For some background, the non-analyticity of the diffusion kernel factor, [$]e^{-d^2/T}[$] at [$]T=0[$] leads many to believe strict asymptotics in [$]T[$] is the only possibility for option values and related solutions for diffusion models. As we explain in the paper, that's not correct. For example, a simple case is the at-the-money Black-Scholes option value [$]V_{BS}(T) = \mbox{Erf}(2^{-3/2} \sqrt{T})[$]. If you divide the right-hand-side by a [$]\sqrt{T}[$], you get an entire function of [$]T[$], and so an associated power series in [$]T[$] that converges for any [$]|T| < \infty[$]. In principle, that or analyticity for [$]|T| < R[$], where [$]R>0[$] is a convergence radius, could hold in the SABR model. We prove it doesn't.

As always, any comments on the paper are appreciated.

Statistics: Posted by Alan — Today, 1:42 pm

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2. I slept in air-conditioning in a different room(my room has terrible air-conditioning and gas that comes out of AC in my room is just thoroughly killing.) which has far better air-conditioning but they still use some light gases in air-conditioner and when I woke up, I was feeling frail and without any energy due to gas I had inhaled. I would have loved to live without air-conditioning but it is way too humid and warm at the moment.

3. When I went out in my car, they charged my head and face with gas that settles on exposed body. It makes me totally dull and takes all energy out of my body.

But still it was a far better day since they decreased laser on my back remarkably especially when I am just moving around and doing nothing very significant.

Statistics: Posted by Amin — Today, 4:39 am

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just in case my question is not crystal-clear, i'm mostly interested on "how to do it" and "why that how is the right approach" in C++ (e.g. one is better off reading the file all at once and then get through each line as it is more memory efficient, oen shall not use conditions like if row M and and column N then catch the value because it is ugly and there is a better way to do it, use boost::tokenizer because it is handy and fast, etc...)..

thank you all!

Statistics: Posted by tagoma — Yesterday, 6:19 pm

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Statistics: Posted by Alan — Yesterday, 3:24 pm

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So yes, there was some let up on torture on my back but it would restart in full swing in a few days again when the whole thing goes out of limelight otherwise they continued to add mind control drugs to food and water just as usual.

Statistics: Posted by Amin — Yesterday, 5:05 am

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Compulsory workplace vaccination rules cannot apply to vegans

"More than half a million vegans will be exempt if companies introduce compulsory vaccination rules in Britain because their beliefs are protected by employment law, legal experts have said."

I’d be comfortable with that as long as said sworn vegans are proscribed from any medical treatment that may harm viruses or bacteria in their bodies."More than half a million vegans will be exempt if companies introduce compulsory vaccination rules in Britain because their beliefs are protected by employment law, legal experts have said."

Statistics: Posted by bearish — August 1st, 2021, 10:35 pm

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Statistics: Posted by tagoma — August 1st, 2021, 8:54 pm

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"More than half a million vegans will be exempt if companies introduce compulsory vaccination rules in Britain because their beliefs are protected by employment law, legal experts have said."

Statistics: Posted by katastrofa — August 1st, 2021, 6:56 pm

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The structure of the file never changes.

As you can see there is now row ID, data/row identifier or anything like that. The 2 first columns ("STUB_1", "STUB_2") relate to measure and geography data dimensions respectively but there several lines with the same combination of "STUB_1" and "STUB_2".

From column 3 to the last row, values correspond to this week, prev week, prev year, this week (4wk ave), this week (4wk ave).

So I know in advance that I will a few data at the intersection of a selected number of rows and columns 3 (this week) & column 4 (prev week).

What is the best way to do this in C++, please? (untold questions include would you read the file row by row ? btw the file is first saved to disk? would you loop over row and columns? are there numpy tools like in C++ nowadays? .. ?)

I'm willing to do this quite consistenly with the way real and modern C++ programmers would do it.

any help much appreciated.

(NO I don't want to use Python, instead)

Statistics: Posted by tagoma — August 1st, 2021, 4:08 pm

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Here is the program.

.

