Related papers: Filtrations
We summarize the current knowledge on the three limit notions: ultrafilter-limits, closed-ultrafilter-limits and FAM-limits. Also, we consider the possibility to perform an iteration which has all the three limits and clarify the problem we…
In Persistent Homology and Topology, filtrations are usually given by introducing an ordered collection of sets or a continuous function from a topological space to $\R^n$. A natural question arises, whether these approaches are equivalent…
We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.
Expository notes about spectral sequences, filtered spectra, and synthetic spectra. We focus on the $\tau$-formalism as it arises in filtered spectra.
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
It is a working version of a lecture on the theory of enlargement of filtration, given at the African Mathematic School in Marrakech, October 19-23, 2015.
For several natural filtrations of a free group S we express the n-th term of the filtration as the intersection of all kernels of homomorphisms from S to certain groups of upper-triangular unipotent matrices. This generalizes a classical…
Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.
The particle filter is a powerful framework for estimating hidden states in dynamic systems where uncertainty, noise, and nonlinearity dominate. This mini-book offers a clear and structured introduction to the core ideas behind particle…
We introduce the notion of filtration between topologies and study its stabilization properties. Descriptive set theoretic complexity plays a role in this study. Filtrations lead to natural transfinite sequences approximating a given…
This article aims to explain essential elements of perturbation theory and their conceptual underpinnings. It is not meant as a summary of popular perturbation methods, though some illustrative examples are given to underline the main…
In all approaches to convergence where the concept of filter is taken as primary, the usual motivation is the notion of neighborhood filter in a topological space. However, these approaches often lead to spaces more general than topological…
The aim of this note is to show that many papers on various kinds of filters (and related concepts) in (subreducts of) residuated structures are in fact easy consequences of more general results that have been known for a long time.
Filtered probability spaces (called "filtrations" for short) are shown to satisfy such a topological zero-one law: for every property of filtrations, either the property holds for almost all filtrations, or its negation does. In particular,…
The filters work in many areas of technology. There constructions are different and substances under filtration are different. It is necessary in some cases to take into account forming of sediments on the walls of the filter since they can…
This paper serves as an introduction to the current book. It provides the basic notions of long-baseline optical/infrared interferome-try prior to reading all the subsequent chapters, and is not an extended introduction to the field.
Implicit particle filters for data assimilation update the particles by first choosing probabilities and then looking for particle locations that assume them, guiding the particles one by one to the high probability domain. We provide a…
Filtration of feed containing multiple species of particles is a common process in the industrial setting. In this work we propose a model for filtration of a suspension containing an arbitrary number of particle species, each with…
Image processing is one of the most immerging and widely growing techniques making it a lively research field. Image processing is converting an image to a digital format and then doing different operations on it, such as improving the…
We introduce a notion of integration defined from filters over families of finite sets. This procedure corresponds to determining the average value of functions whose range lies in any algebraic structure in which finite averages make…