One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the author's lectures, presents several new directions of mathematical research. (...) All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI). (shrink)

We present a novel variant of decision making based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to describe a variety of interesting fallacies and anomalies that have been reported to particularize the decision making of real human beings. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. We demonstrate how the violation of the Savage’s sure-thing principle, known (...) as the disjunction effect, can be explained quantitatively as a result of the interference of intentions, when making decisions under uncertainty. The disjunction effects, observed in experiments, are accurately predicted using a theorem on interference alternation that we derive, which connects aversion-to-uncertainty to the appearance of negative interference terms suppressing the probability of actions. The conjunction fallacy is also explained by the presence of the interference terms. A series of experiments are analyzed and shown to be in excellent agreement with a priori evaluation of interference effects. The conjunction fallacy is also shown to be a sufficient condition for the disjunction effect, and novel experiments testing the combined interplay between the two effects are suggested. (shrink)

The article is devoted to the memory of Vyacheslav Semenovich Stepin and Nikita Nikolaevich Moiseev, whose multifaceted work was integrally focused on philosophical, interdisciplinary and transdisciplinary research of the key ideas and principles of universal human-dimensional evolutionism. Other remarkable Russian scientists V.I. Vernadsky, S.P. Kurdyumov, S.P. Kapitsa, D.S. Chernavsky worked in the same tradition of universal evolutionism. While V.I. Vernadsky and N.N. Moiseev had been the originators of that scientific approach, V.S. Stepin provided philosophical foundations for the ideas of those (...) remarkable scientists and thinkers. The scientific legacy of V.S. Stepin and N.N. Moiseev maintained the formation of a new quality of research into the philosophy of science and technology as well as into the philosophy of culture. This new quality is multidimensional and it is difficult to define unambiguously, but we presume the formation of those areas of philosophical knowledge as constructively oriented languages of interdisciplinary and transdisciplinary co-participation of philosophy in the convergent-evolutionary development of scientific knowledge in general. In this regard, attention is paid to V.S. Stepin’s affirmations about non-classical nature of modern social and humanitarian knowledge. Quantum mechanics teaches us that the reality revealed through it is a hybrid construct, or symbiosis, of both mean and object of cognition. Therefore, the very act of cognitive observation constructs quantum reality. Thus, it is very close to the process of cognition in modern sociology and psychology. V.S. Stepin insisted that these principles are applicable to all complex selfdeveloping systems, and such are all “human-dimensional” objects of modern humanities. In all the phases of homeostasis changes, or crises, there is necessarily a share of chaos, instability, uncertainty in the selection process of future development scenarios, which is ineliminably affected by our observation. Therefore, a cognitive observer in the humanities should be considered as a concept of post-non-classical rationality, that is as an observer of complexity. (shrink)

The decade that has elapsed since the flight of the world's first cosmonaut, Iu. A. Gagarin, has been marked by considerable successes in mastering the cosmos. Lengthy orbital flights and lunar expeditions are already being conducted. Automatic stations are studying the moon, Mars, Venus, and cosmic space. And although we understand that the major trumphs in space are still ahead of us and that today we are merely at the start of the cosmic era, it is nonetheless already possible, in (...) this year of the tenth anniversary of the first human space flight, to draw certain conclusions and discuss the results of human intrusion into the expanses of the universe. (shrink)

At present there is an enormous discrepancy between our nanotechnological capabilities (particularly our nanobiotechnologies), our social wisdom, and consensus on how to apply them. To date, cost considerations have greatly constrained our application of nanotechnologies. However, novel advances in microsystem platform technologies are about to greatly diminish that economic constraint while developing new industries. Properly used in a solid legal and ethical framework, within an educated population, these advances will vastly enrich our quality of life without being intrusive. Improperly used, (...) these technologies could lead to a modern-day Luddism, social turmoil, or possibly even to emulating those societies described in the darkest of novels. These technologies must be developed in tandem with the social and legal frameworks needed to ensure that they improve both individuals and our society. To ensure that this occurs, we need to have the ethical, legal, scientific, and engineering experts working together and with the public. (shrink)

