Related papers: Problem Structures in the Theory and Practice of S…

Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…

Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…

In this era of information technology, abundant information is available on the internet in the form of web pages and documents on any given topic. Finding the most relevant and informative content out of these huge number of documents,…

Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…

This paper surveys the machine learning literature and presents in an optimization framework several commonly used machine learning approaches. Particularly, mathematical optimization models are presented for regression, classification,…

This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present…

This paper presents the methodology for the system requirements and architecture w.r.t. their decomposition and refinement. It also introduces ideas of refinement layers and of refinement-based verification.

Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…

Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical…

This paper has been withdrawn. With the advancement of statistical theory and computing power, data sets are providing a greater amount of insight into the problems of today. Statisticians have an ever increasing number of tools to attack…

With the broad growth of video capturing devices and applications on the web, it is more demanding to provide desired video content for users efficiently. Video summarization facilitates quickly grasping video content by creating a compact…

Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…

In this review we attempt to present an overview of some of the better known quantization techniques found in the current literature and used both by physicists and mathematicians. The treatment is more descriptive than rigorous, for we aim…

Optimization has been becoming a central of studies in mathematic and has many areas with different applications. However, many themes of optimization came from different area have not ties closing to origin concepts. This paper is to…

Asking which sets are fixed-parameter tractable for a given parameterization constitutes much of the current research in parameterized complexity theory. This approach faces some of the core difficulties in complexity theory. By focussing…

Mitigating shortcuts, where models exploit spurious correlations in training data, remains a significant challenge for improving generalization. Regularization methods have been proposed to address this issue by enhancing model…

Decision-making is a central yet under-defined goal in visualization research. While existing task models address decision processes, they often neglect the conditions framing a decision. To better support decision-making tasks, we propose…

We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…

This document is both a synthesis of current notions about complex systems, and a practical approach description. A disambiguation is proposed and exposes possible reasons for controversies related to causation and emergence. Theoretical…

As the development of distributed systems progresses, more and more challenges arise and the need for developing optimized systems and for optimizing existing systems from multiple perspectives becomes more stringent. In this paper I…