Hello,

More philosophy about understanding K-means Clustering in Machine Learning and more..

I am a white arab and i think i am smart since i have also invented many scalable algorithms and algorithms..

I have just read about The K-means clustering algorithm, and i think
it is also for grouping similar data points together and discover underlying patterns, it is why it is used in machine learning, i have just quickly understood it, so i invite you to read about it in the following interesting article:

Understanding K-means Clustering in Machine Learning

https://towardsdatascience.com/understanding-k-means-clustering-in-machine-learning-6a6e67336aa1

And to be more smart, i invite you to look in the following at how K-means Clustering algorithm is used smartly in a delivery store optimization that optimizes the process of good delivery using truck drones by using a combination of k-means to find the optimal number of launch locations and a genetic algorithm to solve the truck route as a traveling salesman problem. And here is a paper from the journal of industrial engineering and management on the subject, you have to read it carefully, since i am reading it and understanding it and i think that i will implement it soon in Delphi and Freepascal using a Particle Swarm Optimization Algorithm for the Traveling Salesman Problem:

Optimization of a Truck-drone in Tandem Delivery Network
Using K-means and Genetic Algorithm

https://upcommons.upc.edu/bitstream/handle/2117/88986/1929-8707-1-pb.pdf?sequence=1&isallowed=y

More precision about more philosophy about human smartness and about artificial intelligence..

I have to be more precision, so here is the definition in the dictionary of "pattern" that i am using in my thoughts of my philosophy below:

Pattern is a particular way in which something is done, is organized, or happens.

Read here in the dictionary to notice it:

https://dictionary.cambridge.org/dictionary/english/pattern

I think i am a philosopher that is smart, so i will ask the following
philosophical question:

What is human smartness or intelligence ?

I will answer it by saying the following:

I think we call it human smartness because it discovers "useful" patterns in the reality, so reality can contain static systems or dynamic systems that contain smartness in form of useful patterns etc., so human smartness uses its smartness to "discover" those useful patterns so that to become more and more smart, and by discovering the useful patterns i also means knowing about there meanings of those useful patterns so that to understand them, it is by logical analogy like discovering the rules so that to become smart, so for example when we are doing mathematics we can discover the useful rules or useful patterns like the theorems in mathematics by using deductive logic and inductive logic, so i can go further and say that Swarm intelligence like PSO(Particle Swarm Optimization) is a self-organization, and Self-organization, also called (in the social sciences) spontaneous order, is a process where some form of overall order arises from local interactions between parts of an initially disordered system. The process can be spontaneous when sufficient energy is available, not needing control by any external agent, so then Swarm intelligence like PSO(Particle Swarm Optimization) is self-organization since notice that the exploration mechanism of PSO that is the global optimization is "collaborating" with the exploitation mechanism of PSO that is the local optimization so that to self-organize by finding the global optimum
, so then we can call Swarm intelligence like PSO(Particle Swarm Optimization) a form of intelligence, this is why we call
it artificial intelligence.

Also you can read more about my thoughts of my philosophy about human smartness in the following web link:

https://groups.google.com/g/alt.culture.morocco/c/Wzf6AOl41xs

Read my following thoughts about artificial intelligence and PSO so that understand:

https://groups.google.com/g/alt.culture.morocco/c/BKGvkTI5FY4

More philosophy about Markov chains and invariants and Petri nets..

I am a white arab and i think i am smart since i have also invented many scalable algorithms and algorithms..

I am also working with Petri Nets and Markov chains in mathematics and structural analysis of Petri nets in mathematics, so i will
talk about it now:

About Markov chains in mathematics and more..

In mathematics, many Markov chains automatically find their own way to an equilibrium distribution as the chain wanders through time. This happens for many Markov chains, but not all. I will talk about the conditions required for the chain to find its way to an equilibrium distribution.

