This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to (...) link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws. (shrink)

Philosophers like Duhem and Cartwright have argued that there is a tension between laws' abilities to explain and to represent. Abstract laws exemplify the first quality, phenomenological laws the second. This view has both metaphysical and methodological aspects: the world is too complex to be represented by simple theories; supplementing simple theories to make them represent reality blocks their confirmation. We argue that both aspects are incompatible with recent developments in nonlinear dynamics. Confirmation procedures and modelling strategies (...) in nonlinear dynamics show that there are simple, abstract theories that can be confirmed without encountering the problems pointed to by Cartwright. (shrink)

In this paper we investigate a number of analytical solutions to the polynomial class of nonlinear Klein-Gordon equations in multidimensional spacetime. This is done in the context of classical φ4 and φ6 field theory, the former with and without the inclusion of an external force field conjugate to φ. Both massive (m≠0) and massless (m=0) cases are considered, as well as tachyonic solutions allowed (v>c). We first present a complete set of translationally invariant solutions for the φ4 model and (...) demonstrate the role of external force fields in altering the form of these solutions. Next, spherically symmetric solutions are discussed in both φ4 and φ6 cases since they provide the most realistic models of elementary particles. (shrink)

We discuss Einstein's ideas on the need for a theory that is both objective and local and also his suggestion for realizing such a theory through nonlinear field equations. We go on to analyze the nonlocality implied by the quantum theory, especially in terms of the experiment of Einstein, Podolsky, and Rosen. We then suggest an objective local field model along Einstein's lines, which might explain quantum nonlocality as a coordination of the properties of pulse-like solutions of the (...) class='Hi'>nonlinear equations that would represent particles. Finally, we discuss the implications of our model for Bell's inequality. (shrink)

More than a simple expository history, A Thousand Years of Nonlinear History sketches the outlines of a renewed materialist philosophy of history in the tradition of Fernand Braudel, Gilles Deleuze, and F lix Guattari, while also engaging the critical new understanding of material processes derived from the sciences of dynamics.Following in the wake of his groundbreaking War in the Age of Intelligent Machines, Manuel De Landa presents a radical synthesis of historical development over the last one thousand years. More (...) than a simple expository history, A Thousand Years of Nonlinear History sketches the outlines of a renewed materialist philosophy of history in the tradition of Fernand Braudel, Gilles Deleuze, and F lix Guattari, while also engaging the critical new understanding of material processes derived from the sciences of dynamics. Working against prevailing attitudes that see history as an arena of texts, discourses, ideologies, and metaphors, De Landa traces the concrete movements and interplays of matter and energy through human populations in the last millennium. De Landa attacks three domains that have given shape to human societies: economics, biology, and linguistics. In every case, what one sees is the self-directed processes of matter and energy interacting with the whim and will of human history itself to form a panoramic vision of the West free of rigid teleology and naive notions of progress, and even more important, free of any deterministic source of its urban, institutional, and technological forms. Rather, the source of all concrete forms in the West's history are shown to derive from internal morphogenetic capabilities that lie within the flow of matter-energy itself. (shrink)

This book reveals the French scientific contribution to the mathematical theory of nonlinear oscillations and its development. The work offers a critical examination of sources with a focus on the twentieth century, especially the period between the wars. Readers will see that, contrary to what is often written, France's role has been significant. Important contributions were made through both the work of French scholars from within diverse disciplines, and through the geographical crossroads that France provided to scientific communication at (...) the time. This study includes an examination of the period before the First World War which is vital to understanding the work of the later period. By examining literature sources such as periodicals on the topic of electricity from that era, the author has unearthed a very important text by Henri Poincaré, dating from 1908. In this work Poincaré applied the concept of limit cycle to study the stability of the oscillations of a device for radio engineering. The “discovery” of this text means that the classical perspective of the historiography of this mathematical theory must be modified. Credit was hitherto attributed to the Russian mathematician Andronov, from correspondence dating to 1929. In the newly discovered Poincaré text there appears to be a strong interaction between science and technology or, more precisely, between mathematical analysis and radio engineering. This feature is one of the main components of the process of developing the theory of nonlinear oscillations. Indeed it is a feature of many of the texts referred to in these chapters, as they trace the significant developments to which France contributed. Scholars in the fields of the history of mathematics and the history of science, and anyone with an interest in the philosophical underpinnings of science will find this a particularly engaging account of scientific discovery and scholarly communication from an era full of exciting developments. (shrink)

The basic concepts appropriate for anS matrix theory for classical nonlinear physics are formulated here. These concepts are illustrated by a discussion of shock wave diffraction patterns. Other information concerning solutions of non-linear conservation laws is surveyed, so that a coherent picture of this theory can be seen. Within thisS matrix framework, a number of open problems as well as a few solved ones will be discussed.

