相关论文: WZ Theory, Chapter II

Society is changing, has always changed, and will keep changing. However, changes are becoming faster and what used to happen between generations, now happens in the same generation. Computing Science is one of the reasons for this speed…

Existence theory in economics is usually in real domains such as the findings of chaotic trajectories in models of economic growth, tatonnement, or overlapping generations models. Computational examples, however, sometimes converge rapidly…

We present evidence for the factorization of the world-sheet path integrals for 2d conformal field theories on the disk into bulk and boundary contributions. This factorization is then used to reinterpret a shift in closed string…

Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…

Solid modeling is a technique underlying CAD software as we see it today, and its theories and algorithms are among the most fundamental milestones in the historical development of CAD. Basically, it has answered the question of what…

In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…

This article focuses on the connection between the possibility of quantum computers, the predictability of complex quantum systems in nature, and the issue of free will.

Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described…

Illusions are fascinating and immediately catch people's attention and interest, but they are also valuable in terms of giving us insights into human cognition and perception. A good theory of human perception should be able to explain the…

This essay examines the relationship between artificial intelligence and the historical evolution of modern Mathematics. Rather than viewing AI as an external rupture, we argue that its effectiveness reveals a structural tendency already…

We stand at the foot of a significant inflection in the trajectory of scientific discovery. As society continues on its fast-paced digital transformation, so does humankind's collective scientific knowledge and discourse. We now read and…

The aim of this paper is to discuss some applications of general topology in computer algorithms including modeling and simulation, and also in computer graphics and image processing. While the progress in these areas heavily depends on…

A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.

This paper considers the potential impact that the nascent technology of quantum computing may have on society. It focuses on three areas: cryptography, optimization, and simulation of quantum systems. We will also discuss some ethical…

Since its inception at the beginning of the twentieth century, quantum mechanics has challenged our conceptions of how the universe ought to work; however, the equations of quantum mechanics can be too computationally difficult to solve…

Energy consumption of computing has found increasing prominence but the area still suffers from the lack of a consolidated formal theory. In this paper, a theory for the energy consumption of computing is structured as an axiomatic system.…

This review introduces Markov Chain Monte Carlo simulations in causal set theory, with a focus on the study of the 2d orders. It will first introduce the Benincasa-Dowker action on causal sets, and cover some musings on the philosophy of…

This book provides a comprehensive and accessible introduction to the emerging field of AI for mathematics. It covers the core principles and diverse applications of using artificial intelligence to advance mathematical research. Through…

The theory of quantum computation is presented in a self contained way from a computer science perspective. The basics of classical computation and quantum mechanics is reviewed. The circuit model of quantum computation is presented in…

In the half century since the 1950s computer simulation has transformed our understanding of physics. The rare, expensive, slow, and bulky mainframes of World War II have given way to today's millions of cheap, fast, desksized workstations…