If in mathematics we give a Markov chain on a finite state space and asks if it converges to an equilibrium distribution as t goes to infinity. An equilibrium distribution will always exist for a finite state space. But you need to check whether the chain is irreducible and aperiodic. If so, it will converge to equilibrium. If the chain is irreducible but periodic, it cannot converge to an equilibrium distribution that is independent of start state. If the chain is reducible, it may or may not converge.

So i will give an example:

Suppose that for the course you are currently taking there are two volumes on the market and represent them by A and B. Suppose further that the probability that a teacher using volume A keeps the same volume
next year is 0.4 and the probability that it will change for volume B
is 0.6. Furthermore the probability that a professor using B this
year changes to next year for A is 0.2 and the probability that it
again uses volume B is 0.8. We notice that the matrix of transition is:

| 0.4 0.6 |
| |
| 0.2 0.8 |

The interesting question for any businessman is whether his
market share will stabilize over time. In other words, does it exist
a probability vector (t1, t2) such that:

(t1, t2) * (transition matrix above) = (t1, t2) [1]

So notice that the transition matrix above is irreducible and aperiodic,
so it will converge to an equilibrum distribution that is (t1, t2) that
i will mathematically find, so the system of equations of [1] above is:

0.4 * t1 + 0.2 * t2 = t1
0.6 * t1 + 0.8 * t2 = t2

this gives:

-0.6 * t1 + 0.2 * t2 = 0
0.6 * t1 - 0.2 * t2 = 0

But we know that (t1, t2) is a vector of probability, so we have:

t1 + t2 = 1

So we have to solve the following system of equations:

t1 + t2 = 1
0.6 * t1 - 0.2 * t2 = 0

So i have just solved it with R, and this gives the vector:

(0.25,0.75)

Which means that in the long term, volume A will grab 25% of the market
while volume B will grab 75% of the market unless the advertising campaign does change the probabilities of transition.

So notice that in my previous post i have talked about invariants of the system, here is my previous post read it carefully:

About Turing completeness and parallel programming..

You have to know that a Turing-complete system can be proven mathematically to be capable of performing any possible calculation or computer program.

So now you are understanding what is the power of "expressiveness" that
is Turing-complete.

For example i am working with the Tool that is called "Tina"(read about it below), it is a powerful tool that permits to work on Petri nets and be able to know about the boundedness and liveness of Petri nets, for example Tina supports Timed Petri nets that are Turing-complete , so the power of there expressiveness is Turing-complete, but i think this level of expressiveness is good for parallel programming and such, but
it is not an efficient high level expressiveness. But still Petri nets are good for parallel programming.

About deadlocks and race conditions in parallel programming..

I have just read the following paper:

Deadlock Avoidance in Parallel Programs with Futures

https://cogumbreiro.github.io/assets/cogumbreiro-gorn.pdf

So as you are noticing you can have deadlocks in parallel programming
by introducing circular dependencies among tasks waiting on future values or you can have deadlocks by introducing circular dependencies among tasks waiting on windows event objects or such synchronisation objects, so you have to have a general tool that detects deadlocks, but if you are noticing that the tool called Valgrind for C++ can detect deadlocks only happening from Pthread locks , read the following to notice it:

http://valgrind.org/docs/manual/hg-manual.html#hg-manual.lock-orders

So this is not good, so you have to have a general way that permits
to detect deadlocks on locks , mutexes, and deadlocks from introducing
circular dependencies among tasks waiting on future values or deadlocks
you may have deadlocks by introducing circular dependencies among tasks
waiting on windows event objects or such synchronisation objects etc.
this is why i have talked before about this general way that detects
deadlocks, and here it is, read about it in my following thoughts:

Yet more precision about the invariants of a system..

I was just thinking about Petri nets , and i have studied more Petri nets, they are useful for parallel programming, and what i have noticed by studying them, is that there is two methods to prove that there is no deadlock in the system, there is the structural analysis with place invariants that you have to mathematically find, or you can use the reachability tree, but we have to notice that the structural analysis of Petri nets learns you more, because it permits you to prove that there is no deadlock in the system, and the place invariants are mathematically calculated by the following system of the given
Petri net: