Physica a Econophysics and Sociophysics
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Lecture 13: Financial Disasters and Econophysics
Lecture 13: Financial Disasters and Econophysics Big problem: Power laws in economy and finance vs Great Moderation: (Source: http://www.mckinsey.com/business-functions/strategy-and-corporate-finance/our-insights/power-curves-what- natural-and-economic-disasters-have-in-common Analysis of big data, discontinuous change especially of financial sector, where efficient market theory missed the boat has drawn attention of specialists from physics and mathematics. Wall Street“quant”models may have helped the market implode; and collapse spawned econophysics work on finance instability. NATURE PHYSICS March 2013 Volume 9, No 3 pp119-197 : “The 2008 financial crisis has highlighted major limitations in the modelling of financial and economic systems. However, an emerging field of research at the frontiers of both physics and economics aims to provide a more fundamental understanding of economic networks, as well as practical insights for policymakers. In this Nature Physics Focus, physicists and economists consider the state-of-the-art in the application of network science to finance.” The financial crisis has made us aware that financial markets are very complex networks that, in many cases, we do not really understand and that can easily go out of control. This idea, which would have been shocking only 5 years ago, results from a number of precise reasons. What does physics bring to social science problems? 1- Heterogeneous agents – strange since physics draws strength from electron is electron is electron but STATISTICAL MECHANICS --- minority game, finance artificial agents, 2- Facility with huge data sets – data-mining for regularities in time series with open eyes. 3- Network analysis 4- Percolation/other models of “phase transition”, which directs attention at boundary conditions AN INTRODUCTION TO ECONOPHYSICS Correlations and Complexity in Finance ROSARIO N. -
Processes on Complex Networks. Percolation
Chapter 5 Processes on complex networks. Percolation 77 Up till now we discussed the structure of the complex networks. The actual reason to study this structure is to understand how this structure influences the behavior of random processes on networks. I will talk about two such processes. The first one is the percolation process. The second one is the spread of epidemics. There are a lot of open problems in this area, the main of which can be innocently formulated as: How the network topology influences the dynamics of random processes on this network. We are still quite far from a definite answer to this question. 5.1 Percolation 5.1.1 Introduction to percolation Percolation is one of the simplest processes that exhibit the critical phenomena or phase transition. This means that there is a parameter in the system, whose small change yields a large change in the system behavior. To define the percolation process, consider a graph, that has a large connected component. In the classical settings, percolation was actually studied on infinite graphs, whose vertices constitute the set Zd, and edges connect each vertex with nearest neighbors, but we consider general random graphs. We have parameter ϕ, which is the probability that any edge present in the underlying graph is open or closed (an event with probability 1 − ϕ) independently of the other edges. Actually, if we talk about edges being open or closed, this means that we discuss bond percolation. It is also possible to talk about the vertices being open or closed, and this is called site percolation. -
From Big Data to Econophysics and Its Use to Explain Complex Phenomena
Journal of Risk and Financial Management Review From Big Data to Econophysics and Its Use to Explain Complex Phenomena Paulo Ferreira 1,2,3,* , Éder J.A.L. Pereira 4,5 and Hernane B.B. Pereira 4,6 1 VALORIZA—Research Center for Endogenous Resource Valorization, 7300-555 Portalegre, Portugal 2 Department of Economic Sciences and Organizations, Instituto Politécnico de Portalegre, 7300-555 Portalegre, Portugal 3 Centro de Estudos e Formação Avançada em Gestão e Economia, Instituto de Investigação e Formação Avançada, Universidade de Évora, Largo dos Colegiais 2, 7000 Évora, Portugal 4 Programa de Modelagem Computacional, SENAI Cimatec, Av. Orlando Gomes 1845, 41 650-010 Salvador, BA, Brazil; [email protected] (É.J.A.L.P.); [email protected] (H.B.B.P.) 5 Instituto Federal do Maranhão, 65075-441 São Luís-MA, Brazil 6 Universidade do