Abstract

Error bars commonly appear in figures in publications, but experimental biologists are often unsure how they should be used and interpreted. In this article we illustrate some basic features of error bars and explain how they can help communicate data and assist correct interpretation. Error bars may show confidence intervals, standard errors, standard deviations, or other quantities. Different types of error bars give quite different ...

Abstract

Using the eigenvalues and eigenvectors of correlations matrices of some of the main financial market indices in the world, we show that high volatility of markets is directly linked with strong correlations between them. This means that markets tend to behave as one during great crashes. In order to do so, we investigate several financial market crises that occurred in the years 1987 (Black Monday), 1989 (Russian crisis), 2001 (Burst of the dot-com bubble and September 11), and 2008 (Subprime Mortgage Crisis), which mark some of the largest ...

Abstract

Abstract Understanding the conditions and dynamics that produce cooperation in evolving systems remains a fundamental goal of evolutionary theory. Significant progress has been made in determining the conditions that support cooperation in simple models, but the evolutionary dynamics that lead from noncooperative conditions to cooperation are still poorly understood. And, in more complex models, even the conditions that support cooperation are not well defined. In this paper we study the dynamics of the evolution of cooperation in both a simple tag-mediated ...

Abstract

Recommendation systems represent an important tool for news distribution on the Internet. In this work we modify a recently proposed social recommendation model in order to deal with no explicit ratings of users on news. The model consists of a network of users which continually adapts in order to achieve an efficient news traffic. To optimize network's topology we propose different stochastic algorithms that are scalable with respect to the network's size. Agent-based simulations reveal the features and the performance of these algorithms. To overcome the resultant drawbacks ...

Abstract

Matrix identities, relations and approximations. A desktop reference for quick overview of mathematics of matrices. ...

Note (first note only)

Version 20081110

Abstract

We demonstrate that it is possible to approximate the mutual information arbitrarily closely in probability by calculating the relative frequencies on appropriate partitions and achieving conditional independence on the rectangles of which the partitions are made. Empirical results, including a comparison with maximum-likelihood estimators, are presented ...

Abstract

Mutual information is useful for investigating the dependence between two experimental time series. It is often used to establish an appropriate time delay in phase-portrait reconstruction from time-series data. A histogram based approach has been used so far to estimate the probabilities. It is shown here that kernel density estimation of the probability density functions needed in estimating the average mutual information across two coordinates can be more effective than the histogram method of Fraser and Swinney [Phys. Rev. A 33, ...

Abstract

Motivation: Clustering co-expressed genes usually requires the definition of `distance' or `similarity' between measured datasets, the most common choices being Pearson correlation or Euclidean distance. With the size of available datasets steadily increasing, it has become feasible to consider other, more general, definitions as well. One alternative, based on information theory, is the mutual information, providing a general measure of dependencies between variables. While the use of mutual information in cluster analysis and visualization of large-scale gene expression data has been ...

Abstract

OpenGL SuperBible, Fourth Edition, begins by illuminating the core techniques of “classic” OpenGL graphics programming, from drawing in space to geometric transformations, from lighting to texture mapping. The authors cover newer OpenGL capabilities, including OpenGL 2.1’s powerful programmable pipeline, vertex and fragment shaders, and advanced buffers. They also present thorough, up-to-date introductions to OpenGL implementations on multiple platforms, including Windows, Mac OS X, GNU/Linux, UNIX, and embedded systems. Coverage includes An entirely new chapter on OpenGL ES programming for handhelds ...

Abstract

Information theory and inference, often taught separately, are here united in one entertaining textbook. These topics lie at the heart of many exciting areas of contemporary science and engineering - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics, and cryptography. This textbook introduces theory in tandem with applications. Information theory is taught alongside practical communication systems, such as arithmetic coding for data compression and sparse-graph codes for error-correction. A toolbox of inference techniques, including message-passing algorithms, Monte Carlo methods, and variational approximations, are developed alongside applications of ...

