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Spontaneous symmetry breaking in photonic lattices: Theory and experiment
Symmetry broken double - well waveguide symmetric potential galerkin truncation photonic crystal lattice
2014/12/29
We examine an example of spontaneous symmetry breaking in a double-well waveguide with a symmetric potential. The ground state of the system beyond a critical power becomes asymmetric. The effect is i...
Symmetry breaking in symmetric and asymmetric double-well potentials
Matter waves light beam the nonlinear schrodinger equation nonlinear solution attractive and nonlinear disturbances
2014/12/25
Motivated by recent experimental studies of matter waves and optical beams in double-well potentials, we study the corresponding solutions of the nonlinear Schrödinger equation. Using a Galerkin-...
Symmetry breaking in linearly coupled dynamical lattices
Two-dimensional model the linear coupling lattice weak coupling lattice
2014/12/25
We examine one- and two-dimensional models of linearly coupled lattices of the discrete-nonlinear-Schrödinger type. Analyzing ground states of the system with equal powers (norms) in the two comp...
SYMMETRY-BREAKING BIFURCATION IN NONLINEAR SCHRODINGER/GROSS-PITAEVSKII EQUATIONS
Nonlinear schrodinger mathematical modeling nonlinear optics macroscopic quantum phenomena the number of particles the mixed pattern
2014/12/25
We consider a class of nonlinear Schrödinger/Gross–Pitaeveskii (NLS-GP) equations, i.e., NLS with a linear potential. NLS-GP plays an important role in the mathematical modeling of nonlinear opti...
Two-dimensional paradigm for symmetry breaking: The nonlinear Schroumldinger equation with a four-well potential
Mechanical systems linear geometric properties nonlinear dynamic equations
2014/12/24
We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derive...
Simple, asymptotically distribution-free, optimal tests for circular reflective symmetry about a known median direction
Circular statistics Fisher information singularity Rayleigh test for uniformity skewed distributions tests for symmetry
2013/4/28
In this paper, we propose optimal tests for circular reflective symmetry about a fixed median direction. The distributions against which optimality is achieved are the so-called k-sine-skewed distribu...
Composite likelihood estimation of sparse Gaussian graphical models with symmetry
Variable selection model selection penalized estimation Gaussian graphical model concentration matrix partial correlation matrix
2012/9/17
In this article, we discuss the composite likelihood estimation of sparse Gaussian graph-ical models. When there are symmetry constraints on the concentration matrix or partial correlation matrix, the...
Improving PSF calibration in confocal microscopic imaging---estimating and exploiting bilateral symmetry
confocal microscopic imaging PSF calibration estimating exploiting bilateral symmetry
2011/3/18
A method for estimating the axis of reflectional symmetry of an image $f(x,y)$ on the unit disc $D=\{(x,y):x^2+y^2\leq1\}$ is proposed, given that noisy data of $f(x,y)$ are observed on a discrete gri...
Decompositions for Extended Double Symmetry Models in Square Contingency Tables with Ordered Categories
decomposition double symmetry marginal double symmetry ordered category quasi double symmetry square contingency table unaided vision data
2009/3/6
For square contingency tables with ordered categories, Tomizawa (1992) proposed three kinds of double symmetry models, whose each has a structure of both symmetry about the main diagonal and asymmetry...
Collapsed Symmetry Model and its Decomposition for Multi-way Tables with Ordered Categories
Collapsed quasi-symmetry collapsed symmetry decomposition marginal homogeneity multi-way tables ordered category quasi-symmetry symmetry
2009/3/5
For r× r tables with ordered categories, Tomizawa (1995) considered the collapsed symmetry model. This model indicates the structure of symmetry for the r−1 ways of collapsing the r× r table int...
Extremal Probabilistic Problems and Hotelling's T2 Test Under Symmetry Condition
Probability inequalities extremal probability problems Hotelling’s T2 test monotonelikelihood ratio stochastic monotonicity
2010/4/26
We consider Hotelling’s T2 statistic for an arbitrary d-dimensional sample.
If the sampling is not too deterministic or inhomogeneous, then under zero
means hypothesis, T2 tends to χ2d in distributi...