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.     

Explicit estimates of sums related to the Nyman–Beurling criterion for the Riemann Hypothesis

We give an estimate for sums appearing in the Nyman–Beurling criterion for the Riemann Hypothesis. These sums contain the Möbius function and are related to the imaginary part of the Estermann zeta function. The estimate is remarkably sharp in comparison to other sums containing the Möbius function. The bound is smaller than the trivial bound – essentially the number of terms – by a fixed power of that number. The exponent is made explicit. The methods intensively use tools from the theory of continued fractions and from the theory of Fourier series.     

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.     

Warm tachyon inflation and swampland criteria

In this study, the scenario of a two-component warm tachyon inflation is considered, where the tachyon field plays the role of the inflaton by driving the inflation. During inflation, the tachyon scalar field interacts with the other component of the Universe, which is assumed to be photon gas, i.e., radiation. The interacting term contains a dissipation coefficient, and the study is modeled based on two different and familiar choices of the coefficient that were studied in the literature. By employing the latest observational data, the acceptable ranges for the free parameters of the model are obtained. For any choice within the estimated ranges, there is an acceptable concordance between the theoretical predictions and observations. Although the model is established based on several assumptions, it is crucial to verify their validity for the obtained values of the free parameters of the model. It is found that the model is not self-consistent for all values of the ranges, and for some cases, the assumptions are violated. Therefore, to achieve both self-consistency and agreement with the data, the parameters of the model must be constrained. Subsequently, we consider the recently proposed swampland conjecture, which imposes two conditions on the inflationary models. These criteria rule out some inflationary models; however, warm inflation is among those that successfully satisfy the swampland criteria. We conduct a precise investigation, which indicates that the proposed warm tachyon inflation cannot satisfy the swampland criteria for some cases. In fact, for the first case of the dissipation coefficient, in which, there is dependency only on the scalar field, the model agrees with observational data. However, it is in direct tension with the swampland criteria. Nevertheless, for the second case, wherein the dissipation coefficient has a dependency on both the scalar field and temperature, the model exhibits acceptable agreement with observational data, and suitably satisfies the swampland criteria.     

Orientation dependent size effects in thermal buckling and post-buckling of nanoplates with cubic anisotropy

In this work, a continuum model is presented for size and orientation dependent thermal buckling and post-buckling of anisotropic nanoplates considering surface and bulk residual stresses. The model with von-Karman nonlinear strains and material cubic anisotropy of single crystals contains two parameters that reflect the orientation effects. Using Ritz method, closed form solutions are given for buckling temperature and post-buckling deflections. Regarding self-instability states of nanoplates and their recovering at higher temperatures, an experiment is discussed based on low pressurized membranes to verify the predictions. For simply supported nanoplates, the size effects are lowest when they are aligned in [100] direction. When the edges get clamped, the orientation dependence is ignorable and the behavior becomes symmetric about [510] axis. The surface residual stress makes drastic increase in buckling temperature of thinner nanoplates for which a minimum thickness is pointed to stay far from material softening at higher temperatures. Deflection of [100]-oriented buckled nanoplates is higher than [110] ones but this reverses at higher temperatures. The results for long nanoplates show that the buckling mode numbers are changed by orientation which is verified by FEM.     

基于图像处理的光学谐振腔自准直研究方法

针对我国氧碘化学激光器输出能量不断提高的情况下,主要限制光束质量的因素之一是出光过程中的光腔失调,提出了一种基于图像处理的光学谐振腔自准直研究方法。该研究方法利用氦氖穿腔光通过凹腔镜中心孔,并在凸腔镜后方放置工业相机,在屏幕上方形成一个干涉同心圆环。通过借助OpenCV库中二值化、霍夫圆检测等图像处理的方法,获得干涉同心圆环的圆心坐标,再通过以圆心为中心将图像分成上下左右四个部分,通过判断这四部分亮点像素的数量差值来预估干涉同心圆环的偏移状态,进而获得空腔条件下光学谐振腔发生变化的理论判据。实验结果表明,该方法可以获得相当精准的光学谐振腔失调判据,其失调判据选取左右亮点像素差值30000,上下亮点像素差值45000,为今后失调判据与步进电机自动调腔的结合做好充足的准备。     

