Hardy potential versus lower order terms in Dirichlet problems: regularizing effects

<abstract><p>In this paper, dedicated to Ireneo Peral, we study the regularizing effect of some lower order terms in Dirichlet problems despite the presence of Hardy potentials in the right hand side.</p></abstract>

The Tangled Webs We Wreak: Examining the Structure of Aggressive Personality Using Psychometric Networks

Trait aggression is a prominent construct in the psychological literature, yet little work has sought to situate trait aggression among broader frameworks of personality. Initial evidence suggests that trait aggression may be best couched within the nomological network of the Five Factor Model (FFM). The current work sought to locate the most appropriate home for trait aggression among the FFM. We applied a preregistered regimen of psychometric network analyses to three datasets (combined N = 2,927) that contained self-reports of trait aggression and the FFM traits. Trait aggression was highly central in the factor-level networks, which contained associations consistent with the conceptualization of this construct as a lower-order component of low agreeableness. The facet-level networks revealed that the behavioral facets of trait aggression reflected low agreeableness, but that the anger and hostility facets reflected high neuroticism. The item-level network suggested that the intent to initiate aggressive encounters was the primary bridge that empirically linked trait aggression to agreeableness. Our results indicate that trait aggression is primarily a lower-order facet of agreeableness, advance our understanding of trait aggression, integrate it with broader frameworks of personality, and suggest future directions to refine this complex dispositional tendency.

The changing pattern of European country groups: Economic, financial, and health indicators, 2000–2015

This study compares the European country groups using economic, financial and health indicators in 2000 and 2015. The “Core” European Union (EU) countries, which are the main progenitors of the deterioration processes within the EU, have changed their cluster memberships from higher-order clusters to lower-order ones. Deposits in banks (assets) to GDP (%) and inflation at consumer prices (annual %) have played a leading role in the formation of EU country groups for 2000 and 2015. The study emphasized the importance of political cohesion and financial stance to mitigate European countries’ financial risks and welfare states.

Quasi-Entropy Closure: A Fast and Reliable Approach to Close the Moment Equations of the Chemical Master Equation

MotivationThe Chemical Master Equation is the most comprehensive stochastic approach to describe the evolution of a (bio-)chemical reaction system. Its solution is a time-dependent probability distribution on all possible configurations of the system. As the number of possible configurations is typically very large, the Master Equation is often practically unsolvable. The Method of Moments reduces the system to the evolution of a few moments of this distribution, which are described by a system of ordinary differential equations. Those equations are not closed, since lower order moments generally depend on higher order moments. Various closure schemes have been suggested to solve this problem, with different advantages and limitations. Two major problems with these approaches are first that they are open loop systems, which can diverge from the true solution, and second, some of them are computationally expensive.ResultsHere we introduce Quasi-Entropy Closure, a moment closure scheme for the Method of Moments which estimates higher order moments by reconstructing the distribution that minimizes the distance to a uniform distribution subject to lower order moment constraints. Quasi-Entropy closure is similar to Zero-Information closure, which maximizes the information entropy. Results show that both approaches outperform truncation schemes. Moreover, Quasi-Entropy Closure is computationally much faster than Zero-Information Closure. Finally, our scheme includes a plausibility check for the existence of a distribution satisfying a given set of moments on the feasible set of configurations. Results are evaluated on different benchmark problems.Abstract Figure

Comparative analysis of mitochondrial genomes in different species reveals the evolution of G-quadruplexes

G-quadruplexes (G4s) are noncanonical structures that can form in the genomes of a range of organisms and are known to play various roles in cellular function. G4s can also form in mitochondrial DNA (mtDNA) because of their high guanine content, and these G4s may play roles in regulating gene expression, DNA replication, and genome stability. However, little is known regarding the evolution and dissemination of G4s in mitochondria. Here we analyzed the potential G4-forming sequences in mtDNA of 16 species from various families and demonstrated that the heavy strand of mtDNA of higher-order organisms contained higher levels of G4 regions than that of lower-order organisms. Analysis of the codons in the light strand revealed enrichment of guanine/cytosine-rich regions in higher eukaryotes and of adenine/thymidine-rich regions in lower-order organisms. Our study showed the diversity of G4s in species ranging from lower to higher orders. In particular, mammals such as humans, chimpanzees, and monkeys display a greater number of G4s than lower-order organisms. These potentially play a role in a range of cellular functions and assist in the evolution of higher organisms.

Existence of Positive Solutions for a Higher-Order Fractional Differential Equation with Multi-Term Lower-Order Derivatives

This paper deals with the study of the existence of positive solutions for a class of nonlinear higher-order fractional differential equations in which the nonlinear term contains multi-term lower-order derivatives. By reducing the order of the highest derivative, the higher-order fractional differential equation is transformed into a lower-order fractional differential equation. Then, combining with the properties of left-sided Riemann–Liouville integral operators, we obtain the existence of the positive solutions of fractional differential equations utilizing some weaker conditions. Furthermore, some examples are given to demonstrate the validity of our main results.