Let P and P' be the laws of two discrete-time stochastic processes defined on the sequence space S, where S is a finite set of points. In this paper we derive a bound on the total variation distance dTV(P,P') in terms of the cylindrical projections of P and P'. We apply the result to Markov chains with finite state space and random walks on Z with not necessarily independent increments, and we consider several examples.

We present the advancements and novelties recently introduced in RNASeqGUI, a graphical user interface that helps biologists to handle and analyse large data collected in RNA-Seq experiments. This work focuses on the concept of reproducible research and shows how it has been incorporated in RNASeqGUI to provide reproducible (computational) results. The novel version of RNASeqGUI combines graphical interfaces with tools for reproducible research, such as literate statistical programming, human readable report, parallel executions, caching, and interactive and web-explorable tables of results.

Reproducible (computational) Research is crucial to produce transparent and high quality scientific papers. First, we illustrate the benefits that scientific community can receive from the adoption of Reproducible Research standards in the analysis of high-throughput omic data. Then, we describe several tools useful to researchers to increase the reproducibility of their works. Moreover, we face the advantages and limits of reproducible research and how they could be addressed and solved.

We prove that positive solutions of the fractional Lane-Emden equation with homogeneous Dirichlet boundary conditions satisfy pointwise estimates in terms of the best constant in Poincaré's inequality on all open sets, and are isolated in $L^1$ on smooth bounded ones, whence we deduce the isolation of the first non-local semilinear eigenvalue .

A product quadrature rule, based on the filtered de la Vallée Poussin polynomial approximation, is proposed for evaluating the finite weighted Hilbert transform in [-1,1]. Convergence results are stated in weighted uniform norm for functions belonging to suitable Besov type subspaces. Several numerical tests are provided, also comparing the rule with other formulas known in literature.

Poisson shot noise processes are natural generalizations of compound Poisson processes that have been widely applied in insurance, neuroscience, seismology, computer science and epidemiology. In this paper we study sharp deviations, fluctuations and the stable probability approximation of Poisson shot noise processes. Our achievements extend, improve and complement existing results in the literature. We apply the theoretical results to Poisson cluster point processes, including generalized linear Hawkes processes, and risk processes with delayed claims. Many examples are discussed in detail.

Age of infection epidemic models [1, 3], based on non-linear integro-dierential equations, naturally describe the evolution of diseases whose infectivity depends on the time since becoming infected. Here we consider a multi-group age of infection model [2] and we extend the investigations in [4], [5] and [6] to provide numerical solutions that retain the main properties of the continuous system. In particular, we use Direct Quadrature methods and prove that the numerical solution is positive and bounded.

In the near future, Exascale systems will need to bridge three technology gaps to achieve high performance while remaining under tight power constraints: energy efficiency and thermal control; extreme computation efficiency via HW acceleration and new arithmetic; methods and tools for seamless integration of reconfigurable accelerators in heterogeneous HPC multi-node platforms. TEXTAROSSA addresses these gaps through a co-design approach to heterogeneous HPC solutions, supported by the integration and extension of HW and SW IPs, programming models, and tools derived from European research.