A positivity result in the theory of Macdonald polynomials

We outline here a proof that a certain rational function Cn(q, t), which has come to be known as the “q, t-Catalan,” is in fact a polynomial with positive integer coefficients. This has been an open problem since 1994. Because Cn(q, t) evaluates to the Catalan number at t = q = 1, it has also been an open problem to find a pair of statistics a, b on the collection

Unifying theory of hypoxia tolerance: molecular/metabolic defense and rescue mechanisms for surviving oxygen lack.

We develop a unifying theory of hypoxia tolerance based on information from two cell level models (brain cortical cells and isolated hepatocytes) from the highly anoxia tolerant aquatic turtle and from other more hypoxia sensitive systems. We propose that the response of hypoxia tolerant systems to oxygen lack occurs in two phases (defense and rescue). The first lines of defense against hypoxia include a balanced suppression of ATP-demand and ATP-supply pathways; this regulation stabilizes (adenylates) at new steady-state levels even while ATP turnover rates greatly decline. The ATP demands of ion pumping are down-regulated by generalized "channel" arrest in hepatocytes and by "spike" arrest in neurons. Hypoxic ATP demands of protein synthesis are down-regulated probably by translational arrest. In hypoxia sensitive cells this translational arrest seems irreversible, but hypoxia-tolerant systems activate "rescue" mechanisms if the period of oxygen lack is extended by preferentially regulating the expression of several proteins. In these cells, a cascade of processes underpinning hypoxia rescue and defense begins with an oxygen sensor (a heme protein) and a signal-transduction pathway, which leads to significant gene-based metabolic reprogramming-the rescue process-with maintained down-regulation of energy-demand and energy-supply pathways in metabolism throughout the hypoxic period. This recent work begins to clarify how normoxic maintenance ATP turnover rates can be drastically (10-fold) down-regulated to a new hypometabolic steady state, which is prerequisite for surviving prolonged hypoxia or anoxia. The implications of these developments are extensive in biology and medicine.

Recruitment and replacement of hippocampal neurons in young and adult chickadees: an addition to the theory of hippocampal learning.

We used [3H]thymidine to document the birth of neurons and their recruitment into the hippocampal complex (HC) of juvenile (4.5 months old) and adult blackcapped chickadees (Parus atricapillus) living in their natural surroundings. Birds received a single dose of [3H]thymidine in August and were recaptured and killed 6 weeks later, in early October. All brains were stained with Cresyl violet, a Nissl stain. The boundaries of the HC were defined by reference to the ventricular wall, the brain surface, or differences in neuronal packing density. The HC of juveniles was as large as or larger than that of adults and packing density of HC neurons was 31% higher in juveniles than in adults. Almost all of the 3H-labeled HC neurons were found in a 350-m-wide layer of tissue adjacent to the lateral ventricle. Within this layer the fraction of 3H-labeled neurons was 50% higher in juveniles than in adults. We conclude that the HC of juvenile chickadees recruits more neurons and has more neurons than that of adults. We speculate that juveniles encounter greater environmental novelty than adults and that the greater number of HC neurons found in juveniles allows them to learn more than adults. At a more general level, we suggest that (i) long-term learning alters HC neurons irreversibly; (ii) sustained hippocampal learning requires the periodic replacement of HC neurons; (iii) memories coded by hippocampal neurons are transferred elsewhere before the neurons are replaced.

An evolutionary theory of the family.

An evolutionary framework for viewing the formation, the stability, the organizational structure, and the social dynamics of biological families is developed. This framework is based upon three conceptual pillars: ecological constraints theory, inclusive fitness theory, and reproductive skew theory. I offer a set of 15 predictions pertaining to living within family groups. The logic of each is discussed, and empirical evidence from family-living vertebrates is summarized. I argue that knowledge of four basic parameters, (i) genetic relatedness, (ii) social dominance, (iii) the benefits of group living, and (iv) the probable success of independent reproduction, can explain many aspects of family life in birds and mammals. I suggest that this evolutionary perspective will provide insights into understanding human family systems as well.

