A kernel-enriched order-dependent nonparametric spatio-temporal process

Spatio-temporal processes are necessary modeling tools for various environmental, biological, and geographical problems. The underlying model is commonly considered to be parametric and to be a Gaussian process. Additionally, the covariance function is expected to be stationary and separable. This structure need not always be realistic. Moreover, attempts have been made to construct nonparametric processes of neither stationary nor separable covariance functions. Nevertheless, as we elucidate, some desirable and necessary spatio-temporal properties are not guaranteed by the existing approaches, thus, calling for further innovative ideas. In this article, using kernel convolution of order-based dependent Dirichlet process, we construct a novel spatio-temporal model. We show that this satisfies desirable properties and includes the stationary, separable, parametric processes as special cases. Our resultant posterior distribution is variable dimensional, which we attack using Transdimensional Transformation based Markov Chain Monte Carlo, which can update all the variables and change dimensions using deterministic transformations of a random variable drawn from some arbitrary density defined on relevant support. We demonstrate our model’s performance on simulated and real data sets. In all situations, the findings are highly encouraging

Simple theoretical analysis of the effective electron mass in semiconductor nanowires

In this paper we study the effective electron mass (EEM) in Nano wires (NWs) of nonlinear optical materials on the basis of newly formulated electron dispersion relation by considering all types of anisotropies of the energy band constants within the framework of k . p formalism. The results for NWs of III-V, ternary and quaternary semiconductors form special cases of our generalized analysis. We have also investigated the EEM in NWs of Bi, IV-VI, stressed Kane type materials, Ge, GaSb and Bi2Te3 by formulating the appropriate 1D dispersion law in each case by considering the influence of energy band constants in the respective cases. It has been found that the 1D EEM in nonlinear optical materials depend on the size quantum numbers and Fermi energy due to the anisotropic spin orbit splitting constant and the crystal field splitting respectively. The 1D EEM is Bi, IV-VI, stressed Kane type semiconductors and Ge also depends on both the Fermi energy and the size quantum numbers which are the characteristic features of such NWs. The EEM increases with increase in concentration and decreasing film thickness and for ternary and quaternary compounds the EEM increases with increase in alloy composition. Under certain special conditions all the results for all the materials get simplified into the well known parabolic energy bands and thus confirming the compatibility test