An inequality connecting entropy distance,Fisher Information and large deviations

In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large deviation rate functional. In addition to possessing various favourable properties, we show that this generalised Fisher Information converges to the classical Fisher Information in an appropriate limit. We then use this generalised Fisher Information and the aforementioned inequality to qualitatively study coarse-graining problems for jump processes on discrete spaces.     

A Multiresponsive Functional AIEgen for Spatiotemporal Pattern Control and All-round Information Encryption

Functional materials with multi-responsive properties and good controllability are highly desired for developing bioinspired and intelligent multifunctional systems. Although some chromic molecules have been developed, it is still challenging to realize in situ multicolor fluorescence changes based on a single luminogen. Herein, we reported an aggregation-induced emission (AIE) luminogen called CPVCM, which can undergo a specific amination with primary amines to trigger luminescence change and photoarrangement under UV irradiation at the same active site. Detailed mechanistic insights were carried out to illustrate the reactivity and reaction pathways. Accordingly, multiple-colored images, a quick response code with dynamic colors, and an all-round information encryption system were demonstrated to show the properties of multiple controls and responses. It is believed that this work not only provides a strategy to develop multiresponsive luminogens but also develops an information encryption system based on luminescent materials.     

Diboraanthracene-Doped Polymer Systems for Colour-Tuneable Room-Temperature Organic Afterglow

Organic ultralong room temperature phosphorescence (RTP), or organic afterglow, is a unique phenomenon, gaining widespread attention due to its far-reaching application potential and fundamental interest. Here, two laterally expanded 9,10-dimesityl-dihydro-9,10-diboraanthracene (DBA) derivatives are demonstrated as excellent afterglow materials for red and blue-green light emission, which is traced back to persistent thermally activated delayed fluorescence and RTP. The lateral substitution of polycyclic DBA scaffold, together with weak transversal electron-donating mesityl groups, ensures the optimal molecular properties for (reverse) intersystem crossing and long-lived triplet states in a rigid poly(methyl methacrylate) matrix. The achieved afterglow emission quantum yields of up to 3 % and 15 %, afterglow lifetimes up to 0.8 s and 3.2 s and afterglow durations up to 5 s and 25 s (for red and blue-green emitters, respectively) are attributed to the properties of single molecules.     

A Photo- and Thermo-Driven Azoarene-Based Circularly Polarized Luminescence Molecular Switch in a Liquid Crystal Host

The development of chiral optical active materials with switchable circularly polarized luminescence (CPL) signals remains a challenge. Here an azoarene-based circularly polarized luminescence molecular switch, (S, R, S)-switch 1 and (R, R, R)-switch 2 , are designed and prepared with an (R)-binaphthyl azo group as a chiral photosensitive moiety and two (S)- or (R)-binaphthyl fluorescent molecules with opposite or the same handedness as chiral fluorescent moieties. Both switches exhibit reversible trans/cis isomerization when irradiated by 365 nm UV light and 520 nm green light in solvent and liquid crystal (LC) media. In contrast with the control (R, R, R)-switch 2 , when switch 1 is doped into nematic LCs, polarization inversion and switching-off of the CPL signals are achieved in the resultant helical superstructure upon irradiation with 365 nm UV and 520 nm green light, respectively. Meanwhile, the fluorescence intensity of the system is basically unchanged during this switching process. In particular, these variations of the CPL signals could be recovered after heating, realizing the true sense of CPL reversible switching. Taking advantage of the unique CPL switching, the proof-of-concept for “a dual-optical information encryption system” based on the above CPL active material is demonstrated.