Search results for "vector space"

Multivariate GARCH estimation via a Bregman-proximal trust-region method

2011

The estimation of multivariate GARCH time series models is a difficult task mainly due to the significant overparameterization exhibited by the problem and usually referred to as the "curse of dimensionality". For example, in the case of the VEC family, the number of parameters involved in the model grows as a polynomial of order four on the dimensionality of the problem. Moreover, these parameters are subjected to convoluted nonlinear constraints necessary to ensure, for instance, the existence of stationary solutions and the positive semidefinite character of the conditional covariance matrices used in the model design. So far, this problem has been addressed in the literature only in low…

Monte Carlo investigations of phase transitions: status and perspectives

2000

Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies of Ising models are discussed, as well as the extension to models of polymer mixtures and solutions. It is shown that using appropriate cluster algorithms, even the scaling functions describing the crossover from the Ising universality class to the mean-field behavior with increasing interaction range can be described. Additionally, the issue of finite-size scaling in Ising models above the marginal dimension (d*=4) is discussed.

Dimension reduction for time series in a blind source separation context using r

2021

Funding Information: The work of KN was supported by the CRoNoS COST Action IC1408 and the Austrian Science Fund P31881-N32. The work of ST was supported by the CRoNoS COST Action IC1408. The work of JV was supported by Academy of Finland (grant 321883). We would like to thank the anonymous reviewers for their comments which improved the paper and package considerably. Publisher Copyright: © 2021, American Statistical Association. All rights reserved. Multivariate time series observations are increasingly common in multiple fields of science but the complex dependencies of such data often translate into intractable models with large number of parameters. An alternative is given by first red…

An algebraic representation of Steiner triple systems of order 13

2021

Abstract In this paper we construct an incidence structure isomorphic to a Steiner triple system of order 13 by defining a set B of twentysix vectors in the 13-dimensional vector space V = GF ( 5 ) 13 , with the property that there exist precisely thirteen 6-subsets of B whose elements sum up to zero in V , which can also be characterized as the intersections of B with thirteen linear hyperplanes of V .

Constrained and unconstrained problems in location theory and inner products

1997

In a real normed space X the optimization problem associated to a finite subset and to a family of positive weights with the objective function [UM0001] has some well known properties when X is an ...

Experiments in Value Function Approximation with Sparse Support Vector Regression

2004

We present first experiments using Support Vector Regression as function approximator for an on-line, sarsa-like reinforcement learner. To overcome the batch nature of SVR two ideas are employed. The first is sparse greedy approximation: the data is projected onto the subspace spanned by only a small subset of the original data (in feature space). This subset can be built up in an on-line fashion. Second, we use the sparsified data to solve a reduced quadratic problem, where the number of variables is independent of the total number of training samples seen. The feasability of this approach is demonstrated on two common toy-problems.

2014

For locating inaccurate problem of the discrete localization criterion proposed by Demigny, a new criterion expression of “good localization” is proposed. Firstly, a discrete expression of good detection and good localization criterion of two dimension edge detection operator is employed, and then an experiment to measure optimal parameters of two dimension Canny's edge detection operator is introduced after. Moreover, a detailed performance comparison and analysis of two dimension optimal filter obtained via utilizing tensor product for one dimension optimal filter are provided which can prove that least square support vector regression (LS-SVR) is a smoothness filter and give the construc…

Multi-dimensional Function Approximation and Regression Estimation

2002

In this communication, we generalize the Support Vector Machines (SVM) for regression estimation and function approximation to multi-dimensional problems. We propose a multi-dimensional Support Vector Regressor (MSVR) that uses a cost function with a hyperspherical insensitive zone, capable of obtaining better predictions than using an SVM independently for each dimension. The resolution of the MSVR is achieved by an iterative procedure over the Karush-Kuhn-Tucker conditions. The proposed algorithm is illustrated by computers experiments.

Polarity Effects on ZnO Films Grown along the Nonpolar[112¯0]Direction

2005

The surface electrical properties of ZnO thin films grown along the nonpolar $[11\overline{2}0]$ direction have been investigated by Kelvin probe microscopy on a nanometer scale. Two different charge domains, with a 75 meV work function difference, coexist within the ZnO surface, which is covered by rhombohedral pyramids whose sidewalls are shown to be ${10\overline{1}1}$-type planes. The presence and relative orientation of the two kinds of charge domains are explained in terms of the atomic arrangement at the ${10\overline{1}1}$ polar surfaces.

Order and Disorder Phenomena at Surfaces of Binary Alloys

2000

We present recent Monte Carlo results on surfaces of bcc-structured binary alloys which undergo an order-disorder phase transformation in the bulk. In particular, we discuss surface order and surface induced disorder at the bulk transition between the ordered (DO3) phase and the disordered (A2) phase. An intricate interplay between different ordering and segregation phenomena leads to a complex surface behavior, which depends on the orientation of the surface under consideration.