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At least 19 recordsLinked to original sources

arXiv2001

Basic Aspects of Negator Algebra in SOC

Recent developments in loop quantum gravity and topological quantum field theory are being mirrored with a view to the emergent structure of self- organized criticality (SOC). Referring back to an earlier paper [nlin.AO/ 0105064], the relationship of SOC to negator algebra is discussed. It is shown that introducing the categorial perspective leads to further holistic conclusions of considerable universality. This present paper shall serve as a preparation of a concrete research project under way designed to illustrate this very universality. Hence, it belongs to a series of recent publications discussing the modern and fruitful interaction between philosophy and the sciences, beyond mere historical aspects and the traditional rephrasing of well-known scientific results.

nlin.AO↗

arXiv2009

Saturation of Stationary Inversion States in a Three-Level Traveling-Wave Quantum Amplifier with Bistable Resonator Pumping

The inversion states of a saturated traveling-wave three-level quantum paramagnetic amplifier have been investigated under conditions of bistable resonator pumping. The equations of motion for the vectorial order parameter have been obtained using adiabatic elimination of fast variables. The exact solutions for stationary inversion states have been found from these equations. For high-quality pump resonators, the isolated and the semi-isolated branches of the inversion ratio have been revealed in stationary solutions. The existence of the semi-isolated branches means a possibility of collapse of the inversion state under influence of a saturating signal. Revival of inversion is possible in this case only by the hard excitation of the pump system. This nonlinear phenomenon is of a qualitatively another nature than one described by us in arXiv:0901.0449v1 [nlin.AO], and may be observed at moderate Q-factor of pump resonator.

nlin.SI↗

arXiv2008

Turing patterns on networks

Turing patterns formed by activator-inhibitor systems on networks are considered. The linear stability analysis shows that the Turing instability generally occurs when the inhibitor diffuses sufficiently faster than the activator. Numerical simulations, using a prey-predator model on a scale-free random network, demonstrate that the final, asymptotically reached Turing patterns can be largely different from the critical modes at the onset of instability, and multistability and hysteresis are typically observed. An approximate mean-field theory of nonlinear Turing patterns on the networks is constructed.

nlin.PS↗

arXiv2019

Self-organized critical balanced networks: a unified framework

Asynchronous irregular (AI) and critical states are two competing frameworks proposed to explain spontaneous neuronal activity. Here, we propose a mean-field model with simple stochastic neurons that generalizes the integrate-and-fire network of Brunel (2000). We show that the point with balanced inhibitory/excitatory synaptic weight ratio $g_c \approx 4$ corresponds to a second order absorbing phase transition usual in self-organized critical (SOC) models. At the synaptic balance point $g_c$, the network exhibits power-law neuronal avalanches with the usual exponents, whereas for nonzero external field the system displays the four usual synchronicity states of balanced networks. We add homeostatic inhibition and firing rate adaption and obtain a self-organized quasi-critical balanced state with avalanches and AI-like activity. Our model might explain why different inhibition levels are obtained in different experimental conditions and for different regions of the brain, since at least two dynamical mechanisms are necessary to obtain a truly balanced state, without which the network may hover in different regions of the presented theoretical phase diagram.

nlin.AO↗

arXiv2019

Lévy noise induced transitions and enhanced stability in a birhythmic van der Pol system

This work describes the effects of Lévy noise on a birhythmic van der Pol like oscillator. Numerical simulations demonstrate that the noise induced escapes from an attractor to another are not markedly different from escapes between stable points in an ordinary potential, albeit the attractors are separated by a barrier of a quasi (or pseudo) potential. However, some differences appear, and are more pronounced when the Lévy distribution index is close to two.

cond-mat.stat-mech↗

arXiv2007

Multi-Agent Approach to the Self-Organization of Networks

Is it possible to link a set of nodes without using preexisting positional information or any kind of long-range attraction of the nodes? Can the process of generating positional information, i.e. the detection of ``unknown'' nodes and the estabishment of chemical gradients, \emph{and} the process of network formation, i.e. the establishment of links between nodes, occur in parallel, on a comparable time scale, as a process of co-evolution? The paper discusses a model where the generation of relevant information for establishing the links between nodes results from the interaction of many \emph{agents}, i.e. subunits of the system that are capable of performing some activities. Their collective interaction is based on (indirect) communication, which also includes memory effects and the dissemination of information in the system. The relevant (``pragmatic'') information that leads to the establishment of the links then emerges from an evolutionary interplay of selection and reamplification.

nlin.AO↗

arXiv2007

Self-organization processes in laser system with nonlinear absorber and external force influence

