Search results for " basis"
showing 10 items of 224 documents
Gabor-like systems in ${cal L}^2({bf R}^d)$ and extensions to wavelets
2008
In this paper we show how to construct a certain class of orthonormal bases in starting from one or more Gabor orthonormal bases in . Each such basis can be obtained acting on a single function with a set of unitary operators which operate as translation and modulation operators in suitable variables. The same procedure is also extended to frames and wavelets. Many examples are discussed.
Hamiltonians defined by biorthogonal sets
2017
In some recent papers, the studies on biorthogonal Riesz bases has found a renewed motivation because of their connection with pseudo-hermitian Quantum Mechanics, which deals with physical systems described by Hamiltonians which are not self-adjoint but still may have real point spectra. Also, their eigenvectors may form Riesz, not necessarily orthonormal, bases for the Hilbert space in which the model is defined. Those Riesz bases allow a decomposition of the Hamiltonian, as already discussed is some previous papers. However, in many physical models, one has to deal not with o.n. bases or with Riesz bases, but just with biorthogonal sets. Here, we consider the more general concept of $\mat…
Quantum Walk Search on Johnson Graphs
2016
The Johnson graph $J(n,k)$ is defined by $n$ symbols, where vertices are $k$-element subsets of the symbols, and vertices are adjacent if they differ in exactly one symbol. In particular, $J(n,1)$ is the complete graph $K_n$, and $J(n,2)$ is the strongly regular triangular graph $T_n$, both of which are known to support fast spatial search by continuous-time quantum walk. In this paper, we prove that $J(n,3)$, which is the $n$-tetrahedral graph, also supports fast search. In the process, we show that a change of basis is needed for degenerate perturbation theory to accurately describe the dynamics. This method can also be applied to general Johnson graphs $J(n,k)$ with fixed $k$.
Artificial neural network comparison for a SHM procedure applied to composite structures.
2013
In this paper different architectures of Artificial Neural Networks (ANNs) for structural damage detection are studied. The main objective is to create an ANN able to detect and localize damage without any prior knowledge on its characteristics so as to serve as a realtime data processor for SHM systems. Two different architectures are studied: the standard feed-forward Multi Layer Perceptron (MLP) and the Radial Basis Function (RBF) ANNs. The training data are given, in terms of a Damage Index ℑD, properly defined using the piezoelectric sensor signal output to obtain suitable information on the damage position and dimensions. The electromechanical response of the assembled structure has b…
Prediction of banana quality indices from color features using support vector regression
2015
Banana undergoes significant quality indices and color transformations during shelf-life process, which in turn affect important chemical and physical characteristics for the organoleptic quality of banana. A computer vision system was implemented in order to evaluate color of banana in RGB, L*a*b* and HSV color spaces, and changes in color features of banana during shelf-life were employed for the quantitative prediction of quality indices. The radial basis function (RBF) was applied as the kernel function of support vector regression (SVR) and the color features, in different color spaces, were selected as the inputs of the model, being determined total soluble solids, pH, titratable acid…
A Review of Kernel Methods in ECG Signal Classification
2011
Kernel methods have been shown to be effective in the analysis of electrocardiogram (ECG) signals. These techniques provide a consistent and well-founded theoretical framework for developing nonlinear algorithms. Kernel methods exhibit useful properties when applied to challenging design scenarios, such as: (1) when dealing with low number of (potentially high dimensional) training samples; (2) in the presence of heterogenous multimodalities; and (3) with different noise sources in the data. These characteristics are particularly appropriate for biomedical signal processing and analysis, and hence, the widespread of these techniques in biomedical signal processing in general, and in ECG dat…
Applications of Kernel Methods
2009
In this chapter, we give a survey of applications of the kernel methods introduced in the previous chapter. We focus on different application domains that are particularly active in both direct application of well-known kernel methods, and in new algorithmic developments suited to a particular problem. In particular, we consider the following application fields: biomedical engineering (comprising both biological signal processing and bioinformatics), communications, signal, speech and image processing.
Orientation of a Surface
2012
We know from Chap. 4 that in order to evaluate the flux of a vector field across a regular surface S, we need to choose a unit normal vector at each point of S in such a way that the resulting vector field is continuous. For instance, if we submerge a permeable sphere into a fluid and we select the field of unit normal outward vectors on the sphere, then the flux of the velocity field of the fluid across the sphere gives the amount of fluid leaving the sphere per unit time. However, if we select the field of unit normal inward vectors on the sphere, then the flux of the velocity field of the fluid across the sphere gives the amount of fluid entering the sphere per unit time (which is the ne…
Learning non-linear time-scales with kernel -filters
2009
A family of kernel methods, based on the @c-filter structure, is presented for non-linear system identification and time series prediction. The kernel trick allows us to develop the natural non-linear extension of the (linear) support vector machine (SVM) @c-filter [G. Camps-Valls, M. Martinez-Ramon, J.L. Rojo-Alvarez, E. Soria-Olivas, Robust @c-filter using support vector machines, Neurocomput. J. 62(12) (2004) 493-499.], but this approach yields a rigid system model without non-linear cross relation between time-scales. Several functional analysis properties allow us to develop a full, principled family of kernel @c-filters. The improved performance in several application examples suggest…
IL LEGISLATORE TEDESCO ALLARGA LE MAGLIE DELLA REVISIONE CONTRA REUM: L'ASSOLUZIONE PER DELITTI GRAVI E IMPRESCRITTIBILI PUÒ ESSERE MESSA IN DISCUSSI…
2022
Il legislatore tedesco ha ampliato il novero dei casi di revisione in peius. Ha previsto la possibilità di impugnare una sentenza definitiva di assoluzione per omicidio o crimini internazionali, qualora – in base a nuovi fatti o mezzi di prova – emergano “ragioni stringenti” per una condanna. La riforma ha già sollecitato dubbi di legittimità costituzionale e, per la sua rilevanza, suscita varie riflessioni.