Estado da Bahia, 41 150-000 Salvador, BA, Brazil * Correspondence: [email protected] Received: 5 June 2020; Accepted: 10 July 2020; Published: 13 July 2020 Abstract: Big data has become a very frequent research topic, due to the increase in data availability. In this introductory paper, we make the linkage between the use of big data and Econophysics, a research field which uses a large amount of data and deals with complex systems. Different approaches such as power laws and complex networks are discussed, as possible frameworks to analyze complex phenomena that could be studied using Econophysics and resorting to big data. Keywords: big data; complexity; networks; stock markets; power laws 1. Introduction Big data has become a very popular expression in recent years, related to the advance of technology which allows, on the one hand, the recovery of a great amount of data, and on the other hand, the analysis of that data, benefiting from the increasing computational capacity of devices. -
The Physical Modelling of Society: a Historical Perspective
Physica A 314 (2002) 1–14 www.elsevier.com/locate/physa The physical modelling ofsociety: a historical perspective Philip Ball Nature, 4-6 Crinan St, London N1 9XW, UK Abstract By seeking to uncover the rules ofcollective human activities, today’s statistical physicists are aiming to return to their roots. Statistics originated in the study ofsocial numbers in the 17th century, and the discovery ofstatistical invariants in data on births and deaths, crimes and marriages led some scientists and philosophers to conclude that society was governed by immutable “natural” laws beyond the reach ofgovernments, ofwhich the Gaussian “error curve” became regarded as the leitmotif. While statistics .ourished as a mathematical tool of all the sciences in the 19th century, it provoked passionate responses from philosophers, novelists and social commentators. Social statistics also guided Maxwell and Boltzmann towards the utilization ofprobability distributions in the development ofthe kinetic theory ofgases, the foundationof statistical mechanics. c 2002 Elsevier Science B.V. All rights reserved. Keywords: Statistics; History ofphysics; Statistical mechanics; Social science; Gaussian 1. Introduction The introduction ofprobability into the fundamentalnature ofthe quantum world by Bohr, Born and Schr8odinger in the 1920s famously scandalized some scholars ofscience’s philosophical foundations.But arguments about chance, probability and determinism were no less heated in the mid-19th century, when statistical ideas entered classical physics. James Clerk Maxwell (1878) let probabilistic physics bring him to the verge of mysticism: “it is the peculiar function of physical science to lead us to the conÿnes of the incomprehensible, and to bid us behold and receive it in faith, till such time as the E-mail address: [email protected] (P. -
John Von Neumann Between Physics and Economics: a Methodological Note
Review of Economic Analysis 5 (2013) 177–189 1973-3909/2013177 John von Neumann between Physics and Economics: A methodological note LUCA LAMBERTINI∗y University of Bologna A methodological discussion is proposed, aiming at illustrating an analogy between game theory in particular (and mathematical economics in general) and quantum mechanics. This analogy relies on the equivalence of the two fundamental operators employed in the two fields, namely, the expected value in economics and the density matrix in quantum physics. I conjecture that this coincidence can be traced back to the contributions of von Neumann in both disciplines. Keywords: expected value, density matrix, uncertainty, quantum games JEL Classifications: B25, B41, C70 1 Introduction Over the last twenty years, a growing amount of attention has been devoted to the history of game theory. Among other reasons, this interest can largely be justified on the basis of the Nobel prize to John Nash, John Harsanyi and Reinhard Selten in 1994, to Robert Aumann and Thomas Schelling in 2005 and to Leonid Hurwicz, Eric Maskin and Roger Myerson in 2007 (for mechanism design).1 However, the literature dealing with the history of game theory mainly adopts an inner per- spective, i.e., an angle that allows us to reconstruct the developments of this sub-discipline under the general headings of economics. My aim is different, to the extent that I intend to pro- pose an interpretation of the formal relationships between game theory (and economics) and the hard sciences. Strictly speaking, this view is not new, as the idea that von Neumann’s interest in mathematics, logic and quantum mechanics is critical to our understanding of the genesis of ∗I would like to thank Jurek Konieczny (Editor), an anonymous referee, Corrado Benassi, Ennio Cavaz- zuti, George Leitmann, Massimo Marinacci, Stephen Martin, Manuela Mosca and Arsen Palestini for insightful comments and discussion. -
