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AbstractMorphodynamics is a general theory of stationay complex system, such as living systems, or mental and social systems it is based on the thermodynamics of physical systems and built on the same lines. By means of the ergodic hypothesis thermodynamics is known to connect the particle dynamics to the energence of order parameters in the equation of state. In the same way, morphodynamics connects order parameters to the emergence of higher level variables; through recurrent applications of the ergodic hypothesis, a hierarchy of equations of state is established which describes a series of successive levels of organization. The equation support a cogmitiveist interpretation that leads to general principles of evolution: the principles determine thespontaneous and irreversible complexification of systems living in their natural environment.

This work represents the current state of the most important economic applications of dynamical systems theory. The volume features not only a survey of modern analytical approaches and nonlinear models but also an anthology of the numerical and graphical methods (represented in 90 illustrations) that are essential to an understanding of dynamical behavior. The first chapters present accessible (though not elementary) introductions to local analysis and the linear approximation, deep issues regarding chaos and complexity, the ergodic approach and probabilistic properties of dynamical systems

1.3 Myopia of an organization: NASA and the space shuttle accidentsNormalization of deviance; The culture of production; Structural secrecy; 1.4 Other cases of myopia; The tragedy of the commons; When numbers do not mean strength; 1.5 Positive myopia and the principle of the hiding hand; 2 Uncertainty and predictability in organizations; 2.1 Risk and uncertainty in complex non-ergodic systems; Risk and uncertainty; Uncertainty and ambiguity; 2.2 Organizations and the future; 2.3 Predictable surprises versus bolts from the blue; Predictable surprises; The hindsight bias problem

1. David Pines and Me -- 2. To err is human: the complex nature of human reproduction and prenatal development -- 3. Short notes on theories of species diversity -- 4. Museum Workshop, evolution of human intelligence and education -- 5. Anomalous behavior of random walks on disordered media -- 6. Pollution, Human Capital, and Growth Cycles -- 7. Productive Consumption in a Two-Sector Model of Economic Development -- 8. Time and Mnemonic Morphism -- 9. Universality and the Role of Limitations Influencing Interdisciplinary Scientific and Cultural Advances -- 10. Some Conceptual Principles with Mathematical Background for Interdisciplinary Developments in the Sciences and Beyond -- 11. The Role of Paradox in the Development of Interdisciplinary Scientific and Cultural Advances -- 12. Elucidation of Chaotic Market Hypothesis Based on Ergodic Theory -- 13 -- Itinerant-Electron Magnetism and Spin Fluctuations− Aspects of Theories and Experiments -- 14. Quantum-size effect probed by NMR measurements -- 15. Recent Topics on Organic Spin Liquid Candidates -- 16. Impact of Reactive Oxygen Species and G-quadruplexes in Telomeres and Mitochondria -- 17.Evolution, Motor of the Changing Biosphere -- 18. New horizons in brain science -- 19. Evolutionary perspective on Suffering : Murase's "Self-Nonself circulation theory of life" applied to PRISM (Pictorial Representation of Illness and Self Measure) -- 20. Machine Learning for Metabolic Identification -- 21. Ignorance, Creation, Destruction -- 22. A Unified Theory and Practice of Creative Complex Systems: Challenging to the Systemic Problems Spanning the Inside and Outside World. .

AbstractFoundations of thermodynamics are reviewed in terms of the elementary processes driving spontaneous evolution in physical systems. These processes lead to ergodic and mixing behavior as well as to conservation of macroscopic quantities such as total energy; finally a tendency towards order through instabilities results when the environment is cold enough. Instabilities are in turn considered as processes driving a spontaneous evolution in complex systems in their natural environment; again ergodic and mixing behavior is exhibited as well as new conserved quantities. As a result, a second thermodynamics is built which relates complexity to the corpuscular nature of matter. Thus, general properties of complex systems are pointed out, such as spontaneous and irreversible tendency towards complexity, development by stages and information flow between systems of different complexity.

Why do we play games and why do we play them on computers? The contributors of »Games and Rules« take a closer look at the core of each game and the motivational system that is the game mechanics. Games are control circuits that organize the game world with their (joint) players and establish motivations in a dedicated space, a »Magic Circle«, whereas game mechanics are constructs of rules designed for interactions that provide gameplay. Those rules form the base for all the excitement and frustration we experience in games. This anthology contains individual essays by authors with backgrounds in Game Design and Game Studies, who lead the discourse to get to the bottom of game mechanics in video games and the real world.

Abstract
This paper deals with linear impulse dynamical systems on ℝd whose parameters depend on an ergodic piece-wise constant Markov process with values from some phase space 𝕐 and on a small parameter ɛ. Trajectories of Markov process x(t,y)∈ ℝd satisfy a system of linear differential equations with close to constant coefficients on its continuity intervals, while its phase coordinate changes discontinuously when Markov process switching occur. Jump sizes depend linearly on the phase coordinate and are proportional to the small parameter ɛ. We propose a method and an algorithm for choosing the base 𝔹(t,y) of the space ℝd that provides approximation of average phase trajectories E{x(t,y)} by a solution of a system of linear differential equations with constant coefficients.

