Breakthrough in the theory of stochastic differential equations and their simulation

Amin · May 15th, 2023, 6:25 am

Friends, my persecution did decrease for a bit as many friends might have judged since I have not been writing posts about corrupt people in Pentagon. But one reason might have been that I was extra careful about my food and tried to make sure that I get food from random sources I have not thought about before.
Yesterday night I bought two sandwiches from a bakery and only after eating them I realized that they were drugged. They must have drugged food at more then a dozen bakeris in the area. After eating the sandwiches all my drive for my research work was gone and I simply sat on the chair for hours trying to think what to do and had absolutely no motivation to do any work.
Just one hour earlier, I bought cold bottled water from a shop in a close by market. Water was good and I really liked it also because weather has already become very hot. I was feeling bad that I bought only one water bottle and went back an hour later to buy a few more cold water bottles. When I drank water again, it was thoroughly drugged and I was very disappointed.
I really want to say that good for nothing scum in Pentagon had very high hopes that Jewish Goldfather would give them jobs paying millions of dollars after retarding me and several other innocent victims like me. The way scum believed in their great luck and believed that that despite being good for nothing, they would get jobs for the rest of their life paying millions of dollars. Now when good Americans realize the true motives of corrupt scum at Pentagon, it is very hard for the scum to come into terms with the reality that their dreams of millions of dollars were just a mirage and scum becomes even more motivated to do something to change the reality again. Again Jewish Goldfather is in no way obliged to hire scum at millions of dollars paying jobs and would do that only if scum at Pentagon shows some progress on ground in retarding the mind control victims pointed out by the Goldfather.
Believe me or not, retarding victims with mind control to please the jewish Goldfather and his likes is the largest money making business among corrupt scum at Pentagon.

Amin · May 15th, 2023, 9:18 pm

Friends, I tried to make the optimization work for finding coefficients of standard gamma series so that its moments match with the moments of random variable in question. But a strategy like I used for finding coefficients of hermite polynomials series does not seem to work well here.
I came across this paper and decided to try its strategy. Here is the paper https://adsabs.harvard.edu/full/2005rdra.book...55M
I want to first find the density in native random variable as done in the above cited paper and later convert it from native random variable to powers of standard gamma and powers of standard normal random variable using the work I have already done. Once we have derived a density representation in native random variable, it is very simple to convert it to powers of standard gamma(alternatively Laguerre polynomial series) or standard normal random variable(or hermite polynomials series).
I should be able to complete this work in next three to four days.

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Friends, I have coded most of the above method to construct the density with Laguerre polynomials that matches specified moments in matlab and I hope it should be ready in another day. Then I will go on to taking derivatives between density constructed with this method and the standard normal density/standard gamma density. And these derivatives would be used to construct the power series in standard normal (or equivalently in hermite polynomials ) that I have been calling Z-series. You could also construct the power series in standard gamma variable. I hope all of this work will be ready in a few days.

Its already summers and temperature during the day is very high so I try to avoid going out during the day in Sun's heat. I go out regularly after sunset when temperature has somewhat decreased. Also I try to work till late at night (It is 2:00 AM here in Lahore) and I usually use a pedestal fan in the porch/garage of our house where I work. There is a ceiling fan in the garage but sparrows have made a nest inside the hole in roof above the fan and its electric wire is broken/disconnected. I decided to not repair and use the ceiling fan until the birds abandon the nest. But pedestal fan used to work fine and there was not a problem. Last night when I slept, I took the pedestal fan inside my room and placed it inside the window of my room to pull colder air from outside the window. I had an absolutely fantastic sleep after that. Mind control agents spend a lot of time at night when I sleeping to try to control my neurotransmitters and fast moving air and fresh air without gases create problems with their operations. Fast moving air decreases the accuracy of EM resonance and fresh air restores the original neurotransmitters. Anyway, when I went out after sunset and then came back and started to work in the garage again, I brought the pedestal fan outside but was horrified to know there was some sick gas or special charges and it was impossible to work in the air of the pedestal fan. I tried to brave through and keep using the fan since it was still too warm but then realized that I was being more and more sick and unable to do any work. And then I turned off the fan and started working without any fan. I will not be able to use the fan inside my room anymore since it would be far more difficult to sleep in its gas mixed air of the fan inside the closed room.
This is a standard practice of inhuman animals of mind control. Whenever I get some comfort in anything like a fan or some other thing, these animals are very quick to create problems with that thing right away. Somebody has to teach humanity 101 to scum at Pentagon.

Amin · May 18th, 2023, 11:20 am

Friends, yesterday night, I was able to complete the work I was doing. But I was slightly disappointed with results. There could be a possibility that I made errors, but when I tried finding a density with Laguerre polynomials applied to gamma density, I noticed that many times the resulting density would go into negative territory and there were large oscillations in density. I found that taking first four Laguerre polynomials usually resulted in a stable well defined density but it was usually somewhat away from true density that had been fit perfectly to first eight moments. Whenever I tried more than first four polynomials, the procedure usually resulted in very large oscillations and unstable density.
However, I might have made some errors in the implementation of the method.
Once a density was ready using first four Laguerre polynomials, I was able to convert it to Z-series quite faithfully (with very small error) into Z-series density by matching the derivatives of Gamma + Laguerre density and a standard normal density at their median. This part worked quite well.
I will be posting the code with comments and minor changes tomorrow.

Amin · May 18th, 2023, 11:30 am

Friends, I have ideas for research on Z-series neural networks and I hope that they would go one step beyond Z-series hermite polynomial regressions in predicting the target variables. I have thought about optimizing them in a semi-analytic way first to quickly find a suitable starting point and after finding a very good guess,these Z-series neural networks would be optimized after that with full-fledged optimization techniques. Lot of ideas here would be based on mathematics and there will be no black-box thing. I really hope that these neural networks will work better than plain hermite orthogonal rgressions in time series predictions.
I have an antipsychotic injection due at the end of next week so I have 8-9 days and I really will try to complete as much work before that time as possible.

Amin · May 19th, 2023, 7:58 pm

Friends, when I went out to get food after sunset, mind control agencies were able to drug some food that I later bought. I have been feeling very bad and have no drive to do anything as if my mind is frozen.
Though mind control agents were trying to retard me all the time even before, they have set out with unprecedented strength after I wrote the post in which mentioned that people of pentagon were scum. I seriously think that, for past few days, hundreds of Pakistan army soldiers try to drug food when I go out at night and I have to be very lucky to escape them. I think most of the things I bought were good but I picked something bad and it has had very adverse effect on me. I think I am able to survive since most of the food was good. I really want to request friends to please ask the corrupt people at Pentagon to end my persecution. Retarding innocent and intelligent people of different nations on behest of rich people in US is an extremely lucrative and multi-billion dollar business for corrupt people at Pentagon and it is very difficult for these corrupt people to accept the alternative world where they would be forced to live without huge corruption money just like as an average American lives.
I do not expect people to blindly believe me. I have just raised voice about something that nobody else was ready to talk about. But I am sure most intelligent people in United States are smart enough to use their resources to investigate the truth on their own about who are the people being retarded and who are the people convincing others that retarding of mind control victims is a good thing and who points to people of Pentagon about retarding innocent people. If corrupt people at Pentagon, as I say they are, are in fact good, they should be willing to convince Americans by presenting any argument and proof that they have about their being good instead of trying to stifle my voice. The way they have been trying to stifle my voice by increasing the persecution and drugging of food to a whole new degree in past few days, should tell people that they are threatened by my allegations and have no sound arguments against my allegations of corruption. If they really had any strong arguments, they would already be presenting those arguments to people to convince them that their mind control drive was indeed a good thing.
Do not expect that mediocre people of Pentagon would voluntarily follow any laws or good human/American ethics or virtues. Not only are they mediocre, they are above the law. A large number of them are simply maximizing their personal profits leveraging the power they have over good, innocent and intelligent people. I really do not believe that unbridled power in hands of mediocre people who are above the law is a good thing for any society.
Sorry, but due to the effect of drugs in my food, I was really not able to write comments and make the work presentable to post it today. I would be posting it tomorrow. I also lost a lot of enthusiasm about it when I noticed that I could not fit any Laguerre polynomial after fourth order. Anyway, I would be posting it tomorrow.

Amin · May 22nd, 2023, 2:23 pm

Friends, I wanted to share some ideas about time series modelling and forecasts.
I suppose we can do a hermite orthogonal regression on lagged variables in so many ways using hermite polynomial correlations of target variable with lagged variables.
Suppose Y is regressed on N lagged variables denoted by [$]X_n, n=1,2, \ldots , N[$] each.

[$]Y \, = \, a_0 \, + a_1 \, Z_{y} \,+ a_2 \, ({Z_{y}}^2-1) \,+ a_3 \, ({Z_{y}}^3 - 3 Z_y) \, + \, \ldots[$]
[$]=a_0 \, + Y_1 \, + \, Y_2 \, + \, Y_3 \,[$]
Above, we have divided Y into three orthogonal hermite components.

We can decompose each [$]X_n[$] into orthogonal hermite polynomial parts as

[$]X_n \, = \, c_0 \, + c_1 \, Z_{n} \,+ c_2 \, ({Z_{n}}^2-1) \,+ c_3 \, ({Z_{n}}^3 - 3 Z_n) \, + \, \ldots[$]

The idea is to construct covariance matrices from realized values of each of the above hermite polynomials and find its orthonormal eigenvectors. One set of orthonormal eigenvectors would come from covariane matrix of first hermite polynomial, second set of orthonormal eigenvectors would come from covariance matrix of second hermite polynomials and so on.
Suppose vector of observed values of first hermite polynomial is given as

[$]Z_t=\begin{pmatrix}Z_{1,t}\\Z_{2,t}\\ \vdots\\ Z_{N,t}\end{pmatrix}[$]

We find the covariance matrix as

[$] Cov_1= \frac{1}{T} \, \sum_{t=1}^{T} \, Z_t \, tr({Z_t})[$]

now we do eigenvalue decomposition of the above covariance matrix to find N orthogonal eigenvectors [$]\zeta_1, \zeta_2, \ldots , \zeta_N[$]

We know that N orthogonal vectors span the entire space of N dimensional vectors, we can represent [$]Z_t[$] at any point in time as

[$]Z_t \, = b_{t,1} \, \zeta_1 \, + \, b_{t,2} \, \zeta_2 + \, \ldots \, + b_{t,N} \, \zeta_N[$]
where
[$]b_{t,1} = Z_t \, . \, \zeta_1[$]
[$]b_{t,2} = Z_t \, . \, \zeta_2[$]
i.e the above coefficients are found by inner product with particular orthonormal eigenvector. We can understand it as that [$]b_{t,1}[$] is the portion of first eigenvector in particular realization of [$]Z_t[$]

What we can do is that we can find correlation between [$]Z_{y,t}[$] and [$]b_{t,1}[$] as proxy for correlation between first eigenvector [$]\zeta_1[$] and [$]Y_1[$] where [$]Y_1[$] represents the first hermite component of [$]Y_t[$].
Suppose
[$]\rho_1 = corr<Z_{y,t},b_{t,1}>, t=1,2, \, \ldots, T[$]
[$]\rho_2 = corr<Z_{y,t},b_{t,2}>, t=1,2, \, \ldots, T[$]
Luckily correlation with only first few eigenvectors would be significant. So we could write first hermite polynomial component of our regression in totally orthogonal coordinates as
[$]\, Y_1 \, = \, \rho_1 \, b_{t,1} \,+\, \rho_2 \, b_{t,2} \,+ \, \ldots \, [$]

This is important since we can get information from movement of eigenvectors that are realized out of movements of a large number of assets.
This is also important since first few eigenvectors usually have their interpretations as level, slope and twist etc so their significant move can help us give more information about the market movement and we can use them in some special ways in our algos.
Though we use a full rank matrix to determine these eigenvectors, only first few eigenvectors would usually be significant and rest will be noise and we might not want to add them in our regression.

In the above explanation, we have specifically done eigenvector decomposition of first hermite polynomial part of regression. We will have to repeat the above process for each of the orthogonal hermite polynomial.
So we not only orthogonalize the non-gaussian densities using hermite polynomials, we also orthogonalize covariances/correlations from each hermite polynomial into orthogonal eigenvectors. Since everything is orthogonal, we can try to understand changing correlations in a more simpler one dimensional setting.

