Lecture 13: Financial Disasters and Econophysics
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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. -
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. -
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. -
An Application of Econophysics to the History of Economic Thought: the Analysis of Texts from the Frequency of Appearance of Key Words
Discussion Paper No. 2015-51 | July 15, 2015 | http://www.economics-ejournal.org/economics/discussionpapers/2015-51 An Application of Econophysics to the History of Economic Thought: The Analysis of Texts from the Frequency of Appearance of Key Words Estrella Trincado and José María Vindel Abstract This article poses a new methodology applying the statistical analysis to the economic literature. This analysis has never been used in the history of economic thought, albeit it may open up new possibilities and provide us with further explanations so as to reconsider theoretical issues. With that purpose in mind, the article applies the intermittency of the turbulence in different economic texts, and specifically in three important authors: William Stanley Jevons, Adam Smith, and Karl Marx. JEL B16 B40 C18 Z11 Keywords Econophysics; history of economic thought; bibliometrics; applications of statistical analysis Authors Estrella Trincado, Universidad Complutense de Madrid, Spain, [email protected] José María Vindel, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, Madrid, Spain Citation Estrella Trincado and José María Vindel (2015). An Application of Econophysics to the History of Economic Thought: The Analysis of Texts from the Frequency of Appearance of Key Words. Economics Discussion Papers, No 2015-51, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2015-51 Received July 7, 2015 Accepted as Economics Discussion Paper July 13, 2015 Published July 15, 2015 © Author(s) 2015. Licensed under the Creative Commons License - Attribution 3.0 1. INTRODUCTION The most obvious and usual way to deal with economic texts is to try to understand in an analytical way the theories put forward by the authors providing a scientific, social and economic context for that specific literature. -
A Critique of Econophysics
Munich Personal RePEc Archive Toolism! A Critique of Econophysics Kakarot-Handtke, Egmont University of Stuttgart, Institute of Economics and Law 30 April 2013 Online at https://mpra.ub.uni-muenchen.de/46630/ MPRA Paper No. 46630, posted 30 Apr 2013 13:04 UTC Toolism! A Critique of Econophysics Egmont Kakarot-Handtke* Abstract Economists are fond of the physicists’ powerful tools. As a popular mindset Toolism is as old as economics but the transplants failed to produce the same successes as in their aboriginal environment. Economists therefore looked more and more to the math department for inspiration. Now the tide turns again. The ongoing crisis discredits standard economics and offers the chance for a comeback. Modern econophysics commands the most powerful tools and argues that there are many occasions for their application. The present paper argues that it is not a change of tools that is most urgently needed but a paradigm change. JEL A12, B16, B41 Keywords new framework of concepts; structure-centric; axiom set; paradigm; income; profit; money; invariance principle *Affiliation: University of Stuttgart, Institute of Economics and Law, Keplerstrasse 17, D-70174 Stuttgart. Correspondence address: AXEC, Egmont Kakarot-Handtke, Hohenzollernstraße 11, D- 80801 München, Germany, e-mail: [email protected] 1 1 Powerful tools When Arnold Schwarzenegger, in his most popular roles, has seen and suffered enough evil he makes up his mind and first of all breaks into a gun store. With the eyes of an expert he spots the most suitable devices for the upcoming tasks. When he leaves the store with maximum firepower and determination we can rely upon that in the sequel humankind will be better off. -
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. -
Percolation Theory Are Well-Suited To
Models of Disordered Media and Predictions of Associated Hydraulic Conductivity A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science By L AARON BLANK B.S., Wright State University, 2004 2006 Wright State University WRIGHT STATE UNIVERSITY SCHOOL OF GRADUATE STUDIES Novermber 6, 2006 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY L Blank ENTITLED Models of Disordered Media and Predictions of Associated Hydraulic Conductivity BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science. _______________________ Allen Hunt, Ph.D. Thesis Advisor _______________________ Lok Lew Yan Voon, Ph.D. Department Chair _______________________ Joseph F. Thomas, Jr., Ph.D. Dean of the School of Graduate Studies Committee on Final Examination ____________________ Allen Hunt, Ph.D. ____________________ Brent D. Foy, Ph.D. ____________________ Gust Bambakidis, Ph.D. ____________________ Thomas Skinner, Ph.D. Abstract In the late 20th century there was a spill of Technetium in eastern Washington State at the US Department of Energy Hanford site. Resulting contamination of water supplies would raise serious health issues for local residents. Therefore, the ability to predict how these contaminants move through the soil is of great interest. The main contribution to contaminant transport arises from being carried along by flowing water. An important control on the movement of the water through the medium is the hydraulic conductivity, K, which defines the ease of water flow for a given pressure difference (analogous to the electrical conductivity). The overall goal of research in this area is to develop a technique which accurately predicts the hydraulic conductivity as well as its distribution, both in the horizontal and the vertical directions, for media representative of the Hanford subsurface. -
