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

The time dependence of the recently introduced minimum spanning tree description of correlations between stocks, called the ‘‘asset tree’’ has been studied in order to reflect the financial market taxonomy. The nodes of the tree are identified with stocks and the distance between them is a unique function of the corresponding element of the correlation matrix. By using the concept of a central vertex, chosen as the most strongly connected node of the tree, an important characteristic is defined by the mean occupation layer. During crashes, due to the strong global correlation in the market, the tree shrinks topologically, and this is shown by a low value of the mean occupation layer . The tree seems to have a scale-free structure where the scaling exponent of the degree distribution is different for ‘‘business as usual’’ and ‘‘crash’’ periods. The basic structure of the tree topology is very robust with respect to time. We also point out that the diversification aspect of portfolio optimization results in the fact that the assets of the classic Markowitz portfolio are always located on the outer leaves of the tree. Technical aspects such as the window size dependence of the investigated quantities are also discussed.

/pdf/dynamics-of-market-correlations-taxonomy-and-portfolio-1sjj6k2bg9.pdf

Dynamics of market correlations: taxonomy and portfolio analysis.

We consider a simple model of a closed economic system where the total money is conserved and the number of economic agents is fixed. Analogous to statistical systems in equilibrium, money and the average money per economic agent are equivalent to energy and temperature, respectively. We investigate the effect of the saving propensity of the agents on the stationary or equilibrium probability distribution of money. When the agents do not save, the equilibrium money distribution becomes the usual Gibb's distribution, characteristic of non-interacting agents. However with saving, even for individual self-interest, the dynamics becomes cooperative and the resulting asymmetric Gaussian-like stationary distribution acquires global ordering properties. Intriguing singularities are observed in the stationary money distribution in the market, as functions of the marginal saving propensity of the agents.

/pdf/statistical-mechanics-of-money-how-saving-propensity-affects-1z8m2ljcay.pdf

Statistical mechanics of money: how saving propensity affects its distribution

The minimum spanning tree, based on the concept of ultrametricity, is constructed from the correlation matrix of stock returns. The dynamics of this asset tree can be characterised by its normalised length and the mean occupation layer, as measured from an appropriately chosen centre called the ‘central node’. We show how the tree length shrinks during a stock market crisis, Black Monday in this case, and how a strong reconfiguration takes place, resulting in topological shrinking of the tree.

/pdf/dynamic-asset-trees-and-black-monday-2s65hu004b.pdf

Dynamic asset trees and Black Monday

This article and the companion paper aim at reviewing recent empirical and theoretical developments usually grouped under the term Econophysics. Since the name was coined in 1995 by merging the words ‘Economics’ and ‘Physics’, this new interdisciplinary field has grown in various directions: theoretical macroeconomics (wealth distribution), microstructure of financial markets (order book modeling), econometrics of financial bubbles and crashes, etc. We discuss the interactions between Physics, Mathematics, Economics and Finance that led to the emergence of Econophysics. We then present empirical studies revealing the statistical properties of financial time series. We begin the presentation with the widely acknowledged ‘stylized facts’, which describe the returns of financial assets—fat tails, volatility clustering, autocorrelation, etc.—and recall that some of these properties are directly linked to the way ‘time’ is taken into account. We continue with the statistical properties observed on order books ...