Amin · May 22nd, 2023, 7:48 pm

Friends, here is my other program that constructs density of a random variable so that resulting density is product of a base gamma density multiplied with a fourth order polynomial whose coefficients are chosen so that first four moments of the Gamma + polynomial series density match the input moments of the random variable. We then find median of this gamma + polynomial density and find the derivatives of the density with respect to the random variable at the median. These derivatives are matched with derivatives of standard normal density with respect to standard normal random variable at its median. We then find the first seven derivatives of the input random variable whose Gamma + polynomial multiple series was found with respect to standard normal variable. These derivatives are used to construct the Z-series of the variable whose gamma + multiplied polynomial density was found.
I wanted to post the program yesterday but was hit with bad food and could not properly concentrate at night. Sorry for the delay.

Here are matlab program files:

function [c0,c] = ZSeriesFromGammaDensityExpansion(rMu)


% mu=-.2;
% sigma=.65;
% for n=1:8
%     rMu(n)=exp(n*mu+n^2/2*sigma^2);
% end
% 
 rMu(1)=0.000012499863483*10^5;   
 rMu(2)=0.000021197093700*10^5;
 rMu(3)=0.000050274347857*10^5;
 rMu(4)=0.000171368317209*10^5;
 rMu(5)=0.000856094970826*10^5;
 rMu(6)=0.006320436615909*10^5;
 rMu(7)=0.068698344472325*10^5;
 rMu(8)=1.084082326087001*10^5;
 



[Coeffii,k,theta,a] = CalculateLaguerreSeriesDensityFromMoments(rMu);

a=0;%parameter a is used to shift the gamma density as in shifted gamma 
%density. I have kept it at 0 in my experiments.
%Sorry for bad notation but please do not confuse parameter a of shifted
%gamma density with a0,a1,a2,a3,a4 which are coefficients of respective 
%powers of x in the polynomial that multiplies the base gamma density.

a0=Coeffii(1);
a1=Coeffii(2);
a2=Coeffii(3);
a3=Coeffii(4);
a4=Coeffii(5);
%The above functions "CalculateLaguerreSeriesDensityFromMoments" takes 
%raw moments.It returns a density representation
%of the random variable which is of the form
%p(y)= (y-a)^v * exp(-(y-a)/theta)/theta^(v+1)/Gamma(v+1) * ...
%(a0+a1*(y-a)/theta +a2*((y-a)/theta)^2+a3*((y-a)/theta)^3 + ...
%a4* ((y-a)/theta)^4;
%where v=k-1;
% k is the shape parameter, and v is the parameter asscoaited with
%generalized Laguerre coefficients.
%If you have solved for density in terms of Laguerre polynomials, you will
%have to convert it into a single polynomial form as above by adding
%together coefficients on the same powers of x in different Laguerre
%polynomials.



Nn=5000;
dNn=.002;

v=k-1;
%Y(1:Nn)=a+((1:Nn)-1)/theta*dNn;
Y(1:Nn)=((1:Nn)-1)*dNn;
fY0(1:Nn)=((Y(1:Nn)-a)).^v .* exp((a-Y(1:Nn))/theta) ./ theta^(v+1)/gamma(v+1);

%fY0(1:Nn) represents the discretized version of base gamma density
%given as: (y-a)^v * exp(-(y-a)/theta)/theta^(v+1)/Gamma(v+1)


Ph(1:Nn)=a0;

for ll=1:4
  Ph(1:Nn)=Ph(1:Nn)+Coeffii(ll+1).*((Y(1:Nn)-a)/theta).^ll;
end

%Ph(1:Nn) above represents the discretized version of 
%(a0+a1*(y-a)/theta +a2*((y-a)/theta)^2+a3*((y-a)/theta)^3 + ...
%a4* ((y-a)/theta)^4;
%This is the discretized version of polynomial that multiplies the
%discretized version of gamma density.

%NormConst=sum(EataL(1:5))
NormConst=sum(fY0(2:Nn).*Ph(2:Nn))*dNn;
fY(1:Nn)=fY0(1:Nn).*Ph(1:Nn)/NormConst;

%fY(1:Nn) is a product of base gamma density and fourth order polynomial
%discretized at all points on the grid. This is effective density.

plot(Y(1:Nn),fY(1:Nn),'r');

str=input("Look at graph of gamma density multiplied with fourth order polynomial");


[Xmedian] = FindMedianOfGammaSeriesDensity(a,a0,a1,a2,a3,a4,k,theta);

%Above function finds median of the new effective density. We find the
%median since we compare derivatives there.


Xmedian

str=input("Look at Xmedian");
[px,dpdx] = DerivativesOfGammaSeriesDensityAtMedian(Xmedian,a,a0,a1,a2,a3,a4,k,theta);

%Above function finds derivatives of the effective density at its median
%with respect to its random variable.
%Please note that the effective density is given as
%p(y)= (y-a)^v * exp(-(y-a)/theta)/theta^(v+1)/Gamma(v+1) * ...
%(a0+a1*(y-a)/theta +a2*((y-a)/theta)^2+a3*((y-a)/theta)^3 + ...
%a4* ((y-a)/theta)^4;
%where v=k-1;
% k is the shape parameter, and v is the parameter asscoaited with
%generalized Laguerre coefficients.


dpxdX=dpdx(1);
d2pxdX2=dpdx(2);
d3pxdX3=dpdx(3);
d4pxdX4=dpdx(4);
d5pxdX5=dpdx(5);
d6pxdX6=dpdx(6);


%Below are derivatives of standard normal density at its median.
Zm=0;
pz=exp(-0.5* (Zm.^2))/sqrt(2*pi);
dpzdZ=-Zm*exp(-0.5* (Zm.^2))/sqrt(2*pi);
d2pzdZ2=(Zm^2-1)*exp(-0.5* (Zm.^2))/sqrt(2*pi);
d3pzdZ3=-(Zm^3-3*Zm)*exp(-0.5* (Zm.^2))/sqrt(2*pi);
d4pzdZ4=(Zm^4-6*Zm^2+3)*exp(-0.5* (Zm.^2))/sqrt(2*pi);
d5pzdZ5=-(Zm^5-10*Zm^3+15*Zm)*exp(-0.5* (Zm.^2))/sqrt(2*pi);
d6pzdZ6=(Zm^6-15*Zm^4+45*Zm.^2-15)*exp(-0.5* (Zm.^2))/sqrt(2*pi);


%Below are the derivatives of the random variable whose gamma expansion
%density was found with respect to standard normal random variable.

dXdZ=pz/px;

d2XdZ2=(dpzdZ-(dpxdX *dXdZ^2))/px 

d3XdZ3=(d2pzdZ2- (2* dpxdX* dXdZ *d2XdZ2+dXdZ *(dXdZ^2* d2pxdX2+dpxdX *d2XdZ2)))/px 

d4XdZ4=(d3pzdZ3-(3* d2XdZ2* (dXdZ^2* d2pxdX2+dpxdX *d2XdZ2)+3* dpxdX *dXdZ *d3XdZ3+dXdZ* (3 *dXdZ* d2pxdX2* d2XdZ2+dXdZ^3* d3pxdX3+dpxdX* d3XdZ3)))/px 

d5XdZ5=(d4pzdZ4- (6 *(dXdZ^2 *d2pxdX2+dpxdX *d2XdZ2) *d3XdZ3+4 *d2XdZ2* (3* dXdZ *d2pxdX2 *d2XdZ2+dXdZ^3* d3pxdX3+dpxdX* d3XdZ3)+4* dpxdX* dXdZ* d4XdZ4+dXdZ *(3* d2pxdX2* d2XdZ2^2+6* dXdZ^2* d2XdZ2* d3pxdX3+4 *dXdZ* d2pxdX2* d3XdZ3+dXdZ^4* d4pxdX4+dpxdX* d4XdZ4)))/px 

d6XdZ6=(d5pzdZ5- (10* d3XdZ3 *(3 *dXdZ* d2pxdX2* d2XdZ2+dXdZ^3* d3pxdX3+dpxdX *d3XdZ3)+10* (dXdZ^2* d2pxdX2+dpxdX *d2XdZ2)* d4XdZ4+5* d2XdZ2* (3* d2pxdX2* d2XdZ2^2+6* dXdZ^2* d2XdZ2* d3pxdX3+4 *dXdZ* d2pxdX2* d3XdZ3+dXdZ^4* d4pxdX4+dpxdX* d4XdZ4)+5 *dpxdX* dXdZ* d5XdZ5+dXdZ *(15* dXdZ* d2XdZ2^2* d3pxdX3+10* d2pxdX2* d2XdZ2* d3XdZ3+10* dXdZ^2 *d3pxdX3* d3XdZ3+10* dXdZ^3* d2XdZ2* d4pxdX4+5* dXdZ* d2pxdX2* d4XdZ4+dXdZ^5* d5pxdX5+dpxdX* d5XdZ5)))/px 

d7XdZ7=(d6pzdZ6- (20 *(3* dXdZ* d2pxdX2* d2XdZ2+dXdZ^3 *d3pxdX3+dpxdX *d3XdZ3)* d4XdZ4+15* d3XdZ3* (3 *d2pxdX2 *d2XdZ2^2+6* dXdZ^2* d2XdZ2* d3pxdX3+4 *dXdZ* d2pxdX2* d3XdZ3+dXdZ^4* d4pxdX4+dpxdX* d4XdZ4)+15* (dXdZ^2* d2pxdX2+dpxdX* d2XdZ2)* d5XdZ5+6* d2XdZ2* (15* dXdZ* d2XdZ2^2* d3pxdX3+10* d2pxdX2* d2XdZ2 *d3XdZ3+10 *dXdZ^2 *d3pxdX3 *d3XdZ3+10 *dXdZ^3 *d2XdZ2* d4pxdX4+5 *dXdZ *d2pxdX2 *d4XdZ4+dXdZ^5 *d5pxdX5+dpxdX* d5XdZ5)+6* dpxdX* dXdZ *d6XdZ6+dXdZ* (15 *d2XdZ2^3 *d3pxdX3+60 *dXdZ *d2XdZ2 *d3pxdX3* d3XdZ3+10 *d2pxdX2 *d3XdZ3^2+45 *dXdZ^2* d2XdZ2^2 *d4pxdX4+20* dXdZ^3 *d3XdZ3* d4pxdX4+15 *d2pxdX2* d2XdZ2 *d4XdZ4+15 *dXdZ^2* d3pxdX3 *d4XdZ4+15 *dXdZ^4* d2XdZ2* d5pxdX5+6 *dXdZ *d2pxdX2* d5XdZ5+dXdZ^6* d6pxdX6+dpxdX *d6XdZ6)))/px 


c0=Xmedian
c(1)=dXdZ
c(2)=1/2*1*d2XdZ2
c(3)=1/6*1*d3XdZ3
c(4)=1/24*1*d4XdZ4
c(5)=1/120*1*d5XdZ5
c(6)=1/720*1*d6XdZ6
c(7)=1/720/7*1*d7XdZ7

%Above are coefficients of Z_series density
%We have the power series in standard normal given as
%Y=c0+c(1) Z + c(2) Z^2 + c(3) Z^3 + c(4) Z^4 +c(5) z^5 +c(6) Z^6 +c(7)
%Z^7;


%Below we graph the Z_series density from its coefficients


dNn=.1/2;   % Normal density subdivisions width. would change with number of subdivisions
Nn=45*4;  % No of normal density subdivisions
NnMid=((1+Nn)/2)*dNn;
Z(1:Nn)=(((1:Nn)*dNn)-NnMid);

%Now construct random variable from its Z-series coefficients
X(1:Nn)=c0;
for nn=1:7
    X(1:Nn)=X(1:Nn)+c(nn)*Z(1:Nn).^nn;
end

%Find change of density derivative with respect to normal for construction
%of density
DfX(1:Nn)=0;
for nn=2:Nn-1
    
    DfX(nn) = (X(nn + 1) - X(nn - 1))/(Z(nn + 1) - Z(nn - 1));
    
    %Change of variable derivative for densities
end
DfX(Nn)=DfX(Nn-1);
DfX(1)=DfX(2);

%Find lognormal density at the normal grid
pX(1:Nn)=0;
for nn = 1:Nn
    pX(nn) = (normpdf(Z(nn),0, 1))/abs(DfX(nn));
end

plot(X(1:Nn),pX(1:Nn),'r');

end

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function [Coeffii,k,theta,a] = CalculateLaguerreSeriesDensityFromMoments(rMu)


POrder=4; % we use first four Laguerre Polynomials 
a=0;
k=(rMu(1)-a).^2/(rMu(2)-rMu(1).^2);
v=k-1;
theta=(rMu(2)-rMu(1).^2)./(rMu(1)-a);

%Above we have chosen shape variable k and scale variable theta so that
%first two given moments are matched with the base gamma density.

for mm=1:4
    rMu(mm)=rMu(mm)/theta^(mm);
end


[EataL,CoeffL]=CalibrateLaguerreSeriesCoefficients(POrder,rMu,v,1);

%The above function returns the coefficients of powers of x that define
%generalized Laguerre polynomials of various orders.
%EataL are coefficients of each Laguerre polynomial so that when Laguerre
%polynomials series with these coefficients EataL is multiplied with base
%gamma density, first four moments of the resulting density match with
%first four iput moments.


