Detection of hidden structures for arbitrary scales in complex physical systems

Ronhovde, Peter; Chakrabarty, Saurish; Hu, Dandan; Sahu, Manjulata; Sahu, Κ. K.; Kelton, K. F.; Mauro, N. A.; Nussinov, Zohar

doi:10.1038/srep00329

Cited by 49 publications

(42 citation statements)

References 57 publications

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“…This article constitutes a longer companion work to an earlier summary [1] in which the basic notions to be detailed here for complex physical systems were succinctly outlined. We begin by briefly reviewing a special class of complex physical systems that is of great fundamental and technological importance -that of amorphous materials.…”

Section: Introductionmentioning

confidence: 99%

Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering

Ronhovde

Chakrabarty

et al. 2011

Eur. Phys. J. E

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Abstract. We elaborate on a general method that we recently introduced for characterizing the "natural" structures in complex physical systems via a multi-scale network based approach for the data mining of such structures. The approach is based on "community detection" wherein interacting particles are partitioned into "an ideal gas" of optimally decoupled groups of particles. Specifically, we construct a set of network representations ("replicas") of the physical system based on interatomic potentials and apply a multiscale clustering ("multiresolution community detection") analysis using information-based correlations among the replicas. Replicas may be (i) different representations of an identical static system or (ii) embody dynamics by when considering replicas to be time separated snapshots of the system (with a tunable time separation) or (iii) encode general correlations when different replicas correspond to different representations of the entire history of the system as it evolves in space-time. Inputs for our method are the inter-particle potentials or experimentally measured two (or higher order) particle correlations. We apply our method to computer simulations of a binary Kob-Andersen Lennard-Jones system in a mixture ratio of A80B20, a ternary model system with components "A", "B", and "C" in ratios of A88B7C5 (as in Al88Y7Fe5), and to atomic coordinates in a Zr80Pt20 system as gleaned by reverse Monte Carlo analysis of experimentally determined structure factors. We identify the dominant structures (disjoint or overlapping) and general length scales by analyzing extrema of the information theory measures. We speculate on possible links between (i) physical transitions or crossovers and (ii) changes in structures found by this method as well as phase transitions associated with the computational complexity of the community detection problem. We briefly also consider continuum approaches and discuss the shear penetration depth in elastic media; this length scale increases as the system becomes increasingly rigid.

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Section: Introductionmentioning

confidence: 99%

Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering

Ronhovde

Chakrabarty

et al. 2011

Eur. Phys. J. E

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“…Augmenting Refs. [5], [6], [7], [8], [9], [10], we further also note the more recent work of Ref. [15] in which the authors demonstrate that the inference algorithms based on evolving interactions between replicated solutions in a cavity type approach have better performance in the binary Ising percepton problem.…”

Section: Introductionmentioning

confidence: 94%

“…By "replicas" we here allude to independent copies of the same problem. Since then these notions have been applied to a variety of complex system physics (both static and dynamic) and image segmentation problems [6], [7], [8], [9]. More recently, other works applied similar notions to a host of interesting problems [11], [12], [13].…”

Section: Introductionmentioning

confidence: 99%

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An interacting replica approach applied to the traveling salesman problem

Sun

Leonard

Ronhovde

et al. 2016

2016 SAI Computing Conference (SAI)

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Abstract-We present a physics inspired heuristic method for solving combinatorial optimization problems. Our approach is specifically motivated by the desire to avoid trapping in metastable local minima-a common occurrence in hard problems with multiple extrema. Our method involves (i) coupling otherwise independent simulations of a system ("replicas") via geometrical distances as well as (ii) probabilistic inference applied to the solutions found by individual replicas. The ensemble of replicas evolves as to maximize the inter-replica correlation while simultaneously minimize the local intra-replica cost function (e.g., the total path length in the Traveling Salesman Problem within each replica). We demonstrate how our method improves the performance of rudimentary local optimization schemes long applied to the NP hard Traveling Salesman Problem. In particular, we apply our method to the well-known "k-opt" algorithm and examine two particular cases-k = 2 and k = 3. With the aid of geometrical coupling alone, we are able to determine for the optimum tour length on systems up to 280 cities (an order of magnitude larger than the largest systems typically solved by the bare k = 3 opt). The probabilistic replica-based inference approach improves k − opt even further and determines the optimal solution of a problem with 318 cities and find tours whose total length is close to that of the optimal solutions for other systems with a larger number of cities.

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“…In the limit of progressively larger number of nodes per community n in power-law graphs, the size of the parameter space region which supported the "hard" phase steadily decreased [8] suggesting that this phase might disappear in the large n limit. The existence of these phases and their physical content is made visible in some applications such as image segmentation [29] and a graph theory based analysis of the structure of glass formers [33,34]. In a companion paper, we illustrate how our edge density based criteria for community detection (in particular that of Eq.…”

Section: A Transitions In Algorithmic Approaches To Community Detectionmentioning

confidence: 99%

Algorithm independent bounds on community detection problems and associated transitions in stochastic block model graphs

et al. 2014

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We derive rigorous bounds for well-defined community structure in complex networks for a stochastic block model (SBM) benchmark. In particular, we analyze the effect of inter-community "noise" (inter-community edges) on any "community detection" algorithm's ability to correctly group nodes assigned to a planted partition, a problem which has been proven to be NP complete in a standard rendition. Our result does not rely on the use of any one particular algorithm nor on the analysis of the limitations of inference. Rather, we turn the problem on its head and work backwards to examine when, in the first place, well defined structure may exist in SBMs. The method that we introduce here could potentially be applied to other computational problems. The objective of community detection algorithms is to partition a given network into optimally disjoint subgraphs (or communities). Similar to k−SAT and other combinatorial optimization problems, "community detection" exhibits different phases. Networks that lie in the "unsolvable phase" lack well-defined structure and thus have no partition that is meaningful. Solvable systems splinter into two disparate phases: those in the "hard" phase and those in the "easy" phase. As befits its name, within the easy phase, a partition is easy to achieve by known algorithms. When a network lies in the hard phase, it still has an underlying structure yet finding a meaningful partition which can be checked in polynomial time requires an exhaustive computational effort that rapidly increases with the size of the graph. When taken together, (i) the rigorous results that we report here on when graphs have an underlying structure and (ii) recent results concerning the limits of rather general algorithms, suggest bounds on the hard phase.

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Detection of hidden structures for arbitrary scales in complex physical systems

Cited by 49 publications

References 57 publications

Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering

Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering

An interacting replica approach applied to the traveling salesman problem

Algorithm independent bounds on community detection problems and associated transitions in stochastic block model graphs

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