Econophysics Point of View of Trade Liberalization: Community Dynamics, Synchronization, and Controllability As Example of Collective Motions
DPRIETI Discussion Paper Series 16-E-026 Econophysics Point of View of Trade Liberalization: Community dynamics, synchronization, and controllability as example of collective motions IKEDA Yuichi AOYAMA Hideaki Kyoto University RIETI IYETOMI Hiroshi MIZUNO Takayuki Niigata University National Institute of Informatics OHNISHI Takaaki SAKAMOTO Yohei University of Tokyo Kyoto University WATANABE Tsutomu University of Tokyo The Research Institute of Economy, Trade and Industry http://www.rieti.go.jp/en/ RIETI Discussion Paper Series 16-E-026 March 2016 Econophysics Point of View of Trade Liberalization: Community dynamics, synchronization, and controllability as example of collective motions* IKEDA Yuichi 1, AOYAMA Hideaki 2 IYETOMI Hiroshi 3, MIZUNO Takayuki 4, OHNISHI Takaaki 5, SAKAMOTO Yohei2, WATANABE Tsutomu 6 1 Graduate School of Advanced Integrated Studies in Human Survivability, Kyoto University, 2 Graduate School of Science, Kyoto University 3 Graduate School of Science and Technology, Niigata University 4 Information and Society Research Division, National Institute of Informatics, 5 Graduate School of Information Science and Technology, University of Tokyo 6 Graduate School of Economics, University of Tokyo Abstract In physics, it is known that various collective motions exist. For instance, a large deformation of heavy nuclei at a highly excited state, which subsequently proceeds to fission, is a typical example. This phenomenon is a quantum mechanical collective motion due to strong nuclear force between nucleons in a microscopic system consisting of a few hundred nucleons. Most national economies are linked by international trade and consequently economic globalization forms a giant economic complex network with strong links, i.e., interactions due to increasing trade. In Japan, many small and medium enterprises could achieve higher economic growth by free trade based on the establishment of an economic partnership agreement (EPA), such as the Trans-Pacific Partnership (TPP). -
Econophysics: a Brief Review of Historical Development, Present Status and Future Trends
1 Econophysics: A Brief Review of Historical Development, Present Status and Future Trends. B.G.Sharma Sadhana Agrawal Department of Physics and Computer Science, Department of Physics Govt. Science College Raipur. (India) NIT Raipur. (India) [email protected] [email protected] Malti Sharma WQ-1, Govt. Science College Raipur. (India) [email protected] D.P.Bisen SOS in Physics, Pt. Ravishankar Shukla University Raipur. (India) [email protected] Ravi Sharma Devendra Nagar Girls College Raipur. (India) [email protected] Abstract: The conventional economic 1. Introduction: approaches explore very little about the dynamics of the economic systems. Since such How is the stock market like the cosmos systems consist of a large number of agents or like the nucleus of an atom? To a interacting nonlinearly they exhibit the conservative physicist, or to an economist, properties of a complex system. Therefore the the question sounds like a joke. It is no tools of statistical physics and nonlinear laughing matter, however, for dynamics has been proved to be very useful Econophysicists seeking to plant their flag in the underlying dynamics of the system. In the field of economics. In the past few years, this paper we introduce the concept of the these trespassers have borrowed ideas from multidisciplinary field of econophysics, a quantum mechanics, string theory, and other neologism that denotes the activities of accomplishments of physics in an attempt to Physicists who are working on economic explore the divine undiscovered laws of problems to test a variety of new conceptual finance. They are already tallying what they approaches deriving from the physical science say are important gains. -
Response to “Worrying Trends in Econophysics” Joseph L. Mccauley Physics Department University of Houston Houston, Tx. 77204
Response to “Worrying Trends in Econophysics” Joseph L. McCauley Physics Department University of Houston Houston, Tx. 77204 [email protected] and Senior Fellow COBERA Department of Economics J.E.Cairnes Graduate School of Business and Public Policy NUI Galway, Ireland Abstract This article is a response to the recent “Worrying Trends in Econophysics” critique written by four respected theoretical economists [1]. Two of the four have written books and papers that provide very useful critical analyses of the shortcomings of the standard textbook economic model, neo-classical economic theory [2,3] and have even endorsed my book [4]. Largely, their new paper reflects criticism that I have long made [4,5,6,7,] and that our group as a whole has more recently made [8]. But I differ with the authors on some of their criticism, and partly with their proposed remedy. 1. Money, conservation laws, and neo-classical economics Our concerns are fourfold. First, a lack of awareness of work which has been done within economics itself. Second, resistance to more rigorous and robust statistical methodology. Third, the belief that universal empirical regularities can be found in many areas of economic activity. Fourth, the theoretical models which are being used to explain empirical phenomena. The latter point is of particular concern. Essentially, the models are based upon models of statistical physics in which energy is conserved in exchange processes. Gallegati, Keen, Lux, and Ormerod [1] Since the authors of “Worrying” [1] begin with an attack on assumptions of conservation of money and analogs of conservation of energy in economic modelling, let me state from the outset that it would generally be quite useless to assume conserved quantities in economics and finance (see [4], Ch.