/pdf/econophysics-review-i-empirical-facts-v4458xh4qk.pdf

Econophysics review: I. Empirical facts

Preface. List of Contributors. 1 A Thermodynamic Formulation of Economics (Juergen Mimkes). 1.1 Introduction. 1.2 Differential Forms. 1.3 The First Law of Economics. 1.4 The Second Law of Economics. 1.5 Statistics. 1.6 Entropy in Economics. 1.7 Mechanism of Production and Trade. 1.8 Dynamics of Production: Economic Growth. 1.9 Conclusion. References. 2 Zero-intelligence Models of Limit-order Markets (Robin Stinchcombe). 2.1 Introduction. 2.2 Possible Zero-intelligence Models. 2.3 Data Analysis and Empirical Facts Regarding Statics. 2.4 Dynamics: Processes, Rates, and Relationships. 2.5 Resulting Model. 2.6 Results from the Model. 2.7 Analytic Studies: Introduction and Mean-field Approach. 2.8 Random-walk Analyses. 2.9 Independent Interval Approximation. 2.10 Concluding Discussion. References. 3 Understanding and Managing the Future Evolution of a Competitive Multi-agent Population (DavidM.D. Smith and Neil F. Johnson). 3.1 Introduction. 3.2 A Game of Two Dice. 3.3 Formal Description of the System's Evolution. 3.4 Binary Agent Resource System. 3.5 Natural Evolution: No System Management. 3.6 Evolution Management via Perturbations to Population's Composition. 3.7 Reducing the Future-Cast Formalism. 3.8 Concluding Remarks and Discussion. References. 4 Growth of Firms and Networks (Yoshi Fujiwara, Hideaki Aoyama, and Wataru Souma). 4.1 Introduction. 4.2 Growth of Firms.1 4.3 Pareto-Zipf and Gibrat under Detailed Balance. 4.4 Small and Mid-sized Firms. 4.5 Network of Firms. 4.6 Conclusion. References. 5 A Review of Empirical Studies and Models of Income Distributions in Society (Peter Richmond, Stefan Hutzler, Ricardo Coelho, and Przemek Repetowicz). 5.1 Introduction. 5.2 Pareto and Early Models of Wealth Distribution. 5.3 Current Studies. 5.4 A Case Study of UK Income Data. 5.5 Conclusions. References. 6 Models of Wealth Distributions - A Perspective (Abhijit Kar Gupta). 6.1 Introduction. 6.2 Pure Gambling. 6.3 Uniform Saving Propensity. 6.4 Distributed Saving Propensity. 6.5 Understanding by Means of the Transition Matrix. 6.6 Role of Selective Interaction. 6.7 Measure of Inequality. 6.8 Distribution by Maximizing Inequality. 6.9 Confusions and Conclusions. References. 7 The Contribution of Money-transfer Models to Economics (Yougui Wang, Ning Xi, and Ning Ding). 7.1 Introduction. 7.2 Understanding Monetary Circulation. 7.3 Inspecting Money Creation and its Impacts. 7.4 Refining Economic Mobility. 7.5 Summary. References. 8 Fluctuations in Foreign Exchange markets (Yukihiro Aiba and Naomichi Hatano). 8.1 Introduction. 8.2 Modeling Financial Fluctuations with Concepts of Statistical Physics. 8.3 Triangular Arbitrage as an Interaction among Foreign Exchange Rates. 8.4 A MacroscopicModel of a Triangular Arbitrage Transaction. 8.5 A Microscopic Model of Triangular Arbitrage Transaction. 8.6 Summary. References. 9 Econophysics of Stock and Foreign Currency Exchange Markets (Marcel Ausloos). 9.1 A Few Robust Techniques 251 9.2 Statistical, Phenomenological and "Microscopic" Models. 9.3 The Lux-MarchesiModel. References. 10 A Thermodynamic Formulation of Social Science (Juergen Mimkes). 10.1 Introduction. 10.2 Probability. 10.3 Elements of Societies. 10.4 Homogenious Societies. 10.5 Heterogeneous Societies. 10.6 Dynamics of Societies. 10.7 Conclusion. References. 11 Computer Simulation of Language Competition by Physicists (Christian Schulze and Dietrich Stauffer). 11.1 Introduction. 11.2 Differential Equations. 11.3 Microscopic Models. 11.4 Conclusion. 11.5 Appendix. References. 12 Social Opinion Dynamics (Gerard Weisbuch). 12.1 Introduction. 12.2 Binary Opinions. 12.3 Continuous Opinion Dynamics. 