Universal laws and economic phenomena

Despite the idiosyncratic behavior of individuals, empirical regularities exist in social and economic systems. These regularities often arise from simple underlying mechanisms which, analogous to the natural sciences, can be expressed as universal principles or laws. In this essay, I discuss the similarities between economic and natural phenomena and argue that it is advantageous for economists to adopt methods from the natural sciences to discover “universal laws” in economic systems. © 2011 Wiley Periodicals, Inc. Complexity, 2011     

Agent‐based computational models and generative social science

This article argues that the agent‐based computational model permits a distinctive approach to social science for which the term “generative” is suitable. In defending this terminology, features distinguishing the approach from both “inductive” and “deductive” science are given. Then, the following specific contributions to social science are discussed: The agent‐based computational model is a new tool for empirical research. It offers a natural environment for the study of connectionist phenomena in social science. Agent‐based modeling provides a powerful way to address certain enduring—and especially interdisciplinary—questions. It allows one to subject certain core theories—such as neoclassical microeconomics—to important types of stress (e.g., the effect of evolving preferences). It permits one to study how rules of individual behavior give rise—or “map up”—to macroscopic regularities and organizations. In turn, one can employ laboratory behavioral research findings to select among competing agent‐based (“bottom up”) models. The agent‐based approach may well have the important effect of decoupling individual rationality from macroscopic equilibrium and of separating decision science from social science more generally. Agent‐based modeling offers powerful new forms of hybrid theoretical‐computational work; these are particularly relevant to the study of non‐equilibrium systems. The agent‐based approach invites the interpretation of society as a distributed computational device, and in turn the interpretation of social dynamics as a type of computation. This interpretation raises important foundational issues in social science—some related to intractability, and some to undecidability proper. Finally, since “emergence” figures prominently in this literature, I take up the connection between agent‐based modeling and classical emergentism, criticizing the latter and arguing that the two are incompatible. © 1999 John Wiley & Sons, Inc.     

THE TRANSFORMATION OF LANDSCAPE: MODELING POLICY AND SOCIAL IMPACTS ON THE AGRICULTURAL LANDSCAPE OF LESVOS

ABSTRACT. The term landscape is more and more used as an “umbrella‘ concept, covering a series of cultural, productive and ecological processes. In order to uncover mechanisms, monitor transformations and predict changes, a complicated set of interacting factors has to be taken into account. This paper presents a model for estimating social and policy impacts on agricultural landscapes, based on the assumption that agricultural landscapes are shaped at” macro “(landscape) level by” micro “interventions at farm level. The model consists of three parts: an” ecological processes “part, which deals with processes that shape the ecological and aesthetic value of a landscape, a” population dynamics “part, which examines farmer population dynamics and a” policy impact “part, which deals with direct or indirect impacts on farming systems and farmer dynamics and refers to CAP Rural Development Measures. The model is applied for the olive and graze land agricultural landscapes of Lesvos (Greece). Results, apart from revealing landscape change patterns; help to illustrate some mechanisms behind this change and indicate that Rural Development Measures are inherent with minor but important malfunctions that cannot lead to sustainable landscape management and rural development in the area.     

A threshold phenomenon in the Field-Noyes model of the Belousov-Zhabotinskii reaction

The Belousov-Zhabotinskii reaction is one of the most interesting and best understood chemical oscillators. It has been conjectured that certain biological phenomena have important features in common with this reaction. We investigate the Field-Noyes model of this reaction and demonstrate that there is a range of values of the stoichiometric parameter, f, over which the model exhibits “threshold phenomena.” That is, if a perturbation from the steady state exceeds a certain “threshold” value then a solution in the form of a “spike” results followed by its return to the steady state. We show that the underlying mathematical structure of this model resembles very closely the underlying mathematical structure of the Hodgkin-Huxley nerve conduction equations which exhibit the same sort of threshold phenomena.     

Inferring social structure from continuous‐time interaction data

Relational event data, which consist of events involving pairs of actors over time, are now commonly available at the finest of temporal resolutions. Existing continuous‐time methods for modeling such data are based on point processes and directly model interaction “contagion,” whereby one interaction increases the propensity of future interactions among actors, often as dictated by some latent variable structure. In this article, we present an alternative approach to using temporal‐relational point process models for continuous‐time event data. We characterize interactions between a pair of actors as either spurious or as resulting from an underlying, persistent connection in a latent social network. We argue that consistent deviations from expected behavior, rather than solely high frequency counts, are crucial for identifying well‐established underlying social relationships. This study aims to explore these latent network structures in two contexts: one comprising of college students and another involving barn swallows.     

Nonlinear processes in Hamiltonian reconnection

The generation of small spatial scales and their interplay with large scale coherent structures is one of the outstanding phenomena of plasma physics and fluid mechanics. In high temperature space and laboratory plasmas dissipative effects become important at length scales that are much smaller than those where microscopic dynamical effects, related e.g., to electron inertia, come into play. Here we discuss the role of this dissipationless small scale dynamics on the nonlinear evolution of collisionless magnetic reconnection within the framework of the so called “two-field” and “four-field models”.     

