*}<= t

this implies in particular f*(y)<=t.

You most welcome

Houda

The main idea of construction is to build irregularly distributed set of zeros, and after that to build an entire function with this set of zeros, using the canonical product.

See Chapter 2, section 5  "Examples" of the following (really brilliant) Goldberg and Ostrovskii book "Value Distribution of Meromorphic Functions" AMS Translations of Mathematical Monographs, vol. 236

I learned this reference from Anna Vishnyakova

She is a former student of Iossif V. Ostrovskii, so if you have more questions, she can help you.

Another reason why you can't use class-specific normalization is that if you do, you can normalize one class, say, between -2 and -1 and the other one between 1 and 2 and get perfect results with 100% accuracy on the training data.

If H(x) is your heaviside function with a step from 0 to 1 at x=0, then you will need something like this:

H(x) - 2H(x-0.5) + H(x-1)

Check it

What is "the same situation"?

Dear Eman,

About what catfishes are you talking? Some catfishes has two cranial fontanelles, others have only one, others have none.

Regards,

Gloria Arratia

Looks good!

You could start with the paper of Ioffe :

Ioffe, A. D. Nonsmooth analysis: differential calculus of nondifferentiable mappings. Trans. Amer. Math. Soc. 266 (1981), no. 1, 1–56.

Before computing the limit one has to fix the precise meaning of the expression. The functions $g(z) = z^s$ and $h(z) = \ln(z)$ are multi-valued, so the question will be correctly posed only after selecting appropriate branches of all expressions that  include these functions. Outside of this I see no difficulties.

As per Wikipedia,

The term "hypergeometric series" was first used by John Wallis in his 1655 book Arithmetica Infinitorum.

Hypergeometric series were studied by Leonhard Euler, but the first full systematic treatment was given by Carl Friedrich Gauss (1813).

Studies in the nineteenth century included those of Ernst Kummer (1836), and the fundamental characterisation by Bernhard Riemann (1857) of the hypergeometric function by means of the differential equation it satisfies.

Riemann showed that the second-order differential equation for 2F1(z), examined in the complex plane, could be characterised (on the Riemann sphere) by its three regular singularities.

The cases where the solutions are algebraic functions were found by Hermann Schwarz (Schwarz's list).

Excuse me Dear searchers, I will not answer the question, but I will reminder by:

Conditions of flagging an answer as cited in RG:

Flagging is a way for us to make sure that Q&A remains useful and relevant. Help us out by flagging answers that are offensive, of a commercial nature, or spam.

For those who flag an answer outside those provided in bold, it is shame and reveals of a bad mind and soul.

I hope your function is from R-->R. What is the meaning of h <=f <= g? Do you mean, h(x)<=f(x)<=g(x) for all x?

h can be called as subordinate of f, or f is a dominant of h.

Karunakaran (Complex Analysis book Author) uses the word, super-ordinate and subordinate for g and h respectively.

Pareto gives the whole picture of the optimization, when the approximation is estimated after several intents, some of which give the optimal solution to one of the objective functions. 

I don't believe there is general case for the setup of your example problem. MATLAB's fminsearch might be useful in approximating solutions, given an initial solution close to the actual. Given input vectors of the form:

psi = [y1;y2;y3;y4]

and coefficients

A = [a1,b1,c1,d1,e1,f1,g1,h1,i1; ...]

Let:

% x = [x1,x2,x3]

X = @(x) [x(1); x(2); x(3); x(1)*x(2); x(1)*x(3); x(2)*x(3); x(1)^2; x(2)^2; x(3)^2]

Y = @(X) A * X

ferr= @(Y) sum( (psi - Y).^2 )

xbest = fminsearch( @(x) ferr( Y( X( x ) ) ), xi )

Using randomly large signed elements for A and x, fminsearch finds near-exact answers given a suitably close initial. The coefficients of your actual data may warrant useful simplifications, esp. if the initial condition can be approximated via the squares of your domain.

Thank you Mithun.

I shall check them out.

