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Amin
Topic Author
Posts: 1943
Joined: July 14th, 2002, 3:00 am

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

Friends, I did some initial work on the above project for 2-3 days but latter stopped working on it. I have been spending most of my time on crypto trading algorithms.
Though it is quite a nice thing to contribute to mathematics, for several years I have been under an extreme pressure to be able to make some money. CIA and mind control agencies stubbornly stopped people from working with me and at this stage I have almost totally given up approaching people for any consulting work to avoid constant embarrassment. After the lesson I got when I went to UK on tier one visa, I do not want to go to any foreign country to work to make myself a game for CIA hunters.
I get very limited money from my parents and I only spend it on food, petrol and some clothes. Since petrol prices increased, I do not even use my car and only have to use a motorcycle (though I am happy to decrease my carbon footprint and think this is what people should use unless otherwise necessary.)  I almost never have the luxury to eat expensive food and I myself avoid foot at restaurants where they take time to prepare food in order to avoid drugged food. I only eat at bakeries or inexpensive restaurants who have already prepared their food and I can take food off the fly. However since recent food inflation, I have to be very careful in what to eat and a lot of bakeries and street restaurants have become out of my approach. I really have to compromise quality of food to save money.
I again have this urgency that I have to somehow make real money and I cannot devote all my time to unpaid research.
However I want to tell friends that this is a temporary break and if I succeed in writing some interesting money making algorithms, I will love to restart my research at stochastics, probability theory and derivatives.
I know that mind control agencies would also love that I am temporarily stopping my research in mathematics and they would increase their machinations and attempts to retard me so I would continue posting here about their victimization tactics.
I really would love to re-start working on my last project in a few weeks or when I would find some time from my trading research so I really hope to post some material soon but it will still be a few weeks.
You think life is a secret, Life is only love of flying, It has seen many ups and downs, But it likes travel more than the destination. Allama Iqbal

Amin
Topic Author
Posts: 1943
Joined: July 14th, 2002, 3:00 am

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

My next antipsychotic injection in due on Friday in another two days. I am writing this since I am perfectly sure that mind control agencies would try their best to give me a "drugged injection". I know that some good people in Europe asked some mainland European Embassies to try to protect me in the past. I really want to request them to keep a vigil and ask their country's embassy to force Pakistani army (and ask other influential people in Pakistan)  to not drug fluanxol antipsychotic injections in Lahore in another day or two. Please ask your country's embassy to keep a watch on this.  If they succeeded in giving me a bad injection, I would not be able to work properly for several weeks. I would be extremely thankful to friends for this and all their earlier favors.
You think life is a secret, Life is only love of flying, It has seen many ups and downs, But it likes travel more than the destination. Allama Iqbal

Amin
Topic Author
Posts: 1943
Joined: July 14th, 2002, 3:00 am

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

I am writing this post to update friends with what has been going on with me in recent days.
I had earlier told friends that I want to trade on Binance to make some money. I downloaded Binance historical Data and tried some reasonably high frequency algorithms on that. I was able to find some high Sharpe ( >1 ) algorithms that worked very well. But when trading costs were added, the algorithms were not profitable. Binance has very high commissions of .1% of trade notional. Compare this to Interactive Broker's .0035% commission on US stocks. So Binance's commissions are on cryptocurrencies about 28 times higher than IB's commissions on US stocks. Well comparing commissions in two different markets might not be fair but this is just to give an idea. Secondly on Binance, cryptocurrency spreads are very small as compared to spreads of many stocks where one can do profitable trading. BTC is so volatile but generally has a spread of no more than .1 USD for a notional of 20000 USD despite its high volatility so strategies that depend on earning high spreads might not work so easily(at least for me) on cryptocurrencies.
I was very worried but found out that Binance had a promotion going that allowed zero commissions on currency pairs with stable currency BUSD. So I am lucky that I can profitably run my algorithms on those pairs and I have verified profitability of my algorithms on those pairs. I hope to start trading in two to three weeks since I still have to write callback programs with the API and later play around to optimize everything. The zero commissions promotion ends close to end of year 2022 but since my algorithm trades almost every minute(or two), even if I use a small notional of 5000 USD, I can get into Binance high volume categories where I will be able to get a small rebate on futures trading from Binance. So things look good and I am very confident that I will make it.
But I am very sure that mind control agencies will really continue their machinations to somehow fail me. In this world when some intelligent Chinese, Indian, Korean or anybody else works their ass off, they become very successful but when some intelligent muslim tries to work hard, racist scumbags of American army valiantly spring into action to fail them based on their habitual trickery, lies and machinations even more so since they pavlovianly start salivating in anticipation of huge rewards they would get from anti-muslim billionaires. My persecution would never have succeeded if it were not were brazen and completely fabricated lies of racist scumbags in American army. This is despite that I do not believe in religion and I am far more liberal than these scumbag racist conservatives in American army.
Friends would notice that I started my post on a good note and usually I would not like to end it with anything unpleasant but I am extremely sure that scumbags of American army will continue their trickery and machinations to somehow fail me otherwise they will not be able to get any rewards from some billionaires they so anticipate.
Anyway, I do hope that things go well and if it does go well, I will come back in a few weeks to end the work on stochastics and option pricing that I had started. I have a lot of good ideas about the calibration of options and their evolution with Z-series densities and I would really like to take my ideas to conclusion.
You think life is a secret, Life is only love of flying, It has seen many ups and downs, But it likes travel more than the destination. Allama Iqbal

