Convolution quadrature time-domain boundary element method for 2-D fluid-saturated porous media

For large-scale wave analyses of fluid-saturated porous media, a conventional time-domain boundary element method (BEM) cannot be applied because of the following reasons: (1) no time-domain fundamental solutions are known for some problems, (2) the method sometimes suffers from instability, and (3) the analyses require large amounts of computational time and memory. In this study, an innovative time-domain BEM is developed for a fluid-saturated porous medium. The formulation presented herein overcomes the above disadvantages using a convolution quadrature method (CQM), first proposed by Lubich, and hybrid-parallelization with both MPI and OpenMP. Problems involving the scattering of an incident plane wave by cavities in a 2-D poroelastic medium are solved as a means of validating the proposed method.     

DeepAdd: Protein function prediction from k-mer embedding and additional features

With the application of new high throughput sequencing technology, a large number of protein sequences is becoming available. Determination of the functional characteristics of these proteins by experiments is an expensive endeavor that requires a lot of time. Furthermore, at the organismal level, such kind of experimental functional analyses can be conducted only for a very few selected model organisms. Computational function prediction methods can be used to fill this gap. The functions of proteins are classified by Gene Ontology (GO), which contains more than 40,000 classifications in three domains, Molecular Function (MF), Biological Process (BP), and Cellular Component (CC). Additionally, since proteins have many functions, function prediction represents a multi-label and multi-class problem. We developed a new method to predict protein function from sequence. To this end, natural language model was used to generate word embedding of sequence and learn features from it by deep learning, and additional features to locate every protein. Our method uses the dependencies between GO classes as background information to construct a deep learning model. We evaluate our method using the standards established by the Computational Assessment of Function Annotation (CAFA) and have noticeable improvement over several algorithms, such as FFPred, DeepGO, GoFDR and other methods compared on the CAFA3 datasets.     

Hypercyclic convolution operators on Fréchet spaces of analytic functions

A result of Godefroy and Shapiro states that the convolution operators on the space of entire functions on Cn, which are not multiples of identity, are hypercyclic. Analogues of this result have appeared for some spaces of holomorphic functions on a Banach space. In this work, we define the space holomorphic functions associated to a sequence of spaces of polynomials and determine conditions on this sequence that assure hypercyclicity of convolution operators. Some known results come out as particular cases of this setting. We also consider holomorphic functions associated to minimal ideals of polynomials and to polynomials of the Schatten-von Neumann class.     

Relations between different types of spectra and spectral characterizations

In the study of the asymptotic behaviour of solutions of differential-difference equations the -spectrum has been useful, where and implies Fourier transform , with given , φ∈L ^∞(ℝ,X), X a Banach space, (half)line. Here we study and related concepts, give relations between them, especially weak Laplace half-line spectrum of φ, and thus ⊂ classical Beurling spectrum = Carleman spectrum =  ; also  = Beurling spectrum of “φ modulo ” (Chill-Fasangova). If satisfies a Loomis type condition (L _U ), then countable and uniformly continuous ∈U are shown to imply ; here (L _U ) usually means , indefinite integral Pf of f in U imply Pf in (the Bohl-Bohr theorem for = almost periodic functions, U=bounded functions). This spectral characterization and other results are extended to unbounded functions via mean classes , ℳ ^m U ((2.1) below) and even to distributions, generalizing various recent results for uniformly continuous bounded φ. Furthermore for solutions of convolution systems S*φ=b with in some we show . With these above results, one gets generalizations of earlier results on the asymptotic behaviour of solutions of neutral integro-differential-difference systems. Also many examples and special cases are discussed.     

Convolution and restriction estimates for measures on curves in

We study convolution and Fourier restriction estimates for some degenerate curves in .

     

From light tails to heavy tails through multiplier

Let X and Y be two independent nonnegative random variables, of which X has a distribution belonging to the class or for some γ ≥ 0 and Y is unbounded. We study how their product XY inherits the tail behavior of X. Under some mild technical assumptions we prove that the distribution of XY belongs to the class or accordingly. Hence, the multiplier Y builds a bridge between light tails and heavy tails.      

Discrete Approximation of a Mixture Distribution via Restricted Divergence

Mixture distributions arise in many application areas, for example, as marginal distributions or convolutions of distributions. We present a method of constructing an easily tractable discrete mixture distribution as an approximation to a mixture distribution with a large to infinite number, discrete or continuous, of components. The proposed DIRECT (divergence restricting conditional tesselation) algorithm is set up such that a prespecified precision, defined in terms of Kullback–Leibler divergence between true distribution and approximation, is guaranteed. Application of the algorithm is demonstrated in two examples. Supplementary materials for this article are available online.     

A unified class of k-uniformly convex functions defined by the Dziok–Srivastava linear operator

The main purpose of this paper is to introduce a new class of functions which are analytic in the open unit disk . We obtain various results including characterization, coefficient estimates, and distortion and covering theorems, for functions belonging to the class .     

Note on the wave equation and tensor products

In this study we apply convolution and tensor products of distribution to solve the non-homogenous wave equation with initial condition and discuss the uniqueness and continuity of solution. We also show that the tensor product can be applied to compute the some singular integrals.