Existence and Regularity of Periodic Solutions to Certain First-Order Partial Differential Equations

We present conditions on the coefficients of a class of vector fields on the torus which yield a characterization of global solvability as well as global hypoellipticity, in other words, the existence and regularity of periodic solutions. Diophantine conditions and connectedness of certain sublevel sets appear in a natural way in our results.     

Statistical characteristics of continuous functions and statistically weakly invariant sets of controllable system

We continue the investigation of expansion of a concept of invariance for sets which consists in studying statistically invariant sets with respect to control systems and differential inclusions. We consider the statistical characteristics of continuous functions: Upper and lower relative frequency of containing for graph of a function in a given set. We obtain conditions under which statistical characteristics of two various asymptotical equivalent functions coincide; then by the value of one of them it is possible to calculate the value of another one. We adduce the equality for finding relative frequencies of hitting functions the given set in the case when the distance from the graph of one of functions to the given set is a periodic function. A consequence of these statements are conditions of statistically weak invariance of a set with respect to controlled system. For some almost periodic functions we obtain the formulas by which we can calculate the mean values and the statistical characteristics. We also consider the following problem. Let the number λ₀ ∈ [0, 1] be given. It is necessary to find the value c(λ₀) such that the upper solution z(t) of the Cauchy problem does not exceed c(λ₀) with the relative frequency being equal λ₀. Depending on statement of the problem, a value z(t) can be interpreted as the size of population, energy of a particle, concentration of substance, size of manufacture or the price of production.     

On Constructive number fields and computability of solutions of PDEs

In this paper we find a connection between constructive number fields and computable reals. This connection is applied to prove the computability in the rigorous sense of computable analysis) of solutions of some important systems of partial differential equations, by means of algorithms which are really used in numerical analysis.     

Hybrid genetic algorithms with selective crossover for the capacitated p-median problem

Central European Journal of Operations Research - The paper suggests two ways of combining a genetic algorithm with integer programming to improve the quality of the problem solution. The...     

Measuring centrality by a generalization of degree

Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes, for which purpose a number of centrality measures have been developed. This paper proposes a new parametric family of centrality measures called generalized degree. It is based on the idea that a relationship to a more interconnected node contributes to centrality in a greater extent than a connection to a less central one. Generalized degree improves on degree by redistributing its sum over the network with the consideration of the global structure. Application of the measure is supported by a set of basic properties. A sufficient condition is given for generalized degree to be rank monotonic, excluding counter-intuitive changes in the centrality ranking after certain modifications of the network. The measure has a graph interpretation and can be calculated iteratively. Generalized degree is recommended to apply besides degree since it preserves most favourable attributes of degree, but better reflects the role of the nodes in the network and has an increased ability to distinguish among their importance.     

Power and reversal power links for binary regressions: An application for motor insurance policyholders

In binary regression, symmetric links such as logit and probit are usually considered as standard. However, in the presence of unbalancing of ones and zeros, these links can be inappropriate and inflexible to fit the skewness in the response curve and likely to lead to misspecification. This is the case of covering some type of insurance, where it can be observed that the probability of a given binary response variable approaches zero at different rates than it approaches one. Furthermore, when usual links are considered, there is not a skewness parameter associated with the distribution chosen that, regardless of the linear predictor, is easily interpreted. In order to overcome such problems, a proposal for the construction of a set of new skew links is developed in this paper, where some of their properties are discussed. In this context, power links and their reversal versions are presented. A Bayesian inference approach using MCMC is developed for the presented models. The methodology is illustrated considering a sample of motor insurance policyholders selected randomly by gender. Results suggest that the proposed link functions are more appropriate than other alternative link functions commonly used in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Computer-Assisted Analysis of the Anderson–Hájek Ontological Controversy

A universal reasoning approach based on shallow semantical embeddings of higher-order modal logics into classical higher-order logic is exemplarily employed to analyze several modern variants of the ontological argument on the computer. Several novel findings are reported which contribute to the clarification of a long-standing dispute between Anderson and Hájek. The technology employed in this work, which to some degree realizes Leibniz’s dream of a characteristica universalis and a calculus ratiocinator for solving philosophical controversies, is ready to be fruitfully adopted in larger scale by philosophers.     

Novel Tdp1 Inhibitors Based on Adamantane Connected with Monoterpene Moieties via Heterocyclic Fragments

Tyrosyl-DNA phosphodiesterase 1 (Tdp1) is a promising target for anticancer therapy due to its ability to counter the effects topoisomerase 1 (Top1) poison, such as topotecan, thus, decreasing their efficacy. Compounds containing adamantane and monoterpenoid residues connected via 1,2,4-triazole or 1,3,4-thiadiazole linkers were synthesized and tested against Tdp1. All the derivatives exhibited inhibition at low micromolar or nanomolar concentrations with the most potent inhibitors having IC₅₀ values in the 0.35–0.57 µM range. The cytotoxicity was determined in the HeLa, HCT-116 and SW837 cancer cell lines; moderate CC₅₀ (µM) values were seen from the mid-teens to no effect at 100 µM. Furthermore, citral derivative 20c, α-pinene-derived compounds 20f, 20g and 25c, and the citronellic acid derivative 25b were found to have a sensitizing effect in conjunction with topotecan in the HeLa cervical cancer and colon adenocarcinoma HCT-116 cell lines. The ligands are predicted to bind in the catalytic pocket of Tdp1 and have favorable physicochemical properties for further development as a potential adjunct therapy with Top1 poisons.