Amin
Topic Author
Posts: 1943
Joined: July 14th, 2002, 3:00 am

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

Friends, I have been working with my algorithms to predict the crypto prices. In past few months BTC and ETH have been volatile like anything and very difficult to predict but I have had enough success. But when I was trying to find parameters for various stochastic process, I had great difficulty finding something that makes a good profit. Until I wrote a good stochastic optimization routine for finding the optimum values of stochastic parameters. Since I always believe that I should share basic fundamental research with friends even though sometimes I might not want to share everything like complete trading algorithms as in this case. Therefore, I decided to share my stochastic optimization program with friends.
It is a surprisingly simple program but worked like gold for me. You have to provide some reasonable guess for the stochastic parameters that are to be optimized. And define a reasonable large step. The algorithm then iterates in the direction of increasing objective function with the large and coarse step added and subtracted to parameters iteratively. When the algorithm stops improving the objective function, the step is cut to .8 of the initial value and the algorithm starts iterating again. Each time algorithm stops improving the objective function, we decrease the step size by a ratio of .8 (or some other suitable ratio). Finally, the algorithm converges to some point with little variation and the best value of objective function. Due to random nature of stochastic processes, many times, the final convergence point is entirely different from the points where the algorithm converged with coarse steps.
The good thing about the algorithm is that it explores the whole territory in the direction of increasing objective function with large and coarse steps at the start, so it does not easily get bogged down by local minima. And as it refines the step size in successive rounds of searches, it almost always finds a suitable value of the parameters that optimize the objective function very well.
In my case all the parameters shared the same probable range in which they can take values and therefore shared the same step change but in general the domain in which different stochastic parameters could take values would be different for every parameter of the stochastic process and in those cases the step change in each stochastic parameter would be made proportional to the standard deviation of the probable range(in the same common step ratio multiplied with standard deviation of every parameter) in which the particular parameter can take values. The above modification should work well but there will be some cases in which you will need to modify it for different step of some of the parameters.
I am sure that friends who optimize their stochastic neural networks with other optimization routines will really find my new function valuable for them. I am sure if the algorithm does not always work better than existing optimization algorithms for stochastic processes, quite a few times it will be very valuable as I found it of great value in my research.
I will be posting my program tomorrow after making a few changes and adding comments.
You think life is a secret, Life is only love of flying, It has seen many ups and downs, But it likes travel more than the destination. Allama Iqbal

Amin
Topic Author
Posts: 1943
Joined: July 14th, 2002, 3:00 am

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

Friends, I am posting the stochastic parameter optimization function below. It is written in matlab but just uses elementary functions and you can instantly copy it in any language just after inspecting the code and understanding it. Explanation of the code follows in next post.

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function [w1,w2,w3,w4,w5,w6] = OptimizeCoeffsPredictWilmott(Xt1,Xt2,Price0,Tl,VarLogR,IValue)

w1=IValue(1,1);
w2=IValue(1,2);
w3=IValue(1,3);
w4=IValue(1,4);
w5=IValue(1,5);
w6=IValue(1,6);

[ObjOld] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w3,w4,w5,w6);
Delta=.15;
for nn=1:1000
Update=0;
w10=w1+Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w10,w2,w3,w4,w5,w6);
if(ObjNew>ObjOld)
w1=w10;
Update=1;
ObjOld=ObjNew;
else
w10=w1-Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w10,w2,w3,w4,w5,w6);
if(ObjNew>ObjOld)
w1=w10;
Update=1;
ObjOld=ObjNew;

end
end

w20=w2+Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w20,w3,w4,w5,w6);
if(ObjNew>ObjOld)
w2=w20;
Update=1;
ObjOld=ObjNew;
else
w20=w2-Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w20,w3,w4,w5,w6);
if(ObjNew>ObjOld)
w2=w20;
Update=1;
ObjOld=ObjNew;

end
end
w30=w3+Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w30,w4,w5,w6);
if(ObjNew>ObjOld)
w3=w30;
Update=1;
ObjOld=ObjNew;
else
w30=w3-Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w30,w4,w5,w6);
if(ObjNew>ObjOld)
w3=w30;
Update=1;
ObjOld=ObjNew;

end
end
w40=w4+Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w3,w40,w5,w6);
if(ObjNew>ObjOld)
w4=w40;
Update=1;
ObjOld=ObjNew;
else
w40=w4-Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w3,w40,w5,w6);
if(ObjNew>ObjOld)
w4=w40;
Update=1;
ObjOld=ObjNew;

end
end
w50=w5+Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w3,w4,w50,w6);
if(ObjNew>ObjOld)
w5=w50;
Update=1;
ObjOld=ObjNew;
else
w50=w5-Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w3,w4,w50,w6);
if(ObjNew>ObjOld)
w5=w50;
Update=1;
ObjOld=ObjNew;

end
end

w60=w6+Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w3,w4,w5,w60);
if(ObjNew>ObjOld)
w6=w60;
Update=1;
ObjOld=ObjNew;
else
w60=w6-Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w3,w4,w5,w60);
if(ObjNew>ObjOld)
w6=w60;
Update=1;
ObjOld=ObjNew;

end
end
if(Update==0)
Delta=Delta*.85;
end
end

end



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I will follow on next page with explanation of the function
You think life is a secret, Life is only love of flying, It has seen many ups and downs, But it likes travel more than the destination. Allama Iqbal

Amin
Topic Author
Posts: 1943
Joined: July 14th, 2002, 3:00 am

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

The function in the post above optimizes the weights/parameters when it is given an objective function that has to be optimized. In my case the objective function is the output of a small independent function that takes some time series parameters.
In a neural network, the objective function will represent the goodness of fit to the target output. In optimizing weights of a neural network, you can also use mean squared error between network output and the target value, but this mean squared error would have to be minimized while I am maximizing my objective function. I want to explain the program in context of neural networks.

