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Inspired by some new advances on normal factor graphs (NFGs), we introduce NFGs as a simple and intuitive diagrammatic approach towards encoding some concepts from linear algebra. We illustrate with examples the workings of such an approach…

Imagery is frequently used to model, represent and communicate knowledge. In particular, graphs are one of the most powerful tools, being able to represent relations between objects. Causal relations are frequently represented by directed…

The purpose of this paper is to point to the usefulness of applying a linear mathematical formulation of fuzzy multiple criteria objective decision methods in organising business activities. In this respect fuzzy parameters of linear…

Maps are arguably one of the most fundamental concepts used to define and operate on manifold surfaces in differentiable geometry. Accordingly, in geometry processing, maps are ubiquitous and are used in many core applications, such as…

Concept Bottleneck Models (CBMs) provide explicit interpretations for deep neural networks through concepts and allow intervention with concepts to adjust final predictions. Existing CBMs assume concepts are conditionally independent given…

We propose to take a look at a new approach to the study of integral polyhedra. The main idea is to give an integral representation, or matrix model representation, for the key combinatorial characteristics of integral polytopes. Based on…

The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…

Computer vision applications are omnipresent nowadays. The current paper explores the use of fuzzy logic in computer vision, stressing its role in handling uncertainty, noise, and imprecision in image data. Fuzzy logic is able to model…

This book has four chapters. In the first chapter interval bistructures (biinterval structures) such as interval bisemigroup, interval bigroupoid, interval bigroup and interval biloops are introduced. Throughout this book we work only with…

After a concise introduction to the square of opposition, in particular, and, Aristotelian Diagrams, in general, I describe how one can create a mathematical universe to host these objects. Since these objects assume that the underlying…

MindSculpt enables users to generate a wide range of hybrid geometries in Grasshopper in real time simply by thinking about those geometries. This design tool combines a brain-computer interface (BCI) with the parametric design platform…

Neuromorphic computing seeks to replicate the remarkable efficiency, flexibility, and adaptability of the human brain in artificial systems. Unlike conventional digital approaches, which suffer from the Von Neumann bottleneck and depend on…

Parametric human body models play a crucial role in computer graphics and vision, enabling applications ranging from human motion analysis to understanding human-environment interactions. Traditionally, these models use surface meshes,…

Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear…

This book introduces several new classes of groupoid, like polynomial groupoids, matrix groupoids, interval groupoids,polynomial interval groupoids, matrix interval groupoids and their neutrosophic analogues. Interval groupoid happens to be…

Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…

One of the major barriers to the training of algorithms on knowledge graph schemas, such as vocabularies or ontologies, is the difficulty that scientists have in finding the best input resource to address the target prediction tasks. In…

A famous biologically inspired hierarchical model firstly proposed by Riesenhuber and Poggio has been successfully applied to multiple visual recognition tasks. The model is able to achieve a set of position- and scale-tolerant recognition,…

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

For the first time, we have introduced the concept of N-groups, N-semigroups, N-loops, and N-groupoids. We also define a mixed N-algebraic structure. The main aim of this book is to attract young mathematicians to this interesting field. It…