Ergodic stationary distribution and practical application of a hybrid stochastic cholera transmission model with waning vaccine-induced immunity under nonlinear regime switching

Considering the effect of stochasticity including white noise and colored noise, this paper aims to study a hybrid stochastic cholera epidemic model with waning vaccine-induced immunity and nonlinear telegraph perturbations. First, we derive a critical value ${?}_0^C$ related to the basic reproduction number ${?}_0$ of the deterministic model. The key aim of this paper is to generalize the θ-stochastic criterion method proposed by the recent work (Han et al. in Chaos Solit Fract 140:110238, 2020) to eliminate nonlinear telegraph perturbations. Next, via constructing several θ-stochastic Lyapunov functions and using the generalized method, we further prove that the stochastic model have a unique ergodic stationary distribution under ${?}_0^C>1$. Results show that the prevention and control of cholera epidemic depend on low transmission rate and small telegraph perturbations. Finally, the corresponding numerical simulations are performed to illustrate our analytical results and a practical application on the Somalia cholera outbreak is shown at the end of this paper.     

The martingale problem for a class of nonlocal operators of diagonal type

We consider systems of stochastic differential equations of the form $$\begin{array}{c}\hfill d{X}_t^i=\sum _{j=1}^d{A}_{ij}\left(X_{t?}\right)d{Z}_t^j\end{array}$$ for $i=1,?,d$ with continuous, bounded and non‐degenerate coefficients. Here $Z_t^1,?,Z_t^d$ are independent one‐dimensional stable processes with ${\alpha }_1,?,{\alpha }_d\in (0,2)$. In this article we research on uniqueness of weak solutions to such systems by studying the corresponding martingale problem. We prove the uniqueness of weak solutions in the case of diagonal coefficient matrices.     

Poisson discretizations of Wiener functionals and Malliavin operators with Wasserstein estimates

This article proposes a global, chaos-based procedure for the discretization of functionals of Brownian motion into functionals of a Poisson process with intensity $\lambda >0$. Under this discretization we study the weak convergence, as the intensity of the underlying Poisson process goes to infinity, of Poisson functionals and their corresponding Malliavin-type derivatives to their Wiener counterparts. In addition, we derive a convergence rate of $O\left({\lambda }^{?1∕4}\right)$ for the Poisson discretization of Wiener functionals by combining the multivariate Chen–Stein method with the Malliavin calculus. Our proposed sufficient condition for establishing the mentioned convergence rate involves the kernel functions in the Wiener chaos, yet we provide examples, especially the discretization of some common path dependent Wiener functionals, to which our results apply without committing the explicit computations of such kernels. To the best our knowledge, these are the first results in the literature on the universal convergence rate of a global discretization of general Wiener functionals.     

Distribution dependent stochastic differential equations

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems.     

Hyperparameter on-line learning of stochastic resonance based threshold networks

Aiming at training the feed-forward threshold neural network consisting of nondifferentiable activation functions, the approach of noise injection forms a stochastic resonance based threshold network that can be optimized by various gradient-based optimizers. The introduction of injected noise extends the noise level into the parameter space of the designed threshold network, but leads to a highly non-convex optimization landscape of the loss function. Thus, the hyperparameter on-line learning procedure with respective to network weights and noise levels becomes of challenge. It is shown that the Adam optimizer, as an adaptive variant of stochastic gradient descent, manifests its superior learning ability in training the stochastic resonance based threshold network effectively. Experimental results demonstrate the significant improvement of performance of the designed threshold network trained by the Adam optimizer for function approximation and image classification.     

Going Off the Grid: Iterative Model Selection for Biclustered Matrix Completion

We consider the problem of performing matrix completion with side information on row-by-row and column-by-column similarities. We build upon recent proposals for matrix estimation with smoothness constraints with respect to row and column graphs. We present a novel iterative procedure for directly minimizing an information criterion to select an appropriate amount of row and column smoothing, namely, to perform model selection. We also discuss how to exploit the special structure of the problem to scale up the estimation and model selection procedure via the Hutchinson estimator, combined with a stochastic Quasi-Newton approach. Supplementary material for this article is available online.     

Gravitational wave imprint of new symmetry breaking

It is believed that there are more fundamental gauge symmetries beyond those described by the Standard Model of particle physics. The scales of these new gauge symmetries are usually too high to be reachable by particle colliders. Considering that the phase transition (PT) relating to the spontaneous breaking of new gauge symmetries to the electroweak symmetry might be strongly first order, we propose considering the stochastic gravitational waves (GW) arising from this phase transition as an indirect way of detecting these new fundamental gauge symmetries. As an illustration, we explore the possibility of detecting the stochastic GW generated from the PT of \begin{document}$ {\bf{B}}-{\bf{L}}$\end{document} in the space-based interferometer detectors. Our study demonstrates that the GW energy spectrum is reachable by the LISA, Tianqin, Taiji, BBO, and DECIGO experiments only for the case where the spontaneous breaking of \begin{document}$ {\bf{B}}-{\bf{L}}$\end{document} is triggered by at least two electroweak singlet scalars.     

Stochastic and upscaled analytical modeling of fines migration in porous media induced by low-salinity water injection

Fines migration induced by injection of low-salinity water(LSW) into porous media can lead to severe pore plugging and consequent permeability reduction. The deepbed filtration(DBF) theory is used to model the aforementioned phenomenon, which allows us to predict the effluent concentration history and the distribution profile of entrapped particles. However, the previous models fail to consider the movement of the waterflood front. In this study, we derive a stochastic model for fines migration during LSW flooding, in which the Rankine-Hugoniot condition is used to calculate the concentration of detached particles behind and ahead of the moving water front. A downscaling procedure is developed to determine the evolution of pore-size distribution from the exact solution of a large-scale equation system. To validate the proposed model,the obtained exact solutions are used to treat the laboratory data of LSW flooding in artificial soil-packed columns. The tuning results show that the proposed model yields a considerably higher value of the coefficient of determination, compared with the previous models, indicating that the new model can successfully capture the effect of the moving water front on fines migration and precisely match the effluent history of the detached particles.