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• W1645275320 abstract "Glossary Nonlinear system A system composed by parts whose combined effects are different from the sum of the effects of each part. Extended system A system composed bymany parts connected by a network of interactions thatmay be regular (lattice) or irregular (graph). Graph, lattice, tree A graph is set of nodes connected by links, oriented or not. If the graph is translationally invariant (it looks the same when changing nodes), it is called a (regular) lattice. A disordered lattice is a lattice with a fraction of removed links or nodes. An ordered set of nodes connected by links is called a path. A closed path not passing on the same links is a loop. A cluster is a set of connected nodes. A graph can be composed by one cluster (a connected graph) or more than one (a disconnected graph). A tree is a connected graph without loops. Percolation The appearance of a “giant component” (a cluster that contains essentially all nodes or links) in a graph or a lattice, after adding or removing nodes or links. Below the percolation threshold the graph is partitioned into disconnected clusters, none of which contains a substantial fraction of nodes or links, in the limit of infinite number of nodes/links. State of a system A complete characterization of a system at a given time, assigning or measuring the positions, velocities and other dynamical variables of all the elements (sometimes called a configuration). For completely discrete systems (cellular automata) of finite size, the state of the system is just a set of integer numbers, and therefore the state space is numerable. Trajectory A sequence of states of a system, labeled with the time, i. e., a path in the state space. Probability distribution The probability of finding a system in a given state, for all the possible states. Mean field An approximate technique for computing the value of the observables of an extended system, neglecting correlations among parts. If necessary, the dynamics is first approximated by a stochastic process. In its simpler version, the probability of a state of the system is approximated by the product of the probability of each component, neglecting correlations. Since the state of two components that depend on a common “ancestor” (that interact with a common node) is in general not uncorrelated, and this situation corresponds to an interaction graph with loops, the simplest mean field approximation consists in replacing the graph or the lattice of interactions with a tree. Monte-Carlo A method for producing stochastic trajectories in the state space designed in such a way that the time-averaged probability distribution is the desired one. Critical phenomenon A condition for which an extended system is correlated over extremely long distances." @default.
• W1645275320 created "2016-06-24" @default.
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• W1645275320 date "2017-01-01" @default.
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• W1645275320 title "Interaction-Based Computing in Physics" @default.
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