We discuss mechanisms of self-organization processes in two-level solid-state class-B laser system. The model is considered under assumptions of influence of nonlinear absorber and external force, separately. It was found that self-organization occurs through the Hopf bifurcation and results to a stable pulse radiation. Analysis is performed according to the Floquet exponent investigation. It was found that influence of the nonlinear absorber extends the domain of control parameters that manage a stable periodic radiation processes. An external force suppresses self-organization processes. A combined influence of both external force and nonlinear absorber results to more complicated picture of self-organization with two reentrant Hopf bifurcations.

nlin.AO↗

arXiv2007

Non-coding DNA programs express adaptation and its universal law

Significant fraction (98.5% in humans) of most animal genomes is non- coding dark matter. Its largely unknown function (1-5) is related to programming (rather than to spontaneous mutations) of accurate adaptation to rapidly changing environment. Programmed adaptation to the same universal law for non-competing animals from anaerobic yeast to human is revealed in the study of their extensively quantified mortality (6-21). Adaptation of animals with removed non-coding DNA fractions may specify their contribution to genomic programming. Emergence of new adaptation programs and their (non-Mendelian) heredity may be studied in antibiotic mini-extinctions (22-24). On a large evolutionary scale rapid universal adaptation was vital for survival, and evolved, in otherwise lethal for diverse species major mass extinctions (25-28). Evolutionary and experimental data corroborate these conclusions (6-21, 29-32). Universal law implies certain biological universality of diverse species, thus quantifies applicability of animal models to humans). Genomic adaptation programming calls for unusual approach to its study and implies unanticipated perspectives, in particular, directed biological changes.

q-bio.GN↗

arXiv2007

Diversity Begets Stability in an Evolving Network

Complex evolving systems such as the biosphere, ecosystems and societies exhibit sudden collapses, for reasons that are only partially understood. Here we study this phenomenon using a mathematical model of a system that evolves under Darwinian selection and exhibits the spontaneous growth, stasis and collapse of its structure. We find that the typical lifetime of the system increases sharply with the diversity of its components or species. We also find that the prime reason for crashes is a naturally occurring internal fragility of the system. This fragility is captured in the network organizational character and is related to a reduced multiplicity of pathways between its components. This work suggests new parameters for understanding the robustness of evolving molecular networks, ecosystems, societies, and markets.

nlin.AO↗

arXiv2007

A New Model for the Organizational Knowledge Life Cycle

Actual organizations, in particular the ones which operate in evolving and distributed environments, need advanced frameworks for the management of the knowledge life cycle. These systems have to be based on the social relations which constitute the pattern of collaboration ties of the organization. We demonstrate here, with the aid of a model taken from the theory of graphs, that it is possible to provide the conditions for an effective knowledge management. A right way could be to involve the actors with the highest betweeness centrality in the generation of discussion groups. This solution allows the externalization of tacit knowledge, the preservation of knowledge and the raise of innovation processes.

physics.gen-ph↗

arXiv2007

Graph spectra as a systematic tool in computational biology

We present the spectrum of the (normalized) graph Laplacian as a systematic tool for the investigation of networks, and we describe basic properties of eigenvalues and eigenfunctions. Processes of graph formation like motif joining or duplication leave characteristic traces in the spectrum. This can suggest hypotheses about the evolution of a graph representing biological data. To this data, we analyze several biological networks in terms of rough qualitative data of their spectra.

nlin.AO↗

arXiv2007

What Makes a System Complex? an Approach to Self-Organization and Emergence

The fast changing reality in technical and natural domains perceived by always more accurate observations has drawn attention on new and very broad class of systems with specific behaviour represented under the common wording complexity. From elementary system graph representation with components as nodes and interactions as vertices, systems are shown to belong to only three states : simple, complicated, and complex, the main properties of which are discussed. The first two states have been studied at length over past centuries, and last one finds its origin in the elementary fact that when system performance is pushed up, there exists a threshold above which interaction between components overtake outside interaction. Then system self-organizes and filters corresponding outer action, making it more robust to outer effect, with emergence of new behaviour not predictable from only components study. Examples in Physics and Biology are given. Three main classes of complexity behaviour are distinguished corresponding to different grades of difficulty to handle their dynamics. The interest of using complex state properties in man-made systems is stressed. Important issues concentrating on the difficult balance between relative system isolation when becoming complex and required delegation of corresponding new capability from (outside) operator are discussed. This implies giving the system some intelligence in an adequate frame between new augmented system state and supervising operator, with consequences on canonical system triplet {effector-sensor-controller} to be reorganized in this new setting. Moreover, entering complexity state opens the possibility for function to feedback onto structure, ie to mimic at technical level the invention of Nature over Her very long history.

nlin.AO↗

arXiv2007

Emergence and resilience of cooperation in the spatial Prisoner's Dilemma via a reward mechanism

