Geometric complexity theory and matrix powering

Valiant's famous determinant versus permanent problem is the flagship problem in algebraic complexity theory. Mulmuley and Sohoni (Siam J Comput 2001, 2008) introduced geometric complexity theory, an approach to study this and related problems via algebraic geometry and representation theory. Their approach works by multiplying the permanent polynomial with a high power of a linear form (a process called padding) and then comparing the orbit closures of the determinant and the padded permanent. This padding was recently used heavily to show no-go results for the method of shifted partial derivatives (Efremenko, Landsberg, Schenck, Weyman, 2016) and for geometric complexity theory (Ikenmeyer Panova, FOCS 2016 and B\"urgisser, Ikenmeyer Panova, FOCS 2016). Following a classical homogenization result of Nisan (STOC 1991) we replace the determinant in geometric complexity theory with the trace of a variable matrix power. This gives an equivalent but much cleaner homogeneous formulation of geometric complexity theory in which the padding is removed. This radically changes the representation theoretic questions involved to prove complexity lower bounds. We prove that in this homogeneous formulation there are no orbit occurrence obstructions that prove even superlinear lower bounds on the complexity of the permanent. This is the first no-go result in geometric complexity theory that rules out superlinear lower bounds in some model. Interestingly---in contrast to the determinant---the trace of a variable matrix power is not uniquely determined by its stabilizer

ABO genetic system, sexually transmitted infections and androgen-associated dermatoses

In the middle of 20th century, it was proved that ABO genetic system was the result of play of selection, including the infectious mortality due to two deadly epidemic collisions in the antiquity and with the main scene being Asian societies. It was discovered that plague tended to kill blood group O while smallpox blood group A carriers. Onwards no link was sought between this evolutionary phenomenon and blood group-related sexually transmitted infections and recurrent androgen-associated dermatoses (such as pityriasis versicolor and acne vulgaris) as well as sexual and fertility activity. Here we Dance Round such possible links. We found that these are expressed more strongly by blood group B carriers, and an attempt at translation of some relationships into population (intercontinental) level. We emphasize the genesis of blood group-related population gene pool equilibrium level and its attributes such as complex defense responses and co-operated immune reactions.Biomedical Reviews 2011; 22: 77-80

The effect of multiple paternity on genetic diversity during and after colonisation

In metapopulations, genetic variation of local populations is influenced by the genetic content of the founders, and of migrants following establishment. We analyse the effect of multiple paternity on genetic diversity using a model in which the highly promiscuous marine snail Littorina saxatilis expands from a mainland to colonise initially empty islands of an archipelago. Migrant females carry a large number of eggs fertilised by 1 - 10 mates. We quantify the genetic diversity of the population in terms of its heterozygosity: initially during the transient colonisation process, and at long times when the population has reached an equilibrium state with migration. During colonisation, multiple paternity increases the heterozygosity by 10 - 300 % in comparison with the case of single paternity. The equilibrium state, by contrast, is less strongly affected: multiple paternity gives rise to 10 - 50 % higher heterozygosity compared with single paternity. Further we find that far from the mainland, new mutations spreading from the mainland cause bursts of high genetic diversity separated by long periods of low diversity. This effect is boosted by multiple paternity. We conclude that multiple paternity facilitates colonisation and maintenance of small populations, whether or not this is the main cause for the evolution of extreme promiscuity in Littorina saxatilis.Comment: 7 pages, 5 figures, electronic supplementary materia

Финансы в России и мире: концептуальные аспекты

The modern digital economy requires “new finance”. The subject of the study is to clarify their content, and the goal is to develop the author’s view of the term of “finance”. The relevance of the topic is dictated by the need to analyze complex theoretical questions of technological transformation of financial markets and activities of financial intermediaries. The scientific novelty consists of the theoretical contribution of the theory of finance evolution in the digital era. The main research methods are systemic and logical approaches, the method of theoretical cognition, the historical method and the method of scientific abstraction. The results of the study are clarification the essence of finance and applied issues of their use in Russia and abroad. It will contribute to the development of a scientific doctrine of digital assets circulation; will allow to refine the model of the activities of financial intermediaries’ regulation in our country and lay the foundation for the formation of global norms and rules for the development of national and international financial markets of the CIS, the EAEU, the SCO, and BRICS countries. The conclusions of the study are: a) confirmation of the author’s position on the essence of finance. The paper indicates that, in the context of the economy’s digital revolution, the substance of economic categories stays constant, although their forms vary according to innovation, behavioral characteristics, and other factors; b) without rejecting the rational knowledge formed in the Western scientific school, the authors emphasize that the social sciences cannot be global, they have a national character; c) based on the investigation, the author defines “finance” as a distribution category in the development and utilization of financial resources.Современная цифровая экономика требует «новых финансов». Предметом исследования является выяснение их содержания, а целью — разработка авторской позиции толкования дефиниции «финансы». Актуальность темы продиктована необходимостью исследовать сложные теоретические вопросы технологической трансформации финансовых рынков и деятельности финансовых посредников. Научная новизна состоит в обосновании эволюции теории финансов в цифровую эпоху. Основными методами исследования являются системный, логический, теоретического познания, исторический и  научной абстракции. Результаты исследования включают выяснение сущности и прикладных вопросов использования финансов в России и за рубежом, что, по мнению авторов, будет способствовать развитию научной доктрины обращения цифровых активов; позволит скорректировать модель регулирования деятельности финансовых посредников в нашей стране и заложить основу формирования наднациональных норм и  правил развития национальных и  международных финансовых рынков стран СНГ, ЕАЭС, ШОС, БРИКС. Выводы исследования включают: а) обоснование авторской позиции о сущности финансов. В статье подчеркивается, что в условиях цифровой трансформации экономики сущность экономических категорий остается неизменной, в то время как их формы видоизменяются под влиянием инноваций, поведенческих аспектов и других факторов; б) не отвергая рациональное знание, сформировавшееся в западной научной школе, авторы подчеркивают, что общественные науки не могут быть глобальными, они имеют национальный характер; в) на основе проведенного анализа дано авторское определение дефиниции «финансы» как распределительной категории в процессе формирования и использования финансовых ресурсов

