New variants of pairwise classification

Pairwise classification is the technique that deals with multi-class problems by converting them into a series of binary problems, one for each pair of classes. Typically, K-class classification rules tend to be easier to learn for K = 2 than for K > 2 – only one decision boundary requires attention.     

Photooxidation of ethanol on Cu-layer silicate/TiO2 composite thin films

Thin film composites of copper-montmorillonite and TiO₂ were prepared and their optical and catalytic properties for ethanol photooxidation were evaluated. The efficiency of composite Cu-clay/TiO₂ = 20/80 was two-fold higher than the standard TiO₂(P25) photocatalyst.     

A model of immune system with time-dependent immune reactivity

In this paper we deal with the Marchuk model of an immune system. Among the main parameters of the model are the coefficients which describe the state of infected organism and the rate of production of antibodies. In the classical model these coefficients are constants. We consider the case when these coefficients are time-dependent. In particular, we are interested in the case of periodic coefficients which can describe periodic changes of the immune reactivity due to periodic changes of the environment. We examine the asymptotic behaviour of solutions. Under some assumptions we prove that the solutions tend to periodic functions. We also present the results of numerical simulations to illustrate the behaviour of solutions.     

Spatial Central Limit Theorem for Supercritical Superprocesses

We consider a measure-valued diffusion (i.e., a superprocess). It is determined by a couple \((L,\psi )\), where L is the infinitesimal generator of a strongly recurrent diffusion in \(\mathbb {R}^{d}\) and \(\psi \) is a branching mechanism assumed to be supercritical. Such processes are known, see for example, (Englander and Winter in Ann Inst Henri Poincaré 42(2):171–185, 2006), to fulfill a law of large numbers for the spatial distribution of the mass. In this paper, we prove the corresponding central limit theorem. The limit and the CLT normalization fall into three qualitatively different classes arising from “competition” of the local growth induced by branching and global smoothing due to the strong recurrence of L. We also prove that the spatial fluctuations are asymptotically independent of the fluctuations of the total mass of the process.     

Block partitions: an extended view

Given a sequence \({S=(s_1, \ldots,s_m) \in [0, 1]^m}\), a block B of S is a subsequence \({B=(s_i,s_{i+1}, \ldots,s_j)}\). The size b of a block B is the sum of its elements. It is proved in [1] that for each positive integer n, there is a partition of S into n blocks B₁, \({\ldots,}\) B _n with \({|b_i - b_j| \le 1}\) for every i, j. In this paper, we consider a generalization of the problem in higher dimensions.     

On properties and applications of (p,q)-extended τ-hypergeometric functions

We introduce the $(p,q)$-extended τ-hypergeometric and confluent hypergeometric functions along with their integral representations. We also present closed integral expressions for the Mathieu-type a-series and for the associated alternating versions whose terms contain the $(p,q)$-extended τ-hypergeometric functions with related contiguous functional relations.     

Chemical Evolution of the Universe and its Consequences for Gravitational-Wave Astrophysics

Gravitational waves (GW) emitted by merging black holes (BH) and neutron stars are now routinely detected. Those are the afterlives of massive stars that formed all across the Universe—at different cosmic times and with different metallicities. Birth metallicity plays an important role in the evolution of massive stars. Consequently, the population properties of mergers are sensitive to the metallicity dependent cosmic star formation history (f_SFR(Z,z)). In particular, within the isolated formation scenarios (the focus of this paper), a strong low metallicity preference of the formation of BH mergers is found. The origin of this dependence and its consequences are discussed. Most importantly, uncertainty in the f_SFR(Z,z) (substantial even at low redshifts) cannot be ignored in the models. This poses a challenge for the interpretation of the observed GW source population properties. Possible improvements and the role of future GW detectors are considered. Recent efforts to determine f_SFR(Z,z) and the factors that dominate its uncertainty are summarized. Many of those factors stem from the uncertain properties of faint and distant galaxies. The fact that they leave imprint on the redshift-dependent properties of mergers makes GW a promising (and complementary to electromagnetic observations) tool to study galaxy chemical evolution.