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We introduce the notion of dynamical metric order of a continuous map on a compact metric space, study its basic properties, and compute it for several classes of maps. This concept which is a counterpart of the metric mean dimension with…

This paper draws attention to the potential of computational methods in reworking data generated in past qualitative studies. While qualitative inquiries often produce rich data through rigorous and resource-intensive processes, much of…

The main purpose of this paper is to study complex valued metric-like spaces as an extension of metric-like spaces, complex valued partial metric spaces, partial metric spaces, complex valued metric spaces and metric spaces. In this…

Powerspaces of directed spaces play an important role in modeling the semantics of nondeterministic functional programming languages. The notions of upper,lower and convex powerspace of a directed space are defined by the way of free…

Disentangled latent spaces usually have better semantic separability and geometrical properties, which leads to better interpretability and more controllable data generation. While this has been well investigated in Computer Vision, in…

In this paper we use finite vector spaces (finite dimension, over finite fields) as a non-standard computational model of linear logic. We first define a simple, finite PCF-like lambda-calculus with booleans, and then we discuss two finite…

In this book the authors introduce the notion of DSm vector spaces of refined labels. They also realize the refined labels as a plane and a n-dimensional space. Further, using these refined labels, several algebraic structures are defined.…

In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. We define a notion of diagonalization of square matrices whose coefficients are intervals. But in this case, with…

Skew-symmetric forms possess unique capabilities. The properties of closed exterior and dual forms, namely, invariance, covariance, conjugacy and duality, either explicitly or implicitly appear in all invariant mathematical formalisms. This…

We present in this paper a new way to define weighted Sobolev spaces when the weight functions are arbitrary small. This new approach can replace the old one consisting in modifying the domain by removing the set of points where at least…

In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…

In this study, we define a new triangle matrix $\hat{W}=\{w_{nk}^{\lambda}(r,s,t)\}$ which derived by using multiplication of $\lambda=(\lambda_{nk})$ triangle matrix with $B(r,s,t)$ triple band matrix. Also, we introduce the sequence…

Can one inject new concepts into an already trained generative model, while respecting its existing structure and knowledge? We propose a new task - domain expansion - to address this. Given a pretrained generator and novel (but related)…

In the last years many results in the area of semidefinite programming were obtained for invariant (finite dimensional, or infinite dimensional) semidefinite programs - SDPs which have symmetry. This was done for a variety of problems and…

We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.

Learning representations of well-trained neural network models holds the promise to provide an understanding of the inner workings of those models. However, previous work has either faced limitations when processing larger networks or was…

The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…

This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…

It is shown that a covariant derivative on any d-dimensional manifold M can be mapped to a set of d operators acting on the space of functions on the principal Spin(d)-bundle over M. In other words, any d-dimensional manifold can be…

This work seeks to tackle the inherent complexity of dataspaces by introducing a novel data structure that can represent datasets across multiple levels of abstraction, ranging from local to global. We propose the concept of a multilevel…