In the present article, I propose to give a positive characterization of ontological emergence from a relational perspective that, in opposition both to atomism and to holism, defends that the existence-conditions, the identity and the behavior or causal role of any emergent entity are to be conceived, and explained, as constructed by diverse systems of qualitatively transformative relations. I argue that from this relational perspective, the notion of emergence can be seen as ontologically and epistemologically coherent and significant. Finally, I (...) try to show in what sense, and to what extent, the Nonlinear Quantum Physics, as developed by Croca and his team, expresses such a relational and emergentist view of physical reality. (shrink)

Although its roots can be traced to the 19th century, progress in the study of nonlinear dynamical systems has taken off in the last 30 years. While pertinent source material exists, it is strewn about the literature in mathematics, physics, biology, economics, and psychology at varying levels of accessibility. A compendium research methods reflecting the expertise of major contributors to NDS psychology, Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data examines the techniques proven to be (...) the most useful in the behavioral sciences. The editors have brought together constructive work on new practical examples of methods and application built on nonlinear dynamics. They cover dynamics such as attractors, bifurcations, chaos, fractals, catastrophes, self-organization, and related issues in time series analysis, stationarity, modeling and hypothesis testing, probability, and experimental design. The analytic techniques discussed include several variants of the fractal dimension, several types of entropy, phase-space and state-space diagrams, recurrence analysis, spatial fractal analysis, oscillation functions, polynomial and Marquardt nonlinear regression, Markov chains, and symbolic dynamics. The book outlines the analytic requirements faced by social scientists and how they differ from those of mathematicians and natural scientists. It includes chapters centered on theory and procedural explanations for running the analyses with pertinent examples and others that illustrate applications where a particular form of analysis is seen in the context of a research problem. This combination of approaches conveys theoretical and practical knowledge that helps you develop skill and expertise in framing hypotheses dynamically and building viable analytic models to test them. (shrink)

Behaviors of chaotic systems are unpredictable. Chaotic systems are deterministic, their evolutions being governed by dynamical equations. Are the two statements contradictory? They are not, because the theory of chaos encompasses two levels of description. On a higher level, unpredictability appears as an emergent property of systems that are predictable on a lower level. In this talk, we examine the structure of dynamical theories to see how they employ multiple descriptive levels to explain chaos, bifurcation, and other complexities of (...) nonlinear systems.. (shrink)

A general solution is obtained for a model of a nonlinear quantum theory for gravitating particles proposed by H. Efinger. The solution procedure is easily generalized to space-time or stochastic formulations.

A critical review of gravitational wave theory is made. It is pointed out that the usual linear approach to the gravitational wave theory is neither conceptually consistent nor mathematically justified. Relying upon that analysis it is argued that—analogously to a Yang-Mills propagating field, which must be nonlinear to carry its gauge charge—a gravitational wave must necessarily be nonlinear to transport its own charge—that is, energy-momentum.

This book reports recent landmark developments and the state of the art in NDS science in psychological theory and research.

Today a change is imperative in approaching global problems: what is needed is not arm-twisting and power politics, but searching for ways of co-evolution in the complex social and geopolitical systems of the world. The modern theory of self-organization of complex systems provides us with an understanding of the possible forms of coexistence of heterogeneous social and geopolitical structures at different stages of development regarding the different paths of their sustainable co-evolutionary development. The theory argues that the evolutionary channel to (...) the observed increasing complexity is extremely narrow and only certain discrete spectra of relatively stable self-maintained structures are feasible in complex systems. There exists a restricted set of ways of assembling a complex evolutionary whole from diverse parts. The law of nonlinear synthesis of complex structures reads: the integration of structures in more complex ones occurs due to the establishment of a common tempo of their evolution. On the basis of the theory, we can see not only desirable but also attainable futures. (shrink)