Black Swans, Dragons-Kings and Prediction
Black Swans, Dragons-Kings and Prediction Professor of Entrepreneurial Risks Didier SORNETTE Professor of Geophysics associated with the ETH Zurich Department of Earth Sciences (D-ERWD), ETH Zurich Professor of Physics associated with the Department of Physics (D-PHYS), ETH Zurich Professor of Finance at the Swiss Finance Institute Director of the Financial Crisis Observatory co-founder of the Competence Center for Coping with Crises in Socio-Economic Systems, ETH Zurich (http://www.ccss.ethz.ch/) Black Swan (Cygnus atratus) www.er.ethz.ch EXTREME EVENTS in Natural SYSTEMS •Earthquakes •Volcanic eruptions •Hurricanes and tornadoes •Landslides, mountain collapses •Avalanches, glacier collapses •Lightning strikes •Meteorites, asteroid impacts •Catastrophic events of environmental degradations EXTREME EVENTS in SOCIO-ECONOMIC SYSTEMS •Failure of engineering structures •Crashes in the stock markets •Social unrests leading to large scale strikes and upheavals •Economic recessions on regional and global scales •Power blackouts •Traffic gridlocks •Social epidemics •Block-busters •Discoveries-innovations •Social groups, cities, firms... •Nations •Religions... Extreme events are epoch changing in the physical structure and in the mental spaces • Droughts and the collapse of the Mayas (760-930 CE)... and many others... • French revolution (1789) and the formation of Nation states • Great depression and Glass-Steagall act • Crash of 19 Oct. 1987 and volatility smile (crash risk) • Enron and Worldcom accounting scandals and Sarbanes-Oxley (2002) • Great Recession 2007-2009: consequences to be4 seen... The Paradox of the 2007-20XX Crisis (trillions of US$) 2008 FINANCIAL CRISIS 6 Jean-Pierre Danthine: Swiss monetary policy and Target2-Securities Introductory remarks by Mr Jean-Pierre Danthine, Member of the Governing Board of the Swiss National Bank, at the end-of-year media news conference, Zurich, 16 December 2010. -
Understanding Complex Systems: a Communication Networks Perspective
1 Understanding Complex Systems: A Communication Networks Perspective Pavlos Antoniou and Andreas Pitsillides Networks Research Laboratory, Computer Science Department, University of Cyprus 75 Kallipoleos Street, P.O. Box 20537, 1678 Nicosia, Cyprus Telephone: +357-22-892687, Fax: +357-22-892701 Email: [email protected], [email protected] Technical Report TR-07-01 Department of Computer Science University of Cyprus February 2007 Abstract Recent approaches on the study of networks have exploded over almost all the sciences across the academic spectrum. Over the last few years, the analysis and modeling of networks as well as networked dynamical systems have attracted considerable interdisciplinary interest. These efforts were driven by the fact that systems as diverse as genetic networks or the Internet can be best described as complex networks. On the contrary, although the unprecedented evolution of technology, basic issues and fundamental principles related to the structural and evolutionary properties of networks still remain unaddressed and need to be unraveled since they affect the function of a network. Therefore, the characterization of the wiring diagram and the understanding on how an enormous network of interacting dynamical elements is able to behave collectively, given their individual non linear dynamics are of prime importance. In this study we explore simple models of complex networks from real communication networks perspective, focusing on their structural and evolutionary properties. The limitations and vulnerabilities of real communication networks drive the necessity to develop new theoretical frameworks to help explain the complex and unpredictable behaviors of those networks based on the aforementioned principles, and design alternative network methods and techniques which may be provably effective, robust and resilient to accidental failures and coordinated attacks. -
The Social Physics Collective Matjaž Perc 1,2,3 Editorial More Than Two Centuries Ago Henri De Saint-Simon Envisaged Physical Laws to Describe Human Societies