% %Below is the program to graph the density.
% Nn=2000;
% dNn=.005;
% 
% 
% %Y(1:Nn)=a+((1:Nn)-1)/theta*dNn;
% Y(1:Nn)=((1:Nn)-1)*dNn;
% 
% %fY0(1:Nn)=(Y(1:Nn)-a).^v .* exp((a-Y(1:Nn))/theta) ./ theta^(v+1)/gamma(v+1);
% fY0(1:Nn)=((Y(1:Nn)-a)).^v .* exp((a-Y(1:Nn))/theta) ./ theta^(v+1)/gamma(v+1);

Coeffii(1:5)=0;
Coeffii(1)=1;
for ll=1:4
    for ii=0:ll
        Coeffii(ii+1)=Coeffii(ii+1)+CoeffL(ll+1,ii+1).*EataL(ll+1);
    end
end

% Coeffii(2:5)=Coeffii(2:5); %Check and verify this theta multiplication
% a0=Coeffii(1);
% a1=Coeffii(2);
% a2=Coeffii(3);
% a3=Coeffii(4);
% a4=Coeffii(5);
% 
% Ph(1:Nn)=a0;
% 
% Ph(1:Nn)=Ph(1:Nn)+a1.*((Y(1:Nn)-a)/theta) + ...
%     +a2.*((Y(1:Nn)-a)/theta).^2 + ...
%     +a3.*((Y(1:Nn)-a)/theta).^3 + ...
%     +a4.*((Y(1:Nn)-a)/theta).^4;
% 
% 
% %NormConst=sum(EataL(1:5))
% NormConst=sum(fY0(2:Nn).*Ph(2:Nn))*dNn
% fY(1:Nn)=fY0(1:Nn).*Ph(1:Nn)/NormConst;
% plot(Y(1:Nn),fY(1:Nn),'r');
% 
% str=input("Look at integral");
end

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function [EataL,CoeffL] = CalibrateLaguerreSeriesCoefficients(POrder,rMu,alpha,theta)




[CoeffL] = CalculateGeneralizedLaguerreCoefficients(POrder,alpha)

%OrthognalityConst(mm)=gamma(mm+alpha+1)/gamma(alpha+1)/factorial(mm);

for mm=0:POrder
    OrthognalityConst(mm+1)=gamma(mm+alpha+1)/gamma(alpha+1)/factorial(mm)/theta;%*gamma(alpha+1);
    EataL(mm+1)=0;
    for nn=0:mm
        if(nn==0)
            
            EataL(mm+1)=EataL(mm+1)+CoeffL(mm+1,nn+1);
        else
            
            EataL(mm+1)=EataL(mm+1)+CoeffL(mm+1,nn+1).*rMu(nn);
        end
    end
    EataL(mm+1)=EataL(mm+1)./OrthognalityConst(mm+1);
end


end

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function [CoeffL] = CalculateGeneralizedLaguerreCoefficients(POrder,alpha)

%This function finds the coefficients of powers of x for a particular Laguerre polynomial.
%CoeffL(nn+1,ii+1) indicates the coefficients of iith power in nnth
%Laguerre polynomial.
%POrder is the number of highest Laguerre polynomial whose coefficients are
%calulcated

CoeffL(1,1)=1;
for nn=1:POrder
    for ii=0:nn
        mm=nn+alpha;

        CoeffL(nn+1,ii+1)=(-1)^ii .*gamma(mm+1)/gamma(ii+alpha+1)/factorial(nn-ii)/factorial(ii);
    end
end

end

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function [ymedian] = FindMedianOfGammaSeriesDensity(a,a0,a1,a2,a3,a4,k,theta)
%This program uses neton-raphson to find median of the following density
%p(y)=(y - a)^(alpha - 1) *exp((a - y)/theta)/theta^alpha/gamma(alpha)*(a0 + a1* (y - a)/theta + a2 *((y - a)/theta)^2 + ... 
%   a3* ((y - a)/theta)^3 + a4* ((y - a)/theta)^4);



alpha=k; % shape parameter.
%integral a to y.
   

%Initial guess
 y=  theta*(k-1/3+8/405/k + 184/25515/k^2+2248/3444525/k^3-19006408/15345358875/k^4);
 
 
 
 
Xtheta= (-a + y)/theta;
Integral=theta^(-4 - alpha).* ((1/theta)^-alpha .*(-a^4.* a4 + a^3.* a3 .*theta - a^2.* a2 .*theta^2 + a.* a1.* theta^3 + ...
    alpha.* (a1 + (1 + alpha).* (a2 + (2 + alpha).* (a3 + a4 .*(3 + alpha)))).* theta^4) + ...
    (1/gamma(alpha)).*(-a + y)^alpha .*((-a + y)/theta)^-alpha.* ((a^4 .*a4 - a^3.* a3.* theta + a^2 .*a2 .*theta^2 - a.* a1.* theta^3 + ...
    a0.* theta^4).* gamma(alpha) - theta^4.* (a0.* igamma(alpha,Xtheta) + a1.* igamma(1 + alpha,Xtheta) + ... 
         a2.* igamma(2 + alpha,Xtheta) + a3 .*igamma(3 + alpha,Xtheta) + a4.* igamma(4 + alpha,Xtheta))));
  % y0=y;  
  % alpha1=alpha+1;
  % alpha2=alpha+2;
  % alpha3=alpha+3;
  % alpha4=alpha+4;
 %(1/gamma(alpha)).*theta^(-alpha) .* (y0/theta)^(-alpha).* ((1/theta)^(4 - alpha).* (a0 *(1/theta)^(-4 + alpha)* y0^alpha + ... 
 %     alpha *(a1 + (1 + alpha)* (a2 + (2 + alpha)* (a3 + a4* (3 + alpha)))) *theta^4 *(y0/theta)^alpha)* gamma(alpha) - ... 
 %  y0^alpha* (a0* gammainc(y0/theta,alpha) + a1* gammainc(y0/theta,alpha1) +a2 *gammainc(y0/theta,alpha2) + ...
 %  a3* gammainc(y0/theta,alpha3) + a4 *gammainc(y0/theta,alpha4)))    

% Xtheta=(-a+y)/theta;
% Integral=theta^(-4 - alpha).* ((1/theta)^-alpha .*(-a^4.* a4 + a^3.* a3 .*theta - a^2.* a2 .*theta^2 + a.* a1.* theta^3 + ...
%     alpha.* (a1 + (1 + alpha).* (a2 + (2 + alpha).* (a3 + a4 .*(3 + alpha)))).* theta^4) + ...
%     (1/gamma(alpha)).*(-a + y)^alpha .*((-a + y)/theta)^-alpha.* ((a^4 .*a4 - a^3.* a3.* theta + a^2 .*a2 .*theta^2 - a.* a1.* theta^3 + ...
%     a0.* theta^4).* gamma(alpha) - theta^4.* (a0.* gammainc(alpha, Xtheta) + a1.* gammainc(1 + alpha, Xtheta) + ... 
%          a2.* gammainc(2 + alpha, Xtheta) + a3 .*gammainc(3 + alpha, Xtheta) + a4.* gammainc(4 + alpha, Xtheta))))
%      
     
     dIntegraldy=(y - a)^(alpha - 1) *exp((a - y)/theta)/theta^alpha/gamma(alpha)*(a0 + a1* (y - a)/theta + a2 *((y - a)/theta)^2 + ... 
   a3* ((y - a)/theta)^3 + a4* ((y - a)/theta)^4);

%Integral
%dIntegraldy

%str=input("Inside the loop---look at y");

 nn=0;
while (abs(Integral-.5)>.000000001) 
 %nn
 %y
 %Integral
    
    
    nn=nn+1;
y=y-(Integral-.5)/dIntegraldy;      
    
Xtheta= (-a + y)/theta;
Integral=theta^(-4 - alpha).* ((1/theta)^-alpha .*(-a^4.* a4 + a^3.* a3 .*theta - a^2.* a2 .*theta^2 + a.* a1.* theta^3 + ...
    alpha.* (a1 + (1 + alpha).* (a2 + (2 + alpha).* (a3 + a4 .*(3 + alpha)))).* theta^4) + ...
    (1/gamma(alpha)).*(-a + y)^alpha .*((-a + y)/theta)^-alpha.* ((a^4 .*a4 - a^3.* a3.* theta + a^2 .*a2 .*theta^2 - a.* a1.* theta^3 + ...
    a0.* theta^4).* gamma(alpha) - theta^4.* (a0.* igamma(alpha,Xtheta) + a1.* igamma(1 + alpha,Xtheta) + ... 
         a2.* igamma(2 + alpha,Xtheta) + a3 .*igamma(3 + alpha,Xtheta) + a4.* igamma(4 + alpha,Xtheta))));

dIntegraldy=(y - a)^(alpha - 1) *exp((a - y)/theta)/theta^alpha/gamma(alpha)*(a0 + a1* (y - a)/theta + a2 *((y - a)/theta)^2 + ... 
   a3* ((y - a)/theta)^3 + a4* ((y - a)/theta)^4);

end
 
 
ymedian=y;   



end

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function [py,dpdy] = DerivativesOfGammaSeriesDensityAtMedian(ymedian,a,a0,a1,a2,a3,a4,k,theta)
y=ymedian;

alpha=k;

py=(y - a)^(alpha - 1) *exp((a - y)/theta)/theta^alpha/gamma(alpha)*(a0 + a1* (y - a)/theta + a2 *((y - a)/theta)^2 + ... 
   a3* ((y - a)/theta)^3 + a4* ((y - a)/theta)^4);


dpdy(1)=(1/gamma(alpha)) * theta^(-5 - alpha) *exp((a - y)/theta)* (-a + y)^(-2 + alpha)* (-theta *(a - y)* (a1* theta^3 + 3* a3 *theta* (a - y)^2 - ... 
      4* a4* (a - y)^3 + 2* a2* theta^2 *(-a + y)) - (1 - alpha) *theta* (a0* theta^4 + a2* theta^2* (a - y)^2 - ... 
      a3 *theta* (a - y)^3 + a4* (a - y)^4 + a1* theta^3* (-a + y)) + (a - y)* (a0* theta^4 + a2* theta^2* (a - y)^2 - a3* theta* (a - y)^3 + ... 
      a4* (a - y)^4 + a1* theta^3* (-a + y)));

dpdy(2)=(1/gamma(alpha))*theta^(-4 - alpha)* exp((a - y)/theta)* (-a + y)^(-3 + alpha) *(2 *(a - y)^2* (a2* theta^2 + 6 *a4 *(a - y)^2 + ...
      3 *a3* theta* (-a + y)) + (1/theta)*2 *(a + (-1 + alpha)* theta - y)* (-a + y)* (a1 *theta^3 + 3 *a3 *theta* (a - y)^2 - ...
      4* a4* (a - y)^3 + 2 *a2 *theta^2* (-a + y)) + (1/(theta^2))*(a^2 + 2* a *(-1 + alpha)* theta + (-2 + alpha)* (-1 + alpha)* theta^2 - ... 
      2* a* y - 2* (-1 + alpha)* theta* y + y^2)* (a0* theta^4 + a2 *theta^2 *(a - y)^2 - a3 *theta* (a - y)^3 + a4* (a - y)^4 + a1* theta^3 *(-a + y)));
      
