Search results for "Nonlinear"
showing 10 items of 3684 documents
HOW SMART DOES AN AGENT NEED TO BE?
2005
The classic distributed computation is done by atoms, molecules or spins in vast numbers, each equipped with nothing more than the knowledge of their immediate neighborhood and the rules of statistical mechanics. These agents, 1023 or more, are able to form liquids and solids from gases, realize extremely complex ordered states, such as liquid crystals, and even decode encrypted messages. We will describe a study done for a sensor-array "challenge problem" in which we have based our approach on old-fashioned simulated annealing to accomplish target acquisition and tracking under the rules of statistical mechanics. We believe the many additional constraints that occur in the real problem ca…
A Tool for Implementing and Exploring SBM Models: Universal 1D Invertible Cellular Automata
2005
The easiest form of designing Cellular Automata rules with features such as invertibility or particle conserving is to rely on a partitioning scheme, the most important of which is the 2D Margolus neighborhood. In this paper we introduce a 1D Margolus-like neighborhood that gives support to a complete set of Cellular Automata models. We present a set of models called Sliding Ball Models based on this neighborhood and capable of universal computation. We show the way of designing logic gates with these models, propose a digital structure to implement them and finally we present SBMTool, a software development system capable of working with the new models.
Diagrammatic approach to cellular automata and the emergence of form with inner structure
2018
We present a diagrammatic method to build up sophisticated cellular automata (CAs) as models of complex physical systems. The diagrams complement the mathematical approach to CA modeling, whose details are also presented here, and allow CAs in rule space to be classified according to their hierarchy of layers. Since the method is valid for any discrete operator and only depends on the alphabet size, the resulting conclusions, of general validity, apply to CAs in any dimension or order in time, arbitrary neighborhood ranges and topology. We provide several examples of the method, illustrating how it can be applied to the mathematical modeling of the emergence of order out of disorder. Specif…
Pseudo-Bosons, So Far
2011
In the past years several extensions of the canonical commutation relations have been proposed by different people in different contexts and some interesting physics and mathematics have been deduced. Here, we review some recent results on the so-called {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^\dagger$. We start discussing some of their mathematical properties and then we discuss several examples.
Multi-rogue waves solutions: from the NLS to the KP-I equation
2013
Our discovery of multi-rogue wave (MRW) solutions in 2010 completely changed the viewpoint on the links between the theory of rogue waves and integrable systems, and helped explain many phenomena which were never understood before. It is enough to mention the famous Three Sister waves observed in oceans, the creation of a regular approach to studying higher Peregrine breathers, and the new understanding of 2 + 1 dimensional rogue waves via the NLS-KP correspondence. This article continues the study of the MRW solutions of the NLS equation and their links with the KP-I equation started in a previous series of articles (Dubard et al 2010 Eur. Phys. J. 185 247–58, Dubard and Matveev 2011 Natur…
Analytical design of nonlinear optical loop mirrors for fiber-optic communication systems
2006
International audience; We propose an easy and efficient method for analytically designing nonlinear optical loop mirrors (NOLMs) for fiber-optic communication systems. This analytical design is based on a Taylor series expansion of the transfer function of the NOLM, from which highly stable dynamical regimes can be readily obtained for any desired pulse parameters. We present numerical simulations showing dramatically improved performances in a 160 Gb/s transmission system that incorporates the NOLMs designed analytically.
Quantum versus Probabilistic One-Way Finite Automata with Counter
2001
The paper adds the one-counter one-way finite automaton [6] to the list of classical computing devices having quantum counterparts more powerful in some cases. Specifically, two languages are considered, the first is not recognizable by deterministic one-counter one-way finite automata, the second is not recognizable with bounded error by probabilistic one-counter one-way finite automata, but each recognizable with bounded error by a quantum one-counter one-way finite automaton. This result contrasts the case of one-way finite automata without counter, where it is known [5] that the quantum device is actually less powerful than its classical counterpart.
Multiple Usage of Random Bits in Finite Automata
2012
Finite automata with random bits written on a separate 2-way readable tape can recognize languages not recognizable by probabilistic finite automata. This shows that repeated reading of random bits by finite automata can have big advantages over one-time reading of random bits.
Local automata and completion
1993
The problem of completing a finite automata preserving its properties is here investigated in the case of deterministic local automata. We show a decision procedure and give an algorithm which complete a deterministic local automaton (if the completion exists) with another one, having the same number of states.
Ultrametric Finite Automata and Turing Machines
2013
We introduce a notion of ultrametric automata and Turing machines using p-adic numbers to describe random branching of the process of computation. These automata have properties similar to the properties of probabilistic automata but complexity of probabilistic automata and complexity of ultrametric automata can differ very much.