Anatomy of Malicious Singularities

As well known, the b-boundaries of the closed Friedman world model and of Schwarzschild solution consist of a single point. We study this phenomenon in a broader context of differential and structured spaces. We show that it is an equivalence relation $\rho$, defined on the Cauchy completed total space $\bar{E}$ of the frame bundle over a given space-time, that is responsible for this pathology. A singularity is called malicious if the equivalence class $[p_0]$ related to the singularity remains in close contact with all other equivalence classes, i.e., if $p_0 \in \mathrm{cl}[p]$ for every $p \in E$. We formulate conditions for which such a situation occurs. The differential structure of any space-time with malicious singularities consists only of constant functions which means that, from the topological point of view, everything collapses to a single point. It was noncommutative geometry that was especially devised to deal with such situations. A noncommutative algebra on $\bar{E}$, which turns out to be a von Neumann algebra of random operators, allows us to study probabilistic properties (in a generalized sense) of malicious singularities. Our main result is that, in the noncommutative regime, even the strongest singularities are probabilistically irrelevant.Comment: 16 pages in LaTe

Geometry of Non-Hausdorff Spaces and Its Significance for Physics

Hausdorff relation, topologically identifying points in a given space, belongs to elementary tools of modern mathematics. We show that if subtle enough mathematical methods are used to analyze this relation, the conclusions may be far-reaching and illuminating. Examples of situations in which the Hausdorff relation is of the total type, i.e., when it identifies all points of the considered space, are the space of Penrose tilings and space-times of some cosmological models with strong curvature singularities. With every Hausdorff relation a groupoid can be associated, and a convolutive algebra defined on it allows one to analyze the space that otherwise would remain intractable. The regular representation of this algebra in a bundle of Hilbert spaces leads to a von Neumann algebra of random operators. In this way, a probabilistic description (in a generalized sense) naturally takes over when the concept of point looses its meaning. In this situation counterparts of the position and momentum operators can be defined, and they satisfy a commutation relation which, in the suitable limiting case, reproduces the Heisenberg indeterminacy relation. It should be emphasized that this is neither an additional assumption nor an effect of a quantization process, but simply the consequence of a purely geometric analysis.Comment: 13 LaTex pages, no figure

State Vector Reduction as a Shadow of a Noncommutative Dynamics

A model, based on a noncommutative geometry, unifying general relativity with quantum mechanics, is further develped. It is shown that the dynamics in this model can be described in terms of one-parameter groups of random operators. It is striking that the noncommutative counterparts of the concept of state and that of probability measure coincide. We also demonstrate that the equation describing noncommutative dynamics in the quantum gravitational approximation gives the standard unitary evolution of observables, and in the "space-time limit" it leads to the state vector reduction. The cases of the spin and position operators are discussed in details.Comment: 20 pages, LaTex, no figure

Neurological disorders associated with COVID-19

The aim of the study - to evaluate the features of the manifestation of neurological disorders associated with COVID-19 in students of Volgograd State Medical University (VolgSMU).Цель исследования – оценить особенности проявления неврологических расстройств, ассоциированных с COVID-19, у студентов Волгоградского государственного медицинского университета (ВолгГМУ)

Conceptual Unification of Gravity and Quanta

We present a model unifying general relativity and quantum mechanics. The model is based on the (noncommutative) algebra \mbox{{\cal A}} on the groupoid \Gamma = E \times G where E is the total space of the frame bundle over spacetime, and G the Lorentz group. The differential geometry, based on derivations of \mbox{{\cal A}}, is constructed. The eigenvalue equation for the Einstein operator plays the role of the generalized Einstein's equation. The algebra \mbox{{\cal A}}, when suitably represented in a bundle of Hilbert spaces, is a von Neumann algebra \mathcal{M} of random operators representing the quantum sector of the model. The Tomita-Takesaki theorem allows us to define the dynamics of random operators which depends on the state \phi . The same state defines the noncommutative probability measure (in the sense of Voiculescu's free probability theory). Moreover, the state \phi satisfies the Kubo-Martin-Schwinger (KMS) condition, and can be interpreted as describing a generalized equilibrium state. By suitably averaging elements of the algebra \mbox{{\cal A}}, one recovers the standard geometry of spacetime. We show that any act of measurement, performed at a given spacetime point, makes the model to collapse to the standard quantum mechanics (on the group G). As an example we compute the noncommutative version of the closed Friedman world model. Generalized eigenvalues of the Einstein operator produce the correct components of the energy-momentum tensor. Dynamics of random operators does not ``feel'' singularities.Comment: 28 LaTex pages. Substantially enlarged version. Improved definition of generalized Einstein's field equation

FLORA: a novel method to predict protein function from structure in diverse superfamilies