 
dpdy(3)=(1/gamma(alpha)) *theta^(-4 - alpha)* exp((a - y)/theta) *(-a + y)^(-4 + alpha)* (6 *(-a + y)^3* (-4 *a *a4 + a3 *theta + 4* a4* y) + ...
    (1/theta)*6 *(a - y)^2 *(a + (-1 + alpha)* theta - y) *(6* a^2 *a4 + a2* theta^2 + 3 *y *(a3* theta + 2* a4* y) - 3* a* (a3* theta + 4* a4* y)) + ... 
    (1/(theta^3))*(a0* theta^4 + a2* theta^2* (a - y)^2 - a3* theta* (a - y)^3 + a4* (a - y)^4 + a1* theta^3 *(-a + y))* (a^3 + (-3 + alpha)* (-2 + alpha) * ...
    (-1 + alpha)* theta^3 + 3* a^2 *((-1 + alpha)* theta - y) - 3 *(-2 + alpha)* (-1 + alpha)* theta^2* y + 3* (-1 + alpha) *theta *y^2 -y^3 + ...
    3* a* ((-2 + alpha)* (-1 + alpha) *theta^2 - 2 *(-1 + alpha)* theta* y + y^2)) + ...
    (1/(theta^2))*3 *(-a + y)* (a^2 + 2* a *(-1 + alpha)* theta + (-2 + alpha) *(-1 + alpha)* theta^2 - ... 
      2 *a *y - 2 *(-1 + alpha)* theta* y + y^2)* (-4* a^3* a4 + a1* theta^3 + 3* a^2 *(a3* theta + 4 *a4* y) + ... 
      y *(2* a2* theta^2 + 3 *a3* theta* y + 4* a4* y^2) - 2* a* (a2* theta^2 + 3* y* (a3 *theta + 2* a4* y))));
      
dpdy(4)=(1/gamma(alpha))*theta^(-4 - alpha)* exp((a - y)/theta)* (-a + y)^(-5 + alpha)* (24* a4 *(a - y)^4 + ...
    (24* (a + (-1 + alpha)* theta - y)* (-a + y)^3 *(-4* a* a4 + a3* theta + 4* a4* y))/theta + ...
    ((-4 + alpha)* (-3 + alpha)* (-2 + alpha)* (-1 + alpha) + (4 *(-3 + alpha)* (-2 + alpha)* (-1 + alpha)* (a - y))/theta + ...
    (6* (-2 + alpha) *(-1 + alpha)* (a - y)^2)/theta^2 + ...
    (4* (-1 + alpha) *(a - y)^3)/theta^3 + (a - y)^4/theta^4) *(a0 *theta^4 + a2* theta^2* (a - y)^2 - a3* theta* (a - y)^3 + a4* (a - y)^4 + a1* theta^3* (-a + y)) + ...
    (1/(theta^2))*12* (a - y)^2 *(a^2 + 2* a* (-1 + alpha)* theta + (-2 + alpha)* (-1 + alpha)* theta^2 - 2* a *y - 2 *(-1 + alpha) *theta* y + y^2)* ...
    (6* a^2 *a4 + a2 *theta^2 + 3 *y *(a3* theta + 2* a4* y) - 3 *a *(a3* theta + 4* a4 *y)) + ...
    (1/(theta^3))*4 *(-a + y)* (a1* theta^3 + 3* a3* theta *(a - y)^2 - 4* a4* (a - y)^3 + 2* a2* theta^2 *(-a + y))* ...
    (a^3 + (-3 + alpha)* (-2 + alpha)* (-1 + alpha)* theta^3 + 3* a^2* ((-1 + alpha)* theta - y) - ... 
      3 *(-2 + alpha) *(-1 + alpha)* theta^2* y + 3* (-1 + alpha)* theta* y^2 -y^3 + 3* a *((-2 + alpha)* (-1 + alpha)* theta^2 - 2* (-1 + alpha)* theta* y + y^2)));
         
  dpdy(5)=(1/gamma(alpha))*theta^(-4 - alpha)* exp((a - y)/theta) *(-a + y)^(-6 + alpha) * ...
      ((120* a4* (a - y)^4 *(a + (-1 + alpha)* theta - y))/theta + (1/(theta^2))*60 *(-a + y)^3* (-4* a* a4 + a3* theta + 4* a4* y)* ...
      (a^2 + 2* a *(-1 + alpha)* theta + (-2 + alpha)* (-1 + alpha)* theta^2 - 2* a* y - 2 *(-1 + alpha)* theta* y + y^2) + ... 
      5* ((-4 + alpha)* (-3 + alpha)* (-2 + alpha)* (-1 + alpha) + (4 *(-3 + alpha)* (-2 + alpha)* (-1 + alpha)* (a - y))/theta + ...
      (6 *(-2 + alpha) *(-1 + alpha) *(a - y)^2)/theta^2 + (4* (-1 + alpha)* (a - y)^3)/theta^3 + (a - y)^4/theta^4)* ...
      (-a + y)* (a1* theta^3 + 3 *a3* theta* (a - y)^2 - 4* a4* (a - y)^3 + 2* a2* theta^2* (-a + y)) + ((-5 + alpha)* (-4 + alpha) * ...
      (-3 + alpha)* (-2 + alpha)* (-1 + alpha) + (5 *(-4 + alpha)* (-3 + alpha)* (-2 + alpha)* (-1 + alpha)* (a - y))/theta + ...
      (10* (-3 + alpha)* (-2 + alpha)* (-1 + alpha)* (a - y)^2)/theta^2 + (10 *(-2 + alpha)* (-1 + alpha) *(a - y)^3)/theta^3 + ...
      (5* (-1 + alpha)* (a - y)^4)/theta^4 + (a - y)^5/theta^5) *(a0 *theta^4 + a2* theta^2* (a - y)^2 - a3* theta* (a - y)^3 + a4 *(a - y)^4 + ...
      a1* theta^3 *(-a + y)) + (1/(theta^3))*20 *(a - y)^2 *(6* a^2 *a4 + a2* theta^2 + 3 *y* (a3* theta + 2* a4* y) - ...
      3* a *(a3* theta + 4 *a4* y))* (a^3 + (-3 + alpha)* (-2 + alpha)* (-1 + alpha)* theta^3 + 3 *a^2* ((-1 + alpha)* theta - y) - ... 
      3 *(-2 + alpha)* (-1 + alpha)* theta^2* y + 3* (-1 + alpha)* theta* y^2 -y^3 + 3* a *((-2 + alpha)* (-1 + alpha)* theta^2 - ... 
         2* (-1 + alpha)* theta *y + y^2)));
         
         
   dpdy(6)=(1/gamma(alpha))*theta^(-4 - alpha)* exp((a - y)/theta)* (-a + y)^(-7 + alpha)* ...
       ((1/(theta^2))*360 *a4 *(a - y)^4* (a^2 + 2* a* (-1 + alpha)* theta + (-2 + alpha)* (-1 + alpha)* theta^2 - ... 
      2 *a *y - 2* (-1 + alpha)* theta* y + y^2) + ... 
   30* ((-4 + alpha)* (-3 + alpha)* (-2 + alpha) *(-1 + alpha) + ( 4 *(-3 + alpha)* (-2 + alpha)* (-1 + alpha)* (a - y))/theta + ...
   (6* (-2 + alpha) *(-1 + alpha)* (a - y)^2)/theta^2 + (4* (-1 + alpha)* (a - y)^3)/theta^3 + (a - y)^4/theta^4)* ...
   (a - y)^2* (a2 *theta^2 + 6* a4* (a - y)^2 + 3* a3* theta *(-a + y)) + ... 
   6* ((-5 + alpha)* (-4 + alpha)* (-3 + alpha)* (-2 + alpha)* (-1 + alpha) + ...
   (5 *(-4 + alpha)* (-3 + alpha)* (-2 + alpha)* (-1 + alpha)* (a - y))/theta + (10* (-3 + alpha)* (-2 + alpha)* (-1 + alpha) *(a - y)^2)/theta^2 + ...
   (10* (-2 + alpha)* (-1 + alpha)* (a - y)^3)/theta^3 + (5 *(-1 + alpha) *(a - y)^4)/theta^4 + (a - y)^5/theta^5)* ...
   (-a + y)* (a1 *theta^3 + 3 *a3* theta* (a - y)^2 - 4* a4 *(a - y)^3 + 2* a2 *theta^2 *(-a + y)) + ((-6 + alpha)* (-5 + alpha)* ...
   (-4 + alpha)* (-3 + alpha)* (-2 + alpha)* (-1 + alpha) + (6 *(-5 + alpha) *(-4 + alpha)* (-3 + alpha)* (-2 + alpha)* (-1 + alpha)* ...
   (a - y))/theta + (15* (-4 + alpha)* (-3 + alpha)* (-2 + alpha) *(-1 + alpha)* (a - y)^2)/theta^2 + ...
   (20* (-3 + alpha)* (-2 + alpha)* (-1 + alpha)* (a - y)^3)/theta^3 + (15* (-2 + alpha) *(-1 + alpha)* (a - y)^4)/theta^4 + ...
   (6* (-1 + alpha)* (a - y)^5)/theta^5 + (a - y)^6/theta^6)* (a0 *theta^4 + a2* theta^2 *(a - y)^2 - a3* theta* (a - y)^3 + ...
      a4* (a - y)^4 + a1 *theta^3* (-a + y)) - (1/(theta^3))*120 *(a - y)^3 *(-4* a* a4 + a3* theta + 4* a4* y)* ...
      (a^3 + (-3 + alpha)* (-2 + alpha)* (-1 + alpha)* theta^3 + 3* a^2* ((-1 + alpha)* theta - y) - ...
      3* (-2 + alpha)* (-1 + alpha) *theta^2* y + 3* (-1 + alpha)* theta* y^2 -y^3 + 3* a* ((-2 + alpha)* (-1 + alpha)* theta^2 - ... 
         2 *(-1 + alpha) *theta* y + y^2)));      
         
      
    
end

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Amin · May 23rd, 2023, 8:40 am

I will suggest friends who are interested in above post(where I calculated Z-series of Gamma expansion density) to please also read the post # 1636 here: https://forum.wilmott.com/viewtopic.php?f=4&t=99702&start=1635

In post 1636, I have used the same method to find Z-series of lognormal density that I used to find Z-series of Gamma-Laguerre expansion density in previous post. In fact, I borrowed most of matlab program in my previous post(other than construction of gamma expansion density) from the matlab program given in post 1636 for lognormal density.

Comparing both programs in previous post and in post 1636, will give a very good idea where to replace the program with derivatives of the input density with continuous derivatives and let rest of the program(which is common in both matlab programs) run unchanged to get good results.

In fact decommenting some of the code in post 1636 and making small changes, you can find an expansion to 10th power of Z-series for lognormal density or any other input density.

Please also read post 1637 for detailed explanation of the method.

If a density with continuous derivatives is not well-constructed by the method, there could be to reasons. Our numerical calculation of median might be off. Or more derivatives i.e higher order Z-series might be required for a faithful construction of density.