Abstract

The advent of large-scale distributed systems poses unique engineering challenges. In open systems such as the internet it is not possible to prescribe the behaviour of all of the components of the system in advance. Rather, we attempt to design infrastructure, such as network protocols, in such a way that the overall system is robust despite the fact that numerous arbitrary, non-certified, third-party components can connect to our system. Economists have long understood this issue, since it is analogous to the ...

Abstract

For a number of years we have been working towards the goal of automatically creating auction mechanisms, using a range of techniques from evolutionary and multi-agent learning. This paper gives an overview of this work. The paper presents results from several experiments that we have carried out, and tries to place these in the context of the overall task that we are engaged in. ...

Abstract

The nature of distributed computation in complex systems has often been described in terms of the component operations of universal computation: information storage, transfer and modification. This thesis makes the original contribution of a complete framework to quantify each of these individual operations on information on a local scale in space and time within a system. We call this the study of information dynamics. The framework is based on information theory, and describes the manner in which these operations interact to create non-trivial computation where “the ...

Abstract

Engineered systems are designed to deftly operate under predetermined conditions yet are notoriously fragile when unexpected perturbations arise. In contrast, biological systems operate in a highly flexible manner; learn quickly adequate responses to novel conditions, and evolve new routines/traits to remain competitive under persistent environmental change. A recent theory on the origins of biological flexibility has proposed that degeneracy - the existence of multi-functional components with partially overlapping functions - is a primary determinant of the robustness and adaptability found in evolved systems. While degeneracy's contribution to biological flexibility ...

Abstract

The nature of distributed computation has often been described in terms ofthe component operations of universal computation: information storage,transfer and modification. We introduce the first complete framework thatquantifies each of these individual information dynamics on a local scalewithin a system, and describes the manner in which they interact to createnon-trivial computation where "the whole is greater than the sum of the parts".We apply the framework to cellular automata, a simple yet powerful model ofdistributed computation. In this application, the framework is ...

Abstract

We present a measure of local information transfer, derived from an existing averaged information-theoretical measure, namely, transfer entropy. Local transfer entropy is used to produce profiles of the information transfer into each spatiotemporal point in a complex system. These spatiotemporal profiles are useful not only as an analytical tool, but also allow explicit investigation of different parameter settings and forms of the transfer entropy metric itself. As an example, local transfer entropy is applied to cellular automata, where it is demonstrated ...

Abstract

We study the coevolution of networks and action choices in a Prisoners' Dilemma. Agents in our model learn about both action choices and choices of interaction partners (links) by imitating successful behavior of others. The resulting dynamics yields outcomes where both cooperators and defectors coexist under a wide range of parameters. Two scenarios can arise. Either there is “full separation” of defectors and cooperators, i.e. they are found in two different, disconnected components. Or there is “marginalization” of defectors, i.e. connected ...

Abstract

Most animals exhibit significant neurological and morphological change throughout their lifetime. No robots to date, however, grow new morphological structure while behaving. This is due to technological limitations but also because it is unclear that morphological change provides a benefit to the acquisition of robust behavior in machines. Here I show that in evolving populations of simulated robots, if robots grow from anguilliform into legged robots during their lifetime in the early stages of evolution, and the anguilliform body plan is ...

Abstract

The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example- and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology, and finance. The book teaches "Matlab-style" and procedural programming as well as object-oriented programming. High school mathematics is a required background, and it is advantageous to study classical and numerical one-variable calculus in parallel with reading this book. Besides learning how to program computers, the reader will also learn how to solve mathematical ...

Abstract

Written by one of the preeminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, economics, philosophy, cognitive science, and the health and social sciences. Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations. The book will open the ...

Abstract

The past twenty years have seen an extraordinary growth in the use of quantitative methods in financial markets. Finance professionals now routinely use sophisticated statistical techniques in portfolio management, proprietary trading, risk management, financial consulting, and securities regulation. This graduate-level textbook is intended for PhD students, advanced MBA students, and industry professionals interested in the econometrics of financial modeling. The book covers the entire spectrum of empirical finance, including: the predictability of asset returns, tests of the Random Walk Hypothesis, the ...