www.nature.com/scientificreports OPEN The social physics collective Matjaž Perc 1,2,3 EDITORIAL More than two centuries ago Henri de Saint-Simon envisaged physical laws to describe human societies. Driven by advances in statistical physics, network science, data analysis, and information technology, this vision is becoming a reality. Many of the grandest challenges of our time are of a societal nature, and methods of physics are increasingly playing a central role in improving our understanding of these challenges, and helping us to fnd innovative solutions. The Social physics Collection at Scientifc Reports is dedicated to this research. lthough we are unique and hardly predictable as individuals, research has shown that in a collective we ofen behave no diferently than particles in matter1. Indeed, many aspects of collective behavior in human societies have turned out to be remarkably predictable, and this fact has paved the way for methods of Aphysics to be applied to many contemporary societal challenges. Examples include trafc2, crime3, epidemic pro- cesses4, vaccination5, cooperation6, climate inaction7, as well as antibiotic overuse8 and moral behavior9, to name just some examples. In fact, possible synergies between physical and social sciences have been foating around in the scientifc literature for centuries. Over two centuries ago, the French political and economic theorist Henri de Saint-Simon was amongst the frst to propose that society could be described by laws similar to those in physics10. However, similar ideas have been around already in the 17th century, when Tomas Hobbes based his theory of the state on the laws of motion, in particular on the principle of inertia, which was then deduced by his contemporary Galileo Galilei11. -
Critical Percolation As a Framework to Analyze the Training of Deep Networks
Published as a conference paper at ICLR 2018 CRITICAL PERCOLATION AS A FRAMEWORK TO ANALYZE THE TRAINING OF DEEP NETWORKS Zohar Ringel Rodrigo de Bem∗ Racah Institute of Physics Department of Engineering Science The Hebrew University of Jerusalem University of Oxford [email protected]. [email protected] ABSTRACT In this paper we approach two relevant deep learning topics: i) tackling of graph structured input data and ii) a better understanding and analysis of deep networks and related learning algorithms. With this in mind we focus on the topological classification of reachability in a particular subset of planar graphs (Mazes). Doing so, we are able to model the topology of data while staying in Euclidean space, thus allowing its processing with standard CNN architectures. We suggest a suitable architecture for this problem and show that it can express a perfect solution to the classification task. The shape of the cost function around this solution is also derived and, remarkably, does not depend on the size of the maze in the large maze limit. Responsible for this behavior are rare events in the dataset which strongly regulate the shape of the cost function near this global minimum. We further identify an obstacle to learning in the form of poorly performing local minima in which the network chooses to ignore some of the inputs. We further support our claims with training experiments and numerical analysis of the cost function on networks with up to 128 layers. 1 INTRODUCTION Deep convolutional networks have achieved great success in the last years by presenting human and super-human performance on many machine learning problems such as image classification, speech recognition and natural language processing (LeCun et al. -
Social Thermodynamics, Social Hydrodynamics and Some Mathematical Applications in Social Sciences
International Journal of Modern Social Sciences, 2013, 2(2): 94-108 International Journal of Modern Social Sciences ISSN: 2169-9917 Journal homepage: www.ModernScientificPress.com/Journals/IJMSS.aspx Florida, USA Article Social Thermodynamics, Social Hydrodynamics and Some Mathematical Applications in Social Sciences Yi-Fang Chang Department of Physics, Yunnan University, Kunming, 650091, China Email: [email protected] Article history: Received 16 May 2013, Received in revised form 17 July 2013, Accepted 18 July 2013, Published 19 July 2013. Abstract: Based on the sameness for men or any elements in the social systems, we search the social thermodynamics, and possible entropy decrease in social sciences. Next, using the similar formulas of the preference relation and the utility function, we propose the confidence relations and the corresponding influence functions that represent various interacting strengths of different families, cliques and