BackgroundPublic awareness and engagement are among the main prerequisites for protecting the rights of research participants and for successful and sustainable functioning of research biobanks. The aim of our study was to analyse public awareness and attitudes towards research biobanks in Latvia, and to compare these data with the results of the 2010 Eurobarometer study. We also analysed the influence of awareness and attitudes towards biobanks on willingness to participate in biobank studies and on preferred type of informed consent.MethodsWe developed (...) a 12-question survey repeating seven questions about biobanks from the 2010 Eurobarometer questionnaire and adding five others. After describing the study variables, we performed a two-stage analysis of the results. In the first stage we analysed differences between the answers from 2010 and 2019 and conducted univariate analyses of relationships among particular variables, and between those variables and the socio-demographic characteristics of participants. In the second stage we investigated multivariable associations of willingness to participate and type of consent with awareness, trust and the socio-economic characteristics of participants.ResultsAccording to our study, the general public in Latvia is still not well informed about research biobanks. Fewer respondents have heard about research biobanks than in 2010. At the same time, the number of respondents who are willing to donate biological samples and personal data to a biobank has increased, e.g. the number of respondents who would definitely or probably be willing to provide information about themselves has increased from 25.8.% to 40.7 since 2010. Overall, concerns about the donation of different types of biological samples and data to a biobank have slightly decreased.ConclusionsPublic awareness about biobanks is important for their sustainability. It needs to be increased not only by traditional methods of informing the public, but also by more innovative and participatory approaches, e.g. by citizen science projects. There is a need to strengthen the public visibility and trustworthiness of ethics committees in Latvia in the field of biobanking. (shrink)

I should like to supplement somewhat the interpretation of the data presented by D.E. Furman. It seems to me that to understand current processes, we must have a clearer idea of the starting point of the present intellectual movement—the "mass atheism" of the preceding period. What was this mass atheism?

Aleksei Fedorovich Losev did not share the hereditary Russian prejudice that science and philosophy exclude religion . Although he did not leave any specialized works in theology, the history of religion, or the foundations of the Christian worldview, many of his books, lines from letters, and fragments of conversations and, most importantly, his whole way of life and life journey show that all his life he reflected continuously and intensely on themes of the Christian faith and, primarily, of the Orthodox (...) faith that he confessed. Not only did he reflect on them, he lived by them. For Aleksei Fedorovich Christianity was never just an object of knowledge, a preoccupation of the reflective mind, but rather the profound foundation of his relationship with the world and with people. It constituted not only his thought and its foundation, but his very life. Religion, as Aleksei Fedorovich understood it, is first of all a certain kind of life, not just a personal worldview, however religious and mystical it might be. It was not a personal morality, however lofty or religious it might be, nor personal feeling or esthetics, however ardent the feeling might be or however perfectly mystical the esthetics. Religion, in his mind, is the realization of a worldview, the material substance of morality, the real affirmation of feeling; it is the life of the person directed to the persons substantial self-affirmation, to self-affirmation in eternity . In recounting the facts of Aleksei Fedorovichs spiritual biography I shall not follow their chronological order. The basic facts can be found in the works of A.A. Takho-Godi, D. Dzhokhadze, M. Gogotishvili, and others. (shrink)

Aging is associated with decreased functional connectivity in the main brain networks, which can underlie changes in cognitive and emotional processing. Neurofeedback is a promising non-pharmacological approach for the enhancement of brain connectivity. Previously, we showed that a single session of infra-low frequency neurofeedback results in increased connectivity between sensory processing networks in healthy young adults. In the current pilot study, we aimed to evaluate the possibility of enhancing brain connectivity during aging with the use of infra-low frequency neurofeedback. Nine (...) females aged 52 ± 7 years with subclinical signs of emotional dysregulation, including anxiety, mild depression, and somatoform symptoms, underwent 15 sessions of training. A resting-state functional MRI scan was acquired before and after the training. A hypothesis-free intrinsic connectivity analysis showed increased connectivity in regions in the bilateral temporal fusiform cortex, right supplementary motor area, left amygdala, left temporal pole, and cerebellum. Next, a seed-to-voxel analysis for the revealed regions was performed using the post- vs. pre-neurofeedback contrast. Finally, to explore the whole network of neurofeedback-related connectivity changes, the regions revealed by the intrinsic connectivity and seed-to-voxel analyses were entered into a network-based statistical analysis. An extended network was revealed, including the temporal and occipital fusiform cortex, multiple areas from the visual cortex, the right posterior superior temporal sulcus, the amygdala, the temporal poles, the superior parietal lobule, and the supplementary motor cortex. Clinically, decreases in alexithymia, depression, and anxiety levels were observed. Thus, infra-low frequency neurofeedback appears to be a promising method for enhancing brain connectivity during aging, and subsequent sham-controlled studies utilizing larger samples are feasible. (shrink)