Abstract

Previous work on mathematical models of cultural evolution has mainly focused on the diffusion of simple cultural elements. However, a characteristic feature of human cultural evolution is the seemingly limitless appearance of new and increasingly complex cultural elements. Here, we develop a general modelling framework to study such cumulative processes, in which we assume that the appearance and disappearance of cultural elements are stochastic events that depend on the current state of culture. Five scenarios are explored: evolution of independent cultural ...

Abstract

Abstract This article proposes a new mathematical theory of communication. The basic concepts of meaning and information are defined in terms of complex systems theory. Meaning of a message is defined as the attractor it generates in the receiving system; information is defined as the difference between a vector of expectation and one of perception. It can be sown that both concepts are determined by the topology of the receiving system. © 2010 Wiley Periodicals, Inc. Complexity 16: 10–26, 2011 ...

Abstract

We investigated dynamics of group decision making on complex problems when agents can form mental models of others from discussion history. Results indicated that as the agents' memory capacity increases, the group reaches superficial consensus more easily. Surprisingly, however, the shared mental model of the problem develops only within a limited area of the problem space, because incorporating knowledge from others into one's own knowledge quickly creates local agreement on where relevant solutions are, leaving other potentially useful solutions beyond the ...

Abstract

Sexual reproduction presents significant challenges to formal treatment of evolutionary processes. A starting point for systematic treatments of ecological and evolutionary phenomena has been provided by the gene-centered view of evolution which assigns effective fitness to each allele instead of each organism. The gene-centered view can be formalized as a dynamic mean-field approximation applied to genes in reproduction and selection dynamics. We show that the gene-centered view breaks down for symmetry breaking and pattern formation within a population and show that ...

Abstract

We introduce a broadened framework to study aspects of coevolution based on the NKclass of statistical models of rugged fitness landscapes. In these models the fitness contribution of each of Ngenes in a genotype depends epistatically on Kother genes. Increasing epistatic interactions increases the rugged multipeaked character of the fitness landscape. Coevolution is thought of, at the lowest level, as a coupling of landscapes such that adaptive moves by one player deform the landscapes of its immediate partners. In these models ...

Abstract

We present a comprehensive study of Vicsek-style self-propelled particle models in two and three space dimensions. The onset of collective motion in such stochastic models with only local alignment interactions is studied in detail and shown to be discontinuous (first-order-like). The properties of the ordered, collectively moving phase are investigated. In a large domain of parameter space including the transition region, well-defined high-density and high-order propagating solitary structures are shown to dominate the dynamics. Far enough from the transition region, on ...

Abstract

An important characteristic of flocks of birds, schools of fish, and many similar assemblies of self-propelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added into the system, the onset of such collective order occurs through a dynamical phase transition controlled by the noise intensity. While originally thought to be continuous, the phase transition has been claimed to be discontinuous on the basis of recently reported numerical evidence. ...

Abstract

This is the second of a two-part paper, investigating the stability properties of a system of multiple mobile agents with double integrator dynamics. In this second part, we allow the topology of the control interconnections between the agents in the group to vary with time. Specifically, the control law of an agent depends on the state of a set of agents that are within a certain neighborhood around it. As the agents move around, this set changes giving rise to a ...

Abstract

We consider disorder-order phase transitions in the three-dimensional version of the scalar noise model (SNM) of flocking. Our results are analogous to those found for the two-dimensional case. For small velocity (v <= 0.1) a continuous, second-order phase transition is observable, with the diffusion of nearby particles being isotropic. By increasing the particle velocities the phase transition changes to first order, and the diffusion becomes anisotropic. The first-order transition in the latter case is probably caused by the interplay between anisotropic diffusion and periodic boundary conditions, leading to ...

Abstract

In this paper we complete the analysis of Vicsek's model of distributed coordination among kinematic planar agents. The model is a simple discrete time heading update rule for a set of kinematic agents (or self-propelled particles as referred to by Vicsek) moving in a finite plane with periodic boundary conditions. Contrary to existing results in the literature, we do not make any assumptions on connectivity but instead prove that under the update scheme, the network of agents stays jointly connected infinitely ...