I take the phrase ''the theory of nonlinear oscillations'' to identify a historical phenomenon. Under this heading a powerful school in Soviet science, L. I. Mandelstam's school, developed its version of what was later called ''nonlinear dynamics''. The theory of nonlinear oscillations was formed around the concept of self-oscillations, which was elaborated by Mandelstam's graduate student A. A. Andronov. This concept determined the paradigm of the theory of nonlinear oscillations as well as its ideology, that is, (...) a set of characteristic ideas which, together with the corresponding examples and analogues, allowed the expansion of the theory into associated areas where it indicated new interesting phenomena and posed new problems. It was the ideology that made possible the broader application of the theory of nonlinear oscillations, whose domain was originally lumped systems, to continuous media and its subsequent progress toward synergetics. In the course of its ideological application, the concept of self-oscillations was greatly extended, became vague and diffuse, and related concepts such as self-waves and self-structures appeared. (shrink)

This paper is a study of the consequences that follow from modeling a nonlinear and nonrelativistic quantum theory for gravitating particles. At present there exists no relativistic generalizations that do not sacrifice certain assumptions which are standard in covariant field theories.

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 12.3 (2005) 229-234 [Access article in PDF] Nonlinear Dynamics at the Cutting Edge of Modernity: A Postmodern View Gordon Globus Keywords nonlinear dynamics, modernity, postmodernity, quantum brain theory, free will, self-organization, autopoiesis, autorhoesis Although nonlinear dynamical conceptu-alizations have been applied to psychia-try for over 20 years,1 they have not had significant impact on the field. Unfortunately Heinrichs' very thoughtful contribution to the (...) discussion is unlikely to move such disinterest. Pragmatically successful paradigms in the phase of Kuhnian "normal science" are highly resistant to change. There is no crisis that besets triumphalist biological psychiatry that might lead to clinical or scientific revolution. At the same time, as I suggest at the end of this commentary, the ideas of nonlinear dynamics may not be revolutionary enough, remaining staunchly within the framework of modernity.In what follows I discuss four issues related to Heinrichs' article. First, I try to enrich his presentation of nonlinear dynamics by bringing in the role of self-organization in the evolution of nonlinear dynamical brain systems and by making the nonlinear dynamics "tunable." Second, I discuss whether Heinrichs succeeds in avoiding the dualism of the biopsychosocial model that he criticizes. Third, I look at the issue of "free will," which Heinrichs would understandably like to avoid. Finally, I mention a new form of dynamics, namely thermofield dynamics, which I think is more promising than nonlinear dynamics. Self-Organizing Self-Tuning Nonlinear Dynamical Systems In the case of psychiatry, we are not considering nonlinear dynamical systems like the weather or an ecosystem, but the brain's neural networks in terms of nonlinear dynamics with all its chaos. There is a principle of such systems of neural networks that Heinrichs does not bring out, although it is extremely important for them. These systems are self-organizing under a Hamiltonian principle of "least energy." To use Hopfield and Tank's (1986) terms, nonlinear dynamical neural networks self-organize toward attractors that minimize the "computational energy" of the system, or for Smolensky (1988), self-organize toward "harmony," or for Globus (1995, 2003), in a Heideggerian vein, self-organize to maximize "belonging-together." In this elaborated framework, rational deliberation is one constraint among many on a self-organizing nonlinear dynamical process. [End Page 229]Heinrichs brings out beautifully the nonlinear dynamical way of thinking clinically. This is not the dynamics of mechanistic psychodynamics, which features psychological forces in vectorial conflict—id versus superego and their compromises—but a flowing evolution of states in which small changes in initial state may have large effects (nonlinearity) on the state trajectory. To live a life is often to feel surprise, which nonlinear dynamics with its chaotic regimes well portrays.But there is a way that classical Freud and nonlinear dynamical neural networks do come together—in the "economics," discharges and conservations of libidinal energy, expenditures and credits in Derrida's (1978) accounting. Heinrichs does not mention this similarity. The economic principles differ between Freud's late nineteenth-century thermodynamics and Heinrichs' late twentieth-century nonlinear dynamics, it is true, but it is all economics.Freud called this economic functioning the "pleasure principle" in which "libido" seeks to discharge its instinctual energy store, reducing the level of instinctual tension. This "primary process" proceeds to an attractor by the quickest, most direct way possible, whereas the "secondary process" defers reduction in instinctual tension, subjecting the primary process to thought. Self-organizing directly to the attractor is the primary process with which the secondary process interferes, introducing deferral.The economy of nonlinear dynamics pictures a "landscape," a variegated topography with peaks and valleys. Each point on the topography represents a state. Peak points are repellors—for example, states in which the phobic object is approached—and the lowest points of the valleys are attractors—for example, obsessions and compulsions. The path of occupied states self-organizes away from repellors and toward attractors. This topography is an energy landscape. Its dynamics spontaneously tends—"self-organizes"—toward least energy/high-constraint satisfaction. Freud's pleasure principle is just the Hamiltonian least energy... (shrink)

