We define pseudo-reality and pseudo-adjointness of a Hamiltonian, H, as ρHρ−1 = H∗ and μHμ−1 = H ′, respectively. We prove that the former yields the necessary condition for spectrum to be real whereas the latter helps in fixing a definition for inner-product of the eigenstates. Here we separate out adjointness of an operator from its Hermitian-adjointness. It turns out that a Hamiltonian posse...

In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

In this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. Weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

This paper explores possible strategies for the recombination of independent multi-resolution sub-band based recognisers. The multi-resolution approach is based on the premise that additional cues for phonetic discrimination may exist in the spectral correlates of a particular sub-band, but not in another. Weights are derived via discriminative training using the ‘Minimum Classification Error’ ...

This paper deals with asymptotically efficient estimation in exchangeable nonlinear dynamic panel models with common unobservable factor. These models are especially relevant for applications to large portfolios of credits, corporate bonds, or life insurance contracts, and are recommended in the current regulation in Finance (Basel II and Basel III) and Insurance (Solvency II). The specificatio...

Introduction Kulldorff’s spatial scan statistic1 detects significant spatial clusters of disease by maximizing a likelihood ratio statistic over circular spatial regions. The fast localized subset scan2 enables scalable detection of proximity-constrained subsets and increases power to detect irregularly-shaped clusters, However, unconstrained subset scanning within each circular neighborhood2, ...

There has been significant interest in sparse inverse covariance estimation in areas such as statistics, machine learning, and signal processing. In this problem, the sparse inverse of a covariance matrix of a multivariate normal distribution is estimated. A Penalised LogLikelihood (PLL) optimisation problem is solved to obtain the matrix estimator, where the penalty is responsible for inducing...

Nonparametric estimation procedures that can flexibly account for varying levels of smoothness among different functional parameters, such as penalized likelihoods, have been developed in a variety of settings. However, geometric constraints on power spectra have limited the development of such methods when estimating the power spectrum of a vector-valued time series. This article introduces a ...

Binomial data with unknown sizes often appear in biological and medical sciences and are usually overdispersed. All previous methods used parametric models and only considered overdispersion due to the variation of sizes. The proposed semiparametric model considers overdispersion due to the variation of sizes and that of probabilities. By doing this, it can include variations caused by observat...

In statistics, an expectationmaximization (EM) algorithm is an iterative method for finding maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated usin...