Related papers: An Introduction to Multisets
Fusion is a common tool for the analysis and utilization of available datasets and so an essential part of data mining and machine learning processes. However, a clear definition of the type of fusion is not always provided due to…
We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are…
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates,…
The article continues the study of the 'regular' arrangement of a collection of sets near a point in their intersection. Such regular intersection or, in other words, transversality properties are crucial for the validity of qualification…
Multimodal learning leverages the integration of diverse data modalities to enhance performance in complex tasks. Yet, it frequently encounters incomplete or redundant modality data in real-world scenarios. This paper presents a…
The concept of sequency holds a fundamental significance in signal analysis using Walsh basis functions. In this study, we closely examine the concept of sequency and explore the properties of sequency-complete and sequency-ordered…
Here we generalize the concept of spatial tensor product, introduced by Skeide, of two product systems via a pair of normalized units. This new notion is called amalgamated tensor product of product systems, and now the amalgamation can be…
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…
In this paper we propose a framework inspired by interacting particle physics and devised to perform clustering on multidimensional datasets. To this end, any given dataset is modeled as an interacting particle system, under the assumption…
In the first part of this paper, we express the generalized Bessel function associated with dihedral systems and a constant multiplicity function as a infinite series of confluent Horn functions. The key ingredient leading to this…
This paper studies partitions in the space of antimonotonic boolean functions on sets of n elements. The antimonotonic functions are the antichains of the partially ordered set of subsets. We analyse and characterise a natural partial…
The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts…
We study generalized permutohedra and supermodular functions. Specifically we analyze decomposability and irreducibility for these objects and establish some asymptotic behavior. We also study a related problem on irreducibility for…
We introduce the notion of functionally compact sets into the theory of nonlinear generalized functions in the sense of Colombeau. The motivation behind our construction is to transfer, as far as possible, properties enjoyed by standard…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
Many natural notions of additive and multiplicative largeness arise from results in Ramsey theory. In this paper, we explain the relationships between these notions for subsets of $\mathbb{N}$ and in more general ring-theoretic structures.…
This paper introduces the concept of Bessel multipliers. These operators are defined by a fixed multiplication pattern, which is inserted between the Analysis and synthesis operators. The proposed concept unifies the approach used for Gabor…
We consider sets of operations on a set A that are closed under permutation of variables, addition of dummy variables and composition. We describe these closed sets in terms of a Galois connection between operations and systems of pointed…
Multisequences over finite fields play a pushing role in the applications that relate to parallelization, such as word-based stream ciphers and pseudorandom vector generation. It is interesting to study the complexity measures for…
A gapset is the complement of a numerical semigroup in N. In this paper, we characterize all gapsets of multiplicity m $\le$ 4. As a corollary, we provide a new simpler proof that the number of gapsets of genus g and fixed multiplicity m…