Here is the function I am using to calculate the objective function

[ObjOld] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w3,w4,w5,w6);
.
Here network evaluation function gives the result ObjOld that you can substitute with sum of mean squared errors between neural network calculated values of the target function and actual values of the target function. Xt1, Xt2, Price0, VarLogR, T1 are input arrays that are required to calculate the objective function given the network weights w1, w2, w3, w4, w5, w6.
We want to calculate the weights w1, w2, w3, w4, w5, w6 in a neural network so that ObjFunction/ObjOld is maximized or alternatively any mean squared error/loss function is minimized.
If you have a multi-layered neural network, just add all the various weights on different layers sequentially (possibly even using looping to calculate objective function with all weights sequentially one after the other) in main optimization loop and the algorithm would optimize it well.

Here is the main optimization loop of the program that repeats the optimization over six weights a thousand times.
In my case all parameters were supposed to be between -1 and 1 and therefore I used just one single value of Delta (which is projected change in weights in a single optimization) for all the weights. You will need some idea about the domain on which weights will take values. if domains of various weights are different you can use a different value of Delta proportional to domain and decrease values in larger domain slightly faster.
As I mentioned Delta is the projected change in weights and this starts with large values as if we are evaluating on a coarse grid. I have taken an initial value of Delta =.15 when my domain is for weights is between -1 and 1 but I think an initial value of .2 or .25 might have worked even better in some difficult cases.
We do 1000 iterations of the optimization over weights loop. At the start of the optimization, we set the value of variable Update equal to zero. Whenever even a single weight is updated, the value of update turns true. However, when no value is updates, we know it is time to decrease the step size Delta by a suitable value. I have chosen this value to .8 but please feel free to experiment. After decreasing the value of Delta, the optimization starts again with a smaller step size as if on a slightly finer grid. This way value of optimization step Delta continues to decrease and optimization search for best weights is done on a successively finer grid.

Delta=.15;
for nn=1:1000
Update=0;
w10=w1+Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w10,w2,w3,w4,w5,w6);
if(ObjNew>ObjOld)
w1=w10;
Update=1;
ObjOld=ObjNew;
else
w10=w1-Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w10,w2,w3,w4,w5,w6);
if(ObjNew>ObjOld)
w1=w10;
Update=1;
ObjOld=ObjNew;

end
end

w20=w2+Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w20,w3,w4,w5,w6);
if(ObjNew>ObjOld)
w2=w20;
Update=1;
ObjOld=ObjNew;
else
w20=w2-Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w20,w3,w4,w5,w6);
if(ObjNew>ObjOld)
w2=w20;
Update=1;
ObjOld=ObjNew;

end
end
w30=w3+Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w30,w4,w5,w6);
if(ObjNew>ObjOld)
w3=w30;
Update=1;
ObjOld=ObjNew;
else
w30=w3-Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w30,w4,w5,w6);
if(ObjNew>ObjOld)
w3=w30;
Update=1;
ObjOld=ObjNew;

end
end
w40=w4+Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w3,w40,w5,w6);
if(ObjNew>ObjOld)
w4=w40;
Update=1;
ObjOld=ObjNew;
else
w40=w4-Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w3,w40,w5,w6);
if(ObjNew>ObjOld)
w4=w40;
Update=1;
ObjOld=ObjNew;

end
end
w50=w5+Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w3,w4,w50,w6);
if(ObjNew>ObjOld)
w5=w50;
Update=1;
ObjOld=ObjNew;
else
w50=w5-Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w3,w4,w50,w6);
if(ObjNew>ObjOld)
w5=w50;
Update=1;
ObjOld=ObjNew;

end
end

w60=w6+Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w3,w4,w5,w60);
if(ObjNew>ObjOld)
w6=w60;
Update=1;
ObjOld=ObjNew;
else
w60=w6-Delta;
[ObjNew] = NetworkEvaluationFunction(Xt1,Xt2,Price0,VarLogR,Tl,w1,w2,w3,w4,w5,w60);
if(ObjNew>ObjOld)
w6=w60;
Update=1;
ObjOld=ObjNew;

end
end
if(Update==0)
Delta=Delta*.85;
end
end

In the start of the program, I assign initial starting values to the weights being optimized using the following lines
w1=IValue(1,1);
w2=IValue(1,2);
w3=IValue(1,3);
w4=IValue(1,4);
w5=IValue(1,5);
w6=IValue(1,6);

I would urge friends to try this program on training their neural networks.
If you have a simple enough objective function that can be coded in matlab, and you would like me to optimize it for you, please feel free to email me and I would love to see how my optimization routine works on it.

