Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture "Maxmin=lim⁡vn=lim⁡vλMaxmin=\lim v_n=\lim v_\lambda"

We study two-player zero-sum recursive games with a countable state space and finite action spaces at each state. When the family of $n$-stage values $\{v_n,n\geq 1\}$ is totally bounded for the uniform norm, we prove the existence of the uniform value. Together with a result in Rosenberg and Vieille (2000), we obtain a uniform Tauberian theorem for recursive games: $(v_n)$ converges uniformly if and only if $(v_\lambda)$ converges uniformly. We apply our main result to finite recursive games with signals (where players observe only signals on the state and on past actions). When the maximizer is more informed than the minimizer, we prove the Mertens conjecture $Maxmin=\lim_{n\to\infty} v_n=\lim_{\lambda\to 0}v_\lambda$. Finally, we deduce the existence of the uniform value in finite recursive game with symmetric information.Comment: 32 page

Limit value for optimal control with general means

We consider optimal control problem with an integral cost which is a mean of a given function. As a particular case, the cost concerned is the Ces\`aro average. The limit of the value with Ces\`aro mean when the horizon tends to infinity is widely studied in the literature. We address the more general question of the existence of a limit when the averaging parameter converges, for values defined with means of general types. We consider a given function and a family of costs defined as the mean of the function with respect to a family of probability measures -- the evaluations -- on R_+. We provide conditions on the evaluations in order to obtain the uniform convergence of the associated value function (when the parameter of the family converges). Our main result gives a necessary and sufficient condition in term of the total variation of the family of probability measures on R_+. As a byproduct, we obtain the existence of a limit value (for general means) for control systems having a compact invariant set and satisfying suitable nonexpansive property.Comment: 21 pages, 2 figure

Scientific development and a new green deal

After 30 years of reform and opening, China has become the world's second largest economy. However, the fast growth has come at the high cost of environmental degradation and resource consumption. The existing resource reserves and environment will not able to sustain the rapid economic development of the future, which demands China to transform its model for development. China should keep pace with the trend of world civilization and grasp the opportunity for green development

Semantic technology for management of data recorded during therapy of cardiac arrest patients

Master's thesis in Computer scienceThe topic of this thesis is the integration of data recorded during cardiopulmonary resuscitation (CPR). In the process of CPR many important data should be recorded, such as: time of the cardiac arrest witnessed, number of shocks given to the patient and parameters for each shock. These data will be used for the coming analysis and producing the report of the therapy. The analysis and comparison of the CPR data and reports may improve the survival rate. However the formats and terminologies of CPR data vary greatly between EMS (Emergency Medical Services) systems in different places. So it is inconvenient to access, compare and transfer data between different EMS systems. In this thesis we use semantic way to solve the heterogeneity problem. An ontology is defined to provide a standardized representation of the heterogeneous data from different EMSs. In this ontology we defined standardized CPR terminologies and report style, and the “dialect” from different EMS systems can be mapped onto this ontology. An interface is defined to map the different databases from different EMS systems onto this ontology. And we provide a uniform way based on the ontology to query all of the databases as if they are one huge database

Applications of nonparametric regression in survey statistics

Systematic sampling is a frequently used sampling method in natural resource surveys, because of its ease of implementation and its design efficiency. An important drawback of systematic sampling, however, is that no direct estimator of the design variance is available. We propose an estimator of the model-based expectation of the design variance, under a nonparametric model for the population. The nonparametric model is sufficiently flexible that it can be expected to hold at least approximately for many practical situations. We prove that the nonparametric variance estimator is both a consistent estimator for the model-based expectation of the design variance and a consistent predictor for the design variance in the model-based context. This variance estimator\u27s properties are further explored through a simulation study. An application in Forest Inventory and Analysis (FIA) is discussed in the second chapter. We compare the nonparametric variance estimator with the variance estimators for random stratified sampling and simple random sampling. The nonparametric variance estimator performs very well and it also has the advantage of allowing more complex models. A discussion about selecting proper auxiliary variables is also carried out for this application. In the last chapter, we study model averaging in survey estimation. Model averaging is a widely used method as it accounts for uncertainties in model selection. However, its applications in survey estimation are yet to be explored. We propose a model-averaging (MA) regression estimator for the population total. The goal is to provide a method that will work well for a wide range of response variables and situations. Different ways to obtain this estimator are explored through large-scale simulation studies

Robust Bayesian Variable Selection for Gene-Environment Interactions

Gene-environment (G×E) interactions have important implications to elucidate the etiology of complex diseases beyond the main genetic and environmental effects. Outliers and data contamination in disease phenotypes of G×E studies have been commonly encountered, leading to the development of a broad spectrum of robust penalization methods. Nevertheless, within the Bayesian framework, the issue has not been taken care of in existing studies. We develop a robust Bayesian variable selection method for G×E interaction studies. The proposed Bayesian method can effectively accommodate heavy-tailed errors and outliers in the response variable while conducting variable selection by accounting for structural sparsity. In particular, the spike-and-slab priors have been imposed on both individual and group levels to identify important main and interaction effects. An efficient Gibbs sampler has been developed to facilitate fast computation. The Markov chain Monte Carlo algorithms of the proposed and alternative methods are efficiently implemented in C++

How Does Folding Modulate Thermal Conductivity of Graphene

We study thermal transport in folded graphene nanoribbons using molecular dynamics simulations and the non-equilibrium Green's function method. It is found that the thermal conductivity of flat graphene nanoribbons can be modulated by folding and changing interlayer couplings. The analysis of transmission reveals that the reduction of thermal conductivity is due to scattering of low frequency phonons by the folds. Our results suggest that folding can be utilized in the modulation of thermal transport properties in graphene and other two dimensional materials.Comment: published in Applied Physics Letters 201

Interaction Analysis of Repeated Measure Data

Extensive penalized variable selection methods have been developed in the past two decades for analyzing high dimensional omics data, such as gene expressions, single nucleotide polymorphisms (SNPs), copy number variations (CNVs) and others. However, lipidomics data have been rarely investigated by using high dimensional variable selection methods. This package incorporates our recently developed penalization procedures to conduct interaction analysis for high dimensional lipidomics data with repeated measurements. The core module of this package is developed in C++. The development of this software package and the associated statistical methods have been partially supported by an Innovative Research Award from Johnson Cancer Research Center, Kansas State University