Amin · May 24th, 2023, 10:25 pm

Friends, some of my neurotransmitters that mind control agencies had kept blocked for several years have been coming back and becoming active in past one month or so. In the past whenever these special neurotransmitters became active, mind control agencies were quick to block them again fearing that if these neurotransmitters remained active for a longer time, it would be impossible to permanently block them again. So in past twenty four years whenever my neurotransmitters came back, CIA and mind control agencies dropped all semblance of humanity, became true animals and blocked these neurotransmitters with an iron fist by forcefully detaining me. I have been detained at least twenty times in past twenty four years. One doctor, after I returned from London in 2011, forcefully detained me for nine months. At the end of my detention, I wanted to live separately from my family but the doctor threatened to detain me indefinitely if I did not agree to live with my family. Usual average detention times at other places was two months of detention. This is despite I have never hit anyone even once in all of my adult life and have never verbally abused or threatened anyone. I have never done any drugs and have never even smoked a cigarette.
CIA and mind control agencies were foreseeing that some of my neurotransmitters are coming back when they wanted to detain me a month ago and I made a request to friends for help. I am sure several American friends strongly protested to American government and mind control agencies backed off from detaining me at that time.
I want to tell friends that CIA and mind control agencies are becoming very desperate again to control my neurotransmitters again before it is too late. Corrupt Pakistan Army, on behest of CIA, has been drugging food in entire markets of many neigborhoods of Lahore city for past one week. Mind control agencies have been trying their best to block any special neurotransmitters and stop them from being active again. And I am sure they will continue to drug food in the entire neighborhoods everyday where they suspect I would go to get food. I would request friends who sources in mainland European embassies to verify on their own how brazenly food is being drugged at a large number of places in Lahore city. In fact, I would request European embassies to thoroughly investigate how the food is being drugged in Lahore city with mind control chemicals since similar this will help European embassies understand the true nature of mind control and also since similar tactics are used to retard totally innocent European researchers who have some brilliant neurotransmitters. This will also help friends understand why I call Pentagon full of human scum since most animals who work there are devoid of any humanity and they have no conception of good and evil that most good Americans or good humans have. They simply use their position of influence and the fact that they are above the law to please and gain favors from likes of Jewish billionaire Goldfather. I like to say about these animals that they are human because they eat food and have sex like most of us but their humanity is full of cruelty and lacks any compassion for suffering they cause by their torture and heinous deeds. They proudly inflict misery on entire nations and then celebrate their machinations. These moronic people of pentagon say that we are only making america great. It might be a badly constructed metaphor but consider if some guy in a community blinded everyone and after blinding everyone started saying that I have made myself great. Only these scumloads of pentagon cannot retard Chinese, Russians and Turkish people who do not openly allow them to operate on their lands.
I really want to thank so many good American friends who strongly supported me in the past and saved me from forced detention or were able to end the drugging of food in Lahore city. I really want to say that I really need their support because otherwise I am very sure that mind control agencies would certainly detain me again in a few weeks so that they can again block my neurotransmitters that have been coming back. The way I was retarded with iron fist every time my neurotransmitters came back, I am very sure that it will not be any different this time if good Americans did not support me.

Amin · May 27th, 2023, 9:23 am

Friends, I have been trying to analyse time series data. And write small programs to automate handling of the data. I want to play with the data and experiment with various ideas for a week to ten days. I want to be more familiar and at home with various aspects of time series data. I am still trying to use traditional methods of time series analysis in a more novel way by combining them with my previous research and new ideas.
But eventually in a week to ten days, I want to start working with Z-series neural networks and try to build simple basic constructs of Z-series neural networks.
As always, I will be sharing most of the significant work and ideas with friends. And also share my matlab programs for Z-series neural networks.
Eventually I want to develop it towards a broader framework and not merely something for quick prediction of stock markets.
Even though a week ago, I was thinking that I could produce something in ten days, I do not have anything very significant at the moment. I just wrote small basic program for handling, manipulation and analysis of data but these program will be very helpful in the future.
Though I want to aim for Z-series neural networks to be a successful technique for time series and data analysis. doing something significant requires large investments in time. I still recall that I had started research with monte-carlo like methods in 2013-2014 but it was only in late 2016 when I was able to think of iterated integrals method. And it still took me till middle of 2018 to post a full-fledged monte carlo program. But one reason behind slow progress was that I was on very high anti-psychotics and I could be able to work for only one or two days a week on average.
I continued my research on SDEs but again it took several years to make something out of it and it was only in year 2022 and early 2023 when I could produce something reasonable. But again, it was also due to antipsychotics and other difficulties that I could not work properly otherwise I could possibly had made a better progress.
So I think that making something substantial out of Z-series neural networks would take a consistent effort for at least a year or two. I hope this time I would possibly be able to work better since I am on smaller dose of antipsychotics.
I also want to thank friends who supported me in the past by protesting to American government about CIA and mind control agencies about my inhuman treatment. I really think that I was able to do any good work only because my persecution decreased for reasonably large intervals(several weeks) whenever good Americans protested to their government. Without support from good friends, I do not think that I could have any meaningful research.I really cannot thank friends enough who went out of their way to support me. There was earlier a stage in my life when I would become ironic and ask myself where is the human goodness in so many people but my faith in good humanity was only restored when many good people who never knew me personally but still tried to help me after knowing that I was a genuine victim of persecution who also tried to do good research. It is only because of support from good Americans that I have reasonable respect among community due to my research as opposed to a general target of ridicule some people had made out of me.
I am very enthusiastic about learning and exploring more about Z-series neural networks and hope to continue the work until there is very good success. I am very hopeful that it will also be a successful line of research.
I will also be posting my new programs once there is more order in things that are still a bit haphazard.

Amin · May 27th, 2023, 6:21 pm

Friends, I am sure that it would take us several months to perfect Z-series neural networks, I want to share very initial and very basic thoughts about how I want to start work in this domain.
Since a lot of data is available, we will start with stock time series prediction models. We suppose that there are a few stocks in the models whose evolution we want to describe from their time series. Parameters that describe the evolution of stocks would themselves be variables depending upon the "feature space variables" that collectively affect the market trading. Feature space variables would be bullishnes/bearishness of the market, volatility, liquidity, local limit order book imbalances, and other similar variables. We will take distributions of these "feature space variables" possibly as Z-series and determine their point values at any time from appropriate local market data possibly using our hermite regressions or decoders/encoders if they work better. Once we have determined the local factors that affect the market also called feature space variables, we will use them to determine the local values of time series parameter variables. These times series parameter variables for example will change around their mean value as a linear or non-linear function of deviation of feature space variables from their mean. These relationships that determine how time series parameters change as a set of feature space variables could be found by nested Z-series regressions on a long stretch of training data or optimizations on training data. With changing market conditions as quantized by feature space variables, the values of time series parameters would also change along the evolution of market in any day. This could be possible that parameters would have their own Z-series distribution but this would have to be seen carefully.
These are some of the basic starting ideas without any equations but as we put these ideas into practice and the research develops, I expect that a lot of things would also change from these initial ideas.
I expect that it would still be two weeks before the first matlab programs would be ready that try to put the above ideas into practice.

Amin · May 28th, 2023, 4:56 am

Friends, in a previous post I told friends how staff at a lady psychiatrist's hospital started beating me and abused me. During past twenty three years, there have been many many instances of my obvious abuse by different psychiatrists. I will describe some of those instances in this post.
When I came from United States and till fifteen years after that, my father would proudly ask me that I could see any psychiatrist I wish. This was because Pakistan army was managing my persecution and they would force psychiatrists to declare me schizophrenic and my father was told that every psychiatrist would be forced to cooperate. However, by chance in 2016, I came across a psychiatrist who was far better. I never told him that I was under mind control but whenever he interviewed me, he always said after the interview that I was perfectly sane and mentally healthy. When my family would force him to increase the dosage of antipsychotics, the doctor first told me that I should not live with my family and make a comprehensive plan to support myself and become independent (such a plan could never work since Pakistan army was threatening people in Pakistan to not give me any business and CIA was making sure that every contact I would reach for work in Europe (and Singapore/ Japan /Australia) would be approached by CIA telling them that I was a very bad guy and they must not do business with me. I had not told the doctor any such thing that intelligence agencies were after me.) When I told the good doctor how previous psychiatrists had abused me, he would tell me that this used to be a very widespread practice in America hundred years ago to wrong mentally healthy humans by using corrupt psychiatrists as instruments to detain them and strip them of their sanity. The good doctor I am talking about was American national with Pakistan background who had practiced psychiatry in America for over twenty years and had returned to Pakistan. That good doctor kept me on very low antipsychotics (1 mg resperidone per day) and that too on extreme insistence of my family. It was only during that time of treatment by that doctor that I got my first break in research and I solved the problem of high order monte carlo simulations (and analytic series solution of ODEs) and posted that solution on this thread. Ok, when my family was fed with the doctor, they detained me with another doctor. They detained me again two years ago when I requested my family that I wanted to see the same doctor of my choice again( I have been detained every year for past six or seven years by different doctors), they detained me through a different doctor. So my family now stubbornly refuses to allow me to see a professional qualified American psychiatrist of my own choice and detains me every time I try to approach him.
Now back to my obvious abuse by two other psychiatrists. I was detained by this doctor who was running a mental health facility and was not a psychiatrist himself. At that time I did not use to walk very much and my blood pressure used to be somewhat high. Since other antipsychotics had failed to retard me, doctor suggested I take aripperizole injections. These injections affect the heart and also elevate blood pressure but doctor who wanted to retard me had no regard for my health while pretending to cure me. In initial days of my detention, staff at the hospital when checked my blood pressure told me high enough blood pressure in line with what I used to have but after I complained about aripperizole and its effect on blood pressure the staff started doctoring blood pressure and started telling me that my blood pressure was very good or even low. This is a post I wrote on another thread in this forum about it. How to safeguard my research - Page 32 - wilmott.com
.

Amin:

Since I wrote about high blood pressure and mentioned high blood pressure before the hospital staff, they have started to doctor blood pressure. Now, everyday they tell me that my blood pressure is 120/80 or 110/70. While they always told me that my blood pressure was 130/90 or 140/100 prior to injections. I have never had so good blood pressure for years that they have started to tell me now. Friends would recall a previous post when I could not sleep at night and had to take a sleeping pill. When the dispenser came to me at night(The hospital has no MBBS who stays here at night in Ramadan. Dr. AS used to stay here on some nights earlier but has been totally absent in Ramadan). When the dispenser checked my blood pressure, he told me that it upper blood pressure is 110. I did not believe him at all. He asked me to check on my own and put the stethoscope head assembly in my ears. I could easily tell that upper blood pressure was more than 140 and lower was more than 100. The staff has already started to doctor blood pressure. My parents are going to Saudi Arabia for two weeks in a few days. Now Dr. AS has the plan to hold me in detention while my parents are abroad. I had a complete settlement with Dr. N and we(I and the doctor N) both agreed that I would be visiting him every fifteen days and all modalities were agreed. I do think as a patient it is my right to choose the psychiatrist and Dr. AS( who is incharge of facility Pav.) has no right to change the doctor after I have selected a psychiatrist and we both agree on terms of any treatment. Dr. AS has imposed another psychiatrist Dr. M who has not even seen me and has already started giving me injections and increased medicine without looking at my present condition. Dr. N had explicitly stated that I would be free to leave if it were his facility. Most major reason for detaining me now is that Dr.AS wants to continue to detain me while my parents are leaving for abroad for more than two weeks

.
Later after a few days, I was given a second aripperizole injection and released from detention. An injection was due every fifteen days. My parents were in Saudi Arabia and I was living with my sister. She insisted after fifteen days that I get a new aripperizole injection. I complained about too much side effects and other serious problems but my sister insisted that I must get the injection. She talked to another doctor and the doctor told her that if his blood pressure and pulse are fine, just give him the injection. I asked my sister that my blood pressure must be checked before I get the new injection. We went to a small hospital close to her house and when my blood pressure was checked my lower blood pressure was 110. The hospital staff recommended that I stay at the hospital in their care until my blood pressure decreases. It was a totally random blood perssure check. When hospital staff came to know that I had been given aripperizole injections, they told my sister to not give me those injections any more. My sister asked the staff to relieve me and we came home but I was not given aripperizole injections after that.
But this is interesting that the psychiatrist was initially desperate to prescribe aripperizole despite that I had told him about my heart and blood pressure problems and his staff was asked to doctor blood pressure so that I would accept the injections.
Good thing is that only after stopping aripperizole, I started my treatment with good psychiatrist doctor Naeem Aftab (who is an American national) and he gave me enough relief that I was able to get a break in my research and solve the problem of high order monte carlo simulations. I would always be thankful to Dr. Naeem Aftab for giving me relief at such a crucial point in my life.