Also, for friends who have been following my thread, I want to mention that would do more and more work with neural networks in the future and hope to continue to post interesting work and code about machine learning and neural networks.
You think life is a secret, Life is only love of flying, It has seen many ups and downs, But it likes travel more than the destination. Allama Iqbal

Amin
Topic Author
Posts: 1943
Joined: July 14th, 2002, 3:00 am

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

Though I have described in the previous post but let me summarize the algorithm again that it optimizes weights of neural network sequentially in the direction of increasing objective function, initially with a large step as if on a very coarse grid. When coarse grid optimization ends, it slightly refines the grid and starts optimizing again and then refines the grid again after it is finished optimizing at that level. So, it continues to refine the grid and starts optimizing neural network weights on the fine grid successively after it is done optimizing on the coarser grid. Until it reaches very close to the optimum value of weights. There is no fixed grid per se, but the step size towards optimizing direction is quantized as if on a grid.
You think life is a secret, Life is only love of flying, It has seen many ups and downs, But it likes travel more than the destination. Allama Iqbal

Amin
Topic Author
Posts: 1943
Joined: July 14th, 2002, 3:00 am

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

Friends, I had worked with the above algorithm in case of a single neuron with six inputs and it worked great. I was really expecting that it would work well on multi-layered network with one intermediate layer but when I tried the above algorithm on a neural network with intermediate layer of neurons, its performance was poor.
That prompted me to think how we could systematically assign initial weights to a neural network before we enter the optimization loop.
There are so many different kinds of neural networks, but my observations are only valid for neural networks that are meant for prediction.
Let us consider a simple toy neural network with five inputs and three neurons in intermediate hidden layer and finally one neuron at end that collects the output of three hidden layer neurons and gives us the final result as its output.
One observation that I was able to think was that weights between inputs and hidden layer should be so that output of first hidden neuron should be orthogonal to both the outputs of second and third neuron in hidden layer. Similarly, output of second neuron should be orthogonal to first and third neuron and so on for the last third neuron in the hidden intermediate layer.
This prompts us to consider several training strategies. For example, optimize the weights on inputs to first hidden layer neuron with zero weights on inputs to second and third hidden intermediate neurons. Once the final output has been perfectly optimized with initial weights leading to first hidden intermediate layer neuron, it means that one factor has been well calibrated.
Now train the weights leading to second intermediate layer neuron given the weights on first intermediate layer neuron that we had previously optimized. So, we do not alter the pre-optimized weights of first neurons and only alter the weights of second neuron but again do not yet alter the weights of third neuron and keep them at zero value. This way, second intermediate layer neuron will pick the effects of second orthogonal factor after first factor has already been perfectly optimized by first neuron in hidden layer.
In the last, we keep the optimized weights of first and second intermediate layer neurons fixed and alter the weights of third neuron so that it can pick the effects of third orthogonal factor.
After this step, if desired, we can run some iterations of gradient descent optimization algorithm on all of the network and hopefully the final values would not change by a large amount.
There is another strategy that can help us to pick initial weights. This is based on analogy with independent factors/principal components. We run principal component analysis on all five inputs as we have five inputs in our toy neural network. The weights to first neuron in hidden layer would be the weights of inputs on first principal component while weight between first neuron in hidden layer and final neuron would be equal to correlation between first principal component and the output.
Similarly, weights from inputs to 2nd hidden neuron would be equal to weights of inputs with respect to second principal component and weight between second hidden neuron and the final neuron would be equivalent to correlation between variable being predicted and the second eigenvector/principal component.
And similarly, for the weights on the final third neuron in hidden layer would be borrowed from third eigenvector/principal component and correlation between third eigenvector and final predicted variable would give us the weight between third intermediate neuron and the final one neuron in outer layer.
We can find initial values of the weights from above analysis and then use gradient descent to further optimize the output so as to get best results.
Though I am sure it is easily comprehensible to most friends, I will try to explain things with equations if I could find time tomorrow.
You think life is a secret, Life is only love of flying, It has seen many ups and downs, But it likes travel more than the destination. Allama Iqbal

Amin
Topic Author
Posts: 1943
Joined: July 14th, 2002, 3:00 am

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

Friends, I have been working to further improve my algorithms and got extremely good results on validation data. I will start testing my algorithms initially on Biance testnet in another day. I just made some changes just yesterday that further dramatically improved the results of my programs and when I went out on motorcycle for breakfast to a different neighborhood, mind control agencies had made every preparation to drug my food. I was hit by drugged food multiple times. Mind control agencies had drugged drinks at a large number of points. I was careful enough to go to a different neighborhood to take food, but I never expected that they would drug the drinks at so many points. By the time I returned, I noticed that my eyesight had dramatically deteriorated due to the effect of drugged drinks I had taken, and it was becoming very difficult to read smaller words especially from a short distance and there was some sheer uneasiness in the eyes.
I want to tell friends that racist conservative scumbags at pentagon find it verry difficult to allow muslims to get ahead in any walk of life (even though we are the ones who are habitually called intolerant). I want to tell friends that hatred in the hearts of these conservative scumbags of Pentagon is very similar to hatred that lies in the heart of Talibans, the only difference is that these scumbags are far more powerful and do not have to resort to violence to achieve their racist designs and rather use machinations to achieve their similar racist designs.
When I was in London 12 years ago, I wrote on Wilmott that mentality of a lot of racist scumbags of Pentagon is very similar to mentality of Taliban of Afghanistan. I drew logical parallels and explained everything with reason. I will post that article in a day if I can easily find it in my documents. I had stated that Taliban is not name of a group, rather it is name of a mentality and racist scumbags of Pentagon are completely fraught with the same mentality.
You think life is a secret, Life is only love of flying, It has seen many ups and downs, But it likes travel more than the destination. Allama Iqbal

Amin
Topic Author
Posts: 1943
Joined: July 14th, 2002, 3:00 am

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

Here is what I wrote on Wilmott on Thu Apr 21, 2011, 11:00 PM. I have brought it back from my own records.