Code:

`function [] = FPERevisitedTransProb08ABwNew04B()%Copyright Ahsan Amin. Infiniti derivatives Technologies.%Please fell free to connect on linkedin: linkedin.com/in/ahsan-amin-0a53334 %or skype ahsan.amin2999%In this program, I am simulating the SDE given as%dy(t)=mu1 x(t)^beta1 dt + mu2 x(t)^beta2 dt +sigma x(t)^gamma dz(t)%I have not directly simulated the SDE but simulated the transformed %Besse1l process version of the SDE and then changed coordinates to retreive%the SDE in original coo%rdinates.%The present program will analytically evolve only the Bessel Process version of the%SDE in transformed coordinates.dt=.125/16/2/2/2; % Simulation time interval.%Fodiffusions close to zero %decrease dt for accuracy.Tt=128*2*2*2*2; % Number of simulation levels. Terminal time= Tt*dt; //.125/32*32*16=2 year; T=Tt*dt;OrderA=4; %OrderM=4; %dtM=dt*4*2*4;TtM=Tt/4/2/4;dNn=.2/1; % Normal density subdivisions width. would change with number of subdivisionsNn=50; % No of normal density subdivisionsNnMidl=25;%One half density Subdivision left from mid of normal density(low)NnMidh=26;%One half density subdivision right from the mid of normal density(high)NnMid=4.0;x0=1.0; % starting value of SDEbeta1=0.0;beta2=1.0; % Second drift term power.gamma=.95;%50; % volatility power. kappa=4.0;%.950; %mean reversion parameter.theta=.250;%mean reversion targetsigma0=1.50;%Volatility value%you can specify any general mu1 and mu2 and beta1 and beta2.mu1=1*theta*kappa; %first drift coefficient.mu2=-1*kappa; % Second drift coefficient.%mu1=0;%mu2=0;alpha=1;% x^alpha is being expanded. This is currently for monte carlo only.alpha1=1-gamma;%This is for expansion of integrals for calculation of drift %and volatility coefficientsyy(1:Nn)=x0; w(1:Nn)=x0^(1-gamma)/(1-gamma);x(1:Nn)=x0;%Z(1:Nn)=(((1:Nn)-5.5)*dNn-NnMid);Z(1:Nn)=(((1:Nn)-5.5)*dNn-NnMid);Zstr=input('Look at Z');ZProb(1)=normcdf(.5*Z(1)+.5*Z(2),0,1)-normcdf(.5*Z(1)+.5*Z(2)-dNn,0,1);ZProb(Nn)=normcdf(.5*Z(Nn)+.5*Z(Nn-1)+dNn,0,1)-normcdf(.5*Z(Nn)+.5*Z(Nn-1),0,1);ZProb(2:Nn-1)=normcdf(.5*Z(2:Nn-1)+.5*Z(3:Nn),0,1)-normcdf(.5*Z(2:Nn-1)+.5*Z(1:Nn-2),0,1); %Above calculate probability mass in each probability subdivision.%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%sigma11(1:OrderA+1)=0;mu11(1:OrderA+1)=0;mu22(1:OrderA+1)=0;sigma22(1:OrderA+1)=0;% index 1 correponds to zero level since matlab indexing starts at one. sigma11(1)=1;mu11(1)=1;mu22(1)=1;sigma22(1)=1;for k=1:(OrderA+1) if sigma0~=0 sigma11(k)=sigma0^(k-1); end if mu1 ~= 0 mu11(k)=mu1^(k-1); end if mu2 ~= 0 mu22(k)=mu2^(k-1); end if sigma0~=0 sigma22(k)=sigma0^(2*(k-1)); endend%Ft(1:TtM+1,1:(OrderA+1),1:(OrderA+1),1:(OrderA+1),1:(OrderA+1))=0; %General time powers on hermite polynomialsFp(1:(OrderA+1),1:(OrderA+1),1:(OrderA+1),1:(OrderA+1))=0;%General x powers on coefficients of hermite polynomials.Fp1(1:(OrderA+1),1:(OrderA+1),1:(OrderA+1),1:(OrderA+1))=0;%General x powers for bessel transformed coordinates.