Yet another experience for abuse was with a seasoned psychiatrist who is known for his connections with Pakistan army. When army dictator Pervaiz Musharraf ruled the country, he made this doctor the dean(president) of the university of health sciences which regulates most medical universities in Pakistan. He had treated me for three years in year 2001. He started my treatment without interviewing me and gave me electric shocks at the start to jumpstart the therapy. I was given electric shocks for fifteen days in early 2001. I still recall that doctor would place a wooden wedge between my teeth and then give me an injection and I still recall how numbness would move in my body from feet to the upper body after the injection.
When going to that doctor's psychiatrist facility in 2001 I had to travel from Kot Addu to Rawalpindi. My family had given me some drug in my food and I became unconscious after an hour or so. I still recall how I was begging my younger brother to help me that I do not want to go anywhere and if he could help me but he like everybody else in the family refused. Slowly drug in food showed its effect and I have absolutely no memory of being taken in my father's car despite that it would have taken him at least eight hours to take me to Rawalpindi. Psychiatrist did not interview me and detained me and started giving me electric shocks. I still recall how I defecated in my bed there and they had to wash it.
Anyway, I was taken to this psychiatrist in 2017 again. He was very clearly told that I had been given antipsychotic drug larjactil by another doctor and it backfired and I had extremely severe drug-induced jaundice. But the doctor was so haughty and cavalier and so desperate to retard me that he still insisted that I must get the same drug larjactil and said that it was not necessary that it would cause jaundice every time. Problem for the doctor was that most antipsychotics had failed to retard me and he wanted to give me some potent antipsychotic that had not been well-tried on me. Though the drug was given to me earlier and later discontinued, the doctor wanted to take his chances to retard me and he had no regard for my health. This doctor is a big crony of Pakistan army and really wanted to please the generals and therefore he decided to give me larjactil again. And as would already be obvious to most friends, after two weeks, I started to show all signs of drug-induced jaundice again and my body and eyes were all yellow. My Biluribin shot like anything. And it took more than two months to control jaundice after that. Though my biluribin came back to normal after two months, several less known enzymes in my liver remained disturbed for several years after that and continued to show as abnormal in my liver function test reports.

I have been detained more than 30 times by various psychiatrists during past twenty-five years on orders of Pakistan Army. This is despite that I have never been violent all my life. I have never hit anyone in my adult life and I rarely speak with anyone in a loud voice. I have never done anything like breaking a glass or any utensils that is associated with sick people.
Here, I will recall an incident eight years ago when I myself approached a lady psychiatrist for help and how she abused me, and her staff beat me for twenty minutes and then tied me and started my treatment with antipsychotics again.
I am recalling this from early 2015. They had previously put me on extremely high antipsychotics and my creativity was all gone. I could barely do any intellectual work. At that time, I was able to convince my family to decrease the injections and they had agreed since I had already lost most of my creativity and intellectual capability. I think mind control agencies were also thinking that I had lost my creativity forever and they wanted to see if it was right time to decrease my drugs and still make sure that I would remain intellectually dull after injections had ended.
But I slowly started to work on my research and started to regain my brain. When mind control agencies realized that I had started to do better research, they asked my family to do something again to retard me. My father asked a self-stylized religious saint to come to our house and take care of me. He came to our house with one of his followers and told me that he wanted to give me injections and I would go to sleep for 24 hours, and they would take scans of my brain to treat me, but I continued to beg and plead him, and I was able to convince him to allow me to leave the home in my car. The supposed saint allowed me to leave since he was probably sure that he would get me later as I had no other place to go other than my home and, therefore, I was able to convince him to let me go outside. When I left the house, I made posts about the saint on at least two different forums from outside my house and pleaded for help. Enough people were following my story even at that time and the saint had to leave. I also called my father when I was outside and protested against this.
My family still remained very tense with me, and I was very afraid that they would force antipsychotics injections and mind control drugs on me therefore I stayed one night out of the home. Here is the post I made when I was away on April 14th, 2015, 2:09 pm
https://forum.wilmott.com/viewtopic.php?f=15&t=94796&start=315#p748191
"I am staying out of my home for the night since I had realized that my father will try to force me into detention again and I would request a court tomorrow for stay order to stop my father from hospitalizing me forcefully again and I would request the court that if there has to be a check on my mental health, it has to be done and investigated properly by a psychiatrist of my choice and I should remain free at the same time. I do not want to be at the mercy of my father's chosen psychiatrist as we saw in the past year that they continued to quote mental health laws and forcefully manipulate me into taking injections. If my father forcefully hospitalized me, I would be cutoff from the outer world and they would do whatever they like. My father's self-stylized saint(peer) had already hinted that he wanted to give me injections that would put me to sleep for 24 hours and he had no argument for my mental sickness at all.”

Next day, on April 15, 2015, I went to Lahore High Court to find some help but I was told that I had to submit an application that would be considered several weeks later when its turn would arrive. When I realized that there was no possibility of help from the court, I decided to see a psychiatrist on my own. I was driving in Garden town Lahore where I came across B**** psychiatric clinic and decided to see the psychiatrist Dr. N*** there. It was evening but the psychiatrist still not had arrived there. I waited for an hour in the reception and then had a consultation with her. I asked her to listen to my case carefully and then decide if I was sane enough and tell my parents about it. She said that I seemed perfectly fine and asked me that she wanted to hear what my family had to say. I agreed and took an appointment to visit her again at April 20, 2015. I took my mother on the planned day and my mother did not have anything decisive to say about any disease other than that I did not eat at home. The psychiatrist asked me to visit her after one week on 27 April 2015. The next week when I went again to visit the psychiatrist, on April 27, and was sitting in the waiting room so that I could visit the psychiatrist on my turn. Another lady who was a psychologist came to me and asked me to go with her in a different room to have a session with psychologist but I declined and said that I was only interested in seeing the psychiatrist who had promised to see me again the earlier week. After five minutes, at least four men came to the room and started besting me. They gave me slaps on my face with full force and gave me blows and they continued to do it for more than fifteen minutes. I had never been beaten like that ever before in my life. All this time, I was simply trying to raise my hand to somehow protect me. Since I was sitting on the sofa, only my face and head were the target of slaps and blows. They were very violent with all sort of slaps and blows on my face as I earlier mentioned that I was sitting and they were standing. . They literally continued to beat me and I continued to beg them to stop. After fifteen minutes of beating me, they tied my legs and lifted me and put me on a bed in a room in the psychiatrist facility and told me that doctor had gone to America and she could not see me. It was a complete lie and the psychiatrist was in her office and was interviewing other patients when I arrived. I continued to ask them to loosen the knots but they continued to make fun of me. I was totally surprised since Dr. N had behaved very nicely in the previous meeting held at 20th with my mother and myself and I was sure she would declare me mentally sane on this meeting. After I was kept tied for about half an hour, a new guard came and opened my hands and legs and said that they would keep me at the facility for three days. The next day my medication in the form of pills started and I was also given two more injections. I was given about nine pills at night and about eight pills in the morning. I was still not given the opportunity to meet the psychiatrist N, and I was told several different things by different people including that psychiatrist N had gone to America, and she had gone to Islamabad. About three days into my treatment, I saw through the glass walls that psychiatrist N was interviewing her clients in her office. After seven days, I was asked to meet psychiatrist N, and she said that she was unaware of the beating as she was in a meeting. Psychiatrist N also assured me that I had no schizophrenia and previous doctors had very wrongly diagnosed me but it was a case of some mania that she would properly treat this time. Her staff continued to say that they were giving me drugs so that the effect of other drugs given to me by previous psychiatrists would decrease.

Before my computer was taken away from me, I was able to take notes for two days in the hospital on my computer that I write here. After first two days of medication, I was so extremely weak that I could barely walk and I had extreme difficulty speaking.

“My Diary for past two days.

4/27/2015
I had two sessions with the doctor N previously on the 20th of April and once before at 13 or 14th of April. I remained away from home during this time and second meeting on 20th of April, evening after the night when I remained away from home. I had told the doctor about my circumstances in the first meeting with her. She had said that I looked perfectly fine mentally but she needed to talk to my family. On 20th of April, I took my mother for a second joint session of myself and my and the psychiatrist said, after the meeting, that said she really could not call me schizophrenic but she needed one more sessions and asked me to come to her facility on 27th of April.
When I arrived at the psychiatric facility, a psychologist had asked me to accompany her which I did and on the way to the her room, I asked for the reason, after which she replied that she wanted to take a session of mine. I told her that I already had a session with another psyc hologist and also with a psychiatrist so I would prefer to have a new session with the psychiatrist now. She agreed and I returned to the waiting room. I was sitting on a sofa in the waiting room on 27th at 8:00 PM (PST) in the line to see the psychiatrist when about five guards took control of me, while I was sitting on a sofa in the waiting room to see the doctor, and gave me an injection. I was beaten and my legs and hands were very strictly tied for more than hour. Though the doctor was in her consultation room and a lot of people were waiting to see her, I was told again and again that doctor was not present at the facility.
In the previous two sessions, she had given the impression I was healthy mentally but she used force without interviewing for the third time or seeing me and without requests to comply. If she was given any special information, she should have talked to me about it and she should have verified with me any change in circumstances.
One injection was given around 8 PM when I arrived for third session with the doctor N. I really think that the doctor was there since there was a large rush of visitors and her SUV was parked in the hospital but everybody among the staff continued to say that doctor did not come to the facility this evening.
I was kept tied for more than one hour. I was taken tied from the waiting room to my room. All these rooms have video cameras so you can ask Dr. N for a video of the events though she might make the excuse that cameras were not working. One of the staff had mentioned when they brought me into a patient room in the facility, that everything was watched by cameras.I would request people familiar with the matter to request her to show them footage of the cameras. Of course, there could be many excuses that cameras were not working but I insist that cameras were working.
Good Mental health facilities try to avoid treating humans like this.
Another injection was given at night before I slept.
and my internet USB device was also taken. They simply took possession of everything out of my pockets and also took my laptop.
When I asked why they gave me injections, one of the staff told me you were ?hyper? and I was totally surprised since I was quietly sitting on the sofa in the waiting lounge for the doctor. I was told that I would stay in the hospital for three days. I am sure this matter can be resolved who is lying and who is truthful once you look apt video footage of cameras in most rooms.

4/28/2015
One injection was given in the morning. One injection was given around noon. All injections were IM (given in the muscle.)
Unknown pills(some pills in the morning +5 pills around noon + 3 pills at night) were given and I was told,? We will tell you know the names of these pills only when you leave.?
Computer was returned today but I was told that we did not take your mobile and they continued to say we never took my mobile. My mobile was never returned( despite I always keep my mobile on me.)
I was also not given my EVO USB device and I was told you cannot write anything on internet. However the USB device was returned to my mother at night.
I was told today by the psychologist that doctor N had gone to America and will come back after seven days and only then she would be able to see you. I was told we are adjusting your medicine and see what was a good medicine. I was told they were discussing the drugs with her on phone and skype There were several conflicting statements about where Dr. N was. Somebody said she was just out of city and had gone to Islamabad.
When I asked my mother who is living with me at the hospital, I wanted a second opinion, because of beating and other irresponsible behavior of the psychiatrist, my mother would make all sort of excuses while the staff would say that you cannot leave the hospital until Dr. N arrives who is currently out of country.
Earlier today, I was told that I would live at the hospital for fifteen days and later I was told that I would live at the facility for seven days. When I was tied, somebody had told me that I would live in the hospital for three days only.
My mother told me please do not write anything wrong on internet otherwise, they would take your USB forcefully like Dr. A had done more than one year ago. The purpose was to threaten me to not write about any maltreatment so that the doctor would continue to freely manipulate me.
7-8 pills were given in the afternoon and similar number of pills were given at night. At many times during the day, I could barely walk and had extreme difficulty speaking.”

Friends, I have previously described several horror experiences with psychiatrists but there are many more such experiences that I have not posted on this thread. Today I am going to describe a continuing experience in which the psychiatrist did everything in his power to retard me.
This is from year 2004/2005. I had a sound logic at that time and I was working from Lahore at a job with a foreign Japanese company that was paying me $4000 per month. I was still on high antipsychotics and when high dosage of normal antipsychotics did not work, in order to retard me, the psychiatrist employed a procedure that is not known in psychiatric practice in any country. The psychiatrist would give me some drugs in a glucose drip every two/three days in the operation theater. When I would be given the glucose drip, I would gradually start to lose consciousness and when half of the drip bottle would have gone into my blood, I would literally be unconscious, and I would later be taken unconscious to my hospital bed by the hospital staff and I would wake up several hours later on the bed in my hospital room and I would be extremely weak.
It was such a frightening experience that I would shudder from horror as the day of this treatment would come closer and continued to beg the psychiatrist to stop this treatment. The psychiatrist would say that he was giving me vitamins and vitamins were always harmless. He insisted that vitamins had to be given to me. He never told me what drugs he gave me that made me unconscious and never discussed it with me other than mentioning vitamins. The psychiatrist continued to perform this procedure for several weeks after sometimes second or usually third day. Most people cannot imagine how it would feel when the drug in glucose drip would go into my body and I would lose my senses. To this day I shudder from complete horror and recall the extremely sick feeling when I would slowly lose consciousness.
Now when I look back, I realize that they were giving me mind control drugs in the drip to take the intelligent neurotransmitters out of my body. They continued to try to take intelligent neurotransmitters out of my body again and again through this procedure for several weeks. I was completely helpless before my family and the psychiatrist and had to go through such unlawful medical procedures.
As friends would have realized that purpose of mind control agencies was always to retard me since neocon scumbags of pentagon and their backers were not capable of appreciating my humanity and did everything in their power to retard me with an iron fist.
I have seen continuing pain, trauma and torture in my life only because I had some special neurotransmitters that people with hatred and venom were not ready to let me have since they considered it a threat to let a Muslim have those neurotransmitters.

