相关论文: A Problem in Categories
It is known that monoidal categories have a finite definition, whereas multicategories have an infinite (albeit finitary) definition. Since monoidal categories correspond to representable multicategories, it goes without saying that…
An ideal on a set $X$ is a collection of subsets of $X$ closed under the operations of taking finite unions and subsets of its elements. Ideals are a very useful notion in topology and set theory and have been studied for a long time. We…
A set X of partial words over a finite alphabet A is called unavoidable if every two-sided infinite word over A has a factor compatible with an element of X. Unlike the case of a set of words without holes, the problem of deciding whether…
Answering connectivity queries in real algebraic sets is a fundamental problem in effective real algebraic geometry that finds many applications in e.g. robotics where motion planning issues are topical. This computational problem is…
A system is data-independent with respect to a data type X iff the operations it can perform on values of type X are restricted to just equality testing. The system may also store, input and output values of type X. We study model checking…
This survey presents some historical background and recent developments in the area of selections for set-valued mappings along with several open questions. It was written with the hope that the presented material may pique an interest in…
In this paper, we study a polynomial decomposition model that arises in problems of system identification, signal processing and machine learning. We show that this decomposition is a special case of the X-rank decomposition --- a powerful…
We investigate an approach to matroid complexity that involves describing a matroid via a list of independent sets, bases, circuits, or some other family of subsets of the ground set. The computational complexity of algorithmic problems…
Consider the following parameterized counting variation of the classic subset sum problem, which arises notably in the context of higher homotopy groups of topological spaces: Let $\mathbf{v} \in \mathbb{Q}^d$ be a rational vector, $(T_{1},…
Blind system identification is known to be an ill-posed problem and without further assumptions, no unique solution is at hand. In this contribution, we are concerned with the task of identifying an ARX model from only output measurements.…
What makes sets, or more precisely, the category {\bf Set} important in Mathematics are the well known {\it two} specific ways in which arbitrary mappings $f : X \longrightarrow Y$ between any two sets $X, Y$ can {\it fail} to be…
Let X be a countably infinite set, Inj(X) the monoid of all injective endomaps of X, and Sym(X) the group of all permutations of X. We classify all submonoids of Inj(X) that are closed under conjugation by elements of Sym(X).
We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative…
Categories can be identified -- up to isomorphism -- with polynomial comonads on Set. The left Kan extension of a functor along itself is always a comonad -- called the density comonad -- so it defines a category when its carrier is…
A simplicial set is non-singular if the representing map of each non-degenerate simplex is degreewise injective. The simplicial mapping set $X^K$ has $n$-simplices given by the simplicial maps $\Delta[n] \times K \to X$. We prove that $X^K$…
Connections between heaps of modules and (affine) modules over rings are explored. This leads to explicit, often constructive, descriptions of some categorical constructions and properties that are implicit in universal algebra and…
Set visualization facilitates the exploration and analysis of set-type data. However, how sets should be visualized when the data is uncertain is still an open research challenge. To address the problem of depicting uncertainty in set…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
We consider the problem of classification of an object given multiple observations that possibly include different transformations. The possible transformations of the object generally span a low-dimensional manifold in the original signal…
Clustering is an unsupervised technique of Data Mining. It means grouping similar objects together and separating the dissimilar ones. Each object in the data set is assigned a class label in the clustering process using a distance measure.…