Reproducing kernel Hilbert space method is utilized in this paper as an efficient approach to solve singular fourth order ...

Three mathematicians have laid out proof that solves a long-standing problem in mathematics. Even the mathematician—an Abel prize winner—that first posed the problem didn't believe it would ever be ...

David Harper is the CEO and founder of Bionic Turtle. He is also a published author with a popular YouTube channel on expert finance topics. Probability distributions help investors model uncertainty ...

Abstract: A nonlinear filter is developed by representing the state probability density function by a finite sum of Gaussian density kernels whose mean and covariance are propagated from one time-step ...

Operational Laws: Little's Law, response-time law, asymptotic bounds, modification analysis, performance metrics. Markov Chain Theory: both discrete-time and continuous-time, renewal theory, ...

Predicting how complex stochastic systems respond to small external perturbations is central in physics, climate science, and engineering. We combine the generalized fluctuation–dissipation theorem ...

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To mathematicians, equations are art. Just as many are moved by a painting or piece of music, to those who appreciate and understand math, expressions of numbers, variables, operations and relations ...

A long-standing challenge in statistical mechanics has been to quantify the nonequilibrium nature of active systems such as swarming bacteria, schooling fish, and flocking birds. The entropy ...

Abstract: Markov decision processes (MDPs) are widely used for modeling sequential decision-making problems under uncertainty. We propose an online algorithm for solving a class of average-reward MDPs ...