A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic reviews of the relevant material are provided. Further chapters are devoted to the stability of invariant sets, bifurcation theory, chaotic dynamics and the transition to chaos. In the final two chapters the authors approach the subject from a (...) measure-theoretical point of view and compare results to those given for the geometrical or topological approach of the first eight chapters. Includes about one hundred exercises. A Windows-compatible software programme called DMC, provided free of charge through a website dedicated to the book, allows readers to perform numerical and graphical analysis of dynamical systems. Also available on the website are computer exercises and solutions to selected book exercises. See www.cambridge.org/economics/resources. (shrink)

v. 1. Theory of continuous Fokker-Planck systems -- v. 2. Theory of noise induced processes in special applications -- v. 3. Experiments and simulations.

The present article deals with an observer design for nonlinear vehicle lateral dynamics. The contributions of the article concern the nonconsideration of any force model and the consideration that the longitudinal velocity is time varying, which is more realistic than the assumption that it is constant. The vehicle model is then represented by an exact Takagi–Sugeno model via the sector nonlinearity transformation. A proportional multiple integral observer based on the TS model is designed to estimate simultaneously the state vector (...) and the unknown input. The convergence conditions of the estimation error are expressed under LMI formulation using the Lyapunov theory, which guaranties a bounded error. Simulations are carried out for comparison between the conventional PI observer, the enhanced PI observer, and the PMI observer. Finally, experimental results are provided to illustrate the performances of the proposed PMI observer. (shrink)

Much empirical analysis and econometric work recognizes that there are nonlinearities, regime shifts or structural breaks, asymmetric adjustment costs, irreversibilities and lagged dependencies. Hence, empirical work has already transcended neoclassical economics. Some progress has also been made in modeling endogenously generated cyclical growth and fluctuations. All this is inconsistent with neoclassical general equilibrium. Hence there is growing evidence of Kuhnian anomalies. It therefore follows that there is a Kuhnian crisis in economics and further research in nonlinear dynamics and complexity (...) can only increase the Kuhnian anomalies. This crisis can only deepen. However, there is an ideological commitment to general equilibrium that justifies “free enterprise” with only minimal state intervention that may still sustain neoclassical economics despite the growing evidence of Kuhnian anomalies. Thus, orthodox textbook theory continues to ignore this fact and static neoclassical theory remains a dogma with no apparent reformulation to replace it. (shrink)

This essay explores the metaphorical use of the area of nonlinear dynamics popularly known as "chaos theory," surveying its use in one particular field: legal theory. After sketching some of the mistakes encountered in these efforts, I outline the possibility of the fruitful use of nonlinear dynamics for thinking about our legal system. I then offer some general lessons to be drawn from these examples-both cautionary maxims and a limited defense of cross-disciplinary borrowing. I conclude with some reflections (...) on the nature of arguments that seek to establish intellectual authority or epistemic merit by analogical reasoning. (shrink)

This essay explores the metaphorical use of the area of nonlinear dynamics popularly known as “chaos theory,” surveying its use in one particular field: legal theory. After sketching some of the mistakes encountered in these efforts, I outline the possibility of the fruitful use of nonlinear dynamics for thinking about our legal system. I then offer some general lessons to be drawn from these examples—both cautionary maxims and a limited defense of cross-disciplinary borrowing. I conclude with some reflections (...) on the nature of arguments that seek to establish intellectual authority or epistemic merit by analogical reasoning. (shrink)

We study the conditions under which increasing risk raises the optimal control variable when the budget constraint is nonlinear. In contrast to the case when the budget constraint is linear, nonlinearities alter the risk attitudes of the economic agent; that is, the agent’s risk behavior is driven by the interaction between the shape of the utility function and the shape of the budget constraint. This paper complements the classical literature with linear payoff functions in two important ways. First, we (...) derive necessary and sufficient conditions for unambiguous comparative statics of changes in risk when the budget constraint is nonlinear. Second, we highlight the critical role of the coefficients of technological improvement and cross-prudence in technology derived from the nonlinear budget constraint in a similar form to that in which the coefficient of relative risk aversion and the coefficient of relative prudence are derived from the utility function. We show several applications of this theory, including the worker’s decision to work in-person during a pandemic. (shrink)

