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101.
Canonical correlation analysis based on information theory 总被引:2,自引:0,他引:2
In this article, we propose a new canonical correlation method based on information theory. This method examines potential nonlinear relationships between p×1 vector Y-set and q×1 vector X-set. It finds canonical coefficient vectors a and b by maximizing a more general measure, the mutual information, between aTX and bTY. We use a permutation test to determine the pairs of the new canonical correlation variates, which requires no specific distributions for X and Y as long as one can estimate the densities of aTX and bTY nonparametrically. Examples illustrating the new method are presented. 相似文献
102.
A. Sinatra Y. Castin 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》1998,4(3):247-260
In the absence of losses the phase of a Bose-Einstein condensate undergoes collapses and revivals in time due to elastic atomic
interactions. As experiments necessarily involve inelastic collisions, we develop a model to describe the phase dynamics of
the condensates in presence of collisional losses. We find that a few inelastic processes are sufficient to damp the revivals of the phase. For this reason the observability of phase revivals for present experimental
conditions is limited to condensates with a few hundreds of atoms.
Received: 23 February 1998 / Revised: 21 July 1998 / Accepted: 23 July 1998 相似文献
103.
P. L. Chesson 《Journal of multivariate analysis》1976,6(4):526-537
The ordinary notion of a bivariate distribution has a natural generalisation. For this generalisation it is shown that a bivariate distribution can be characterised by a Hilbert space
and a family
p, 0 ≤ p ≤ 1, of subspaces of
.
specifies the marginal distributions whilst
p is a summary of the dependence structure. This characterisation extends existing ideas on canonical correlation. 相似文献
104.
The standard C∗-algebraic version of the algebra of canonical commutation relations, the Weyl algebra, frequently causes difficulties in applications since it neither admits the formulation of physically interesting dynamical laws nor does it incorporate pertinent physical observables such as (bounded functions of) the Hamiltonian. Here a novel C∗-algebra of the canonical commutation relations is presented which does not suffer from such problems. It is based on the resolvents of the canonical operators and their algebraic relations. The resulting C∗-algebra, the resolvent algebra, is shown to have many desirable analytic properties and the regularity structure of its representations is surprisingly simple. Moreover, the resolvent algebra is a convenient framework for applications to interacting and to constrained quantum systems, as we demonstrate by several examples. 相似文献
105.
Zhijun Zhang Ling Mi Xiugui Yin 《Journal of Mathematical Analysis and Applications》2008,348(2):797-805
For more general nonlinear term g, the paper shows the exact blow-up rate of the unique solution ψ(t) to the singular boundary value problem
106.
Holger Dette Lorens A. Imhof 《Transactions of the American Mathematical Society》2007,359(10):4999-5018
We derive strong uniform approximations for the eigenvalues in general Laguerre and Hermite -ensembles by showing that the maximal discrepancy between the suitably scaled eigenvalues and roots of orthogonal polynomials converges almost surely to zero when the dimension converges to infinity. We also provide estimates of the rate of convergence. In the special case of a normalized real Wishart matrix , where denotes the dimension and the degrees of freedom, the rate is , if with , and the rate is , if with . In the latter case we also show the a.s. convergence of the largest eigenvalue of to the corresponding quantile of the Marcenko-Pastur law.
107.
The finite-size scaling technique is extended to a microcanonical ensemble. As an application, equilibrium magnetic properties of anL×L square lattice Ising model are computed using the microcanonical ensemble simulation technique of Creutz, and the results are analyzed using the microcanonical ensemble finite-size scaling. The computations were done on the multitransputer system of the Condensed Matter Theory Group at the University of Mainz. 相似文献
108.
109.
Let be a nontrivial involution, i.e., R=R−1≠±In. We say that is R-symmetric if RGR=G. The set of all -symmetric matrices is denoted by . In this paper, we first give the solvability condition for the following inverse eigenproblem (IEP): given a set of vectors in and a set of complex numbers , find a matrix such that and are, respectively, the eigenvalues and eigenvectors of A. We then consider the following approximation problem: Given an n×n matrix , find such that , where is the solution set of IEP and is the Frobenius norm. We provide an explicit formula for the best approximation solution by means of the canonical correlation decomposition. 相似文献
110.
Abdulmuhsen H. Ali 《International Journal of Theoretical Physics》2009,48(1):194-212
The derivation of the statistical nature of the quantum mechanical wave function is presented within the formalism of quantum
mechanics and the second quantization. The statistical wave function may be derived for non relativistic bosons, non relativistic
fermions, and relativistic bosons by employing the commuting field operator
. For relativistic electrons a strictly anticommuting
must be employed to derive the statistical wave function (spinor). The discussion at the end of the paper aims to show the
physical plausibility of a statistical wave function. 相似文献