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Here we discuss an application of HPC (not high performance computing, instead high precision computing, which is a special case of HPC) applied to dynamical systems such as the logistic map in chaos theory. defined as X(k) = 4 X(k) (1 - X(k-1)).
For all these systems, the loss of precision propagates exponentially, to the point that after 50 iterations, all generated values are completely wrong. Tons of articles have been written on this subject - none of them acknowledging the…Continue
Summary: This is the first in a series about Chatbots. In this first installment we cover the basics including their brief technological history, uses, basic design choices, and where deep learning comes into play. In subsequent articles we’ll describe in more detail about how they are actually programmed and best practice dos and don’ts.…Continue
Data Science Central (DSC) is excited to announce our competition to solve a new, interesting problem in statistical science, pertaining to stochastic processes. DSC members are invited and encouraged, to submit a theoretical solution or an application to real life problems, including but not limited to fintech, operations research, statistical science, computer science, economics, engineering, social, actuarial, biological or physical sciences.
The statistical process central to this…Continue
Here we describe well-known chaotic sequences, including new generalizations, with application to random number generation, highly non-linear auto-regressive models for times series, simulation, random permutations, and the use of big numbers (libraries available in programming languages to work with numbers with hundreds of decimals) as standard computer precision almost always produces completely erroneous results after a few iterations -- a fact rarely if ever mentioned in the scientific…Continue