A previous model for treating electromagnetic nonlinear wave systems is examined in the context of wave mechanics. It is shown that nonlinear wave mechanics implies harmonic generation of new quasiparticle wave functions, which are absent in linear systems. The phenomenon is interpreted in terms of pair (and higher order ensembles) coherence of the interacting particles. The implications are far-reaching, and the present approach might contribute toward a common basis for diverse physical phenomena involving nonlinearity. An intimate relationship connecting (...) coherence, nonlocal interaction, and nonlinearity has been previously noticed in the physics of superconductivity. It is shown here that all these ingredients are consistently contained in the present formalism. The present theory may contribute to elucidate a controversial theory proposed by Panarella, who claims to have measured high-energy photons due to high-intensity laser radiation, which cannot be predicted on the basis of linear quantum theory. Panarella explains the new phenomena by stipulating a nonlinear intensity-dependent photon energy. It is argued here that nonlinearity, manifested in the presence of high intensity, may give rise to high- and low-energy photons, the so-called “effective” and “tired” photons, respectively. However, the present explanation does not involve ad hoc assumptions regarding the foundations of quantum theory. In analogy with the electrodynamic model, the present theory leads to particulate self-focusing in high-density streams of particles. Since such particulate beams are currently under consideration in connection with fusion reactions, this might be of future interest. (shrink)

Much empirical analysis and econometric work recognizes that there are nonlinearities, regime shifts or structural breaks, asymmetric adjustment costs, irreversibilities and lagged dependencies. Hence, empirical work has already transcended neoclassical economics. Some progress has also been made in modeling endogenously generated cyclical growth and fluctuations. All this is inconsistent with neoclassical general equilibrium. Hence there is growing evidence of Kuhnian anomalies. It therefore follows that there is a Kuhnian crisis in economics and further research in nonlinear dynamics and complexity (...) can only increase the Kuhnian anomalies. This crisis can only deepen. However, there is an ideological commitment to general equilibrium that justifies “free enterprise” with only minimal state intervention that may still sustain neoclassical economics despite the growing evidence of Kuhnian anomalies. Thus, orthodox textbook theory continues to ignore this fact and static neoclassical theory remains a dogma with no apparent reformulation to replace it. (shrink)

This paper presents a nonlinear trajectory controller with improved performances for a general model of the waverider based on feedback linearization theory and composite nonlinear feedback technique. First, a nonlinear controller is presented using the dynamic inversion and CNF technique for the MIMO Model, and the robust stability of the proposed controller is proved. Then, the nonlinear model is established on the basis of hypersonic aerodynamic principle, and the dynamic characteristics are analyzed accordingly, and the periodic (...) trajectory is designed and optimized in combination with a fuel optimization problem. Furthermore, the nonlinear controller is applied to the trajectory tracking of the waverider model, and the general design steps are provided the flight controller using this nonlinear control method. Finally, an illustrative example is given to verify the effectiveness of the nonlinear controller of the waverider, and the flight performances are improved accordingly, including system stability, robustness, and tracking ability. (shrink)

Main principles of the complex nonlinear thinking which are based on the notions of the modern theory of evolution and self-organization of complex systems called also synergetics are under discussion in this article. The principles are transdisciplinary, holistic, and oriented to a human being. The notions of system complexity, nonlinearity of evolution, creative chaos, space-time definiteness of structure-attractors of evolution, resonant influences, nonlinear and soft management are here of great importance. In this connection, a prominent contribution made to (...) system analysis and to a necessary reform of education and thinking by Edgar Morin is considered. (shrink)

This article argues that the process of development as such explains a great deal of the forms and properties of individual developmental trajectories, without the necessity of having to rely on either external or internal factors or causes. Both the problem of developmental change and invariance can be explained by employing a dynamic systems conceptualization of development. It is shown that dynamic systems models on the one hand and those of the genuine developmental models in psychology on the other, share (...) a set of important general properties that are able to explain both the universal and the idiosyncratic aspects of developmental processes. The concept of mental and behavioral ecology, which may serve as a starting point for specific theories of development of cognition, social behavior, personality and so forth, is discussed. It is concluded that both long-term and short-term developmental patterns will be shown to follow similar abstract dynamical principles. (shrink)