In my previous post I talked about the ideology of intolerance the word Taliban represents. Here I would like to make a detailed comparison between the two groups of Taliban I mentioned in my previous post , one group of which is the Taliban of Afghanistan and the other group is the racist Taliban of Pentagon. The original Taliban, as the world knows, are characterized by their ignorance, lack of education, indoctrination of hardline versions of religion and of course the two Taliban characteristics which are lack of tolerance and employing violent means to achieve their intolerant version of the world. On the other hand Taliban of Pentagon are reasonably educated, very mediocre, embrace racism, have a lot of resources available and share the taliban characteristics of lack of tolerance and employing sometimes violent and usually cunning means to achieve their racist and intolerant version of the world. However what makes the Taliban of Pentagon worse is that Taliban characteristics of Original Taliban can be blamed on lack of education and backwardness of their society. On the other hand, racism and intolerance of the Taliban of Pentagon cannot be blamed on lack of education and backwardness of their society and it is a characteristics actively chosen by a group that should be decently aware of ideologies of human goodness as represented by the population from which it is chosen. This active adoption of Taliban characteristics as opposed to passive Talibamism of Afghani Talibs makes Taliban of Pentagon more hideous and abominable creatures. Afghani Taliban ruthlessly kill christian missionries while their racist counterparts, the Taliban of Pentagon are more cunning and have sharpshooters who retard innocent and peace living Muslims of other countries with the aim to inflict damage on their nations. Advanced technologies and abundance of money allows them to hide their racist crimes and call themselves "responsible army". The Taliban of Afghanistan show indiscriminate hatred and their acts result in just a few deaths but they earn stigma for their religion while the acts of Taliban of Pentagon are more strategic because they result in making the children of our nations darker forever while earning no stigma for their nations. The acts of Taliban of Pentagon are more hideous for our nations and act of Taliban of Afghanistan really do not matter for anyone bust just a few individuals which of course, cannot be pardoned either but Talibanism of Pentagon is more hideous than the Talibanism of Afghanistan, though underlying characteristics of Talibanism are the same. The Taliban of Afghanistan are stupid while the racist Taliban of Pentagon are cunning, The Taliban of Afghanistan kill ruthlessly while the Taliban of Pentagon retard someone and assign a group of mean mind control satans who continue to insult and humiliate them all their life. I appeal to Taliban of Pentagon to learn from their Afghani counterparts and kill instead of giving a life of humiliation since it is more graceful to die than have a life of humiliation
I would request Americans, who are in fact good and responsible, to eradicate racism from their society and from Pentagon and make sure nobody innocent of any religion is retarded especially if they want to serve their nations and have nothing against America. I would like to point out a fact from history that America was slower than rest of the world to abolish several aspects of racism an example of that is the fact that slavery continued in America longer than could be imagined especially given the advancement and prosperity of its society. Today,The case of racism of Satans of Pentagon is very similar and should be addressed by responsible Americans.
You think life is a secret, Life is only love of flying, It has seen many ups and downs, But it likes travel more than the destination. Allama Iqbal

Amin
Topic Author
Posts: 1943
Joined: July 14th, 2002, 3:00 am

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

Friends, I deposited one BNB in my Binance account and generated API keys so that I can start running my programs on binance testnet. I have installed Linux on an external hard drive with python, Visual studio code and anaconda. There was always a bluetooth connection ON in Unix and I could not close it by simply clicking on the bluetooth icon. I looked up on internet how to close it by going to linux shell and adding a further command so that it does not start when we turn on linux. I also noticed that there was another shell open with suspicious activity and I closed it. I generated my API keys after all of this. I plan to keep my small external hard drive on me when I go out. But I am still sure that CIA crooks would try to install more devices on my laptop so that they can somehow approach the external hard drive from my computer and play with my trading and do not let me succeed.
I have algorithms already set and I hope that after testing my programs on binance testnet for a few days, I will start live trading in 5-10 days.
I want to request friends to convince the american army people to let me move on with my life after the forced coercion of 23 years in which I continued to face trauma and torture again and again.
You think life is a secret, Life is only love of flying, It has seen many ups and downs, But it likes travel more than the destination. Allama Iqbal

Amin
Topic Author
Posts: 1943
Joined: July 14th, 2002, 3:00 am

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

Friends, I have been working during past few days to complete my coding to run my trading strategy on Binance. I have started playing with live data from Binance but some of the coding remains to be done. I will continue coding and testing my programs for next few days and hope that I will start trading live by 10th of October.
I had an antipsychotic injection yesterday and I have not been feeling very good, but I have started working on my programs again.
I had earlier told friends that I had installed linux and python on an external hard drive and I keep the hard drive on me when I leave the house. But I recently start to feel that they have broken into my hard drive since I noticed that my programs were becoming very slow at times and linux system also becomes very slow sometimes. I will try to see what I can do about it, but I would request friends meanwhile to please ask the mind control agencies to not alter my programs or interfere in my trading activity.
I will keep posting here for friends how my trading goes when I start around 10th of October.
You think life is a secret, Life is only love of flying, It has seen many ups and downs, But it likes travel more than the destination. Allama Iqbal