The importance of communities in strengthening the ethics of international collaborative research is increasingly highlighted, but there has been much debate about the meaning of the term ‘community’ and its specific normative contribution. We argue that ‘community’ is a contingent concept that plays an important normative role in research through the existence of morally significant interplay between notions of community and individuality. We draw on experience of community engagement in rural Kenya to illustrate two aspects of this interplay: (i) that (...) taking individual informed consent seriously involves understanding and addressing the influence of communities in which individuals’ lives are embedded; (ii) that individual participation can generate risks and benefits for communities as part of the wider implications of research. We further argue that the contingent nature of a community means that defining boundaries is generally a normative process itself, with ethical implications. Community engagement supports the enactment of normative roles; building mutual understanding and trust between researchers and community members have been important goals in Kilifi, requiring a broad range of approaches. Ethical dilemmas are continuously generated as part of these engagement activities, including the risks of perverse outcomes related to existing social relations in communities and conditions of ‘half knowing’ intrinsic to processes of developing new understandings. (shrink)

The development of the social sciences needs to rely on precise methods. The nomological model of explanation adopted in the natural sciences is ill-suited for the social sciences. An algorithmic model of society can be a promising solution to existing problems. In its most general form, an algorithm is a generally understood prescription for what actions to perform and in what order to achieve the desired result. Any algorithm can be represented as a set of rules of the form «If (...) A, do D to get P». People are the bearers of this kind of rules that apply in different areas of their activities. The rules are subject to change based on personal and collective experience. There is a special mathematical discipline that studies the laws of evolution of such rules. This discipline is called genetic programming. Contrary to the threatening name, the algorithmic model does not imply the deprivation of a person’s right to free choice, but it needs this right as a necessary condition for the evolution of social algorithms. These algorithms allow us to give a non-causal, but law-like explanation of many well-known social phenomena, as well as to effectively model the future, which is critically important today. A retrospective look at the evolution of social algorithms shows that the current global crisis of human society is associated with the approach to the point of singularity in their evolution. This is due to the fact that there is no need for direct human participation in the implementation of social algorithms, which is reflected in a fundamental change in the sphere of employment and less need for further development of the sciences. (shrink)

© 2016 Regents of the University of California.The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 3,062 new measurements from 721 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. All the particle properties and search limits are listed in Summary Tables. We also give numerous (...) tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 117 reviews are many that are new or heavily revised, including those on Pentaquarks and Inflation. The complete Review is published online in a journal and on the website of the Particle Data Group. The printed PDG Book contains the Summary Tables and all review articles but no longer includes the detailed tables from the Particle Listings. A Booklet with the Summary Tables and abbreviated versions of some of the review articles is also available. (shrink)

Предназначено для студентов художественных вузов и факультетов, а также для учащихся профессиональных учебных заведений художественного профиля.

Idealizm Platona -- Skholastika XIX veka -- Pchëly -- Russkoepravitelʹstvo pod pokrovitelʹstvom Shedo-Ferroti -- Russkiĭ Don-Kikhot -- Ocherki iz istorii truda -- Progress v mire zhivotnykh i rasteniĭ -- Populi︠a︡rizatory otrit︠s︡atelʹnykh doktrin -- Genrikh Geĭne -- Mysli︠a︡shchiĭ proletariat.