Search results for "approximation"

Interpolation and approximation in L2(γ)

AbstractAssume a standard Brownian motion W=(Wt)t∈[0,1], a Borel function f:R→R such that f(W1)∈L2, and the standard Gaussian measure γ on the real line. We characterize that f belongs to the Besov space B2,qθ(γ)≔(L2(γ),D1,2(γ))θ,q, obtained via the real interpolation method, by the behavior of aX(f(X1);τ)≔∥f(W1)-PXτf(W1)∥L2, where τ=(ti)i=0n is a deterministic time net and PXτ:L2→L2 the orthogonal projection onto a subspace of ‘discrete’ stochastic integrals x0+∑i=1nvi-1(Xti-Xti-1) with X being the Brownian motion or the geometric Brownian motion. By using Hermite polynomial expansions the problem is reduced to a deterministic one. The approximation numbers aX(f(X1);τ) can be used to descr…

3D digitization of transparent objects by polalization techniques in IR & by triangulation in UV

2011

Two non-conventional methods for the 3D digitization of transparent objects via non-contact measurement are reported in this thesis. 3D digitization is a well acknowledged technique for opaque objects and various commercial solutions based on different measurement approaches are available in the market offering different types of resolution at different prices. Since these techniques require a diffused or lambertian surface, their application to transparent surfaces fails. Indeed, rays reflected by the transparent surface are perturbed by diverse inter-reflections induced by the refractive properties of the object. Therefore, in industrial applications like quality control, the transparent …

Online topology estimation for vector autoregressive processes in data networks

2017

An important problem in data sciences pertains to inferring causal interactions among a collection of time series. Upon modeling these as a vector autoregressive (VAR) process, this paper deals with estimating the model parameters to identify the underlying causality graph. To exploit the sparse connectivity of causality graphs, the proposed estimators minimize a group-Lasso regularized functional. To cope with real-time applications, big data setups, and possibly time-varying topologies, two online algorithms are presented to recover the sparse coefficients when observations are received sequentially. The proposed algorithms are inspired by the classic recursive least squares (RLS) algorit…

A brief overview on the numerical behavior of an implicit meshless method and an outlook to future challenges

2015

In this paper recent results on a leapfrog ADI meshless formulation are reported and some future challenges are addressed. The method benefits from the elimination of the meshing task from the pre-processing stage in space and it is unconditionally stable in time. Further improvements come from the ease of implementation, which makes computer codes very flexible in contrast to mesh based solver ones. The method requires only nodes at scattered locations and a function and its derivatives are approximated by means of a kernel representation. A perceived obstacle in the implicit formulation is in the second order differentiations which sometimes are eccesively sensitive to the node configurat…

A novel numerical meshless approach for electric potential estimation in transcranial stimulation

2015

In this paper, a first application of the method of fundamental solutions in estimating the electric potential and the spatial current density distribution in the brain due to transcranial stimulation, is presented. The coupled boundary value p roblems for the electric potential are solved in a meshless way, so avoiding the use of grid based numerical methods. A multi-spherical geometry is considered and numerical results are discussed.

Fractional model of concrete hereditary viscoelastic behaviour

2016

The evaluation of creep effects in concrete structures is addressed in the literature using different predictive models, supplied by specific codes, and applying the concepts of linear viscoelastic theory with ageing. The expressions used in the literature are mainly based on exponential laws, which are introduced in the integral expression of the Boltzmann principle; this approach leads to the need of finding approximated numerical solutions of the viscoelastic response. In this study, the hereditary fractional viscoelastic model is applied to concrete elements, underlining the convenience of using creep or relaxation functions expressed by power laws. The full reciprocal character of cree…

User-Centered Virtual Reality for Promoting Relaxation: An Innovative Approach

2019

[EN] Virtual reality has been used effectively to promote relaxation and reduce stress. It is possible to find two main approaches to achieve such aims across the literature. The first one is focused on genetic environments filled with relaxing "narratives" to induce control over one's own body and physiological response, while the second one engages the user in virtual reality-mediated activities to empower his/her own abilities to regulate emotion. The scope of the present contribution is to extend the discourse on VR use to promote relaxation, by proposing a third approach. This would be based on VR with personalized content, based on user research to identify important life events. As a…

An analytical study of the ageostrophic motion of an air parcel

1978

The complete ageostrophic motion of an individual air parcel is discussed. It is shown that the general velocity solution of the equation describing this motion may be expressed in terms of the well-known series approximation of Philipps and a rest term; this term describes the inertial motion of the air parcel about a given initial state.

Spatio-Temporal Modeling of Zika and Dengue Infections within Colombia

2018

The aim of this study is to estimate the parallel relative risk of Zika virus disease (ZVD) and dengue using spatio-temporal interaction effects models for one department and one city of Colombia during the 2015&ndash

Time Dependent Case

1999

This chapter is devoted to finite element approximations of scalar time dependent hemivariational inequalities. We start with the parabolic case following closely Miettinen and Haslinger, 1998. At the end of this chapter we discuss, how the results can be extended to constrained problems. Our presentation will follow the structure used for the static case in Chapter 3. First, we introduce an abstract formulation of a class of parabolic hemivariational inequalities (see Miettinen, 1996, Miettinen and Panagiotopoulos, 1999).