Book
History & Mathematics: Economy, Demography, Culture, and Cosmic Civilizations
The present Yearbook (which is the sixth in the series) is subtitled Economy, Demography, Culture, and Cosmic Civilizations. To some extent it reveals the extraordinary potential of scientific research. The common feature of all our Yearbooks, including the present volume, is the usage of formal methods and social studies methods in their synthesis to analyze different phenomena. In other words, if to borrow Alexander Pushkin's words, ‘to verify the algebra with harmony'. One should note that publishing in a single collection the articles that apply mathematical methods to the study of various epochs and scales  from deep historical reconstruction to the pressing problems of the modern world  reflects our approach to the selection of contributions for the Yearbook. History and Mathematics, Social Studies and formal methods, as previously noted, can bring nontrivial results in the studies of different spheres and epochs. This issue consists of three main sections: (I) Historical and Technological Dimensions includes two papers (the first is about the connection between genes, myths and waves of the peopling of Americas; the second one is devoted to quantitative analysis of innovative activity and competition in technological sphere in the Middle Ages and Modern Period); (II) Economic and Cultural Dimensions (the contributions are mostly focused on modern period); (III) Modeling and Theories includes two papers with interesting models (the first one concerns modeling punctuated equilibria apparent in the macropattern of urbanization over time; in the second one the author attempts to estimate the number of Communicative Civilizations). We hope that this issue will be interesting and useful both for historians and mathematicians, as well as for all those dealing with various social and natural sciences.

The paper presents a quantitative analysis of innovative activity and competition in technological sphere in the Middle Ages and Modern Period (till the end of the 20th century). The authors consider the innovative competition in two aspects. The first section of the present paper shows the growth of the number of innovations over halfcentury intervals in Europe and Asia. As is widely accepted at present, by the early 2nd millennium CE Europe lagged far behind the main eastern countries not only in terms of development of the productive forces but in respect of many relevant parameters. According to some data, Europe failed to outrun China (as regards scientifictechnological growth rates) not only in the 12th or 13th, but even in the 14th century. On the other hand, the authors show a rather vigorous acceleration of those rates in Europe since the 12th century with one more such acceleration in the 13th century (when Medieval Europe produced its first paradigm changing inventions  initially, the invention of the spectacles and the mechanical clock). In the 15th century Europe definitely outpaced Asia. After such historical breakthrough, it is very important to trace how the leadership has changed in this respect within Europe. The second and the following sections of the paper are devoted to this aspect. Here we consider the dynamics of technological inventions in Europe from the 15th to the 19th centuries. Our analysis of the technological innovation dynamics shows that: firstly, the British lead began to show up only in the second half of the 17th century; before Britain had clearly lagged behind Italy and Germany. Thus, during the two initial centuries of the Industrial Revolution Britain absorbed the achievements of European societies, and only then was it succeeded to start its own innovative climb. Secondly, though we observe the British evident leadership in the technological innovation from the second half of the 17th century to the first half of the 19th century, for a greater part of that period, the overall innovation activity of ‘the rest of the West' was higher than that of Britain. The primacy of Britain in the field of technological invention was absolute only during a relatively short period in the second half of the 18th century and the early 19th century, i.e. the period of the final phase of the Industrial Revolution. Thirdly, by the first half of the 19th century the British endogenous technological growth rate virtually stagnated against the background of a very fast increase of those rates in France, Germany and the USA, as a result of which those countries caught up with Britain in a rather significant way. Fourthly, in the second half of the 19th century Britain finally lost its technological lead, as in the late 19th century the number of major inventions made in the USA, Germany, and France exceeded the number of British inventions.
The spatial distribution of folkloremythological motifs is shown to correlate rather tightly with the distribution of mitochondrial DNA (mtDNA) and Ychromosome (NRY) haplogroups. The analysis of spatial distribution of folkloremythological motifs confirms earlier findings of geneticists which identified South Siberia as the Old World homeland of the main wave of the peopling of the New World (the diffusion of the respective populations in the New World turns out to be associated with the spread of Clovis and paraClovis archaeological cultures). Indeed, this is just South Siberia where the highest concentration of the Amerindian folkloremythological motifs in Eurasia is observed. On the other hand, it turns out to be possible to connect the penetration of mtDNA HG C and NRY HG Q > Q3 to the New World with this migration wave. The spatial distribution of the ‘CircumgobiAmerindian' folkloremythological motifs follows rather closely the distribution of mtDNA HG C in the New World. This makes it possible to reconstruct up to a considerable detail the mythology brought to the New World from South Siberia by this migration wave. Another migration wave turns out to be associated with the distribution of mtDNA HG B and motifs of ‘Melazonian' mythological complex whose highest concentration is observed in Melanesia, on the one hand, and Amazonia, on the other. These motifs form a few connected sets, which suggest certain possibilities for the reconstruction of some features of ‘protoMelazonian' mythology brought to the New World by the bearers of mtDNA HG B. MtDNA HG A frequencies in Siberian and American populations display a rather strong and statistically significant correlation with the number of the ‘Raven Cycle' motifs in respect of folkloremythological traditions. There are certain grounds to believe that both these motifs and the respective genetic marker (‘Arctic A') were brought to the extreme American NorthWest and extreme NorthEast Asia (‘Transberingia') later than both maternal lines B+C and CircumgobiAmerindian, Melazonian and UralAmerindian motifs had been brought to the New World. The presence of a relatively homogenous Transberingian ‘geneticmythological' zone characterized by high frequencies of both mtDNA HG A and the Transberingian motifs seems to be accounted for, first of all, by the fact that they were brought to this zone relatively later with the migrations apparently corresponding to the movement to this area of Dene, EskoAleut and ChukotkoKamchatkan language speakers and replaced to a considerable extent earlier genetic markers and folkloremythological motifs. But, on the other hand, the same fact seems to be additionally accounted for by the functioning up to the Modern Age of the Transberingian communicative network, as in the Holocene the communication through the Bering straits does not appear to have ever interrupted, and led to additional homogenization of the zone. And the movement through the Bering straits definitely went in both directions, in the framework of which their way to the Old World appears to have been found by both some New World genetic markers (e.g., NRY HG Q3), and apparently some folkloremythological motifs which were developed already in the New World (the possibility of the migration of some Transberingian motifs from the New World to the NE Asia [suggested {in a bit exaggerated way} already by the members of the Jesup Expedition] seems to be supported by a higher concentration of these motifs in the New World part of this zone). The analyzed evidence suggests that the UralAmerindian mythological complex was brought to the New World by a wave of migration which took place between 10,000 and 13,000, i.e. not long after the main wave of the peopling of Americas.