Walter Freeman's theory of nonlinear neurodynamics has had a major impact on brain dynamics in modern cognitive neuroscience. Steven Bressler's theory of neurocognitive networks follows from Freeman's work, and his empirical evidence for the coordination of cortical areas by phase-coupled beta rhythms in large-scale cognitive brain networks supports Freeman's ideas on nonlinear brain dynamics. Bressler's work, taking Freeman's concepts into the realm of cognitive neurodynamics, also supports Scott Kelso's theory of metastability in coordination dynamics. The aims of the (...) present paper are threefold: 1) to explore relevant concepts in Freeman's theoretical framework, 2) unify it and provide empirical support for it, and 3) explore its import for the study of consciousness. We take as our point of departure Bressler and Kelso's 2016 publication on cortical coordination dynamics and the Freeman-Kelso dialogue noted in the literature on this topic. In our view, Freeman's conceptual framework has great explanatory power. Its grounding in a dynamical systems approach to the study of brain function, and its incorporation of embodiment, make it relevant to the study of consciousness. Thus, with Freeman, we argue that the scientific understanding of consciousness must move beyond notions of computationalism and mental representations, to employ concepts of nonlinear brain dynamics and embodiment. (shrink)

This study presents the results of an empirical analysis of the relationship between managerial thinking style and ethical decision-making. Data from 200 managers across multiple organizations and industries demonstrated that managers predominantly adopt a utilitarian perspective when forming ethical intent across a series of business ethics vignettes. Consistent with expectations, managers utilizing a balanced linear/nonlinear thinking style demonstrated a greater overall willingness to provide ethical decisions across ethics vignettes compared to managers with a predominantly linear thinking style. However, results (...) comparing the ethical decision-making of balanced thinking managers and nonlinear thinking managers were generally inconsistent across the ethics vignettes. Unexpectedly, managers utilizing a balanced linear/nonlinear thinking style were least likely to adopt an act utilitarian rationale for ethical decision-making across the vignettes, suggesting that balanced thinkers may be more likely to produce ethical decisions by considering a wider range of alternatives and ruling out those that are justified solely on the basis of their outcomes. Implications are discussed for future research and practice related to management education and development, and ethical decision-making theory. (shrink)

Using the usual matrix representation of Clifford algebra of spacetime, quantities independent of the choice of a representation in the Dirac theory are examined, relativistic invariance of the theory is discussed, and a nonlinear equation is proposed. The equation presents no negative energy waves and gives the same results as the linear theory for hydrogen atom.

This paper presents a theory of algorithms designed to optimize highly interactive systems (multi-diminsional, multi-peak, nonlinear functions). Two applications are discussed: one concerns cognitive systems capable of learning and generalization, and one concerns calculations dealing with the "origin of life" from "organic soups". The algorithms are intrinsically parallel--each function argument processed serves as a carrier for information about a tremendous number of regions (hyperplanes) in the function's domain. Each region is automatically ranked according to the estimated average value of (...) the function over that region, and the rankings are compactly stored in the algorithm's data base (M l-tuples store approximately M-2 l/2 rankings). Thus, the algorithm implicitly processes hyperplanes by manipulating function arguments. (shrink)

We propose a general framework for integrating theory and empiricism in human evolutionary ecology. We specifically emphasize the joint use of stochastic nonlinear dynamics and information theory. To illustrate critical ideas associated with historical contingency and complex dynamics, we review recent research on social preferences and social learning from behavioral economics. We additionally examine recent work on ecological approaches in history, the modeling of chaotic populations, and statistical application of information theory.