%YCoeff0 and YCoeff are coefficents for original coordinates monte carlo.%YqCoeff0 and YqCoeff are bessel/lamperti version monte carlo.YCoeff0(1:(OrderA+1),1:(OrderA+1),1:(OrderA+1),1:(OrderA+1))=0;YqCoeff0(1:(OrderA+1),1:(OrderA+1),1:(OrderA+1),1:(OrderA+1))=0;%Pre-compute the time and power exponent values in small multi-dimensional arraysYCoeff = ItoTaylorCoeffsNew(alpha,beta1,beta2,gamma); %expand y^alpha where alpha=1;YqCoeff = ItoTaylorCoeffsNew(alpha1,beta1,beta2,gamma);%expand y^alpha1 where alpha1=(1-gamma)YqCoeff=YqCoeff/(1-gamma); %Transformed coordinates coefficients have to be %further divided by (1-gamma)for k = 0 : (OrderA) for m = 0:k l4 = k - m + 1; for n = 0 : m l3 = m - n + 1; for j = 0:n l2 = n - j + 1; l1 = j + 1; %Ft(l1,l2,l3,l4) = dtM^((l1-1) + (l2-1) + (l3-1) + .5* (l4-1)); Fp(l1,l2,l3,l4) = (alpha + (l1-1) * beta1 + (l2-1) * beta2 + (l3-1) * 2* gamma + (l4-1) * gamma ... - (l1-1) - (l2-1) - 2* (l3-1) - (l4-1)); Fp1(l1,l2,l3,l4) = (alpha1 + (l1-1) * beta1 + (l2-1) * beta2 + (l3-1) * 2* gamma + (l4-1) * gamma ... - (l1-1) - (l2-1) - 2* (l3-1) - (l4-1)); YCoeff0(l1,l2,l3,l4) =YCoeff(l1,l2,l3,l4).*mu11(l1).*mu22(l2).*sigma22(l3).*sigma11(l4); YqCoeff0(l1,l2,l3,l4) =YqCoeff(l1,l2,l3,l4).*mu11(l1).*mu22(l2).*sigma22(l3).*sigma11(l4); end end endend%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%wnStart=1;%ticZt1(wnStart:Nn)=0.0;Zt2(wnStart:Nn)=0.0;for tt=1:Tt x(isnan(x)==1)=0.00; [xMu0dt,c1] = CalculateDriftAndVolA4Original(x,wnStart,Nn,YCoeff0,Fp,gamma,dt); %Loop below tackles first ten time steps in Bessel coordinates if(tt<=10) w(wnStart:Nn)=x(wnStart:Nn).^(1-gamma)/(1-gamma); [wMu0dt,dwMu0dtdw,c1] = CalculateDriftAndVolA4(w,wnStart,Nn,YqCoeff0,Fp1,gamma,dt); [wMid] = InterpolateOrderN8(8,0,Z(NnMidl-3),Z(NnMidl-2),Z(NnMidl-1),Z(NnMidl),Z(NnMidh),Z(NnMidh+1),Z(NnMidh+2),Z(NnMidh+3),w(NnMidl-3),w(NnMidl-2),w(NnMidl-1),w(NnMidl),w(NnMidh),w(NnMidh+1),w(NnMidh+2),w(NnMidh+3)); Zt1(wnStart:Nn)=w(wnStart:Nn)-wMid; [dwdZ,d2wdZ2A] = First2Derivatives2ndOrderEqSpacedA(wnStart,Nn,dNn,Zt1,Z); C0(wnStart:Nn)=Zt1(wnStart:Nn)-dwdZ(wnStart:Nn).*Z(wnStart:Nn); Zt2(wnStart:Nn)=C0(wnStart:Nn)+abs(sqrt((dwdZ(wnStart:Nn)).^2+sigma0^2*dt)).*Z(wnStart:Nn); %x2(wnStart:Nn)=((1-gamma)*(Zt2(wnStart:Nn)-0*Zt1(wnStart:Nn)+wMid)).