相关论文: The Mesoscopic category, Automata and Tropical Geo…

A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…

The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov-Witten classes, and a…

In this article a stochastic cellular automata model is examined, which has been developed to study a "small" world, where local changes may noticeably alter global characteristics. This is applied to a climate model, where global…

Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such "mesoscopic quantum electrodynamics" is shown to share its dynamical…

We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where some arithmetic properties of a given number field can be…

In the context of the two dimensional sigma model, we show that classical field theory naturally defines a functor from Segal's category of Riemann surfaces to the Guillemin-Sternberg/Weinstein category of canonical relations in symplectic…

We develop the rudiments of a finite-dimensional representation theory of groups over idempotent semifields by considering linear actions on tropical linear spaces. This can be considered a tropical representation theory, a characteristic…

We prove a new symplectic analogue of Kashiwara's Equivalence from D-module theory. As a consequence, we establish a structure theory for module categories over deformation quantizations that mirrors, at a higher categorical level, the…

We explore a field theoretical approach to quantum computing and control. This book consists of three parts. The basics of systems theory and field theory are reviewed in Part I. In Part II, a gauge theory is reinterpreted from a systems…

The original local, discrete example of Linear Unitary Cellular Automata (LUCA) is analyzed in terms of a new representation previously introduced in [1] for classical CA. Several important underlying symmetries are reviewed and their tight…

In Isliker et al. (2000b), an extended cellular automaton (X-CA) model for solar flares was introduced. In this model, the interpretation of the model's grid-variable is specified, and the magnetic field, the current, and an approximation…

Dualities play a central role in the study of quantum spin chains, providing insight into the structure of quantum phase diagrams and phase transitions. In this work we study categorical dualities, which are defined as bounded-spread…

A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…

Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these…

We consider quantum cellular automata on a body-centred cubic lattice and provide a simple derivation of the only two homogenous, local, isotropic, and unitary two-dimensional automata [G. M. D'Ariano and P. Perinotti, Physical Review A 90,…

It has been shown that certain quantum walks give rise to relativistic wave equations, such as the Dirac and Weyl equations, in their long-wavelength limits. This intriguing result raises the question of whether something similar can happen…

The main aim of this paper is to show the interconnections between {\L}ukasiewicz logic and algebraic geometry using algebraic, geometric and logical instruments. We continue our investigation into a new algebraic geometry based on…

Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete…

We describe correlations functions of topological quantum mechanics (TQM) in terms of Morse theory. We review the basics of topological field theories and discuss geometric and algebraic interpretations of TQM. We prove that correlators in…

In this paper we describe a relation between a microscopic stochastic traffic cellular automaton model (i.e., the STCA) and the macroscopic first-order continuum model (i.e., the LWR model). The innovative aspect is that we explicitly…