The rich phase structure of a mutator model
We propose a modification of the Crow-Kimura and Eigen models of biological molecular evolution to include a mutator gene that causes both an increase in the mutation rate and a change in the fitness landscape. This mutator effect relates to a wide range of biomedical problems. There are three possible phases: mutator phase, mixed phase and non-selective phase. We calculate the phase structure, the mean fitness and the fraction of the mutator allele in the population, which can be applied to describe cancer development and RNA viruses. We find that depending on the genome length, either the normal or the mutator allele dominates in the mixed phase. We analytically solve the model for a general fitness function. We conclude that the random fitness landscape is an appropriate choice for describing the observed mutator phenomenon in the case of a small fraction of mutators. It is shown that the increase in the mutation rates in the regular and the mutator parts of the genome should be set independently; only some combinations of these increases can push the complex biomedical system to the non-selective phase, potentially related to the eradication of tumors.
The approaches to the modeling of innovative development of economic systems based on the methodology of nonlinear dynamics are proposed. The generalized nonlinear dynamic models for the analysis of economic development is discussed. The loss of stability of the dynamic mode and the area of deterministic chaos are considered in terms of risk analysis
Main concepts and models of the modern theory of self-organization of complex systems, called also synergetics, are generalized and formulated in the book as principles of a synergetic world view. They are under discussion in the context of philosophical studies of holism, teleology, evolutionism as well as of gestalt-psychology; they are compared with some images from the history of human culture. The original and unfamiliar (to the Western readers) research results of the Moscow synergetic school which has its center at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences are expounded in the book. Complicated and paradoxical concepts of synergetics (structure-attractors, bifurcations, blow-up regimes, non-stationary dissipative structures of self-organization, fractals, non-linearity) are translated into an intelligible language and vividly illustrated by materials and examples from various fields of knowledge, starting with the laser thermonuclear fusion and concluding with mysterious phenomena of human psychology and creativity. The style of writing is close to that of popular-science literature. That's why the book might be of interest and is quite comprehensible for students and specialists in the humanities. It is shown that the development of synergetics entails deep changes in the conceptual net through which we comprehend the world. It means a radical shift of paradigm, a conceptual transition from being to becoming, from stability to sustainability, from images of order to chaos generating new ordered evolving structures, from self-maintaining systems to fast evolution through a nonlinear positive feedback, from evolution to co-evolution, reciprocal evolution of different complex systems. The new synergetic way of thinking is evolutionary, nonlinear and holistic. This is a modern stage of development within the traditions of cybernetics and system-structural analysis. However, many elements of the latter have undergone important changes since their appearance.
Some texts written by me together with corresponding member of the Russian Academy of science Sergei P. Kurdyumov (1928-2004) and under his direct ideological influence are collected in the book. These texts are elaborated, systematized, brought together in the book and supplemented with new materials. Sergei P. Kurdyumov were possessed of a deep metaphysical flair and put forward ideas, the matter of which are not fully clear up to now. These are, first of all, the idea of co-evolution and the notion of complex structures developing at different tempos as co-existing tempo-worlds. Owing to developments in the field of nonlinear dynamics and of synergetics, the classical problem of time and the problems of evolutionary holism disclose some new and non-traditional aspects. The matter of new notions of nonlinearity of the course of time in the processes of evolution and coevolution and of nonlinear links between different modi of time – between the past, the present and the future - come to the light in the book. Analyses of four interconnected aspects of the course of processes in open and nonlinear dissipative systems – of evolutionarity, temporality, emergent nature and holism – are carried out. A whole series of paradoxical notions, such as “the influence of the future upon the present”, “the possibility of touch of a remote future in praesenti”, irreversibility and elements of reversibility of the course of time appear in synergetics, non-traditional and nonlinear notion of time being at the heart of all of them. It is shown that the best pictorial view of the nonlinear time is apparently the tree of evolution or the tree of time that represent one of archetypes in the human psyche. This image is widely used in myths and religious doctrines of the world nations (the tree of evolution of languages from some united parent language or the tree of evolution of biological species), the image is often drawn by children, appears in consciousness of a man in his sleep, etc. The synergetics methodology under development is applied to study of cognitive systems. The emergent structures of evolution and of self-organization of the individual consciousness, their spatiotemporal peculiarities, and the complexity of the human Self are considered in detail. The radical changes in the understanding of the problems of time that occur due to synergetics are compared with images of time and with the notions of connection between the past, the present and the future in the history of philosophy and of culture. The obtained methodological inferences are of great importance for a reform of systems of education, for forecasting (for building of scenarios of future development), for effective management activity in the modern globalizing world, for elaboration of methods of stimulation of the creative thinking, for the growth of personality and its adequate building into the social media.
In this paper, we construct a new distribution corresponding to a real noble gas as well as the equation of state for it.
For a gas mixture, the new concept of number-theoretic internal energy is introduced. This energy does not depend on the masses of the miscible gases.
We construct an example of blow-up in a ”ow of min-plus linear operators arising as solution operators for a Hamilton…Jacobi equation @S/@t+|∇S|/ + U(x, t) = 0, where > 1 and the potential U(x, t) is uniformly bounded together with its gradient. The construction is based on the fact that, for a suitable potential de“ned on a time interval of length T, the absolute value of velocity for a Lagrangian minimizer can be as large as O(log T)2−2/. We also show that this growth estimate cannot be surpassed. Implications of this example for existence of global generalized solutions to randomly forced Hamilton…Jacobi or Burgers equations are discussed.
Main concepts and models of the modern theory of self-organization of complex systems, called also synergetics, are generalized and formulated in the book as principles of a synergetic world view. They are under discussion in the context of philosophical studies of holism, teleology, evolutionism as well as of gestalt-psychology; they are compared with some images from the history of human culture. The original and unfamiliar (to the Western readers) research results of the Moscow synergetic school which has its center at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences are expounded in the book. The heuristic value of the synergetic models of evolution and self-organization of complex systems in epistemology and cognitive psychology, education and teaching, futures studies, social management activities and systems of global security is shown in the book. The book is addressed to a wide circle of readers: students, teachers, scientists who are specialized in different fields of natural sciences and the humanities as well as to all readers who strive for using recent results of science for reflections and achieving success in their own life.
A method based on the spectral analysis of thermowave oscillations formed under the effect of radiation of lasers operated in a periodic pulsed mode is developed for investigating the state of the interface of multilayered systems. The method is based on high sensitivity of the shape of the oscillating component of the pyrometric signal to adhesion characteristics of the phase interface. The shape of the signal is quantitatively estimated using the correlation coefficient (for a film–interface system) and the transfer function (for multilayered specimens).
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.