^(1.0/(1-gamma)); end [dxdZ,d2xdZ2A] = First2Derivatives2ndOrderEqSpacedA(wnStart,Nn,dNn,x,Z); % [xMid] = InterpolateOrderN8(8,0,Z(NnMidl-3),Z(NnMidl-2),Z(NnMidl-1),Z(NnMidl),Z(NnMidh),Z(NnMidh+1),Z(NnMidh+2),Z(NnMidh+3),x(NnMidl-3),x(NnMidl-2),x(NnMidl-1),x(NnMidl),x(NnMidh),x(NnMidh+1),x(NnMidh+2),x(NnMidh+3));% % Zt1(wnStart:Nn)=x(wnStart:Nn)-xMid;% % [dxdZ,d2xdZ2A] = First2Derivatives2ndOrderEqSpacedA(wnStart,Nn,dNn,x,Z);% % C0(wnStart:Nn)=Zt1(wnStart:Nn)-dxdZ(wnStart:Nn).*Z(wnStart:Nn);%-.5*d2xdZ2A(wnStart:Nn).*(Z(wnStart:Nn).^2-1);% % %Zt2(wnStart:Nn)=C0(wnStart:Nn)+abs(sqrt((dxdZ(wnStart:Nn)).^2+sigma0^2*x(wnStart:Nn).^(2*gamma).*dt)).*Z(wnStart:Nn);%+.5.*(sqrt((d2xdZ2A(wnStart:Nn).^2)+(sigma0^2.*(gamma).*x(wnStart:Nn).^(2*gamma-1)*dt).^2)).*(Z(wnStart:Nn).^2-1);% % % %Zt2(wnStart:Nn)=C0(wnStart:Nn)+abs(sqrt((dxdZ(wnStart:Nn).*x(wnStart:Nn).^gamma).^2+c1(wnStart:Nn).^2)).*Z(wnStart:Nn);% [dxdZ,d2xdZ2A] = First2Derivatives2ndOrderEqSpacedA(wnStart,Nn,dNn,Zt2,Z);% x2=Zt2(wnStart:Nn)+xMid; % tt if(tt>10) x(wnStart:Nn)= +x(wnStart:Nn)-sigma0.^2*gamma*x(wnStart:Nn).^(2*gamma-1)*dt ... +xMu0dt(wnStart:Nn) ... +.5*sigma0^2*x(wnStart:Nn).^(2*gamma).*(dxdZ(wnStart:Nn)).^(-2).*(d2xdZ2A(wnStart:Nn)).*dt ... +.5*sigma0^2*x(wnStart:Nn).^(2*gamma).*Z(wnStart:Nn).*(dxdZ(wnStart:Nn)).^(-1)*dt; else %Bessel coordinates evolution associated with first ten steps. w(wnStart:Nn)= wMid+Zt2(wnStart:Nn)+wMu0dt(wnStart:Nn); x(wnStart:Nn)=((1-gamma).*w(wnStart:Nn)).^(1/(1-gamma)); %x(wnStart:Nn)= +x2(wnStart:Nn)-sigma0.^2*gamma*x(wnStart:Nn).^(2*gamma-1)*dt+ ... % xMu0dt(wnStart:Nn);%+Zt2(wnStart:Nn)-Zt1(wnStart:Nn);%+ ... end %yy(wnStart:Nn)=((1-gamma).*w(wnStart:Nn)).^(1/(1-gamma)); w(wnStart:Nn)=x(wnStart:Nn).^(1-gamma)/(1-gamma); % [wE] = InterpolateOrderN6(6,Z(Nn)+dNn,Z(Nn),Z(Nn-1),Z(Nn-2),Z(Nn-3),Z(Nn-4),Z(Nn-5),w(Nn),w(Nn-1),w(Nn-2),w(Nn-3),w(Nn-4),w(Nn-5));% % w1(wnStart:Nn-1)=w(wnStart:Nn-1);% w1(Nn)=x(Nn);% w2(wnStart:Nn-1)=w(wnStart+1:Nn);% w2(Nn)=wE; % w(w1(:)>w2(:))=0;%Be careful;might not universally hold;% % Change 3:7/25/2020: I have improved zero correction in above.% w(w<0)=0.0; for nn=wnStart:Nn if(x(nn)<=0) wnStart=nn+1; end end end%yy(wnStart:Nn)=((1-gamma).*w(wnStart:Nn)).^(1/(1-gamma));yy(wnStart:Nn)=x(wnStart:Nn);Dfyy(wnStart:Nn)=0;for nn=wnStart+1:Nn-1 Dfyy(nn) = (yy(nn + 1) - yy(nn - 1))/(Z(nn + 1) - Z(nn - 1)); %Change of variable derivative for densitiesendpyy(1:Nn)=0;for nn = wnStart:Nn-1 pyy(nn) = (normpdf(Z(nn),0, 1))/abs(Dfyy(nn));endtocItoHermiteMean=sum(yy(wnStart+1:Nn-1).*ZProb(wnStart+1:Nn-1)) %Original process average from coordinates disp('true Mean only applicable to standard SV mean reverting type models otherwise disregard');TrueMean=theta+(x0-theta)*exp(-kappa*dt*Tt)%Mean reverting SDE original variable true averagetheta1=1;rng(29079137, 'twister')paths=200000;YY(1:paths)=x0; %Original process monte carlo.Random1(1:paths)=0;for tt=1:TtM Random1=randn(size(Random1)); HermiteP1(1,1:paths)=1; HermiteP1(2,1:paths)=Random1(1:paths); HermiteP1(3,1:paths)=Random1(1:paths).