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

In this article, we review several techniques to extract information from large-scale stock market data. We discuss recurrence analysis of time series, decomposition of aggregate correlation matrices to study co-movements in financial data, stock level partial correlations with market indices, multidimensional scaling, and minimum spanning tree. We apply these techniques to daily return time series from the Indian stock market. The analysis allows us to construct networks based on correlation matrices of individual stocks on one hand, and on the other, we discuss dynamics of market indices. Thus, both microlevel and macrolevel dynamics can be analyzed using such tools. We use the multidimensional scaling methods to visualize the sectoral structure of the stock market and analyze the co-movements among the sectoral stocks. Finally, we construct a mesoscopic network based on sectoral indices. Minimum spanning tree technique is seen to be extremely useful in order to group technologically related sectors, and the mapping corresponds to actual production relationship to a reasonable extent.

Sectoral Co-movements in the Indian Stock Market: A Mesoscopic Network Analysis

In this paper, we review some of the properties of financial and other spatio-temporal time series generated from coupled map lattices, GARCH(1,1) processes and random processes (for which analytical results are known). We use the Hurst exponent (R/S analysis) and detrended fluctuation analysis as the tools to study the long-time correlations in the time series. We also compare the eigenvalue properties of the empirical correlation matrices, especially in relation to random matrices.

Financial and Other Spatio-Temporal Time Series:. Long-Range Correlations and Spectral Properties

In this paper we discuss some examples of systems composed of $N$ units, which exchange a conserved quantity $x$ according to some given stochastic rule, from some standard kinetic model of condensed matter physics to the kinetic exchange models used for studying the wealth dynamics of social systems. The focus is on the similarity of the equilibrium state of the various examples considered, which all relax toward a canonical Gibbs-Boltzmann equilibrium distribution for the quantity $x$, given by a $\Gamma$-distribution with shape parameter $\alpha = D/2$, which implicitly defines an effective dimension $D$ of the system. We study various systems exploring (continuous) values of $D$ in the interval $[1,\infty)$.

Thermal Equilibrium in D-dimensions: From Fluids and Polymers to Kinetic Wealth Exchange Models

We present an analytical method of studying "extended" electronic eigenstates of a diamond hierarchical lattice, which may be taken as the simplest of the hierarchical models recently proposed for stretched polymers. We use intuitive arguments and a renormalization-group method to determine the distribution of amplitudes of the wave functions corresponding to some of these "extended" eigenstates. An exact analysis of the end-to-end transmission property of arbitrarily large finite lattices reveals an anomalous behavoiur. It is seen that while for a special value of the energy the lattice, however large, becomes completely transparent to an incoming electron, for the other energy eigenvalues the transmission decreases with system size. For one such energy eigenvalue we analytically obtain the precise scaling form of the transmission coefficient. The same method can easily be adopted for other energies.

/pdf/anomalous-transmission-in-a-hierarchical-lattice-2wv7gp8pw2.pdf

Anomalous Transmission in a Hierarchical Lattice

In the framework of complexity theory, which provides a unified framework for natural and social sciences, we study the complex and interesting problem of the internal structure, similarities, and differences between the Mazatec dialects, an endangered Otomanguean language spoken in south-east Mexico. The analysis is based on some databases which are used to compute linguistic distances between the dialects. The results are interpreted in the light of linguistics as well as statistical considerations and used to infer the history of the development of the observed pattern of diversity.

Anirban Chakraborti

Papers

Sectoral Co-movements in the Indian Stock Market: A Mesoscopic Network Analysis

Financial and Other Spatio-Temporal Time Series:. Long-Range Correlations and Spectral Properties

Thermal Equilibrium in D-dimensions: From Fluids and Polymers to Kinetic Wealth Exchange Models

Anomalous Transmission in a Hierarchical Lattice

Patterns of Linguistic Diffusion in Space and Time: The Case of Mazatec