Conditional ergodicity in infinite dimension

The goal of this paper is to develop a general method to establish conditional ergodicity of infinite-dimensional Markov chains. Given a Markov chain in a product space, we aim to understand the ergodic properties of its conditional distributions given one of the components. Such questions play a fundamental role in the ergodic theory of nonlinear filters. In the setting of Harris chains, conditional ergodicity has been established under general nondegeneracy assumptions. Unfortunately, Markov chains in infinite-dimensional state spaces are rarely amenable to the classical theory of Harris chains due to the singularity of their transition probabilities, while topological and functional methods that have been developed in the ergodic theory of infinite-dimensional Markov chains are not well suited to the investigation of conditional distributions. We must therefore develop new measure-theoretic tools in the ergodic theory of Markov chains that enable the investigation of conditional ergodicity for infinite dimensional or weak-* ergodic processes. To this end, we first develop local counterparts of zero-two laws that arise in the theory of Harris chains. These results give rise to ergodic theorems for Markov chains that admit asymptotic couplings or that are locally mixing in the sense of H. F\"{o}llmer, and to a non-Markovian ergodic theorem for stationary absolutely regular sequences. We proceed to show that local ergodicity is inherited by conditioning on a nondegenerate observation process. This is used to prove stability and unique ergodicity of the nonlinear filter. Finally, we show that our abstract results can be applied to infinite-dimensional Markov processes that arise in several settings, including dissipative stochastic partial differential equations, stochastic spin systems and stochastic differential delay equations.Comment: Published in at http://dx.doi.org/10.1214/13-AOP879 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Resonant cyclotron scattering in pulsar magnetospheres and its application to isolated neutron stars

Resonant cyclotron scattering (RCS) in pulsar magnetospheres is considered. The photon diffusion equation (Kompaneets equation) for RCS is derived. The photon system is modeled three dimensionally. Numerical calculations show that there exist not only up scattering but also down scattering of RCS, depending on the parameter space. RCS's possible applications to the spectra energy distributions of magnetar candidates and radio quiet isolated neutron stars (INSs) are point out. The optical/UV excess of INSs may caused by the down scattering of RCS. The calculations for RX J1856.5-3754 and RX J0720.4-3125 are presented and compared with their observational data. In our model, the INSs are proposed to be normal neutron stars, although the quark star hypothesis is still possible. The low pulsation amplitude of INSs is a natural consequence in the RCS model.Comment: 16 pages, 5 figures, 2 tables, accepted for publication in RA

Modelling of Dynamic Strain Aging with a Dislocation-Based Isotropic Hardening Model and Investigation of Orthogonal Loading

Based on experimental results, a dislocation material model describing the dynamic strain aging\ud effect at different temperatures is presented. One and two stage loading tests were performed in\ud order to investigate the influence of the loading direction as well as the temperature influence due\ud to the hardening mechanism. Bergström’s theory of work hardening was used as a basis for the\ud model development regarding the thermal isotropic behavior as well as the Chaboche model to\ud describe the kinematic hardening. Both models were implemented in an in-house FE-Code in\ud order to simulate the real processes. The present paper discusses two hardening mechanisms,\ud where the first part deals with the pure isotropic hardening including dynamic strain aging and the\ud second part involves the influence of the loading direction regarding combined (isotropic and\ud kinematic) hardening behavior

Ergodicity and stability of the conditional distributions of nondegenerate Markov chains

We consider a bivariate stationary Markov chain $(X_n,Y_n)_{n\ge0}$ in a Polish state space, where only the process $(Y_n)_{n\ge0}$ is presumed to be observable. The goal of this paper is to investigate the ergodic theory and stability properties of the measure-valued process $(\Pi_n)_{n\ge0}$, where $\Pi_n$ is the conditional distribution of $X_n$ given $Y_0,...,Y_n$. We show that the ergodic and stability properties of $(\Pi_n)_{n\ge0}$ are inherited from the ergodicity of the unobserved process $(X_n)_{n\ge0}$ provided that the Markov chain $(X_n,Y_n)_{n\ge0}$ is nondegenerate, that is, its transition kernel is equivalent to the product of independent transition kernels. Our main results generalize, subsume and in some cases correct previous results on the ergodic theory of nonlinear filters.Comment: Published in at http://dx.doi.org/10.1214/11-AAP800 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