^2-1; HermiteP1(4,1:paths)=Random1(1:paths).^3-3*Random1(1:paths); HermiteP1(5,1:paths)=Random1(1:paths).^4-6*Random1(1:paths).^2+3; YY(1:paths)=YY(1:paths) + ... (YCoeff0(1,1,2,1).*YY(1:paths).^Fp(1,1,2,1)+ ... YCoeff0(1,2,1,1).*YY(1:paths).^Fp(1,2,1,1)+ ... YCoeff0(2,1,1,1).*YY(1:paths).^Fp(2,1,1,1))*dtM + ... (YCoeff0(1,1,3,1).*YY(1:paths).^Fp(1,1,3,1)+ ... YCoeff0(1,2,2,1).*YY(1:paths).^Fp(1,2,2,1)+ ... YCoeff0(2,1,2,1).*YY(1:paths).^Fp(2,1,2,1)+ ... YCoeff0(1,3,1,1).*YY(1:paths).^Fp(1,3,1,1)+ ... YCoeff0(2,2,1,1).*YY(1:paths).^Fp(2,2,1,1)+ ... YCoeff0(3,1,1,1).*YY(1:paths).^Fp(3,1,1,1))*dtM^2 + ... ((YCoeff0(1,1,1,2).*YY(1:paths).^Fp(1,1,1,2).*sqrt(dtM))+ ... (YCoeff0(1,1,2,2).*YY(1:paths).^Fp(1,1,2,2)+ ... YCoeff0(1,2,1,2).*YY(1:paths).^Fp(1,2,1,2)+ ... YCoeff0(2,1,1,2).*YY(1:paths).^Fp(2,1,1,2)).*dtM^1.5) .*HermiteP1(2,1:paths) + ... ((YCoeff0(1,1,1,3).*YY(1:paths).^Fp(1,1,1,3) *dtM) + ... (YCoeff0(1,1,2,3).*YY(1:paths).^Fp(1,1,2,3)+ ... YCoeff0(1,2,1,3).*YY(1:paths).^Fp(1,2,1,3)+ ... YCoeff0(2,1,1,3).*YY(1:paths).^Fp(2,1,1,3)).*dtM^2).*HermiteP1(3,1:paths) + ... ((YCoeff0(1,1,1,4).*YY(1:paths).^Fp(1,1,1,4)*dtM^1.5 )).*HermiteP1(4,1:paths) + ... (YCoeff0(1,1,1,5).*YY(1:paths).^Fp(1,1,1,5)*dtM^2.0).*HermiteP1(5,1:paths); endYY(YY<0)=0;disp('Original process average from monte carlo');MCMean=sum(YY(:))/paths %origianl coordinates monte carlo average.disp('Original process average from our simulation');ItoHermiteMean=sum(yy(wnStart+1:Nn-1).*ZProb(wnStart+1:Nn-1)) %Original process average from coordinates disp('true Mean only applicble to standard SV mean reverting type models otherwise disregard');TrueMean=theta+(x0-theta)*exp(-kappa*dt*Tt)%Mean reverting SDE original variable true averageMaxCutOff=30;NoOfBins=round(300*gamma^2*4*sigma0/sqrt(MCMean)/(1+kappa));%Decrease the number of bins if the graph is too [YDensity,IndexOutY,IndexMaxY] = MakeDensityFromSimulation_Infiniti_NEW(YY,paths,NoOfBins,MaxCutOff );plot(yy(wnStart+1:Nn-1),pyy(wnStart+1:Nn-1),'r',IndexOutY(1:IndexMaxY),YDensity(1:IndexMaxY),'g'); %plot(y_w(wnStart+1:Nn-1),fy_w(wnStart+1:Nn-1),'r',IndexOutY(1:IndexMaxY),YDensity(1:IndexMaxY),'g',Z(wnStart+1:Nn-1),fy_w(wnStart+1:Nn-1),'b'); title(sprintf('x0 = %.4f,theta=%.3f,kappa=%.2f,gamma=%.3f,sigma=%.2f,T=%.2f,dt=%.5f,M=%.4f,TM=%.4f', x0,theta,kappa,gamma,sigma0,T,dt,ItoHermiteMean,TrueMean));%,sprintf('theta= %f', theta), sprintf('kappa = %f', kappa),sprintf('sigma = %f', sigma0),sprintf('T = %f', T)); legend({'Ito-Hermite Density','Monte Carlo Density'},'Location','northeast') str=input('red line is density of SDE from Ito-Hermite method, green is monte carlo.'); end`