Predicting protein function from structure remains an active area of interest, particularly for the structural genomics initiatives where a substantial number of structures are initially solved with little or no functional characterisation. Although global structure comparison methods can be used to transfer functional annotations, the relationship between fold and function is complex, particularly in functionally diverse superfamilies that have evolved through different secondary structure embellishments to a common structural core. The majority of prediction algorithms employ local templates built on known or predicted functional residues. Here, we present a novel method (FLORA) that automatically generates structural motifs associated with different functional sub-families (FSGs) within functionally diverse domain superfamilies. Templates are created purely on the basis of their specificity for a given FSG, and the method makes no prior prediction of functional sites, nor assumes specific physico-chemical properties of residues. FLORA is able to accurately discriminate between homologous domains with different functions and substantially outperforms (a 2–3 fold increase in coverage at low error rates) popular structure comparison methods and a leading function prediction method. We benchmark FLORA on a large data set of enzyme superfamilies from all three major protein classes (α, β, αβ) and demonstrate the functional relevance of the motifs it identifies. We also provide novel predictions of enzymatic activity for a large number of structures solved by the Protein Structure Initiative. Overall, we show that FLORA is able to effectively detect functionally similar protein domain structures by purely using patterns of structural conservation of all residues

Politicization of COVID-19 health-protective behaviors in the United States:Longitudinal and cross-national evidence

During the initial phase of the COVID-19 pandemic, U.S. conservative politicians and the media downplayed the risk of both contracting COVID-19 and the effectiveness of recommended health behaviors. Health behavior theories suggest perceived vulnerability to a health threat and perceived effectiveness of recommended health-protective behaviors determine motivation to follow recommendations. Accordingly, we predicted that—as a result of politicization of the pandemic—politically conservative Americans would be less likely to enact recommended health-protective behaviors. In two longitudinal studies of U.S. residents, political conservatism was inversely associated with perceived health risk and adoption of health-protective behaviors over time. The effects of political orientation on health-protective behaviors were mediated by perceived risk of infection, perceived severity of infection, and perceived effectiveness of the health-protective behaviors. In a global cross-national analysis, effects were stronger in the U.S. (N = 10,923) than in an international sample (total N = 51,986), highlighting the increased and overt politicization of health behaviors in the U.S

Predictors of adherence to public health behaviors for fighting COVID-19 derived from longitudinal data

The present paper examines longitudinally how subjective perceptions about COVID-19, one's community, and the government predict adherence to public health measures to reduce the spread of the virus. Using an international survey (N = 3040), we test how infection risk perception, trust in the governmental response and communications about COVID-19, conspiracy beliefs, social norms on distancing, tightness of culture, and community punishment predict various containment-related attitudes and behavior. Autoregressive analyses indicate that, at the personal level, personal hygiene behavior was predicted by personal infection risk perception. At social level, social distancing behaviors such as abstaining from face-to-face contact were predicted by perceived social norms. Support for behavioral mandates was predicted by confidence in the government and cultural tightness, whereas support for anti-lockdown protests was predicted by (lower) perceived clarity of communication about the virus. Results are discussed in light of policy implications and creating effective interventions

Using machine learning to identify important predictors of COVID-19 infection prevention behaviors during the early phase of the pandemic

Before vaccines for coronavirus disease 2019 (COVID-19) became available, a set of infection-prevention behaviors constituted the primary means to mitigate the virus spread. Our study aimed to identify important predictors of this set of behaviors. Whereas social and health psychological theories suggest a limited set of predictors, machine-learning analyses can identify correlates from a larger pool of candidate predictors. We used random forests to rank 115 candidate correlates of infection-prevention behavior in 56,072 participants across 28 countries, administered in March to May 2020. The machine-learning model predicted 52% of the variance in infection-prevention behavior in a separate test sample—exceeding the performance of psychological models of health behavior. Results indicated the two most important predictors related to individual-level injunctive norms. Illustrating how data-driven methods can complement theory, some of the most important predictors were not derived from theories of health behavior—and some theoretically derived predictors were relatively unimportant

Domain architecture evolution of pattern-recognition receptors

In animals, the innate immune system is the first line of defense against invading microorganisms, and the pattern-recognition receptors (PRRs) are the key components of this system, detecting microbial invasion and initiating innate immune defenses. Two families of PRRs, the intracellular NOD-like receptors (NLRs) and the transmembrane Toll-like receptors (TLRs), are of particular interest because of their roles in a number of diseases. Understanding the evolutionary history of these families and their pattern of evolutionary changes may lead to new insights into the functioning of this critical system. We found that the evolution of both NLR and TLR families included massive species-specific expansions and domain shuffling in various lineages, which resulted in the same domain architectures evolving independently within different lineages in a process that fits the definition of parallel evolution. This observation illustrates both the dynamics of the innate immune system and the effects of “combinatorially constrained” evolution, where existence of the limited numbers of functionally relevant domains constrains the choices of domain architectures for new members in the family, resulting in the emergence of independently evolved proteins with identical domain architectures, often mistaken for orthologs