The author refl ects upon the book The Sources of culturalhistorical psychology: philosophicalhumanitarian context by V. Zinchenko, B. Pruzhinin, T. Schedrina. Moscow, 2010.
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 stateofthe 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.
The main focus of this paper is the relation between the realisation of the right of the child to express his/her views and democracy in Russia. With this in view, I will study the interconnection between the right to express the views and the right to participate. Further, I will give an overview of the specifics of democracy in Russia, how they influence political participation, and what could be done to prevent the further infantilisation of citizens in Russia. Finally, I will explore traditional perceptions with regard to children’s participation in Russia and the legal framework and practice of the implementation of the child’s right to social and political participation.
This book directly confronts uncomfortable questions that many prefer to brush aside: if economists and other scholars, politicians, and business professionals understand the causes of economic crises, as they claim, then why do such damaging crises continue to occur? Can we trust business and intellectual elites who advocate the principles of Realpolitik and claim the "public good" as their priority, yet consistently favor maximization of profit over ethical issues?
Former deputy prime minister of Russia Grigory Yavlinsky, an internationally respected freemarket economist, makes a powerful case that the oftencited causes of global economic instability—institutional failings, wrong decisions by regulators, insufficient or incorrect information, and the like—are only secondary to a far more significant underlying cause: the failure to understand that universal social norms are essential to thriving businesses and social and economic progress. Yavlinsky explores the widespread disregard for moral values in business decisions and calls for restoration of principled behavior in politics and economic practices. The unwelcome alternative, he warns, will be a twentyfirstcentury global economy in the grip of unending crises.
Grigory Yavlinsky is a Russian economist and founder and member of the Russian United Democratic Party (YABLOKO). As deputy prime minister of Russia in 1990, he wrote the first Russian economic program for transition to a freemarket economy, 500 Days. He lives in Moscow.
Reviews
“Grigory Yavlinsky’s book is an important contribution to understanding the interplay between social norms and modern economy. The current global crisis makes his analysis especially relevant.”—George Soros
“Reading Grigory Yavlinsky's remarkable book, I was reminded of Adam Smith, also a moral philosopher concerned with the correlation between individual aspirations and the enlightened evolution of society. It is invaluable to have the perspective of an intellectual such as Yavlinsky writing in the shadow of swiftly moving events on the global stage. He explains how market mechanisms influence international developments ranging from instability in European markets to the recent ‘Great Recession’ in the United States.”—Vartan Gregorian, President, Carnegie Corporation of New York
“Yavlinsky provides a new and indepth interpretation of the events leading to the current recession and broader interpretations of how to avoid future ones. Realeconomik has my enthusiastic endorsement.”—Michael D. Intriligator, University of California, Los Angeles
“With clarity and eloquence, Yavlinsky argues that the deepest cause of the global recession was the erosion of the world economy’s moral dimensions. As a professional economist who has long been a leader of the Russian opposition, he knows how to splice politics and economics. As a politician who has repeatedly declined high office on grounds of principle, he lends the book additional authority. Realeconomik is a work that will, I believe, help to spark a public debate on issues of profound importance for humankind.”—Peter Reddaway, George Washington University
The economic crisis has revealed three particularly vulnerable development in Russia in the last decade: a growing resource of expertise, aging equipment and the lag in scientific and technological progress, institutional obstacles to the growth of the market economy. The article discusses the components of economic growth. How quickly evolving new economy and whether overcome monocultural specialization of the country? How to make this growth sustainable and irreversible, everything been done to enhance scientific and technological potential of the Russian Federation, that these arguments comes from the myths that Russia  the best country in the world, and that reflects the actual trends that and that helps prevent the escalation of Russia from the industrial society to a postindustrial society.
The article deals with current approaches to research on socialeconomic impacts of cultural events. A systematic approach is proposed to analysis of services provided within cultural events in behalf of different target groups — stakeholders.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnitedimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasisolutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasisolutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasisolutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasisolutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.
Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible crosssection of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a crosssection exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a crosssection in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational crosssection in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational Wequivariant map T   >G/T where T is a maximal torus of G and W the Weyl group.