9,792 research outputs found
Complexified sigma model and duality
We show that the equations of motion associated with a complexified
sigma-model action do not admit manifest dual SO(n,n) symmetry. In the process
we discover new type of numbers which we called `complexoids' in order to
emphasize their close relation with both complex numbers and matroids. It turns
out that the complexoids allow to consider the analogue of the complexified
sigma-model action but with (1+1)-worldsheet metric, instead of
Euclidean-worldsheet metric. Our observations can be useful for further
developments of complexified quantum mechanics.Comment: 15 pages, Latex, improved versio
Canonical gravity in two time and two space dimensions
We describe a program for developing a canonical gravity in 2+2 dimensions
(two time and two space dimensions). Our procedure is similar to the usual
canonical gravity but with two times rather than just one time. Our work may be
of particular interest as an alternative approach to loop quantum gravity in
2+2 dimensions.Comment: 13 pages, Latex, improved versio
Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures
In this article we propose novel Bayesian nonparametric methods using
Dirichlet Process Mixture (DPM) models for detecting pairwise dependence
between random variables while accounting for uncertainty in the form of the
underlying distributions. A key criteria is that the procedures should scale to
large data sets. In this regard we find that the formal calculation of the
Bayes factor for a dependent-vs.-independent DPM joint probability measure is
not feasible computationally. To address this we present Bayesian diagnostic
measures for characterising evidence against a "null model" of pairwise
independence. In simulation studies, as well as for a real data analysis, we
show that our approach provides a useful tool for the exploratory nonparametric
Bayesian analysis of large multivariate data sets
General Approach to Functional Forms for the Exponential Quadratic Operators in Coordinate-Momentum Space
In a recent paper [Nieto M M 1996 Quantum and Semiclassical Optics, 8 1061;
quant-ph/9605032], the one dimensional squeezed and harmonic oscillator
time-displacement operators were reordered in coordinate-momentum space. In
this paper, we give a general approach for reordering multi-dimensional
exponential quadratic operator(EQO) in coordinate-momentum space. An explicit
computational formula is provided and applied to the single mode and
double-mode EQO through the squeezed operator and the time displacement
operator of the harmonic oscillator.Comment: To appear in J. Phys. A: Mathematics and Genera
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