PROPOSING MODEL OF HANDLING LANGUAGE FOR SMART HOME SYSTEM CONTROLLED BY VOICE

Voice interaction control is a useful solution for smart homes. Now it helps bring the house closer to people. In recent years, many smart home-based voice control solutions have been introduced (for example: Google Assistant, Alexa Amazon etc.). However, most of these solutions do not really serve Vietnamese people. In this paper, we study and develop Vietnamese language processing model to apply to smart home system. Specifically, we propose language processing methods and create databases for smart homes. Our main contribution of the paper is the Vietnamese language processing database for smart-home system

Optimal parameters of dynamic vibration absorber for linear damped rotary systems subjected to harmonic excitation

Dynamic vibration absorber (DVA) is a simple and effective device for vibration absorption used in many practical applications. Determination of suitable parameters for DVA is of significant importance to achieve high vibration reduction effectiveness. This paper presents a method to find the optimal parameters of a DVA attached to a linear damped rotary system excited by harmonic torque. To this end, a closed-form formula for the optimum tuning parameter is derived using the fixed-point theory based on an assumption that the damped rotary systems are lightly or moderately damped. The optimal damping ratio of DVA is found by solving a set of non-linear equations established by the Chebyshev's min-max criterion. The performance of the proposed optimal DVA is compared with that obtained by existing optimal solution in literature. It is shown that the proposed optimal parameters allow to obtain superior vibration suppression compared to existing optimal formula. Extended simulations are carried out to examine the performance of the optimally designed DVA and the sensitivity of the optimum parameters. The simulation results show that the improvement of the vibration performance on damped rotary system can be as much as 90% by using DVA

Structural features of geostrophic circulation in open region of the South China Sea

On the basis of observation data of water temperature and salinity the mean seasonal geostrophic circulation in open region of the South China Sea (SCS) was computed by the dynamic method relative to the 800 decibar reference surface. The results of computation let go to following notices: In both main monsoons (winter and summer) there are two main geostrophic eddies: the anticlockwise eddy in the northern and northwestern part, and the clockwise eddy in the southern part of the SCS with corresponding divergent and convergent zones. The main frontal zones go along the middle latitudes of the sea from the southern continental shelf of Vietnam to the area west of Luzon Island. The strength and stability of the current in winter are higher than in summer. The Kuroshio has an enough strong branch intruding into the SCS through Bashi Strait in winter creating in the sea the water structure similar to that of the Northwest Pacific subtropical and tropical regions. In summer the Kuroshio water can intrude directly only into the area southwest of Taiwan

Involving citizens in priority setting for public health research: Implementation in infection research

Background Public sources fund the majority of UK infection research, but citizens currently have no formal role in resource allocation. To explore the feasibility and willingness of citizens to engage in strategic decision making, we developed and tested a practical tool to capture public priorities for research. Method A scenario including six infection themes for funding was developed to assess citizen priorities for research funding. This was tested over two days at a university public festival. Votes were cast anonymously along with rationale for selection. The scenario was then implemented during a three-hour focus group exploring views on engagement in strategic decisions and in-depth evaluation of the tool. Results 188/491(38%) prioritized funding research into drug-resistant infections followed by emerging infections(18%). Results were similar between both days. Focus groups contained a total of 20 citizens with an equal gender split, range of ethnicities and ages ranging from 18 to >70 years. The tool was perceived as clear with participants able to make informed comparisons. Rationale for funding choices provided by voters and focus group participants are grouped into three major themes: (i) Information processing; (ii) Knowledge of the problem; (iii) Responsibility; and a unique theme within the focus groups (iv) The potential role of citizens in decision making. Divergent perceptions of relevance and confidence of “non-experts” as decision makers were expressed. Conclusion Voting scenarios can be used to collect, en-masse, citizens' choices and rationale for research priorities. Ensuring adequate levels of citizen information and confidence is important to allow deployment in other formats