Any absolutely continuous, piecewise smooth, symmetric two-player game can be extended to define a population game in which each player interacts with a large representative subset of the entire population. Assuming that players respond to the payoff gradient over a continuous action space, we obtain nonlinear integro-partial differential equations that are numerically tractable and sometimes a...

In this paper two disturbance decoupling problems without stability and with quadratic stability via dynamic output feedback for switched linear systems are investigated. Firstly, simultaneous (C,A,B)-pair which incorporates both the concept of simultaneous (A,B)-invariant subspace and its dual simultaneous (C,A)-invariant subspace for a family of linear systems are investigated. Secondly, dist...

In this paper we introduce a sequential block iterative method and its simultaneous version with op-timal combination of weights (instead of convex combination) for solving convex feasibility problems.When the intersection of the given family of convex sets is nonempty, it is shown that any sequencegenerated by the given algorithms converges to a feasible point. Additionally for linear feasibil...

This paper studies simultaneous equations models for two or more discrete outcomes. The models allow latent variables to be high dimensional and require latent variables and covariates to be independently distributed. The models may be incoherent, delivering no values of the outcomes at certain values of the latent variables and covariates. The models may be incomplete, delivering more than one...

This article will devise data-driven, mathematical laws that generate optimal, statistical classification systems which achieve Bayes’ error rate for data distributions with unchanging statistics. Thereby, I will design learning machines that minimize the Bayes’ risk or probability of misclassification. I will devise a system of fundamental equations of binary classification for a classificatio...