Evidence against the exon theory of genes derived from the triose-phosphate isomerase gene.

The exon theory of genes proposes that the introns of protein-encoding nuclear genes are remnants of the DNA spacers between ancient minigenes. The discovery of an intron at a predicted position in the triose-phosphate isomerase (EC 5.3.1.1) gene of Culex mosquitoes has been hailed as an evidential pillar of the theory. We have found that that intron is also present in Aedes mosquitoes, which are closely related to Culex, but not in the phylogenetically more distant Anopheles, nor in the fly Calliphora vicina, nor in the moth Spodoptera littoralis. The presence of this intron in Culex and Aedes is parsimoniously explained as the result of an insertion in a recent common ancestor of these two species rather than as the remnant of an ancient intron. The absence of the intron in 19 species of very diverse organisms requires at least 10 independent evolutionary losses in order to be consistent with the exon theory.

Theory of orientation tuning in visual cortex.

The role of intrinsic cortical connections in processing sensory input and in generating behavioral output is poorly understood. We have examined this issue in the context of the tuning of neuronal responses in cortex to the orientation of a visual stimulus. We analytically study a simple network model that incorporates both orientation-selective input from the lateral geniculate nucleus and orientation-specific cortical interactions. Depending on the model parameters, the network exhibits orientation selectivity that originates from within the cortex, by a symmetry-breaking mechanism. In this case, the width of the orientation tuning can be sharp even if the lateral geniculate nucleus inputs are only weakly anisotropic. By using our model, several experimental consequences of this cortical mechanism of orientation tuning are derived. The tuning width is relatively independent of the contrast and angular anisotropy of the visual stimulus. The transient population response to changing of the stimulus orientation exhibits a slow "virtual rotation." Neuronal cross-correlations exhibit long time tails, the sign of which depends on the preferred orientations of the cells and the stimulus orientation.

Taking The 'Sport' Out of Sports Parenting: Toward A Theory of Sport Related Parent-Child Communication Competency

Research has shown that over-emphasis on winning is the number one reason why approximately seventy percent of the forty million children who participate in youth sports will quit by age 13. This study utilized a constructivist grounded theory approach to investigate the role of parent-child communication within the context of youth sports. A total of 22 athletes and 20 parents were recruited through a Western university to discuss messages exchanged during youth sport participation. The results suggest that the delineation between messages of support and pressure is largely dependent on discursive work done by both parent and child. Parents who employed competent communicative strategies to avoid miscommunications regarding participation and sports goals were able to provide support and strengthen the relationship despite pressurized situations. The present study frames the youth sport dilemma within a developing conceptualization of communicative (in)competence and offers theoretical implications for sport related parent-child communication competency (SRPCCC).

Monetary Effervescence: A Sociological Theory of Religion Applied to Money

This project attempts to answer the question "What holds the construction of money together?" by asserting that it is money's religious nature which provides the moral compulsion for people to use, and continue to uphold, money as a socially constructed concept. This project is primarily descriptive and focuses on the religious nature of money by employing a sociological theory of religion in viewing money as a technical concept. This is an interdisciplinary work between religious studies, economics, and sociology and draws heavily from Emile Durkheim's 'The Elementary Forms of Religious Life' as well as work related to heterodox theories of money developed by Geoffrey Ingham, A. Mitchell Innes, and David Graeber. Two new concepts are developed: the idea of monetary sacrality and monetary effervescence, both of which serve to recharge the religious saliency of money. By developing the concept of monetary sacrality, this project shows how money acts to interpret our economic relations while also obfuscating complex power dynamics in society, making them seem naturally occurring and unchangeable. The project also shows how our contemporary fractional reserve banking system contributes to money's collective effervescence and serves to animate economic acting within a monetary network. The project concludes by outlining multiple implications for religious studies, economics, sociology, and central banking.