systems of organization. This produces a multiply connected topological economics. Further, we discuss the binary periods of the political economy by the complex function and the elliptic functions. Using the nonlinear equations of hydrodynamics we may research the formulations of the binary and multiple centers in various social systems. Finally, we propose the developed directions of society and a unification of simplicity and complexity from a new tree-field representation. The application of mathematics and physics will be an important direction of modern social science at 21 century. Keywords: social science, mathematics, thermodynamics, entropy, nonlinearity, hydrodynamics, topology, complex function 1. Introduction It is long time ago that mathematics is applied in various social sciences. This may trace to its source: Chinese Yi (I Ching, or The Book of Change) and Pythagoras. -
Arxiv:1504.02898V2 [Cond-Mat.Stat-Mech] 7 Jun 2015 Keywords: Percolation, Explosive Percolation, SLE, Ising Model, Earth Topography
Recent advances in percolation theory and its applications Abbas Ali Saberi aDepartment of Physics, University of Tehran, P.O. Box 14395-547,Tehran, Iran bSchool of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5531, Tehran, Iran Abstract Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied to describe a large variety of natural, technological and social systems. Percolation models serve as important universality classes in critical phenomena characterized by a set of critical exponents which correspond to a rich fractal and scaling structure of their geometric features. We will first outline the basic features of the ordinary model. Over the years a variety of percolation models has been introduced some of which with completely different scaling and universal properties from the original model with either continuous or discontinuous transitions depending on the control parameter, di- mensionality and the type of the underlying rules and networks. We will try to take a glimpse at a number of selective variations including Achlioptas process, half-restricted process and spanning cluster-avoiding process as examples of the so-called explosive per- colation. We will also introduce non-self-averaging percolation and discuss correlated percolation and bootstrap percolation with special emphasis on their recent progress. Directed percolation process will be also discussed as a prototype of systems displaying a nonequilibrium phase transition into an absorbing state. In the past decade, after the invention of stochastic L¨ownerevolution (SLE) by Oded Schramm, two-dimensional (2D) percolation has become a central problem in probability theory leading to the two recent Fields medals. -
Predicting Porosity, Permeability, and Tortuosity of Porous Media from Images by Deep Learning Krzysztof M
www.nature.com/scientificreports OPEN Predicting porosity, permeability, and tortuosity of porous media from images by deep learning Krzysztof M. Graczyk* & Maciej Matyka Convolutional neural networks (CNN) are utilized to encode the relation between initial confgurations of obstacles and three fundamental quantities in porous media: porosity ( ϕ ), permeability (k), and tortuosity (T). The two-dimensional systems with obstacles are considered. The fuid fow through a porous medium is simulated with the lattice Boltzmann method. The analysis has been performed for the systems with ϕ ∈ (0.37, 0.99) which covers fve orders of magnitude a span for permeability k ∈ (0.78, 2.1 × 105) and tortuosity T ∈ (1.03, 2.74) . It is shown that the CNNs can be used to predict the porosity, permeability, and tortuosity with good accuracy. With the usage of the CNN models, the relation between T and ϕ has been obtained and compared with the empirical estimate. Transport in porous media is ubiquitous: from the neuro-active molecules moving in the brain extracellular space1,2, water percolating through granular soils3 to the mass transport in the porous electrodes of the Lithium- ion batteries4 used in hand-held electronics. Te research in porous media concentrates on understanding the connections between two opposite scales: micro-world, which consists of voids and solids, and the macro-scale of porous objects. Te macroscopic transport properties of these objects are of the key interest for various indus- tries, including healthcare 5 and mining6. Macroscopic properties of the porous medium rely on the microscopic structure of interconnected pore space. Te shape and complexity of pores depend on the type of medium.