In order to develop further the methods of scenario building and to facilitate the paths towards desirable and sustainable futures, we cannot do without a nonlinear evolutionary thinking. The theory of self-organization of complex systems, called also synergetics, is a scientific basis for such a thinking, the main principles of which are under consideration in the paper. Synergetics provides us with the knowledge of constructive principles of coevolution of the complex social systems, coevolution of countries and geopolitical regions being (...) at different stages of development, integration of the East and the West, the North and the South. (shrink)

This research evaluates the production of three dimensional (3D) clouds for geospatial viewing programs such as Google Earth, NASA World Wind, and X3D Earth. This thesis took advantage of iso-standard X3D graphics and X3D Edit in conjunction with manually produced image textures to represent 3D clouds. While a 3D geospatial viewing might never completely characterize the current state of the atmosphere, a sufficiently realistic virtual 3D rendering can be created to present current sky coverage given adequate satellite and model data. (...) Various visualization demonstration results are presented that can be rendered and navigated in real time. Further research and development is needed to match a cloud typing model output with a particular method of 3D cloud production. Data-driven adaptation and production of cloud models for web-based delivery is an achievable capability given continued research and development. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 12.3 (2005) 235-237 [Access article in PDF] Determined by Chaos: The Nonlinear Dynamics of Free Will Jessica Wahman Keywords free will, chaos theory, determinism, materialism In "antidepressants and the Chaotic Brain: Implications for the Respectful Treatment of Selves," Douglas Heinrichs provides an intriguing justification of individuated and longer term therapy for depressive clients. He does not reject medication as a therapeutic strategy, nor does (...) he question the materialist basis of the traditional medical model. Rather, he offers a physically deterministic account of depression that is at the same time compatible with a sense of human agency and individuality. Heinrichs suggests that human physiology and its psychiatric disorders are better accounted for by the nonlinear dynamics of chaos theory than by the traditional account of neurotransmitter production and reuptake. Because the latter, microscopic, explanation suggests a direct cause-and-effect relationship between synaptic activity and subjective affect, it cannot account for the wide variation of responses to the same medications, nor can it satisfy the client's fears that her drug-induced well-being is not fully hers to control. Chaos theory, he asserts, can provide a better explanation by treating the human organism as a complex holistic system whose patterns resemble a topographical map of probability more than they do a unidirectional vector model of cause to effect. Like the weather, human affect and behavior are physically determined but difficult to predict, and so careful attention to both the individual history of the client and the uniqueness of responses to medication are a necessary part of any successful therapeutic program.Connected to this theory of nonlinear physiology is Heinrichs's account of autonomy and agency under this rubric. He notes that a psychology based on chaos theory is not only compatible with the notion of free will, it can better explain why the successful use of medication actually increases freedom and autonomy instead of limiting it. It is here that I wish to focus my comments, because his interpretation of free will may give us, to borrow a phrase from Daniel Dennett, a "variet[y] of free will worth wanting" (1984, title page). Free will, in this case, is not a metaphysical ability to act above and beyond our material causes, but is instead a property of the material system itself, namely when that system feels itself capable of greater psychic mobility around the topographical map of probabilistic patterns.According to this model, our ability to reason, plan, and act on the decisions we make is itself a [End Page 235] part of our chaotically determined neurologic system. When we are healthy, we are able to reason in our best interests and act on those reasons. This is modeled as an ability for the organism to metaphorically "move about" the map of its own possibilities, and more important, to both enter and escape certain states, known as chaotic attractors, into which it is likely to be drawn. "Where" we wind up, psychologically speaking, at any point in time is determined by our own system, and so we may say that in such a case we are autonomous and our choices are made freely. Depression, on the other hand, can be compared to a deep groove in the map, a chaotic attractor that is hard to escape, and so the system quite literally becomes "stuck in a rut." This is subjectively experienced as the tendency for thought processes and activities to fall into negative and self-defeating patterns despite the best efforts of the client to escape these habits. So long as the organism does not have a sense of being "trapped" in an attractor (whether a depressive or, for example, manic or compulsive state), then that organism may be said to be free. Medication and the therapy that accompanies it, so far as it facilitates our ability to escape deep chaotic attractors, promotes our own freedom of will. If a car cannot spin its way out of a ditch, does the tow truck hinder or promote its freedom by hauling it back onto solid pavement where it may again... (shrink)

The shape of the spectral lines of an optically active system interacting with one or more strong radiation fields in the presence of a perturbing bath is studied. A method based on the statistics of the fluctuation of the interaction between the radiator and the perturbing environment (the model Markov microfield theory) is used. This method permits the foundations of line shape theory in modern statistical mechanics to be seen clearly. Multiphoton processes and homogeneous, inhomogeneous, and power broadening mechanisms are (...) included in the analysis. The correlations between radiative and collisional processes which arise in nonlinear spectroscopy are included explicitly. A discussion of the new information that is obtained from these correlations in nonlinear spectroscopy is also presented. Several model systems are presented as illustrative examples of the theory. (shrink)