Related papers: Algebraic Approach to Directed Rough Sets
The author has recently introduced an abstract algebraic framework of analogical proportions within the general setting of universal algebra. The purpose of this paper is to lift that framework from universal algebra to the strictly more…
Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the…
Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated…
Granular operator spaces and variants had been introduced and used in theoretical investigations on the foundations of general rough sets by the present author over the last few years. In this research, higher order versions of these are…
Humans readily generalize abstract relations, such as recognizing "constant" in shape or color, whereas neural networks struggle, limiting their flexible reasoning. To investigate mechanisms underlying such generalization, we introduce…
In real-world tasks, there is usually a large amount of unlabeled data and labeled data. The task of combining the two to learn is known as semi-supervised learning. Experts can use logical rules to label unlabeled data, but this operation…
A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated…
The problem of link prediction is of active interest. The main approach to solving the link prediction problem is based on heuristics such as Common Neighbors (CN) -- more number of common neighbors of a pair of nodes implies a higher…
The human cognitive system exhibits remarkable flexibility and generalization capabilities, partly due to its ability to form low-dimensional, compositional representations of the environment. In contrast, standard neural network…
These notes aim at providing a complete and systematic account of some foundational aspects of algebraic supergeometry, namely, the extension to the geometry of superschemes of many classical notions, techniques and results that make up the…
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…
Determining the attachments of prepositions and subordinate conjunctions is a key problem in parsing natural language. This paper presents a trainable approach to making these attachments through transformation sequences and error-driven…
New concepts of rough natural number systems, recently introduced by the present author, are used to improve most rough set-theoretical measures in general Rough Set theory (\textsf{RST}) and measures of mutual consistency of multiple…
The natural join and the inner union combine in different ways tables of a relational database. Tropashko [18] observed that these two operations are the meet and join in a class of lattices-called the relational lattices- and proposed…
This paper classifies the derivations of group algebras in terms of the generators and defining relations of the group. If $RG$ is a group ring, where $R$ is commutative and $S$ is a set of generators of $G$ then necessary and sufficient…
The identifiability problem arises naturally in a number of contexts in mathematics and computer science. Specific instances include local or global rigidity of graphs and unique completability of partially-filled tensors subject to rank…
In this paper, rough approximations of Cayley graphs are studied and rough edge Cayley graphs are introduced. Furthermore, a new algebraic definition called pseudo-Cayley graphs containing Cayley graphs is proposed. Rough approximation is…
We start an analysis of geometric properties of a structure relative to a reduct. In particular, we look at definability of groups and fields in this context. In the relatively one-based case, every definable group is isogenous to a…
When adopting a model-based formulation, solving inverse problems encountered in multiband imaging requires to define spatial and spectral regularizations. In most of the works of the literature, spectral information is extracted from the…
Robotic manipulation in complex open-world scenarios requires both reliable physical manipulation skills and effective and generalizable perception. In this paper, we propose a method where general purpose pretrained visual models serve as…