We study the problem of the emergence of cooperation in the spatial Prisoner's Dilemma. The pioneering work by Nowak and May showed that large initial populations of cooperators can survive and sustain cooperation in a square lattice with imitate-the-best evolutionary dynamics. We revisit this problem in a cost-benefit formulation suitable for a number of biological applications. We show that if a fixed-amount reward is established for cooperators to share, a single cooperator can invade a population of defectors and form structures that are resilient to re-invasion even if the reward mechanism is turned off. We discuss analytically the case of the invasion by a single cooperator and present agent-based simulations for small initial fractions of cooperators. Large cooperation levels, in the sustainability range, are found. In the conclusions we discuss possible applications of this model as well as its connections with other mechanisms proposed to promote the emergence of cooperation.

q-bio.PE↗

arXiv2007

Stability of Localized Patterns in Neural Fields

We investigate two-dimensional neural fields as a model of the dynamics of macroscopic activations in a cortex-like neural system. While the one-dimensional case has been treated comprehensively by Amari 30 years ago, two-dimensional neural fields are much less understood. We derive conditions for the stability for the main classes of localized solutions of the neural field equation and study their behavior beyond parameter-controlled destabilization. We show that a slight modification of original model yields an equation whose stationary states are guaranteed to satisfy the original problem and numerically demonstrate that it admits localized non-circular solutions. Generically, however, only periodic spatial tessellations emerge upon destabilization of rotationally-invariant solutions.

nlin.AO↗

arXiv2007

Cycles in Nonlinear Macroeconomics

The monograph is concerned with some key problems of the theory of nonlinear economic dynamics. The authors' concept consists in analyzing the problem of structural instability of economic systems within the framework of the synergetic paradigm. As examples, the classical models of macroeconomics are considered. The authors present the results of the study of the phenomenon of self-organization in open and nonequilibrium economic systems. The generation of limit cycles, as well as of more complex periodic structures, is discussed; the character of their stability is examined.

nlin.AO↗

arXiv2008

A model for learning to segment temporal sequences, utilizing a mixture of RNN experts together with adaptive variance

This paper proposes a novel learning method for a mixture of recurrent neural network (RNN) experts model, which can acquire the ability to generate desired sequences by dynamically switching between experts. Our method is based on maximum likelihood estimation, using a gradient descent algorithm. This approach is similar to that used in conventional methods; however, we modify the likelihood function by adding a mechanism to alter the variance for each expert. The proposed method is demonstrated to successfully learn Markov chain switching among a set of 9 Lissajous curves, for which the conventional method fails. The learning performance, analyzed in terms of the generalization capability, of the proposed method is also shown to be superior to that of the conventional method. With the addition of a gating network, the proposed method is successfully applied to the learning of sensory-motor flows for a small humanoid robot as a realistic problem of time series prediction and generation.

nlin.AO↗

arXiv2007

Self-Replicating Space-Cells and the Cosmological Constant

We consider what the implications would be if there were a discrete fundamental model of physics based on locally-finite self-interacting information, in which there is no presumption of the familiar space and laws of physics, but from which such space and laws can nevertheless be shown to be able to emerge stably from such a fundamental model. We argue that if there is such a model, then the familiar laws of physics, including Standard Model constants, etc., must be encodable by a finite quantity C, called the complexity, of self-interacting information I, called a Space-Cell. Copies of Space-Cell I must be distributed throughout space, at a roughly constant and near-Planck density, and copies must be created or destroyed as space expands or contracts. We then argue that each Space-Cell is a self-replicator that can duplicate in times ranging from as fast as near-Planck-times to as slow as Cosmological-Constant-time which is 10^{61} Planck-times. From standard considerations of computation, we argue this slowest duplication rate just requires that 10^{61} is less than about 2^C, the number of length-C binary strings, hence requiring only the modest complexity C at least 203, and at most a few thousand. We claim this provides a reasonable explanation for a dimensionless constant being as large as 10^{61}, and hence for the Cosmological Constant being a tiny positive 10^{-122}. We also discuss a separate conjecture on entropy flow in Hole-Bang Transitions. We then present Cosmological Natural Selection II.

gr-qc↗

arXiv2014

Self-Organized Characteristics of the International System

Various self-organized characteristics of the international system can be identified with the help of a complexity science perspective. The perspective discussed in this article is based on various complexity science concepts and theories, and concepts related to ecology and ecosystems. It can be argued that the Great Power war dynamics of the international system in Europe during the period 1480-1945, showed self-organized critical (SOC) characteristics, resulting in a punctuated equilibrium dynamic. It seems that the SOC-characteristics of the international system and the punctuated equilibrium dynamic were - in combination with chaotic war dynamics - functional in a process of social expansion in Europe. According to a model presented in this article, population growth was a component of the driving force of the international system during this time frame. The findings of this exploratory research project contradict with generally held opinions in International Relations theory.

nlin.AO↗