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.

Here is the output of the program

ItoHermiteMean =

0.249565254868068

true Mean only applicable to standard SV mean reverting type models otherwise disregard

TrueMean =

0.250251596970927

Original process average from monte carlo

MCMean =

0.249542499753951

Original process average from our simulation

ItoHermiteMean =

0.249565254868068

true Mean only applicble to standard SV mean reverting type models otherwise disregard

TrueMean =

0.250251596970927

IndexMax =

651

and here is the output graph(I have changed the scale)

Statistics: Posted by Amin — August 1st, 2021, 10:29 am

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Here is my previous post:

It seems that crooks 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, Crooks 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 crooks 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 crooks retard intelligent people of all color and creed, these ultra right wing army crooks 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 crooks in US army would rather die than let those intelligent blacks succeed in American society in a big way.

I want to request CNN, New York Times, Washington Post 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 crooks in US army on behest of some powerful people in United States and due to rightwing extremist biases of these crooks. 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 crooks 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 crooks. 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 crooks in American army to end their evil practices that their being nice with crooks is a very misguided approach. Since good people do not have the power to forcefully end the evil practices of US army crooks, only way to end the evil practices of US army crooks is by exposing them openly in US public and all across the world.

Statistics: Posted by Amin — August 1st, 2021, 5:55 am

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I have been begging for help for years and years but to no avail and the torture by lowly crooks never ends at all. These lowly racist crooks who are incapable of doing any good in this world want to stop every black, muslim or foreigner from doing anything productive in this world. Is there any justice in this world or the these racist crooks are the last words of justice? Please help me.

Statistics: Posted by Amin — August 1st, 2021, 2:43 am

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Statistics: Posted by tagoma — July 31st, 2021, 10:10 pm

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The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (Oxford Landmark Science) - Roger Penrose

He covers the basic principles of physics, cosmology, mathematics, and philosophy and discusses AI in depth. Nice explorations from a gracious and open minded scientist and interesting to revisit the original ideas twenty years later.

Statistics: Posted by platinum — July 31st, 2021, 2:13 pm

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