Related papers: Filtrations
We explore the structure of $\text{Fil}$, the category of filters and germs of admissible partial functions. In particular, we show that $\text{Fil}$ is a nonsymmetric closed category, as defined elsewhere by this and other authors.
This paper gives an introduction to some results on monodromy groupoids and the monodromy principle, and then develops the notion of monodromy groupoid for group groupoids.
This paper presents the methodology for the system requirements and architecture w.r.t. their decomposition and refinement. It also introduces ideas of refinement layers and of refinement-based verification.
This article defines a complement of a function and conditions for existence of such a complement function and presents few algorithms to construct a complement.
Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of…
In this paper, we give some generalizations the concept of element order and we study some of the properties of these generalized order. In particular, with using this generalization we derive two solvability criteria.
We describe the construction of the slice fibration of a given one.
We define natural A_infinity-transformations and construct A_infinity-category of A_infinity-functors. The notion of non-strict units in an A_infinity-category is introduced. The 2-category of (unital) A_infinity-categories, (unital)…
The goal of this paper is to provide some basic structure information on derivations in finite semirings.
The present document aims at providing a short, didactical introduction to three standard versions of the Kalman filter, namely its variants identified as Basic, Extended, and Unscented. The application of these algorithms in three…
Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…
The aim of this paper is to provide a variational interpretation of the nonlinear filter in continuous time. A time-stepping procedure is introduced, consisting of successive minimization problems in the space of probability densities. The…
We introduce an auxiliary technique, called residual nudging, to the particle filter to enhance its performance in cases that it performs poorly. The main idea of residual nudging is to monitor, and if necessary, adjust the residual norm of…
We review definitions and basic properties of operads, PROPs and algebras over these structures.
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
Fracterms are introduced as a proxy for fractions. A precise definition of fracterms is formulated and on that basis reasonably precise definitions of various classes of fracterms are given. In the context of the meadow of rational numbers…
This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…
We present here definitions and constructions basic for the theory of monoidal and tensor categories. We provide references to the original sources, whenever possible. Group-theoretical categories are used as examples
In this article we focus on evolving information systems. First a delimitation of the concept of evolution is provided, resulting in a first attempt to a general theory for such evolutions. The theory makes a distinction between the…
This document contains a concise and unified reference for one of the existing mechanizations of the UD Kalman filter. The associated matrix algorithms are also included along with the corresponding references.