After starting mind control in Lahore in early 2000's, bad jews (again apologies to good jews) were very emboldened how easy it was to manipulate army and government in Pakistan to start mind control of intelligent people in Pakistan. It was a time when Pervaiz Musharraf who was an army dictator ruled the country. He was very ready to please the CIA in order to get help from American army to prolong his illegal dictatorship in Pakistan. He fixed in place all the required mind control infrastructure in all large cities of Pakistan to please American army who was playing in hand of bad jews to damage the Muslim majority country.
When Americans rightly blame our country for terrorism, they must not forget that many neocon generals in American army have played in the hand of bad jews and have made every effort to systematically destroy talent in Pakistan on a very large scale using mind control technologies to keep it backward forever.
Mind control in Pakistan is ensured by top Pakistani army generals since they are given several hundred million dollars by US army every year and the top brass of Pakistan army divides this money among themselves with bigger fish getting larger share and smaller fish getting a smaller share. Therefore, mind control infrastructure in Pakistan is very detailed and thorough.
From my own experience, there is very large mind control activity in Lahore and Islamabad, the two cities where I have lived during the past twenty years. There are at least more than 500 mind control targets in Pakistan most of whom are computer science majors.
Mind control in Pakistan and many other places increased dramatically like never before. We have in Lahore a huge building called Arfa Towers where all the facilities for technology and IT companies were provided to attract new firms and entrepreneurs and later Arfa Towers became a scene of mind control carnage since tens of aspiring computer scientists and entrepreneurs were retarded and it became very easy for mind control agencies to find the talent since the facility attracted talent and retard it. Time between 2008 and 2016 was like black death for talent in technology in our country (I am not talking about pseudo-talent that American embassy continued to support and showcase heroically in the meantime.) I still recoil with horror when I look back and recall how difficult it was to get good drinking water in Lahore during that time for more than six months in 2013-2014. I would have to go to remote parts of the city, go to villages around the city and sometimes even go to other cities and only then I would be able to get some good water after repeated attempts and my only worry during the day would be to somehow get good food and water.
At this point I like to tell friends that a lot of food and beverages that are drugged with mind control chemicals would be eaten or taken by most of the population that is not on mind control and they would never notice any anomaly in taste or any other effect since these mind control chemicals are inactive and inert and become chemically active only when targeted remotely with precise electromagnetic wave frequencies so only target victims are affected and this is a very cruel method to target intelligent people by drugging the entire supply of food and beverages and then focusing waves on the targeted individuals to activate the mind control chemicals. Pakistan army and mind control agencies would drug the entire public water supply and beverages knowing that the victim would have to drink something somewhere. Ground water is also so thoroughly drugged with mind control chemicals that entire public water supply of the city and several kilometers out of the city would be completely drugged with mind control chemicals. Pakistan army routinely does this in Lahore city on behest of American mind control agencies.
Ten years ago, army soldiers and agents would go to markets to drug the targeted food and beverages with mind control chemicals which they still. Large scale movements of soldiers and agents raise suspicions in general public and therefore mind control chemicals are supplied to beverage and food manufacturing companies in Pakistan, and they simply add the chemicals in food and beverages during the manufacturing process.
In Lahore city, there are more drugged beverages at any time than good beverages in small stores or large supermarkets alike since most of the beverages are drugged at manufacturing source by coca-cola, pepsi-cola and Nestle.
Coffee stimulates the brain and the brain connects in new ways after taking coffee and good coffee creates problems with keeping victims on mind control since their brain starts connecting in many new ways after taking good coffee. All coffee and I repeat that entire coffee in the country present in the stores is drugged with mind control chemicals. Most of the coffee on good stores is imported from foreign countries. I do not know how it works but importer is probably told by army to drug the imported coffee before distributing it in the market. It is even very difficult or rather impossible to get good coffee beans. Two or three years ago it was possible to find some brand of coffee that was good by trying all new brands but it has not worked for past two years now for me despite that I keep trying. I even know of instances that when I was able to buy good coffee of a certain brand from very large and posh stores, they took entire coffee brand off the shelf from all their branches within two to three days. People know that Corrupt Army in Pakistan that ensures mind control is more powerful than any political government here.
Tea used to be good but for past one year most mainstream Pakistani brands of black tea are drugged with mind control drugs. This has still not caught up thoroughly like coffee is thoroughly drugged and it is still possible to find some good foreign brands tea that is good.
All stimulant/energy drinks including red bull are well drugged at manufacturing source. Red bull was better till last year but then it became drugged everywhere. I even tried it at remote places in several cities other than Lahore and it has always been drugged lately.
Most of the soaps, shampoos, creams, toothpastes are drugged with mind control chemicals. I do not use shampoos or creams but whatever rare I tried them once in a while they were drugged and they charged my skin. All of these have mind control chemicals that charge the skin and make mind control extremely effective. Many people would be amazed when I tell them that even though I would be in my full senses before washing my head and face with a soap but after washing my head and face with a drugged soap, my eyesight would deteriorate and my conception of reality would completely change and sometimes I would face extreme anxiety. It is hard to emphasize that even a small thing like this can completely change the victim's state of mind and consciousness. Getting a good soap was very difficult for me till last year and I would drive for several hours in different parts of the city especially looking at all the pharmacies on the way to find some unknown brand or some soap that would have been manufactured several years ago when soaps were not getting completely drugged. I tried all the soaps including beauty soaps that are specially made for women, even many unknown brands, and specially imported soaps(which were all universally drugged thoroughly) and it was very very difficult to find a good soap. After finding a good soap, I would keep it in my pocket all the time. This is a small thing but you cannot live without it. Since our mouth is kept charged and some charges continue to go into victim's body from one's mouth. Therefore toothpastes are also added with mind control chemicals to charge inside of our mouth. You can imagine that after buying five or six tooth pastes of different remote brands, I would get a good tooth paste. I have recently been using toothpaste that is imported from abroad and is good. Toothpastes manufactured in Pakistan are all drugged with mind control chemicals.
Another big problem is that pharmaceutical companies add mind control chemicals to their drugs(pills etc). Most of the mind control victims are targeted due to their talent and intelligence in mind many times might require special minerals that are rare in our food. Most of the mineral and vitamin formulas are also drugged with mind control chemicals. Most mainstream mineral and vitamin pills in the market are thoroughly drugged with mind control chemicals. I never like to take names but I would like to tell friends that greatest crook of all times is Glaxosmithkline( I would invite them to sue me for writing this on Wilmott). GSK's mineral and vitamin formulas, effervescent calcium tablets, and toothpastes are all drugged with mind control chemicals. There is a tablet by the name Kemadrin that has to be taken with antipsychotics and GSK manufactures it and it is also drugged with mind control chemicals. My experience with GSK is so bad that If I have to buy any medicine and if it is made by GSK, I would try my utmost to avoid taking it for the fear of its being drugged with mind control chemicals and look for alternatives.
Injection fluanxol and clopixol are also drugged with mind control chemicals.
Again all this thorough infrastructure took more than fifteen years to develop in Pakistan and Pakistan army continued to work hard to develop it over the years. There are at least five hundred brilliant Pakistanis most of whom are computer scientists who are on active mind control to thwart them to contribute to society in any good way.
All this infrastructure exists in Pakistan and was developed because neocon generals wanted to please bad but rich jews and American mind control agencies continue to perfect it over last twenty years. Again, mind control in Pakistan is ensured by top Pakistani army generals since they are given several hundred million dollars by US army
I have not talked about special infrastructure that is used to project EM waves on the target and this infrastructure is present on all major roads and public places in big cities and major highways and motorways in the country.

Amin · May 28th, 2023, 5:02 am

My Letter To HRW About My Human Rights Abuse

Above is a very incomplete account of how various psychiatrists continued to play in hands of Pakistan army to retard me. It also does not cover all the time till year 2022 and the account stops several years earlier.
Pakistan Army has no personal animosity with me. Chief of Pakistan Army staff is given more than 50 billion rupees every year(exchanged rate has increased three times in past two years and money is paid in dollars) come rain or shine so that army continues American Mind control of intelligent people in Pakistan. Even when the relations between both countries are extremely bad, this bribe is always given to Pakistan army generals in time.

Before writing this post, I want to apologize to good jews but want to tell them there are enough evil jews who are doing everything to tarnish the great goodwill jews have so rightly earned through generations of hard work and being nice and kind to other people in the society. I want to request good jews to Please force these evil(jewish) people to end the bad practices that are starting to take root in American and other societies on their behest and before it is too late. I also really hope that my mind control would finally end(as I have been begging for past twenty years) and I would never have to write a post like this again.

In the past, I continued to mention about my mind control persecution from time to time but only started writing regularly about it when I arrived in UK on a Highly Skilled Migrant work visa. Mind control agencies did everything in their power to fail me in UK. People were asked to not give me a job. People I contacted were routinely told brazen lies about me totally shamelessly. When I realized that I had no future in UK, I returned to Pakistan after a six month stint in UK. Since my hard earned money had thoroughly insulted mind control infrastructure in UK as they had to drug entire cities with mind control chemicals in UK (read briefly about it in my application to HRW in a previous thread) for a nobody like me and American government had to move all their grand and influential puppets in UK (again for a nobody like me) to force people to drug the manufactured food. British Banks went to the extent to steal my money to bleed me. Read here: https://forum.wilmott.com/viewtopic.php?f=15&t=102298#p857494. British police forcefully stopped me from seeing law firms(Brief details are given in my application to HRW attached as a link below). Since my money had given mind control agencies a very tough time, mind control agencies decided to never let me make significant money after that. My old Japanese employer was told to not hire me after I returned to Pakistan. Whoever I would contact someone in Europe for job or consulting, mind control agencies would move American embassy infrastructure in that country and somebody highly influential (or army or secret services of that particular country) in that particular country would approach my target employer and again brazen lies and fabricated stories would be told about me shamelessly. I am a fighter in life and I continued my research despite all economic, coercive and other hardships. All odds were against me but I tried my best to continue. I have been presenting my research to friends on this forum for past five or six years. At this point, I want to request good American and friends from other countries who have come to know me through my research to please use their influence to end my mind control forever.

Since things might heat up after my writing this and my persecution might increase, I want to ask European embassies in Pakistan to keep a vigil. I want to tell Europeans that my writing about mind control is in their great interest since the very same people who instigate retarding of intelligent muslims are behind retarding of dozens of intelligent europeans and once these people are exposed I am sure they will be far more careful in openly retarding European talent(that they do not like).

