Equivalent Conditions for Weak Continuity of Nonlinear Filters

This paper studies weak continuity of nonlinear filters. It is well-known that Borel measurability of transition probabilities for problems with incomplete state observations is preserved when the original discrete-time process is replaced with the process whose states are belief probabilities. It is also known that the similar preservation may not hold for weak continuity of transition probabilities. In this paper we show that the sufficient condition for weak continuity of transition probabilities for beliefs introduced by Kara, Saldi, and Yuksel (2019) is a necessary and sufficient condition for semi-uniform Feller continuity of transition probabilities. The property of semi-uniform Feller continuity was introduced in Feinberg, Kasyanov, and Zgurovsky (2021), and, if the original transition probability has this property, then the transition probability of the process, whose state is a pair consisting of the belief probability and observation, also has this property. Thus, this property implies weak continuity of nonlinear filters. This paper also reviews several necessary and sufficient conditions for semi-uniform Feller continuity.Comment: arXiv admin note: substantial text overlap with arXiv:2108.09232; text overlap with arXiv:2107.02207, arXiv:2103.1325

Synthetic vascular tissue and method of forming same

Disclosed are composite materials that can more closely mimic the mechanical characteristics of natural elastic tissue, such as vascular tissue. Disclosed materials include a combination of elastic nanofibers and non-elastic nanofibers. Also disclosed are a variety of methods for forming the composite materials. Formation methods generally include the utilization of electrospinning methods to form a fibrous composite construct including fibers of different mechanical characteristics

Semi-Uniform Feller Stochastic Kernels

This paper studies transition probabilities from a Borel subset of a Polish space to a product of two Borel subsets of Polish spaces. For such transition probabilities it introduces and studies semi-uniform Feller continuity and a weaker property called WTV-continuity. This paper provides several equivalent definitions of semi-uniform Feller continuity and describes the preservation property of WTV-continuity under integration. The motivation for this study came from the theory of Markov decision processes with incomplete information, and this paper provides fundamental results useful for this theory.Comment: arXiv admin note: text overlap with arXiv:1903.1162