For continuous functions, "midpoint convex" is equivalent to "convex" as Mikkelson's link already noted.   This is very similar to the argument that an additive continuous function has the form f(x)=Ax with discontinuous counterexamples easily constructed in terms of a Hamel base for the reals as a vector space over the rational field.  Indeed, any such an example is also an example here: midpoint convex (with equality!) but not convex.

The continuity is related to uniform convergence of sequences (and series) of functions (including Dini's theorem). On the other hand, for the most Borel measures, Luzin's theorem on approximation by continuous compactly supported functions works. On locally compact spaces, for a large class of measures, the subspace of continuous compactly supported functions is dense in L^p, 1<=p<infinity. For these last assertions see W. Rudin, "Real and complex analysis". Moreover, for a moment determinate positive regular Borel measure on a closed (unbounded) subset A in R^n, any nonnegative continuous compactly supported function (with the support contained in A) can be approximated from above by dominating (hence nonnegative on A) polynomials, in L^1 - norm. This result has applications to the multidimensional moment problem. Concerning the role played by C^2-functions, I recall that the theory of free and constrained extrema is usually proved for such functions.  

Go to page 7 of the document and pages afterwards for matlab code. It shows how to convert Riccati inequality into LMI. 

No, the system isn't inconsistent; just do the math: Integrating the first condition gives that f(x,y)=(a/2)x^2 + c(y). From this one obtains an, apparent,  contradiction, since the derivative of this expression wrt y is a function only of y and can't be equal to bx; unless b=0, which means that c(y)=c(0)=c, is a constant.

If one started out by integrating wrt y, one would've found f(x,y)=bxy + d(x); the derivative of this expression wrt x would then give by + d'(x)=ax=>d'(x)=ax-by, which, once more, is consistent only with b=0. 

So the only solution is f(x,y)=(a/2)x^2+c. Standard, elementary, exercise in undergraduate calculus. A mystery what it's doing on such a forum...

No there are no studies on it!

Thanks Chad, I have solved this problem. 

Watheq,

"In experimental design and we we want to build an efficient model for prediction, it is essential to obtain normal response distribution." - That's just not correct, in several ways. The distribution of the response does not matter - the distribution of the residuals is the key, and this is tightly linked to the formulation of the model. And the predictions of models assuming normal residuals are BLUE, even when the actual residual distribution is non-normal. The important part here is the estimated uncertainty of the predictions, what depends on how the stochastic part of the model is defined. Note that this does not neccesarily need to be based on the normal distribution!

"In regression modeling, it is necessary some times to obtain normal distribution for the response variable for better fit." - Again it is not the distribution of the response variable that really matters, but the distribution of the residuals. Apart from this I do not see how this is related to the quality of a fit. How do you measure this quality? All "quality" measures I know depend on the scale of the response, so transforming the response also transforms the meaning of these quality measures, and comparing them is like comparing apples and peaches. At best, It is just meaningless.

A good model gives estimates of interpretable effect sizes. Most transformations will render the estimates quite uninterpretable, what I consider a major disadvantage (NB: the log-transformation is somewhat special because it just makes a model estimating multiplicative effects instead of additive effects).

Please check the following publications, where the dielectric function of graphene is worked out on the basis of the so-called tight-binding approximation:

1. Stauber et al., Optical conductivity of graphene in the visible region of the spectrum. Phys Rev B 78, 085432 (2008).

2. Falkovsky LA, Pershoguba SS. Optical far-infrared properties of a graphene monolayer and multilayer. Phys Rev B 76, 153410 (2007).

The presented theory is in very good agreement with available experimental data. Please notice that the REAL part of the dielectric function is guided by the so-called "universal optical conductivity of graphene". Check, for example

3. Kuzmenko et al., Universal optical conductance of graphite. Phys Rev Lett.

100, 117401 (2008).

Hydrogenated graphene on SiC is somewhat special in the sense that its Fermi-level is 0.2 to 0.3 eV below the Dirac point (i.e., it is strongly p-type doped). This influences a parameter called "chemical potential" in the above papers. In our recent publication we have done some estimate of the influence of the chemical potential on the optical conductivity (and thereby on the dielectric function), please check I.G. Ivanov et al., Layer-number determination in graphene on SiC by reflectance mapping, Carbon 77, 492 (2014). Check the text discussing Eqs. (7) and further.