Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

/pdf/community-detection-in-graphs-34rogm3r6p.pdf

Community detection in graphs

https://link.springer.com/content/pdf/10.2307%2F3343168.pdf

Development as Freedom

Agent-based modeling of zapping behavior of viewers, television commercial allocation, and advertisement markets by Hiroyuki Kyan and Jun-ichi Inoue.- Agent based modeling of Housing asset bubble: A simple utility function based investigation by Kausik Gangopadhyay and Kousik Guhathakurta.- Urn model-based adaptive Multi-arm clinical trials: A stochastic approximation approach by Sophie Laruelle and Gilles Pages.- Logistic modeling of a Religious Sect features by Marcel Ausloos.- Characterizing financial crisis by means of the three states random field Ising model by Mitsuaki Murota and Jun-ichi Inoue.- Themes and applications of kinetic exchange models: Redux by Asim Ghosh, Anindya S. Chakrabarti, Anjan Kumar Chandra and Anirban Chakraborti.- Kinetic exchange opinion model: solution in the single parameter map limit by Krishanu Roy Chowdhury, Asim Ghosh, Soumyajyoti Biswas and Bikas K. Chakrabarti.- An overview of the new frontiers of Economic Complexity by Matthieu Cristelli, Andrea Tacchella, Luciano Pietronero.- Jan Tinbergen's legacy for economic networks: from the gravity model to quantum statistics by Tiziano Squartini and Diego Garlaschelli.- A macroscopic order of consumer demand due to heterogenous consumer behaviors on Japanese household demand tested by the random matrix theory by Yuji Aruka,Yuichi Kichikawa and Hiroshi Iyetomi.- Uncovering the network structure of the world currency market: Cross-correlations in the fluctuations of daily exchange rates by Sitabhra Sinha and Uday Kovur.- Systemic risk in Japanese credit network by Hideaki Aoyama.- Pricing of goods with Bandwagon properties: The curse of coordination by Mirta B. Gordon, Jean-Pierre Nadal, Denis Phan and Viktoriya Semeshenko.- Evolution of Econophysics by Kishore C. Dash.- Econophysics and sociophysics: Problems and prospects by Asim Ghosh and Anindya S. Chakrabarti.- A discussion on Econophysics by Hideaki Aoyama.

Econophysics of agent-based models

If one places N cities randomly on a lattice of size L, we find that \(\) and \(\) vary with the city concentration p=N/L2, where \(\) is the average optimal travel distance per city in the Euclidean metric and \(\) is the same in the Manhattan metric. We have studied such optimum tours for visiting all the cities using a branch and bound algorithm, giving the exact optimized tours for small system sizes (\(\)) and near-optimal tours for bigger system sizes (\(\)). Extrapolating the results for \(\), we find that \(\) for p=1, and \(\) and \(\) with \(\) as \(\). Although the problem is trivial for p=1, for \(\) it certainly reduces to the standard travelling salesman problem on continuum which is NP-hard. We did not observe any irregular behaviour at any intermediate point. The crossover from the triviality to the NP-hard problem presumably occurs at p=1.

/pdf/the-travelling-salesman-problem-on-randomly-diluted-lattices-2ympq98ncp.pdf

The travelling salesman problem on randomly diluted lattices: Results for small-size systems

In this chapter, we briefly review the different aspects and applications of kinetic exchange models in economics and sociology Our main aim is to show in what manner the kinetic exchange models for closed economic systems were inspired by the kinetic theory of gas molecules The simple yet powerful framework of kinetic theory, first proposed in 1738, led to the successful development of statistical physics of gases towards the end of the nineteenth century This framework was successfully adapted to modelling of wealth distributions in the early 2000s In later times, it was applied to other areas like firm dynamics and opinion formation in the society, as well We have tried to present the flavour of the several models proposed and their applications, intentionally leaving out the intricate mathematical and technical details

Kinetic Exchange Models in Economics and Sociology

The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments. Furthermore, the convergence to the limit distributions can be slow, requiring a huge amount of records to obtain significant statistics, and thus limiting its practical applications. Focussing, instead, on the closely related density of “near-extremes”–the distance between a record and the maximal value–can render the statistical methods to be more suitable in the practical applications and/or validations of models. We apply this recently proposed method in the empirical validation of an adapted financial market model of the intraday market fluctuations.

/pdf/the-near-extreme-density-of-intraday-log-returns-1kztwmrugv.pdf

The near-extreme density of intraday log-returns

We study unit-level expenditure on consumption across multiple countries and multiple years, in order to extract invariant features of consumption distribution. We show that the bulk of it is lognormally distributed, followed by a power law tail at the limit. The distributions coincide with each other under normalization by mean expenditure and log scaling even though the data is sampled across multiple dimension including, e.g. time, social structure and locations. This phenomenon indicates that the dispersions in consumption expenditure across various social and economic groups are significantly similar subject to suitable scaling and normalization. Further, the results provide a measurement of the core distributional features. Other descriptive factors including those of sociological, demographic and political nature, add further layers of variation on the this core distribution. We present a stochastic multiplicative model to quantitatively characterize the invariance and the distributional features.

Anirban Chakraborti

Papers

Econophysics of agent-based models

The travelling salesman problem on randomly diluted lattices: Results for small-size systems

Kinetic Exchange Models in Economics and Sociology

The near-extreme density of intraday log-returns

Quantifying invariant features of within-group inequality in consumption across groups