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The test of homogeneity for normal mixtures has been conducted in diverse research areas, but constructing a theory of the test of homogeneity is challenging because the parameter set for the null hypothesis corresponds to singular points…
This work is focused on constructing space-time covariance functions through a hierarchical mixture approach that can serve as building blocks for capturing complex dependency structures. This hierarchical mixture approach provides a…
Consider an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. In order to establish concentration properties for nonlinear functions $Z(A)$, it is standard to appeal to functional inequalities like Poincar\'e or…
We propose a new method to construct a stationary process and random field with a given decreasing covariance function and any one-dimensional marginal distribution. The result is a new class of stationary processes and random fields. The…
The momentum spectrum and number density of created bosons for two types of arbitrarily polarized electric fields are calculated and compared with those of created fermions, employing the equal-time Feshbach-Villars-Heisenberg-Wigner…
The kernel polynomial method allows to sample overall spectral properties of a quantum system, while sparse diagonalization provides accurate information about a few important states. We present a method combining these two approaches…
We employ a rotating frame of reference to elucidate high-harmonic generation of circularly polarized light by bicircular driving fields. In particular, we show how the experimentally observed circular components of the high-harmonic…
In a spatial-temporal model, structural change and/or spatial heterogeneity can easily affect estimation of parameters. Following the spatial-temporal model in [1], we develop a nonparametric procedure for test-ing the presence of…
High-harmonic generation (HHG) in solids is an emerging method to probe ultrafast electron dynamics in solids at attosecond timescale. In this work, we study HHG from monolayer and bilayer graphene. Bilayer graphenes with AA and AB stacking…
To accomplish correct Bayesian inference from weak lensing shear data requires a complete statistical description of the data. The natural framework to do this is a Bayesian Hierarchical Model, which divides the chain of reasoning into…
We explore a newly proposed channel to create binary black holes of stellar origin. This scenario applies to massive, tight binaries where mixing induced by rotation and tides transports the products of hydrogen burning throughout the…
We conjecture that the Higgs potential can be significantly modified when it is in close proximity to the horizon of an astrophysical black hole, leading to the destabilization of the electroweak vacuum. In this situation, the black hole…
The complexity of composite spectra of close binary star system makes study of the spectra of their component stars extremely difficult. For this reason there exists very little information on the photospheric chemical composition of stars…
Binary galaxies are modeled as point-masses obeying the non-Newtonian MOND and Mannheim-Kazanas (MKG) theories of gravity. Random samples of such systems are generated by means of Monte Carlo simulations of binary orbits. Model pairs have…
We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution nonparametrically, given i.i.d.~data from the mixture model, using ideas from shape…
High harmonic generation (HHG) is a highly nonlinear emission process in which systems driven by intense laser pulses emit integer multiples (harmonics) of the driving field. This feature is considered universal to all occurrences of HHG.…
The possible functional forms of the effective conductivity sigma_{eff} of the randomly inhomogeneous two-phase system at arbitrary values of concentrations are discussed. A new functional equation, generalizing the duality relation, is…
The simulation of stochastic reaction-diffusion systems using fine-grained representations can become computationally prohibitive when particle numbers become large. If particle numbers are sufficiently high then it may be possible to…
The method of spectral disentangling has now created the opportunity for studying the chemical composition in previously inaccessible components of binary and multiple stars. This in turn makes it possible to trace their chemical evolution,…
In addition to rather complicated general methods it is interesting and valuable to develop fast efficient methods for calculating generators of power integral bases in special types of number fields. We consider sextic fields containing a…