Evolution in complex systems

What features characterize complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analyzed to confirm this effect. The strain arises from local frustration. As the strain is released through “quakes,” some system variable undergoes record statistics with accompanying log‐Poisson statistics for the quake event times. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology and show how quantitative indications of aging can be found. © 2004 Wiley Periodicals, Inc. Complexity 10: 49–56, 2004     

Bifurcation and nonsmooth dynamics of solitary waves in the generalized long-short wave equations

Generalized wave equations, which model the resonant interaction between the long wave and the short wave, are considered. To understand the underlying complex dynamics, the bifurcations and nonsmooth behaviors of solitary waves for this system are investigated by qualitative techniques in dynamical systems. These complex behaviors may serve as mechanisms for fascinating physical phenomena such as solitons, chaos and turbulence.     

One-way flow network formation under constraints

We study the effects of institutional constraints on stability and efficiency in the “one-way flow” model of network formation. In this model the information that flows through a link between two players runs only towards the player that initiates and supports the link, so in order for it to flow in both directions, both players must pay whatever the unit cost of a directional link is. We assume that an exogenous “societal cover” consisting of a collection of possibly overlapping subsets covering the set of players specifies the social organization in different groups or “societies,” so that a player may initiate links only with players that belong to at least one society that he/she also belongs to, thus restricting the feasible strategies and networks. In this setting, we examine the impact of such societal constraints on stable/efficient architectures and on dynamics.     

A Poisson random field model for intermittent phenomena with application to laminar-turbulent transition and material microstructure

The alternation of a physical system between two phases or states is referred to as intermittency. Examples of intermittent phenomena abound in applications and include the transition from laminar to turbulent flow over a flight vehicle and the presence of imperfections within material microstructure. It is shown that intermittent phenomena of this type can be modeled by two-state random fields with piecewise constant samples; we refer to the states of the random field as “off” and “on” or, equivalently, 0 and 1. These random fields can be calibrated to the available information, which consists of: (1) the marginal probability that the state of the system is “on”; and (2) the average number of fluctuations between states that occur within a bounded region. The proposed model is defined by a sequence of pulses of prescribed shape and unit magnitude, located at random (Poisson) points within a bounded domain. Properties of the model are discussed, and simple algorithms to generate samples of the random field are provided. Various applications are considered, including voids within material microstructure and the random vibration of a flight vehicle subjected to a transition from laminar to turbulent flow over its surface.     

Learning from similarities and differences: a reflection on the potentials and constraints of cross-national studies in mathematics

Research in mathematics education that crosses national boundaries provides new insights into the development and improvement of the teaching and learning of mathematics. In particular, cross-national comparisons lead researchers to more explicit understanding of their own implicit theories about how teachers teach and how children learn mathematics in their local contexts as well as what is going on in school mathematics in other countries. Further, when researchers from multiple countries and regions study collaboratively aspects of teaching and learning of mathematics, the taken-for-granted familiar practices in the classroom can be questioned. Such cross-national comparisons provide opportunities for researchers and educators to probe typical dichotomies such as “high-performing” versus “low performing”, “teacher-centred versus student-centred”, or even “East versus West”, in searching for similarities and differences in educational policies and practices in different cultural contexts.     

VOLE POPULATION DYNAMICS UNDER THE INFLUENCE OF SPECIALIST AND GENERALIST PREDATION

Abstract To understand the impact of predation by different types of predators on the vole population dynamics, we formulate a three differential equation model describing the population dynamics of voles, the “specialist predator” and the “generalist predator.” First we perform a local stability study of the different steady states of the basic model and deduce that the predation rates of the “specialist” as well as the “generalist” predator are the main parameters controlling the existence/extinction criteria of the concerned populations. Next we analyze the model from a thermodynamic perspective and study the thermodynamic stability of the different equilibria. Finally using stochastic driving forces, we incorporate the exogenous factor of environmental forcing and investigate the stochastic stability of the system. We compare the stability criteria of the different steady states under deterministic, thermodynamic and stochastic situations. The analysis reveals that when the “specialist” and the “generalist” predator are modeled separately, the system exhibits rich dynamics and the predation rates of both types of predators play a major role in controlling vole oscillation and/or stability. These findings are also seen to resemble closely with the observed behavior of voles in the natural setting. Numerical simulations are carried out to illustrate analytical findings.     

