Levy walk dynamics in non-static media

Almost all the media the particles move in are non-static, one of which is the most common expanding or contracting (by a scale factor) non-static medium discussed in this paper. Depending on the expected resolution of the studied dynamics and the amplitude of the displacement caused by the non-static media, sometimes the non-static behaviors of the media can not be ignored. In this paper, we build the model describing L\'evy walks in one-dimension uniformly non-static media, where the physical and comoving coordinates are connected by scale factor. We derive the equation governing the probability density function of the position of the particles in comoving coordinate. Using the Hermite orthogonal polynomial expansions, some statistical properties are obtained, such as mean squared displacements (MSDs) in both coordinates and kurtosis. For some representative non-static media and L\'{e}vy walks, the asymptotic behaviors of MSDs in both coordinates are analyzed in detail. The stationary distributions and mean first passage time for some cases are also discussed through numerical simulations.

Simultaneous Comparison of Sensitivities and Specificities of Two Diagnostic Tests Adjusting for Discrete Covariates

Adjusting for covariates is important in the study of the performance of diagnostic tests. In this manuscript, the simultaneous comparison of the sensitivities and specificities of two binary diagnostic tests is studied when discrete covariates are observed in all of the individuals in the sample. Four methods are presented to simultaneously compare the two sensitivities and the two specificities: a global hypothesis test and three other methods based on individual comparisons. The maximum likelihood method was applied to adjust the overall estimators of sensitivities and specificities. Simulation experiments were carried out to study the asymptotic behaviors of the four proposed methods when the covariate is binary, giving general rules of application. The results were applied to a real example.

Time-Inhomogeneous Feller-Type Diffusion Process in Population Dynamics

The time-inhomogeneous Feller-type diffusion process, having infinitesimal drift α(t)x+β(t) and infinitesimal variance 2r(t)x, with a zero-flux condition in the zero-state, is considered. This process is obtained as a continuous approximation of a birth-death process with immigration. The transition probability density function and the related conditional moments, with their asymptotic behaviors, are determined. Special attention is paid to the cases in which the intensity functions α(t), β(t), r(t) exhibit some kind of periodicity due to seasonal immigration, regular environmental cycles or random fluctuations. Various numerical computations are performed to illustrate the role played by the periodic functions.

Estimation of the Average Kappa Coefficient of a Binary Diagnostic Test in the Presence of Partial Verification

The average kappa coefficient of a binary diagnostic test is a measure of the beyond-chance average agreement between the binary diagnostic test and the gold standard, and it depends on the sensitivity and specificity of the diagnostic test and on disease prevalence. In this manuscript the estimation of the average kappa coefficient of a diagnostic test in the presence of verification bias is studied. Confidence intervals for the average kappa coefficient are studied applying the methods of maximum likelihood and multiple imputation by chained equations. Simulation experiments have been carried out to study the asymptotic behaviors of the proposed intervals, given some application rules. The results obtained in our simulation experiments have shown that the multiple imputation by chained equations method provides better results than the maximum likelihood method. A function has been written in R to estimate the average kappa coefficient by applying multiple imputation. The results have been applied to the diagnosis of liver disease.

On Consensus Index of Triplex Star-Like Networks: A Graph Spectra Approach

In this article, the consensus-related performances of the triplex multi-agent systems with star-related structures, which can be measured by the algebraic connectivity and network coherence, have been studied by the characterization of Laplacian spectra. Some notions of graph operations are introduced to construct several triplex networks with star substructures. The methods of graph spectra are applied to derive the network coherence, and some asymptotic behaviors of the indices have been derived. It is found that the operations of adhering star topologies will make the first-order coherence increase a constant value under the triplex structures as parameters tend to infinity, and the second-order coherence have some equality relations as the node related parameters tend to infinity. Finally, the consensus related indices of the triplex systems with the same number of nodes but non-isomorphic graph structures have been compared and simulated to verify the results.