Amin
Topic Author
Posts: 1943
Joined: July 14th, 2002, 3:00 am

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

I just turned on my linux ubuntu system and installed htop after finding about it on internet. When I used the htop command on linux shell, I noticed that bluetooth process was working in the background even though its icon in the icons tab was dim as if bluetooth were off.  I killed bluetooth and figured that there was another process avahi-daemon for local home Lan was also on. I also stopped and then disabled avahi-daemon as well.
This was interesting. When I tried to disable avahi-daemon, system refused saying there are clients using it. I had to stop it first with stop command and then system allowed me to disable it.
I am not a great expert at inside workings of computer systems and have to look up on internet about various things.
Mind control agencies already have my programs, but I am very afraid that they would start interfering in my trading activity so as to fail me again. I want to request friends to please stop them from doing any interference in my trading activity.
You think life is a secret, Life is only love of flying, It has seen many ups and downs, But it likes travel more than the destination. Allama Iqbal

Amin
Topic Author
Posts: 1943
Joined: July 14th, 2002, 3:00 am

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

Friends, I am fully convinced that mind control agencies have a plan to not let me make any profits in the market. And they have already connived with my family about it.
The way relationships work in our family, everybody including myself tries to behave normally but when my family is asked by the mind control agencies to do anything particular, most of the members of my family start behaving differently.
It has been 23 years since I came back to Pakistan in Feb 1999. I was already more than one year into mind control in United States at that time. When mind control agencies contacted my father (on the insistence of some malicious jews) before I returned to Pakistan. My father agreed to fully cooperate and was in fact very happy about it that Americans had placed so much trust in him. He was so stupid that he simply agreed that anything would be given to him and the family after I would have been retarded. He agreed that if he took any money, it would become obvious to everyone due to change of his circumstances that he had taken bribes from CIA. He was told that it would take only a few years to retard me, and I could not remain sane before their potent mind control drugs, and he was very willing to wait a few years. In early years when I would openly complain, my father would proudly retort that if he had cooperated with Americans, why had he not taken any money. Later, I stopped questioning him.
There were so many times again and again when my family became desperate to somehow retard me and got me detained with psychiatrists on totally flimsy excuses. I have been detained more than thirty times in past twenty three years. They would give me drugs and take away some of my neurotransmitters and my relationship with the family would come back to normal in a few weeks after I would be freed from detention. There would be times when I would be agitated that they have no humanity for me, but I would simply tell myself to behave nicely with them. If I had not remained nice, I would have faced far more trauma and torture. Many times, I would simply wonder how desperate people can become for money.
Ok, since no special money has yet been given to my family. About a month and a half ago, my brother almost begged me to start trading in crypto since he had already become interested in crypto (and made large losses trading on high leverage.) He had been helping me with data download and other simple chores and was very enthusiastic. I still had enough regard for my brother and offered to share 25% of the profits with him.
But since I made improvements to my trading algorithms, things dramatically changed. My brother would visit me once or twice upon my insistence and would tell me that I had to first prove that my algorithms could become profitable (something I really have to do, of course) but a changed and stayed tone makes me realize that something is very wrong. Today, my mother came to my room and asked me out of the blue, "Son, do you think that Binance exchange might create problems for you and interfere in your trading?" Atmosphere in our house has already become silently tense.
I have complete faith in my algorithms. I checked them on large data by running the optimization algorithm on previous days data set and then running them on next day with parameters calculated from previous 24 hours earlier. Other than my optimized parameters from previous 24 hours, nothing is known to trading algorithm about the present data on which it is calculating profit and loss. And I keep sliding my 24 hours parameter learning and validation windows so that nothing is known in the validation window other than the parameters I calculated from previous 24 hours data. And my algorithms make large profits something that really upsets mind control people who have been trying to retard me for past twenty-three years.
They are also continuously breaking into my linux environment that I have saved on a removable hard disk.
I plan to trade with 50 dollars for a few days on Binance and I am sure that they want to stop me in my tracks when I am using little money so that my family can object to my trading saying that it is not turning out to be profitable. And then they would force me to start working with some traditional business to earn money and stop working with mathematical finance. Since they have been waiting for past twenty-three years, my family is already very desperate.
I am very very sure if American friends never protested and stopped hardliners, they would do everything in their power to fail me. I want to tell friends despite my forced persecution of past twenty-three years, I still have enough faith in humanity. Please stop mind control agencies from interfering with my trading and let me live a life free of coercion.
You think life is a secret, Life is only love of flying, It has seen many ups and downs, But it likes travel more than the destination. Allama Iqbal