I had told friends earlier that a jewish billionaire is Godfather of mind control. When my persecution started (in late 1997) at the university in New York which is a big time player in mind control of Muslims, blacks and foreigners, many university officials were very pleased that they were getting written in good books of the billionaire jewish Godfather. Though there are far richer billionaires in US who are staunchly opposed to mind control, they are not ready to shell out hundreds of millions of dollars to bribe anyone to end mind control while mind control Godfather continues to give large bribes to people to continue mind control. Many of the people related to defense in mind control are given extremely high paying jobs in Godfather and his other jewish friends' companies after they retire from mind control and Godfather is extremely generous towards them and it is well established and well known to scum in mind control that after retarding muslims, blacks and others in their career, they will move to paradise(tens of people from army/Pentagon who follow whims of Billionaire Godfather are given jobs paying milllons of dollars by Godfather and his jewish cohort in several companies) after they retire. No wonder there is no let up in mind control whatever good people try.
We know in almost all classic folk lore stories evil is too strong and too sure of itself while good is mostly weak and just trying to protect itself from evil who is bent on damaging and eradicating the weak and the poor good but it is the weak and poor good that finally prevails. I want to tell good American friends that evil at this stage has become too bold and thousands of talented people are retarded every year. And it is just not muslims and blacks that are on the line, several hundreds of brilliant whites are retarded across United States by mind control agency every year that has become too emboldened due to lack of any accountability. Thousands of foreigners are also kept retarded in dozens of countries including many European countries.
My only intention behind this post is that I want mind control to end from our societies. I do not have any joy in mentioning that there are some bad jewish actors behind it. In American society there are a large number of jews who have excelled in the professions of science, education, medicine and have made great contributions to our societies. There are a very large number of jewish professors each of whom would have taught tens of thousands of students on top of making extraordinary contributions to body of human knowledge through their great research. Then there are accomplished jewish scientists whose work, research and inventions make our everyday life better. There are great jewish doctors and surgeons who would treat countless sick people and make them recover from disease. The list of contributions of jewish people to humanity is very long and it continues. Then there are a large number of ordinary jewish folks who are known for their goodness and civility to other people in the society. When we know all of this, we do not want to say anything anti-jewish to hurt the feelings of so many good jewish people. But I still have to say there are really some bad people who are unconnected with most of the nice and accomplished jews and they instigate and continue cruel mind control torture on talented people of other ethnicities, religions and countries based on their personal dislike and hatred. My purpose is only to end the mind control victimization and torture on otherwise nice and talented people and I do not have any hidden intentions beyond that. And I am sure American society knows very well about the contributions of good Jews to both their country and broader humanity and my exposing some bad actors would never have any bad effect of any kind on these good and nice jews who we all respect and who are our role models.I want to tell friends something I have said before here that I am sure American society would eventually end the menace of mind control from their and other countries. I want to request all good Americans and Europeans to come forward and invite any investigative journalist you know to read my threads and ask them to help end the menace of mind control in our societies through their investigative journalism. Without any accountability evil will continue to grow stronger and then mind control would start to threaten even those people who consider themselves safe due to affiliations, status or wealth.
I want to request CNN, New York Times, Washington Post, Al-Jazeera and large reputed European media outlets to run a comprehensive story on mind control torture, retarding and victimization of intelligent people of US and other nations by scum in US army on behest of some powerful people in United States and due to rightwing extremist biases of these scumloads. If you would like to do investigative research about animal practices of US army, one great resource would be mainland European embassies in Muslim countries who keep a detailed account of mind control persecution of intelligent muslims in these countries by scum in US army. Many of the staff in mainland European embassies are very good human beings who abhor such practices and would love to cooperate with good journalists in exposing the evil animal practices of US army scum. Only the accounts of people at mainland European embassies in muslim countries thorough animal practices of American army's mind control wing would be enough to drop a great bombshell in the media and general public all across the world. I want to warn all the good people who try to have a civilized dialogue with scum in American army to end their evil practices that their being nice with US army scumloads is a very misguided approach. Since good people do not have the power to forcefully end the evil practices of US army scum, only way to end the evil practices of US army crooks is by exposing them openly in US public and all across the world.
It seems that scum in American army and mind control are unable to pay a heed to civilized calls by good American people and others to end their animal cruel practices and remain bent on mischief. If crooks in American army and mind control remain adamant on continuing evil practices, the only solution seems that some brave investigative journalists expose them by running a comprehensive story on mind control practices by American army. It seems that doing a civilized dialogue with hardened crooks in mind control gives them a strong sense of weakness of good people and makes the crooks even more adamant to continue their evil practices. Reminds me of Abu-Gharib. Very similarly, scum in defense had no conception that they were doing any wrong thing when there was a culture of openly urinating on human captives. It was an open thing in army and most scumloads thought it was indeed a very right thing to do( and I am sure some of those crooks still believe that it was a right thing they did even after being reprimanded by the broader American society). It was not until brave people at CNN did a daring story against animal practices by crooks that evil practices stopped. Though American army scumloads retard intelligent people of all color and creed, these ultra right wing army scumloads love to retard blacks and muslims with great relish. Blacks are only 8-10% of US population but make a very large proportion of victims in united states since many ultra right wing scum in US army would rather die than let those intelligent blacks succeed in American society in a big way.

Amin · May 28th, 2023, 6:59 am

Friends, after coming back from UK in 2011, I always wanted to live in my country. I tried to do good research and had enough success despite all hardships. Though malicious people spread all kind of lies about me and successfully made me an object of ridicule all over the world, I was till able to earn enough respect among good people due to my research who tried to protect me again and again several times. But at this age of fifty years (I will be fifty this September), it is very difficult for me to simultaneously fight mind control and try to make something out of my future. Conservative army scum shares the same hatred for Muslims that was prevalent in Europe in fifteenth century and US army scum completely refuses to grow out of that hatred for Muslims. On top of that there is a cohort of rich Jews headed by a Jewish billionaire who go out of their way to create multi-million dollar opportunities for officers in American army and Pentagon(after their retirement from American army) who retard Muslims and others targeted by the Jewish Godfather. There is an active network of many jews in US universities who remain in touch with the billionaire Jewish Godfather and american army and continue to point out who to retard.
I am extremely thankful to good people in United States who tried to protect me in the past. I do not have words to describe the gratitude I have towards them. But hardliner conservatives in American army are too strong and they have absolutely no intention of ending my torture and mind control. I really think whatever I try or good people try, my density will surely remain in doldrums. I will be kept on antipsychotics with occassional detentions and mind control will continue.
Twenty five years have passed since my mind control started but I never lost hope that one day I would be free and live in the world without the yoke of mind control on me. I am more optimistic today then ever that my mind control will end one day but American army scum is also, at the same time, more emboldened than ever and are not ready at all to decrease any mind control.
Again I wanted to remain in my own country for the rest of my life but again and again I feel that my life here will remain miserable. I have therefore decided that I will try to approach top five or six universities in China and try to get a research position there. I will tell them in detail about my mind control in Pakistan and several hundred others like me who are forced to live under the constant yoke of mind control by US army. I will also try to describe my academic achievements. I hope that I would be able to get some place in some good Chinese university. I do not think I have any future if I remain in Pakistan. Bad people in US army are stronger than any voice of sanity in that country. So I have made up my mind to try to settle in China.
In fact I urge all Pakistani students who have any special talent to go to China for higher education. Despite whatever good people in US try, there is a strong network of bad people in US universities that looks for Muslim talent and then asks US army to retard them. It is ensured that people who are targeted live a life of total failure and misery after that. if you have any special talent, please do not waste your life. However, if you are in the middle without any very special talent or ambition(sorry for being honest), you can safely go there and have a happy life.
Chinese education is not bad at all. There are two very good professors in NUST(that is the best Pakistani university) who I respect due to their research and one of them did his PhD from China and the other did his PhD from Japan. These two people in my Network have done excellent ground-breaking research in their fields.
I want to spend next week trying to write letters to Chinese professors or admin in Good Chinese universities. I hope that once I am free, I will continue to do good research.

Amin · May 28th, 2023, 7:40 pm

Friends, I wrote a rough subject of the letter I intend to send to various professors and staff in some good Chinese Universities in Beijing or Shanghai. I will make some minor changes to it tomorrow, add title and a resume and start sending it to Chinese friends possibly day after tomorrow since I still have to edit my resume. I want to request good European and American friends in academia if they know any Chinese professors, please tell them about my case and refer them to this thread. I really want to leave Pakistan at the moment and settle in China for several years and try to make something out of my future without yoke of mind control placed constantly on my shoulders.
Here is the rough letter.

I am a Pakistani researcher in stochastics, quantitative finance and statistical learning who has made some special discoveries in the aforementioned fields of mathematics. Unfortunately I am also part of a group of more than 500 very talented Pakistanis who are kept under mind control by US Army to systematically keep our country backward. Since China is a friendly country that also does not allow US Army mind control torture on its soil, I want to start my research at -------- university where I could do interdisciplinary research with other Chinese scholars with complete freedom and without the fear of US state persecution. Under these circumstances, I am looking for a research assistant position in your university.
Before I describe my accomplishments in mathematics research, I want to tell Chinese friends that I was targeted by US Army for mind control because of my creativity and talent for mathematics when I was a masters student at NYU in 1998. US military and other agencies systematically tried to fail me and persecuted me in various countries like Singapore, Japan and UK due to global reach of US military. Unfortunately unlike proud Chinese people, Pakistani government and military are a puppet of US army and they openly allow US military to operate in Pakistan and execute mind control of innocent Pakistani citizens. However just like China, American Army considers Pakistan an enemy country and tries its best to damage the interests of our country even though they pretend to be friends on the veneer. In order to obstruct progress of our country Pakistan, American Army has a group of more than 500 very talented Pakistani computer scientists and researchers who are kept on mind control all the time so they cannot contribute to our country and society in any positive way. I have written about my persecution on hands of US military at several places on Wilmott forum on internet and I am giving links to those threads so that Chinese friends can know about the cruelty with which American military retards innocent and talented people of our poor countries to keep the destinies of our backward countries bleak forever.

My Letter to HRW About My Human Rights Abuses: viewtopic.php?f=15&t=102298

How To Safeguard My Research: viewtopic.php?f=15&t=94796

Breakthrough In the Theory of Stochastic Differential Equations and Their Simulation: viewtopic.php?f=4&t=99702

Please consider my request to join your university as a request for asylum against torture and persecution of American military. I want to assure that I would try to make a very positive contribution towards the research activity of the university in my field of applied mathematics.
Among my previous research achievements in the field of stochastics, I solved the longstanding problem of higher order accurate monte carlo simulations of stochastic differential equations. This problem had evaded large number of brilliant researchers all over the world for several decades without anybody finding a proper solution to the problem.
Later I found an orthogonal hermite polynomial representation of a very large class of random variables encompassing most of the classes of non-cental chi-squared random variables, generalized gamma random variables, lognormal random variables, heavy tailed distributed random variables and many more. The class of random variables that could be represented by hermite polynomial series expansion covers almost all the different types of random variables we come across in qunatitative finance. I discovered a numerical method that would take first eight moments of the random varaibles as input and present a hermite polynomial analytic series representation of the density so that first eight moments of the analytic hermite expression would exactly match the input moments. This method is far superior to earlier used methods like edgeworth or gram-charlier expansions and mostly gives a perfectly exact fit to the density when valid moments are input to the numerical method.
Later I found in my research that prevalent classic method of calculation of pearson correlation was highly suoptimal in general. It was optimal only for perfectly gaussian random variables. In general, the greater the deviation from gausssianity in two random variables, the more suboptimal the classic calculation of pearson correlation would become. I found in my research that a proper way to calculate correlations between two non-gaussian random variables was to represent the random variables as series in hermite orthogonal polynomials and then find correlations independently between hermite polynomials of the same order across two variables. This discovery means that most of the classic models and numerical methods in stochastics and time series that are based on proper calculation of correlations or covariances between two or more random variables have to be properly altered by replacing one gross estimate of Pearson correlation by multiple estimates of correlations between hermite polynomials of the same order across two ariables when the random variables under consideration are non-gaussian.
The observation that pearson correlations have to be calculated independently for each hermite polynomial led to a new ground breaking concept of analytic hermite polynomial regression between two or more non-gaussian variables. This orthogonal regression breaks down every non-gaussian random variable into a series in hermite polynomials and then hermite polynomials of every order are regressed independently on each other depending upon their indpendent pearson correlations and then results from various orthogonal hermite polynomial regressions is added to give planar curves that make a fit to the regression data. As opposed to straight lines making a fit between variables in linear regression, in hermite orthogonal regression, polynomials are used to find a fit to data and this fit is in the form of high-dimensional analytic hyperplanar-curves. Please note that Hermite orthogonal regression I am referring to is a very new discovery that I recently made in Feb 2023 and it is different, far better and unrelated to another classic method known by the name of hermite polynomial regression which has been known for decades. This new method of hermite orthogonal regression is a strong competitor and usually better than most AI and machine learning regresssion methods that fit a curve to data.
One of my articles on interest rate derivatives, "Calibration, Simulation and Hedging in a Heston Libor Market Model with Stochastic Basis" was an invited publication in a risk book here: https://riskbooks.com/interest-rate-mod ... ial-crisis
Please look under table of contents for my article.

Breakthrough in the theory of stochastic differential equations and their simulation

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Re: Breakthrough in the theory of stochastic differential equations and their simulation

Re: Breakthrough in the theory of stochastic differential equations and their simulation