Theory of ferromagnetism in planar heterostructures of (Mn,III)-V semiconductors

A density-functional theory of ferromagnetism in heterostructures of compound semiconductors doped with magnetic impurities is presented. The variable functions in the density-functional theory are the charge and spin densities of the itinerant carriers and the charge and localized spins of the impurities. The theory is applied to study the Curie temperature of planar heterostructures of III-V semiconductors doped with manganese atoms. The mean-field, virtual-crystal and effective-mass approximations are adopted to calculate the electronic structure, including the spin-orbit interaction, and the magnetic susceptibilities, leading to the Curie temperature. By means of these results, we attempt to understand the observed dependence of the Curie temperature of planar δ-doped ferromagnetic structures on variation of their properties. We predict a large increase of the Curie temperature by additional confinement of the holes in a δ-doped layer of Mn by a quantum well.

Cotunneling theory of atomic spin inelastic electron tunneling spectroscopy

We propose cotunneling as the microscopic mechanism that makes possible inelastic electron tunneling spectroscopy of magnetic atoms in surfaces for a wide range of systems, including single magnetic adatoms, molecules, and molecular stacks. We describe electronic transport between the scanning tip and the conducting surface through the magnetic system (MS) with a generalized Anderson model, without making use of effective spin models. Transport and spin dynamics are described with an effective cotunneling Hamiltonian in which the correlations in the magnetic system are calculated exactly and the coupling to the electrodes is included up to second order in the tip MS and MS substrate. In the adequate limit our approach is equivalent to the phenomenological Kondo exchange model that successfully describes the experiments. We apply our method to study in detail inelastic transport in two systems, stacks of cobalt phthalocyanines and a single Mn atom on Cu2N. Our method accounts for both the large contribution of the inelastic spin exchange events to the conductance and the observed conductance asymmetry.

Theory of single-spin inelastic tunneling spectroscopy

I show that recent experiments of inelastic scanning tunneling spectroscopy of single and a few magnetic atoms are modeled with a phenomenological spin-assisted tunneling Hamiltonian so that the inelastic dI/dV line shape is related to the spin spectral weight of the magnetic atom. This accounts for the spin selection rules and dI/dV spectra observed experimentally for single Fe and Mn atoms deposited on Cu2N. In the case of chains of Mn atoms it is found necessary to include both first and second-neighbor exchange interactions as well as single-ion anisotropy.

Diversity for Texts Builds in Language L(MT): Indexes Based in Theory of Information

If one has a distribution of words (SLUNs or CLUNS) in a text written in language L(MT), and is adjusted one of the mathematical expressions of distribution that exists in the mathematical literature, some parameter of the elected expression it can be considered as a measure of the diversity. But because the adjustment is not always perfect as usual measure; it is preferable to select an index that doesn't postulate a regularity of distribution expressible for a simple formula. The problem can be approachable statistically, without having special interest for the organization of the text. It can serve as index any monotonous function that has a minimum value when all their elements belong to the same class, that is to say, all the individuals belong to oneself symbol, and a maximum value when each element belongs to a different class, that is to say, each individual is of a different symbol. It should also gather certain conditions like they are: to be not very sensitive to the extension of the text and being invariant to certain number of operations of selection in the text. These operations can be theoretically random. The expressions that offer more advantages are those coming from the theory of the information of Shannon-Weaver. Based on them, the authors develop a theoretical study for indexes of diversity to be applied in texts built in modeling language L(MT), although anything impedes that they can be applied to texts written in natural languages.

Theory of Systems, Systems Metaphysics and Neoplatonism

Science has been developed from the rational-empirical methods, having as a consequence, the representation of existing phenomena without understanding the root causes. The question which currently has is the sense of the being, and in a simplified way, one can say that the dogmatic religion lead to misinterpretations, the empirical sciences contain the exact rational representations of phenomena. Thus, Science has been able to get rid of the dogmatic religion. The project for the sciences of being looks to return to reality its essential foundations; under the plan of theory of systems necessarily involves a search for the meaning of Reality.