Amin
Topic Author
Posts: 1943
Joined: July 14th, 2002, 3:00 am

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

I am very afraid that after reading my yesterday's post many friends would think that it is all my fault since I did not struggle enough to get me out of this and tried to leave my family.  I am writing this post to dispel that impression.
First important thing is that Pakistan army manages CIA's mind control in Pakistan. Pakistan army facilitates all mind control in Pakistan in return for huge bribes that are paid to generals by CIA. I tried to escape my family several times, but Pakistan army made sure that I was forcefully placed in control of my family every time. Most psychiatrists also follow military's orders, and these psychiatrists also have their own uneducated personnel that are very willing to use force to detain and control the mind control victims and police only helps the most influential people. I also tried several human rights organizations in Pakistan and found out that they were very aware of mind control and drugging of entire markets in the city but made no big deal about it and never were willing to help me. Yes, one psychiatrist tried to help me somewhat, but my family made sure that I was detained whenever I insisted on seeing that psychiatrist.
Here I will describe a few times when I tried to escape my family and how it finally worked out.
One incident is from 2009, as I recall. I did not want to live with my family in Lahore, so I left the city and drove to Karachi by car. Upon arrival in Karachi, my ATM card was disabled upon orders of army. I was stopped and repeatedly harassed by police in Karachi. I was stopped in Clifton by a police car and they took me to Clifton police station on 23rd of February 2009. Police checked my car and said two front seat belts of your car carry different manufacturing dates so "your car must be stolen, and we have to verify it" and reported me to their boss. I asked them to go ahead and also requested that police had repeatedly asked me the same thing that my car must be stolen in past two days so once you have verified, please write me a written statement so I can just show it to police everywhere once they would stop me in future. The Police officer agreed to that and asked me to wait in the other room. I waited there for about half an hour and the officer came again and violently slapped me several times. He said," You are over-educated, and you think of yourself as something." I was surprised since I had not told him anything personal at all. I was seriously humiliated, but I knew they would beat and lock me if I responded in force. I waited another hour sitting next to locker room of the police station. After some time, Navy personnel came in three jeeps to the police station and asked me to accompany them. I was taken to compound of PNS Nigran(Navy) in Karachi where they locked me in the Navy jail. The next morning, I was taken to open compound, and I was circled by more than ten people who wanted to give me injections by force. I seriously tried to resist but they continued to ask me to take injections. They were human enough to not beat me for that. I asked again and again that they were not even telling me what the injection was, but they finally forcefully injected me. And sent me back to Lahore with my brother-in-law. Upon my arrival in Lahore, I was detained for six months by a psychiatrist.
Here I want to tell friends one interesting incident that happened when I was driving towards Karachi. I had entered Sindh province and was normally driving my car listening to music. All of a sudden, I noticed that my right arm was getting paralyzed. It was becoming very difficult to move my arm even very slightly. I knew at once that it had to do with mind control, and I realized that I had to urgently do something. I somehow figured that something (gas) was going into my nose. I had some raw cotton handy on the other seat (as I would force compressed cotton into my ears to decrease the effect of mind control something that I used before 2010) and I put some cotton in my nose using my left hand, and all of a sudden, my right arm was perfectly alright. Cotton probably altered the frequencies of waves going into the nose and they were not effective after that. I am sure if I had not pulled this trick, they would have said later that Amin was a psychiatric patient who escaped his home and ran away and was later found in poor condition helpless. And then psychiatrists would have restricted my free movement.
Another time when I decided to live on my own away from my family was in year 2011 when I returned from London. When I came back to Karachi from London, I wanted to rent a house in Karachi and live alone away from my family who was in Lahore. Pakistan army continued to threaten people to not rent me a house. I continued to call my family everyday despite what they had earlier done to me. My brother-in-law and his friends called me and posed as brokers interested in arranging housing for me over the phone and asked me to come to a thinly populated area. I asked the taxi driver to reach the place they mentioned. My brother-in-law started forcing me to go with him. I continued to ask him that we could talk and settle everything nicely, but he was belligerent. They forced me off me feet on the road and tied both my hands and legs. He wanted to blindfold me in the car by putting a cover on my head, but I forced my head against the roof of the car (my hands and legs were tied) and he could not blindfold me. They took me to a house in DHA Karachi and locked the main gate. Some people continued to come and go from the smaller gate. They gave me some injections and I would fall asleep. I would doze for about half an hour to hour after every injection and when I would wake up, they would give me some other injection. Basically, they were giving me some injection and would wait for about one hour to see the effect of that injection and then would give me another injection after seeing effect of previous injection. They gave me five or six different injections over the course of the day. In the afternoon they gave me some food to eat. While I was eating, a woman I never knew and never had seen before, and all her breasts were exposed came and started eating in the same plate I was eating. I continued to answer what she said but did not do anything at all. They continued to give me more injections after I had taken food and, in the evening, they gave me a final injection and I woke up at a psychiatrist's facility next day. Doctor did not interview me for several days and my heavy medication started again. I was threatened to comply. One of the other patients told me that some people took me out of my room unconscious at night and brought me back in the morning. I told Doctor I to make sure that nobody entered my room when I were sleeping, and doctor agreed. I noticed that people continued to enter my room at night when I was sleeping. After a lot of those incidents and protests, Doctor changed his line and said that we really have to enter your room at night because of your safety. Doctor kept me detained in his facility for more than nine months and only in early 2012, I was allowed to leave his facility. Earlier I had told the doctor that I did not want to live with my family and wanted to live alone but doctor told me that he would free me only if I agreed to live with my family and otherwise detain me indefinitely. I had to live with drug addicts and in a very unprofessional environment. He allowed me to leave after nine months when I knew that there was no other way but to live with my family in Lahore.
