In this paper, we apply the Variation of Parameters Method (VPM) for solving initial and boundary value problems of diversified physical nature. The analytical results are calculated in terms of convergent series with easily computable components. The proposed VPM is applied without any discretization, perturbation, transformation or restrictive assumptions and is free from round off errors and...

The main contribution of this paper, is a new key enumeration algorithm that combines the conceptual simplicity of the rank estimation algorithm of Glowacz et al. (from FSE 2015) and the parallelizability of the enumeration algorithm of Bogdanov et al. (SAC 2015) and Martin et al. (from ASIACRYPT 2015). Our new algorithm is based on histograms. It allows obtaining simple bounds on the (small) r...

We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart of the algorithm is the evaluation of modular functions in several arguments. The fastest one of the presented approaches uses a technique devised by Dupont to evaluate modular functions by Newton ...

This paper presents a model selection procedure which stresses the importance of the classic polynomial models as tools for evaluating the complexity of a given modeling problem, and for removing non-significant input variables. If the complexity of the problem makes a neural network necessary, the selection among neural candidates can be performed in two phases. In an additive phase, the most ...

Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today. Interval methods are useful whenever we have to deal with uncertainties, which can be rigorously bounded. Fuzzy sets, rough sets and probability calculus can perf...

For a given sequence a = (a1, . . . , an) of numbers, a global rounding is an integer sequence b = (b1, . . . , bn) such that the rounding error |∑i∈I (ai − bi )| is less than one in all intervals I ⊆ {1, . . . , n}. We give a simple characterization of the set of global roundings of a. This allows to compute optimal roundings in time O(n logn) and generate a global rounding uniformly at random...

The aim of this note is to indicate that nonparametric orthogonal series estimators of probability densities retain the mean integrated square error (MISE) consistency when observations are grouped to the points of a uniform grid (prebinned). This kind of grouping is typical for computer rounding errors and may also be useful in data compression, before calculating estimates, e.g., using the FF...

Let S denote the price process of a security, and suppose that S follow a geometric Brownian motion with volatility σ. We consider the case when the observations at the discrete time points 0, 1/n, 2/n, · · · , 1 are the rounded-off values Sn i/n = αnbSi/n/αnc (i = 0, · · · , n), where αn > 0 is the round-off level corresponding to the sample frequency n. We investigate the asymptotic behavior ...

Combustion is the source of eighty percent of the energy produced in the world: it is therefore a topic of major interest in the present context of global warming and decreasing fuel resources. Simulating combustors and especially instability mechanisms in these systems has become a central issue in the combustion community in the last ten years. This can be achieved only on massively parallel ...

The paper describes the use of adaptive and non-periodic sampling in different fields of System Theory and Control. The review is organized in a very comprehensive way and it presents results of the last thirty years about the problem of signal applications using as main tool adaptive sampling schemes including results is the improvement of the transient behaviors. Also, related results are pre...