Chemical weathering of lower paleozoic black shales of south Sweden

Lower Paleozoic black shales are widespread in Sweden and form part of the Baltic paleobasin, which deposits are also known in Estonia and the Leningrad Oblast of Russia. These rocks are enriched in a carbon substance and characterized by the significant content of uranium, vanadium, molybdenum, copper, nickel, cobalt, zinc, and lead. Black shales contain high levels of Sr – 968; Ba – 337; U – 229; V – 509; Mo – 165; Zn – 411; Ni – 214; Cu – 112 (ppm) in secondary minerals composition formed on their surface. Retrograde diagenetic conditions facilitate the black shales chemical weathering. Elements of the first (U), second (Mo, Sr, Zn), and third (V) hazard classes are washed out of black shales and secondary minerals and can further enter biological cycles

A ROLE FOR CELLULAR IMMUNITY IN EARLY POSTPARTUM PERIOD

The functioning of the secretory organs is closely related to the activity of the immune system. As is well known, this participation is manifested in the fact that at certain stages of activity, the lymphoid cells migrating to the organ can be involved in the regulation of secretion. In addition, the products of the immune system and even its cellular elements can become components of a number of secrets. Colostrum and milk contain a large number of cells of a wide spectrum (up to 1/3 of the volume), of which the number of lymphocytes is up to 16% of leukocytes. Lymphocytes, in an immunologically active form, entering the newborn’s body with colostrum, activate the cellular immunity system. The transport of lymphokinin mediators plays a certain role in this process. Microphages, T- and B-lymphocytes, penetrating through the intercellular spaces into the lymphoid layer of the intestine, transmit immunoreceptors to the prolymphocytes of the newborn, "armed" with their activity to recognize genetically foreign ones. The lymphocytes contained in colostrum are the cells of the immune system that provide cellular and humoral immunity. They are mainly represented by T-cells, B-cells and killer cells. Milk T-cells produce a full spectrum of immune regulatory proteins such as interferon, tumor necrosis factor alpha. These cells are the cells of the immune memory. Newborns who received the first portion of colostrum no later than an hour after birth are characterized by an increased number of leukocytes, more pronounced phagocytosis, which indicates the stimulation of hemo- and lymphocytosis. When carrying out transmission and scanning electron microscopy in the epithelial layer of the intestine, cellular elements were found that got there from the intestinal lumen. Microsections show how cells of a lymphoid nature, pushing apart the structures of the epithelial layer, bypass natural barriers and, at the same time, retain their physiological usefulness. The possibility of penetration of immunocompetent cells of the mother’s colostrum into the bloodstream of the young is proved using the natural label of the female’s cells – sex chromatin. Naturally, sex chromatin-labeled cells were sought in male newborns. The detection of colostrum cells in the intestinal wall and bloodstream of the young is approximately 25% in the blood, 1% in the lymph, and about 70% in the intestine. There is no doubt that the leukocytes of colostrum are of exceptional importance in creating immunity in newborn animals

MIGRATION FORMS OF CHEMICAL ELEMENTS IN THE INTRUSIVE ROCKS OF THE EASTERN DESERT (EL SELA AREA, EGYPT)

In the Egypt's Eastern Desert intrusive rocks with U-REE mineralization (two-mica granites, microgranites, dolerites, and bostonites) are developed. We estimated the content of chemical elements in reference samples of intrusive rocks and also in their water-soluble (colloid-salt) fraction. This fraction is water-extracted from the rock under certain conditions. The rock sample and its colloid-salt fraction are analyzed using ICP-MS. The chemical characteristic of the extracted fraction reflects the mobile migrating part of the chemical elements in the composition of the rocks. Comparison of the obtained data allows us to estimate the share of migrating and weakly migrating elements