I had received HSMP work visa for UK in 2010. In my fool's paradise, I thought that British are the most civilized people on earth and once I would go to London all the mind control will end and I would live happily ever after. During my three days in Pakistan prior to arrival in London, I had very little food thinking that I would eat better undrugged food once I reach London. Though my first week was better, I started getting hit with drugged food right after my first week in UK. At one stage after a month, all drinks and beverages manufactured by Britvic were drugged. There are five or six large departmental store chains in UK who manufacture their own drinks and beverages and all of them were manufacturing drugged beverages. It was extremely difficult to get a good drink in London.
When I was in London, I posted on a Chinese LinkedIn group about mutual cooperation. A contact in China wanted to start a high performance computing firm targeting finance and he wanted me to work for him in China and did all the required official work for me to get Chinese visa. The visa agency first asked me for extra documents, but my Chinese friends arranged all the documents. When all documents were complete, Visa agency changed their line saying that I had to apply for visa in Pakistan although I was a legal resident in UK with a work visa and their website mentioned that Pakistanis on UK work visa could apply for Chinese visa from London.  I later went to Chinese embassy, but they told me that they had relegated all visa matters to visa collection firm. I had to abandon the idea of going to China since Chinese embassy was not willing to annoy British for a random Pakistani trying to get to China. Of course, some influential people in UK wanted my persecution to continue and Chinese diplomatic staff had far more regard for their British hosts and had no special sympathies with me.
Lot of times such machinations worked since some influential people in UK were telling blatant lies about me.
Later when in UK, I also applied for German visa which was promptly refused. And I figured the hard truth that it was not worth applying to any Schengen country's visa after that.
In 2005, I was asked by my Japanese employer to come to Tokyo (2005) and work in their office there(I was earlier working from Lahore). Japanese authorities drugged large number of places in Tokyo city and mad e my life absolute hell and I resigned only after one month of stay in Tokyo. I did not want to return to Pakistan due to huge persecution by my family and the army so I decided to go somewhere where US military could not go and got Iranian visit visa from Tokyo and went to TehranCrooks in US defense gave huge amount of money to Iranian crooks(crooks everywhere know each other well) and they used huge microwave and gases torture on me. I could never imagine that mind control could ever follow me in Tehran but I had seen extremely unlikely things happen in my life earlier. For that reason, when I reached Tehran and on my first night in Tehran, I again wore an aluminium shield in the hotel and then extreme torture stated. They had already made all preparations for my arrival in Iran. They directed extreme microwaves on me and due to extreme pain, I left the hotel somewhat after midnight and they continued to direct microwaves on me and there was extreme physical pain and I ran on deserted streets to somehow be able to avoid mircrowave torture. I still recall that my hotel was in close vicinity to major government buildings since I still have some memory that some of the buildings I noticed were important places but I forgot the particular details.
And one very interesting incident happened in Iran. I was walking in the city and I came across a major building with tank stationed outside. I thought I may be able to get some possible help and walked inside and asked for help. I was taken to a guy inside the office and he said that he wanted another person who knows English well to write down everything I have to say. Actually they were following me everywhere and that guy had already been told what to say before I was taken to him by security at the gate. Then they took me to a meeting room with a large table and the two people sat on the other side of the table from me. I started telling them about my persecution and the person who knew English started writing and then tea came. They asked me to take tea. I just had a sip of tea that I started to lose my mind but there were several sugar cubes and I realized that sugar must be good and I swallowed several sugar cubes and I was slightly better. I told the Iranians there that I really needed to go to wash room. I walked out of the room and went towards the wash room and in the gallery I noticed that one room had a door wide open and there was a refrigerator there. I opened the refrigerator door and drank plenty of water and I was far better. When I went back to the meeting room and started telling my story again, both guys were no longer interested in anything and told me that they could not help me.
There was a large amount of drugged food in central Tehran and I surely believe that it must have been drugged at the spot by a large number of people at stores and food places when I would get closer or arrive there. I was hit by drugged food again and again.
One of the hotels Azadi Hotel which was located in outskirts of Tehran was a bit better and I started living there but they asked me to leave saying that they had an upcoming conference and they could no longer let me live there. I recall that some Iranian agents came to hotel and told me they had come from Iranian president but it was obvious that they were Iranian intelligence and they wanted me to work for Iran. I knew the meanings of getting associated with Iranian intelligence would spoil my life forever and I just told them that I wanted to live and work in Iran as an ordinary citizen.

Just after two or three days in Tehran, I was trying to find refuge in embassies like Vatican in Tehran asking them to help me on human grounds. I left Tehran after one week and flew back to Pakistan. I still recall that I arrived at Tehran airport a lot earlier than flight departure. I had previously protested somewhere against unnecessary removal of shoes of Muslim passengers and it was known to mind control agencies. They asked Iranians security on airport who approached me inside the departure lounge and took me to a room and asked me to remove my shoes and had my body search.
Those eight days I lived in Tehran were literally some of the most difficult days in my life and I really decided to leave quickly after a week.
Since during all this, mind control agencies could not control me well and several of my neurotransmitters were coming back, they had extremely huge amount of gases in washrooms in Dubai airport where I would stop for transit while going to Karachi. No wonder ultra conservative crooks in US army align so well with Saudi (who dissolve their criticizers in acid) and Dubai.

I had earlier faced mind control in Singapore and Hong Kong towards the end of year 2000.
You think life is a secret, Life is only love of flying, It has seen many ups and downs, But it likes travel more than the destination. Allama Iqbal