Theoretical Studies of the Self Cleavage Pistol Ribozyme Mechanism

Ribozymes are huge complex biological catalysts composed of a combination of RNA and proteins. Nevertheless, there is a reduced number of small ribozymes, the self-cleavage ribozymes, that are formed just by RNA and, apparently, they existed in cells of primitive biological systems. Unveiling the details of these “fossils” enzymes can contribute not only to the understanding of the origins of life but also to the development of new simplified artificial enzymes. A computational study of the reactivity of the pistol ribozyme carried out by means of classical MD simulations and QM/MM hybrid calculations is herein presented to clarify its catalytic mechanism. Analysis of the geometries along independent MD simulations with different protonation states of the active site basic species reveals that only the canonical system, with no additional protonation changes, renders reactive conformations. A change in the coordination sphere of the Mg2+ ion has been observed during the simulations, which allows proposing a mechanism to explain the unique mode of action of the pistol ribozyme by comparison with other ribozymes. The present results are at the center of the debate originated from recent experimental and theoretical studies on pistol ribozyme.

InterModel Vigorish (IMV): A novel approach for quantifying predictive accuracy when outcomes are binary

Understanding the ``fit'' of models meant to predict binary outcomes has been a long-standing problem. We propose a novel metric---the InterModel Vigorish (IMV)---for quantifying the value of change in predictive accuracy between two systems in the case of a binary outcome. The metric is based on an analogy to well-characterized physical systems with tractable probabilities. We first translate a baseline prediction of some binary outcomes into a statement about a canonical system---weighted coins---by equating the entropy of the two systems. We then use the weighted coin for a baseline prediction to establish a fair bet. For a second predictive system that we want to gauge relative to the baseline, we use the notion of expected winnings from a single-blind bet wherein the second weighted coin has replaced the first (the opposing player being blinded to this replacement). The resulting quantity has a scale that is both generally applicable and not dependent on the magnitude of the baseline prediction; moreover, it is always a statement about the change in fit relative to some baseline (which can simply be the prevalence) whereas other metrics (e.g., AUC) are stand-alone measures that need to be further manipulated to yield indices related to differences in fit across models. We illustrate the properties of this metric in simulations, and the value of it in empirical applications related to health, political affiliation, and item responses. We also reconsider results from the recent Fragile Families Challenge using the IMV metric.

Droplet impact onto a spring-supported plate: analysis and simulations

The high-speed impact of a droplet onto a flexible substrate is a highly non-linear process of practical importance, which poses formidable modelling challenges in the context of fluid–structure interaction. We present two approaches aimed at investigating the canonical system of a droplet impacting onto a rigid plate supported by a spring and a dashpot: matched asymptotic expansions and direct numerical simulation (DNS). In the former, we derive a generalisation of inviscid Wagner theory to approximate the flow behaviour during the early stages of the impact. In the latter, we perform detailed DNS designed to validate the analytical framework, as well as provide insight into later times beyond the reach of the proposed analytical model. Drawing from both methods, we observe the strong influence that the mass of the plate, resistance of the dashpot, and stiffness of the spring have on the motion of the solid, which undergo forced damped oscillations. Furthermore, we examine how the plate motion affects the dynamics of the droplet, predominantly through altering its internal hydrodynamic pressure distribution. We build on the interplay between these techniques, demonstrating that a hybrid approach leads to improved model and computational development, as well as result interpretation, across multiple length and time scales.

Some infinite sequences of canonical covers of degree 2

In this note, we construct three new infinite families of surfaces of general type with canonical map of degree 2 onto a surface of general type. For one of these families the canonical system has base points.

On the regulator problem for linear systems over rings and algebras

The regulator problem is solvable for a linear dynamical system Σ \Sigma if and only if Σ \Sigma is both pole assignable and state estimable. In this case, Σ \Sigma is a canonical system (i.e., reachable and observable). When the ring R R is a field or a Noetherian total ring of fractions the converse is true. Commutative rings which have the property that the regulator problem is solvable for every canonical system (RP-rings) are characterized as the class of rings where every observable system is state estimable (SE-rings), and this class is shown to be equal to the class of rings where every reachable system is pole-assignable (PA-rings) and the dual of a canonical system is also canonical (DP-rings).

EQUATIONS OF PLANETARY SYSTEMS MOTION

The study of the dynamically evolution of planetary systems is very actually in relation with findings of exoplanet systems. free spherical bodies problem is considered in this paper, mutually gravitating according to Newton's law, with isotropically variable masses as a celestial-mechanical model of non-stationary exoplanetary systems. The dynamic evolution of planetary systems is learned, when evolution's leading factor is the masses' variability of gravitating bodies themselves. The laws of the bodies' masses varying are assumed to be known arbitrary functions of time. When doing so the rate of varying of bodies' masses is different. The planets' location is such that the orbits of planets don't intersect. Let us treat this position of planets is preserve in the evolution course. The motions are researched in the relative coordinates system with beginning in the center of the parent star, axes that are parallel to corresponding axes of the absolute coordinates system. The canonical perturbation theory is used on the base aperiodic motion over the quasi-canonical cross-section. The bodies evolution is studied in the osculating analogues of the second system of canonical Poincare elements. The canonical equations of perturbed motion in analogues of the second system of canonical Poincare elements are convenient for describing the planetary systems dynamic evolution, when analogues of eccentricities and analogues of inclinations of orbital plane are sufficiently small. It is noted that to obtain an analytical expression of the perturbing function main part through canonical osculating Poincare elements using computer algebra is preferably. If in expansions of the main part of perturbing function is constrained with precision to second orders including relatively small quantities, then the equations of secular perturbations will obtained as linear non-autonomous system. This circumstance meaningful makes much easier to study the non-autonomous canonical system of differential equations of secular perturbations of considering problem.

Pandemic and Crisis of Church-State Relations

The main objective of the article is to expand the problematic field of church historical research by including an analysis of the influence of external conditions generated by the secular environment (global systemic crisis) on the dynamics and quality of systemic processes within institutional churches in recent times. The systemic crisis, into which the world economy entered at the very beginning of the 21st century (the crisis of the growth model based on over-lending to the economy), combined with standard cyclical crises, produces serious social processes, in particular in the religious sphere. Economic instability in society affects the economic activities of religious institutions, stimulates age shifts (aging) and gender movements, and has a definite impact on such religious institutions as liturgical activity and the canonical system. In this context, any measures of state influence on religious institutions (in the specific case, pandemic restrictions) are perceived as attempts, if not persecution, then unjustified pressure. The internal resistance of traditionalist-oriented actors stimulates the development of the internal structural crisis of religious institutions.