Abstract

A simple adaptive network model describing recent swarming experiments is introduced. By exploiting an analogy with human decision-making models, its dynamics is captured using a low-dimensional system of equations permitting analytical investigation. The model reproduces several characteristic features of swarms, including: spontaneous symmetry breaking, noise- and density-driven order-disorder transitions that can be of first or second order, intermittency, and metastable configurations displaying memory effects. By considering only minimal components of the swarming dynamics, it highlights the essential elements required to reproduce the observed behavior. ...

Abstract

The recent banking crises have made it clear that increasingly complex strategies for managing risk in individual banks have not been matched by corresponding attention to overall systemic risks. We explore some simple mathematical caricatures for ‘banking ecosystems’, with emphasis on the interplay between the characteristics of individual banks (capital reserves in relation to total assets, etc.) and the overall dynamical behaviour of the system. The results are discussed in relation to potential regulations aimed at reducing systemic risk. ...

Abstract

In the run-up to the recent financial crisis, an increasingly elaborate set of financial instruments emerged, intended to optimize returns to individual institutions with seemingly minimal risk. Essentially no attention was given to their possible effects on the stability of the system as a whole. Drawing analogies with the dynamics of ecological food webs and with networks within which infectious diseases spread, we explore the interplay between complexity and stability in deliberately simplified models of financial networks. We suggest some policy ...

Abstract

We present an overview of some representative Agent-Based Models in Economics. We discuss why and how agent-based models represent an important step in order to explain the dynamics and the statistical properties of financial markets beyond the Classical Theory of Economics. We perform a schematic analysis of several models with respect to some specific key categories such as agents' strategies, price evolution, number of agents, etc. In the conclusive part of this review we address some open questions and future perspectives and highlight the conceptual importance of some ...

Abstract

NetworkX is a Python language package for exploration and analysis of networks and network algorithms. The core package provides data structures for representing many types of networks, or graphs, including simple graphs, directed graphs, and graphs with parallel edges and self-loops. The nodes in NetworkX graphs can be any (hashable) Python object and edges can contain arbitrary data; this flexibility makes NetworkX ideal for representing networks found in many different scientific fields. In addition to the basic data structures many graph ...

Abstract

This article considers problems that can be characterized by large dynamic graphs. Communication networks provide the prototypical example of such problems where nodes in the graph are network IDs and the edges represent communication between pairs of network IDs. In such graphs, nodes and edges appear and disappear through time so that methods that apply to static graphs are not sufficient. Our definition of a dynamic graph is procedural. We introduce a data structure and an updating scheme that captures, in ...

Abstract

In this paper we present a generic algorithm for drawing sequences of graphs. This algorithm works for different layout algorithms and related metrics and adjustment strategies. It differs from previous work on dynamic graph drawing in that it considers all graphs in the sequence (offline) instead of just the previous ones (online) when computing the layout for each graph of the sequence. We introduce several general adjustment strategies and give examples of these strategies in the context of force-directed graph layout. ...

Abstract

Economic development and underdevelopment is one aspect of the uneven spatial distribution of economic activity. This paper reviews existing literature on geography and development, and argues that rigorous theoretical and empirical analysis is needed to increase understanding of the role of geography in development and to better design development policy. The analytical issues are: why does economic activity cluster in centers of activity? How do new centers develop? And what are the consequences of remoteness from existing centers? Empirical evidence comes ...

Abstract

Over the past years several authors have used the approach of generalized modeling to study the dynamics of food chains and food webs. Generalized models come close to the efficiency of random matrix models, while being as directly interpretable as conventional differential-equation-based models. Here we present a pedagogical introduction to the approach of generalized modeling. This introduction places more emphasis on the underlying concepts of generalized modeling than previous publications. Moreover, we propose a shortcut that can significantly accelerate the formulation of generalized models and introduce an iterative procedure ...

Abstract

We analyze the timescales of conflict decision-making in a primate society. We present evidence for multiple, periodic timescales associated with social decision-making and behavioral patterns. We demonstrate the existence of periodicities that are not directly coupled to environmental cycles or known ultraridian mechanisms. Among specific biological and socially-defined demographic classes, periodicities span timescales between hours and days, and many are not driven by exogenous or internal regularities. Our results indicate that they are instead driven by strategic responses to social interaction patterns. Analyses also reveal that a class of ...