我国“政府主导-社会参与”救灾体制改革的演化路径分析

《关于推进防灾减灾救灾机制体制改革的意见》提出我国救灾工作要“坚持党委领导、政府主导、社会力量和市场机制广泛参与”,但推动改革的具体实施路径尚在探索中。通过归纳中西方两种典型救灾体制的优缺点,构建政府救援部门和社会力量协同救灾的演化博弈分析框架,论证了“政府主导-社会参与”救灾体制改革的多重演化路径、均衡条件和关键影响因素。研究表明,政府与社会力量的协同救援效应和救援工作的阶段特征,是决定救灾体制演化的两个关键性因素。在推进传统救灾模式到理想救灾模式的体制演化过程中,存在“双轨制”协调博弈或“一抓就死、一放就活”周期解等过渡状态的多条演化路径。救灾模式需要随救灾工作的阶段转换进行调整。     

A Canonical Theory of Origins and Development of Social Complexity

The puzzle of origins and future of government and social complexity in human and social dynamics, arguably a characteristic feature of the emergence and long-term evolution of hierarchy and power in the history of civilizations, is an enduring topic that has challenged political scientists, anthropological archaeologists, and other social scientists and historians. This paper proposes a new computational theory for the emergence of social complexity that accounts for the earliest formation of systems of government (pristine polities) in prehistory and early antiquity, as well as present and future political development. This general social theory is based on a “fast process” of crisis and opportunistic decision-making through collective action, which feeds a “slow” process of political development or decay. The “fast” core iterative process is “canonical” in the sense that it undergoes variations on a recurring theme of signal detection, information-processing, problem-solving, successful adaptation and occasional failure. When a group is successful in managing or overcoming serious situational changes (stresses or opportunities, endogenous or exogenous, social or physical) a probabilistic phase transition may occur, under a specified set of conditions, yielding a long-term (slow) probabilistic accrual process of emergent sociopolitical complexity and development. A reverse process may account for decay. The canonical theory is being formally implemented through the “PoliGen” agent-based model (ABM), based on the new Multi-Agent Simulator of Networks and Neighborhoods (MASON). Empirically, the theory is testable with the datasets on polities developed by the Long-Range Analysis of War (LORANOW) Project. This paper focuses on the concepts, mechanisms, and basic formal structure that constitute the canonical theory and inform the subsequent simulation model.     

The Emergence of Social Order by Processes of Typifying: A Computational Model

The article argues that Rational Choice approaches are not sufficient to explain the “how” of the emergence of social order. Therefore, the concept of “typifying” according to the theory of Berger and Luckmann is understood as the most important form of establishing social orders between different social actors. A computational model is described that captures the basic features of the typifying process. Each artifical actor consists of two different neural nets, an “action net” and a “perception net”. These nets allow an actor to establish social rules of interaction with other actors, to remember the other actors after a time and to typify new actors as persons that belong to the same type as actors the first actor is already “acquainted” with. Experimental results and theoretical consequences are also given.     

Control parameters in Boolean networks and cellular automata revisited from a logical and a sociological point of view

The use of “control parameters” as applied to describe the dynamics of complex mathematical systems within models of real social systems is discussed. Whereas single control parameters cannot sufficiently characterize the dynamics of such systems it is suggested that domains of values of certain sets of parameters are appropriately denoting necessary conditions for highly disordered dynamics of social systems. Various of those control parameters permit a straightforward interpretation in terms of properties of social rules and structures. © 1999 John Wiley & Sons, Inc.     

Mathematics learning and tools from theoretical, historical and practical points of view: the productive notion of mathematics laboratories

In our research work, we have looked at the way in which artefacts become, for teachers as well as for students, instruments of their mathematical activity. The issues related to the use of tools and technologies in mathematical education are now widely considered. A look to history highlights the different ways in which the same questions have been studied at different times and in different places. This suggests that the contribution of artefacts to mathematics learning should be considered in terms of various contexts. Our “visits” to these contexts will be guided by the coordination of two main theoretical frameworks, the instrumental approach and the semiotic mediation approach from the perspective of mathematics laboratory. This journey through history and schooling represents a good occasion to address some questions: Are there “good” contexts in which to develop mathematical instruments? Are there “good” teaching practices which assist students’ instrumental geneses and construct mathematical meanings? How is it possible to promote such teaching practices? Some study cases are discussed.     

Nonlinear Questions in Clamped Plate Models

The linear clamped plate boundary value problem is a classical model in mechanics. The underlying differential equation is elliptic and of fourth order. The latter is a peculiar feature with respect to which this equation differs from numerous equations in physics and engineering which are of second order. Concerning the clamped plate boundary value problem, “linear questions” may be considered as well understood. This changes completely as soon as one poses the simplest “nonlinear question”: What can be said about positivity preserving? Does a plate bend upwards when being pushed upwards? It is known that the answer is “no” in general. However, there are many positivity issues as e.g. “almost positivity” to be discussed. Boundary value problems for the “Willmore equation” are nonlinear counterparts for the linear clamped plate equation. The corresponding energy functional involves curvature integrals over the unknown surface. The Willmore equation is of interest in mechanics, membrane physics and, in particular, in differential geometry. Quite far reaching results were achieved concerning closed surfaces. As for boundary value problems, by far less is known. These will be discussed in symmetric situations. This survey article reports upon joint works with A. Dall’Acqua, K. Deckelnick (Magdeburg), S. Fröhlich (Free University of Berlin), F. Gazzola (Milan), F. Robert (Nice), Friedhelm Schieweck (Magdeburg) and G. Sweers (Cologne).