相关论文: Applications of Bimatrices to some Fuzzy and Neutr…

Decision making under uncertainty is a cross-cutting challenge in science and engineering. Most approaches to this challenge employ probabilistic representations of uncertainty. In complicated systems accessible only via data or black-box…

In this paper, we integrate the concepts of feature importance with implicit bias in the context of pattern classification. This is done by means of a three-step methodology that involves (i) building a classifier and tuning its…

Model fusion research aims to aggregate the knowledge of multiple individual models to enhance performance by combining their weights. In this work, we study the inverse problem: investigating whether model fusion can be used to reduce…

Functions that are not differentiable in the classical sense have become a central tool in modern mathematical models for imaging, inverse problems, machine learning, and optimal control of differential equations. These models are…

Many disciplines of science and engineering deal with problems related to compositions, ranging from chemical compositions in materials science to portfolio compositions in economics. They exist in non-Euclidean simplex spaces, causing many…

The sole aim of this book is to give a self-contained introduction to concepts and mathematical tools in Bayesian matrix decomposition in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent…

Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages…

We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…

This paper presents an end-to-end neural architecture based on Diffusion Models for spatial puzzle solving, particularly jigsaw puzzle and room arrangement tasks. In the latter task, for instance, the proposed system "PuzzleFusion" takes a…

Fuzzy simplicial sets have become an object of interest in dimensionality reduction and manifold learning, most prominently through their role in UMAP. However, their definition through tools from algebraic topology without a clear…

Despite the recent success of neural network models in mimicking animal performance on visual perceptual tasks, critics worry that these models fail to illuminate brain function. We take it that a central approach to explanation in systems…

Frequentist and Bayesian methods differ in many aspects, but share some basic optimal properties. In real-life classification and regression problems, situations exist in which a model based on one of the methods is preferable based on some…

The Fuzzy Modeling has been applied in a wide variety of fields such as Engineering and Management Sciences and Social Sciences to solve a number Decision Making Problems which involve impreciseness, uncertainty and vagueness in data. In…

Visual models play a crucial role in both science and science communication. However, the distinction between mere analogies and mathematically sound graphical representations is not easy and can be misunderstood not only by laypeople but…

A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for formalizing algorithms that manipulate mathematical expressions. A theory…

Bigraphs are a universal computational modelling formalism for the spatial and temporal evolution of a system in which entities can be added and removed. We extend bigraphs to probablistic bigraphs, and then again to action bigraphs, which…

In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…

Multi-omics data offer unprecedented insights into complex biological systems, yet their high dimensionality, sparsity, and intricate interactions pose significant analytical challenges. Network-based approaches have advanced multi-omics…

This book studies ultrafilters on connectivity systems, that is, on pairs \((X,f)\) where \(X\) is a finite set and \(f:2^{X}\to \mathbb{N}\) is a symmetric submodular function. Ultrafilters, which play a fundamental role in topology and…

This book discusses computational curiosity, from the psychology of curiosity to the computational models of curiosity, and then showcases several interesting applications of computational curiosity. A brief overview of the book is given as…