Threshold systems are known to be some of the most important nonlinear self-organizing systems in nature, including networks of earthquake faults, neural networks, superconductors and semiconductors, and the World Wide Web, as well as political, social, and ecological systems. All of these systems have dynamics that are strongly correlated in space and time, and all typically display a multiplicity of spatial and temporal scales. Here we discuss the physics of self-organization in earthquake threshold systems at two distinct scales: (i) The "microscopic" laboratory scale, in which consideration of results from simulations leads to dynamical equations that can be used to derive the results obtained from sliding friction experiments, and (ii) the "macroscopic" earthquake fault-system scale, in which the physics of strongly correlated earthquake fault systems can be understood by using time-dependent state vectors defined in a Hilbert space of eigenstates, similar in many respects to the mathematics of quantum mechanics. In all of these systems, long-range interactions induce the existence of locally ergodic dynamics. The existence of dissipative effects leads to the appearance of a "leaky threshold" dynamics, equivalent to a new scaling field that controls the size of nucleation events relative to the size of background fluctuations. At the macroscopic earthquake fault-system scale, these ideas show considerable promise as a means of forecasting future earthquake activity.

In this survey, we present some methods in the dynamics and dimension theory for invariant measures of hyperbolic endomorphisms (smooth non-invertible maps), and for conformal iterated function systems with overlaps. For endomorphisms, we recall the notion of asymptotic degree of an equilibrium measure, which is shown to be related to the folding entropy; this degree is then applied to dimension estimates. For finite iterated function systems, we present the notion of overlap number of a measure, which is related to the folding entropy of a lift transformation, and also give some examples when it can be computed or estimated. We apply overlap numbers to prove the exact dimensionality of invariant measures, and to obtain a geometric formula for their dimension. Then, for countable conformal iterated function systems with overlaps, the projections of ergodic measures are shown to be exact dimensional, and we give a dimension formula. Relations with ergodic number theory, continued fractions, and random dynamical systems are also presented.

1 Demand and Equilibria -- 1.1 Introduction -- 1.2 Individual demand -- 1.3 Market demand -- 1.4 Equilibria -- 1.5 Concluding remarks -- 2 Smoothing Demand by Aggregation -- 2.1 Many different consumers -- 2.2 Convexifying by averaging -- 2.3 Concluding remarks on diversification -- 3 Spaces of Preferences and Large Economies -- 3.1 Introduction -- 3.2 Preference relations -- 3.3 Spaces of preference relations -- 3.4 Large economies -- 4 Heuristic Remarks on Some Basic Concepts -- 4.1 Genericity -- 4.2 Stability -- 4.3 Equal distribution -- 4.4 The law of large numbers -- 5 The Parametric Approach -- 5.1 Introduction -- 5.2 Dispersion of tastes -- 5.3 Continuous mean demand -- 5.4 Differentiable mean demand -- 5.5 Concluding remarks -- 6 The Ergodic Approach -- 6.1 Introduction -- 6.2 G-dispersion -- 6.3 Continuous mean demand -- 6.4 Differentiable mean demand -- 6.5 Concluding remarks -- 7 Other Approaches -- 7.1 Dispersion of unit normals -- 7.2 Infinite dimensional linear spaces of preferences -- 7.3 Random individual demand -- 7.4 The generic approach -- 8 Mathematical Tools -- 8.1 Miscellany -- 8.2 Differential topology -- 8.3 Measure theory -- Notation -- References.

I. On Modeling the Cross-Dual Dynamics of Competition -- The Dynamic Equalization of Profit Rates for Input-Output Models with Fixed Capital -- The Equalization of the Rate of Profit Reconsidered -- A Cross-Over Gravitation Process in Prices and Inventories -- Stability of Production Prices in a Model of General Interdependence -- Ergodic Price Setting with Technical Progress -- II. Microfoundations of Macrodynamics and Limit Cycles -- Swinging along the Autostrada -- Stability and Instability in a Dynamic Model of Capitalist Production -- On a Microdynamics of a Nonlinear Macrocycle Model -- Stabilization Policy in a Nonlinear Business Cycle Model -- III. Linear and Nonlinear Macrodynamics -- Some Extensions of a Classical Growth Cycle Model -- Growth Cycles in a Classical-Keynesian Model -- Problems Concerning the Dynamic Analysis of a Keynesian Model with Perfect Foresight -- Cyclical Growth: The Interdependent Dynamics of Industry and Agriculture -- IV. Econometrics of the Dynamics of Proportions and Nonlinear Macrodynamics -- The Stability of the Reproduction Scheme: Theoretical Discussion and Empirical Evidence for the United States, 1948–1980 -- Testing Non-Linearity in Business Cycles.

Credit contagion refers to the propagation of economic distress from one firm or sovereign government to another. In this paper we model credit contagion phenomena and study the fluctuation of aggregate credit losses on large portfolios of financial positions. The joint dynamics of firms' credit ratings is modeled by a voter process, which is well-known in the theory of interacting particle systems. We clarify the structure of the equilibrium joint rating distribution using ergodic decomposition. We analyze the quantiles of the portfolio loss distribution and in particular their relation to the degree of model risk. After a proper re-scaling taking care of the heavy tails induced by the contagion dynamics, we provide a normal approximation of both the equilibrium rating distribution and the portfolio loss distribution.

Dynamical systems -- Deterministic linear systems -- Deterministic nonlinear systems -- Stochastic difference equations -- Markov processes -- Ergodic theory and stationary processes -- Dynamic optimization -- Markov decision process model -- Finite-horizon dynamic programming -- Infinite-horizon dynamic programming -- Applications -- Linear-quadratic models -- Control under partial information -- Numerical methods -- Structural estimation -- Equilibrium analysis -- Complete markets exchange economies -- Neoclassical growth models -- Bayesian estimation of dsge models using dynare -- Overlapping generations models -- Incomplete markets models -- Search and matching models of unemployment -- Dynamic new keynesian models -- Further topics -- Recursive utility -- Dynamic games -- Recursive contracts -- Mathematical appendixes -- References -- Matlab index -- Name index -- Subject index.