12.4 Diffusion of Culture. 12.5 Conclusions. References. 13 Opinion Dynamics, Minority Spreading and Heterogeneous Beliefs (Serge Galam). 13.1 The Interplay of Rational Choices and Beliefs. 13.2 Rumors and Collective Opinions in a PerfectWorld. 13.3 Arguing by Groups of Size Three. 13.4 Arguing by Groups of Size Four. 13.5 Contradictory Public Opinions in Similar Areas. 13.6 Segregation, Democratic Extremism and Coexistence. 13.7 Arguing in Groups of Various Sizes. 13.8 The Model is Capable of Predictions. 13.9 Sociophysics is a Promising Field. References. 14 Global Terrorism versus Social Permeability to Underground Activities (Serge Galam). 14.1 Terrorism and Social Permeability. 14.2 A Short Introduction to Percolation. 14.3 Modeling a Complex Problem as Physicists do. 14.4 TheWorld Social Grid. 14.5 Passive Supporters and Open Spaces to Terrorists. 14.6 The Geometry of Terrorism is Volatile. 14.7 From the Model to Some Real Facts of Terrorism. 14.8 When Regional Terrorism Turns Global. 14.9 The Situation Seems Hopeless. 14.10 Reversing the Strategy from Military to Political. 14.11 Conclusion and Some Hints for the Future. References. 15 How a "Hit" is Born: The Emergence of Popularity from the Dynamics of Collective Choice (Sitabhra Sinha and Raj Kumar Pan). 15.1 Introduction. 15.2 Empirical Popularity Distributions. 15.3 Models of Popularity Distribution. 15.4 Conclusions. References. 16 Crowd Dynamics (Anders Johansson and Dirk Helbing). 16.1 Pedestrian Modeling: A Survey. 16.2 Self-organization. 16.3 Other Collective Crowd Phenomena. 16.4 Bottlenecks. 16.5 Optimization. 16.6 Summary and Selected Applications. References. 17 Complexities of Social Networks: A Physicist's Perspective (Parongama Sen). 17.1 Introduction. 17.2 The Beginning: Milgram's Experiments. 17.3 Topological Properties of Networks. 17.4 Some Prototypes of Small-world Networks. 17.5 Social Networks: Classification and Examples. 17.6 Distinctive Features of Social Networks. 17.7 Community Structure in Social Networks. 17.8 Models of Social Networks. 17.9 Is it Really a SmallWorld? Searching: Post Milgram. 17.10 Endnote. 17.11 Appendix: The Indian Railways Network. References. 18 Emergence of Memory in Networks of Nonlinear Units: From Neurons to Plant Cells (Jun-ichi Inoue). 18.1 Introduction. 18.2 Neural Networks. 18.3 Summary: Neural Networks. 18.4 Plant Intelligence: Brief Introduction. 18.5 The I-V Characteristics of Cell Membranes. 18.6 A Solvable Plant-intelligence Model and its Replica Analysis. 18.7 Summary and Discussion. References. 19 Self-organization Principles in Supply Networks and Production Systems (Dirk Helbing, Thomas Seidel, Stefan Lammer, and Karsten Peters). 19.1 Introduction. 19.2 Complex Dynamics and Chaos. 19.3 The Slower-is-faster Effect. 19.4 Adaptive Control. 19.5 Summary and Outlook. References. 20 Can we Recognize an Innovation?: Perspective from an Evolving Network Model (Sanjay Jain and Sandeep Krishna). 20.1 Introduction. 20.2 A Framework for Modeling Innovation: Graph Theory and Dynamical Systems. 20.3 Definition of the Model System. 20.4 Time Evolution of the System. 20.5 Innovation. 20.6 Six Categories of Innovation. 20.7 Recognizing Innovations: A Structural Classification. 20.8 Some Possible General Lessons. 20.9 Discussion. 20.10 Appendix A: Definitions and Proofs. 20.11 Appendix B: Graph-theoretic Classification of Innovations. References. Color Plates. Subject Index. Author Index.

Anirban Chakraborti

Papers

Dynamics of market correlations: taxonomy and portfolio analysis.

Statistical mechanics of money: how saving propensity affects its distribution

Dynamic asset trees and Black Monday

Econophysics review: I. Empirical facts

Econophysics and Sociophysics : Trends and Perspectives