This paper considers estimating a parameter $\beta$ that defines an estimating function $U(y,x, \beta)$ for an outcome variable $y$ and its covariate $x$ when the outcome is missing in some of the observations. We assume that, in addition to the outcome and the covariate, a surrogate outcome is available in every observation. Rectly specifying the conditional expectation of $U$ given the surrogate and the covariate. When the conditional expectation is not correctly specified, which is the most likely scenario in practice, the estimation efficiency can be severely compromised even if the propensity function (of missingness) is correctly specified. We propose an estimator that is robust against the choice of the conditional expectation via an empirical likelihood. We demonstrate that the proposed estimator achieves efficiency gain whether the conditional score is correctly specified or not. When the conditional score is correctly specified, the estimator reaches the semiparametric variance bound within the class of estimating functions generated by $U$. The practical performance of the estimator is evaluated using simulation and a dataset based on the 1996 U.S. presidential election.

We find a regularity criterion for the Ostwald-de Waele models like Serrin's condition to the Navier-Stokes equations. Moreover, we show short time existence and estimate the Hausdorff dimension of the set of singular times for the weak solutions .

It is well known that a classical harmonic function (with respect to the Laplacian operator) can be characterized analytically and probabilistically. Recently there are interests resulting from several areas of mathematics in knowing whether the above two notions of harmonicity remain equivalent in a more general context, such as for diffusions on fractals and for discontinuous processes including symmetric L\'evy processes. For instance, due to their importance in theory and in applications, there has been intense interest recently in studying discontinuous processes and non-local (or integro-differential) operators, by both analytical and probabilistic approaches.
In this talk, we will discuss the equivalence of the analytic and probabilistic notions of harmonicity in the context of general symmetric Hunt processes on locally compact separable metric spaces. Extensions to general symmetric right processes on Lusin spaces including infinite dimensional spaces will be mentioned at the end if time permits .

This talk concerns with the classical mild solution of stochastic partial differential equation driven by fractional noises. We represent the L^p norm of the solution by intersection local time and use this relation to study the solution. The tool is the wel-known Feynman-Kac formula.

该报告将介绍随机矩阵的主要成果以及在大维数据分析中的应用.

We are concerned with the finite horizon portfolio selection with transaction costs, which is a singular stochastic control problem. Relying on a PDE approach, we proved that the problem can be reduced to a parabolic double obstacle problem through which the behaviors of the free boundaries can be completely characterized. Our approach essentially indicates a connection between singular control and optimal stopping, which had never been revealed for the present problem before..

We study optimal stopping problems for some functionals of Brownian motion in the case when the decision whether or not to stop before (or at) time $t$ is allowed to be based on the $\delta$-advanced information ${\cal F}_{t+\delta}$, where ${\cal F}_s$ is the $\sigma$-algebra generated by Brownian motion up to time $s$, $s\ge -\delta$, $\delta>0$ being a fixed constant. Our approach involves the forward integral and the Malliavin calculus for Brownian motion .

We present several results on partially hyperbolic dynamical systems, particularly the ones with lower center dimensions. These results include: continuity of topological entropy, abundance of pathological foliations and entropy conjecture for systems with one dimensional center. One of the key ingredients in these results is a new class of topological invariants we introduced for invariant foliations.

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Service operations, such as Telephone Call Centers or Emergency Departments in hospitals, are traditionally analyzed as queueing systems using mathematical queueing models. Recently, statisticians started to supplement these mathematical models with theoretically-interesting and practically-relevant statistical analysis. This is enabled by the availability of transaction-level (or call-by-call) data bases, such as those housed at the Technion's SEE laboratory. In this talk, I shall focus on call centers data. Operationally, the service process in such call centers can be decomposed into three fundamental components: arrivals, customer abandonment, and service durations. Each component has a different mathematical structure, which requires a different style of statistical analysis. I shall discuss several new methodologies that have been developed for the analysis of such call-by-call data. Empirical analysis of the data has validated in some cases, and refuted in others, the applicability of existing queueing models to call-center operations. This has stimulated the development of further models that capture previously unaccounted-for phenomena, such as arrival-rate uncertainty and server heterogeneity. I shall also present some ongoing research aiming at addressing such phenomena.

Through examples of Service Operations, with a focus on Telephone Call Centers, I review empirical findings that motivate or are motivated by (or both) interesting research questions. These findings give rise to features that are prerequisites for useful service models, for example customers' (im)patience, time-varying demand, heterogeneity of customers and servers, over-dispersion in Poisson arrivals, generally-distributed (as opposed to exponential) service- and patience-durations, and more. Empirical analysis also enables validation of existing models and protocols, either supporting or refuting their relevance and robustness.The mathematical framework for my models is asymptotic queueing theory, where limits are taken as the number of servers increases indefinitely, in a way that maintains a delicate balance against the offered-load. Asymptotic analysis reveals an operational regime that achieves, under already moderate scale, remarkably high levels of both service quality and efficiency. This is the QED Regime, discovered by Erlang and characterized by Halfin & Whitt. (QED = Quality- and Efficiency-Driven).My main data-source is a unique repository of call-centers data, designed and maintained at the Technion's SEE Laboratory. (SEE = Service Enterprise Engineering). The data is unique in that it is transaction-based: it details the individual operational history of all the calls handled by the participating call centers. (For example, one source of data is a network of 4 call centers of a U.S. bank, spanning 2.5 years and covering about 1000 agents; there are 218,047,488 telephone calls overall, out of which 41,646,142 where served by agents, while the rest were handled by answering machines.) To support data analysis, a universal data-structure and a friendly interface have been developed, under the logo DataMOCCA = Data MOdels for Call Centers Analysis. (I shall have with me DataMOCCA DVD's for academic distribution.).

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In response to competitive pressures, firms are increasingly adopting revenue management opportunities afforded by advances in information and communication technologies. Motivated by applications in industry, we consider a dynamic pricing problem facing a firm that sells given initial inventories of multiple substitutable and perishable products over a finite selling horizon. In these applications, since individual product demands are linked through consumer choices,the seller must formulate a joint dynamic pricing strategy while explicitly incorporating consumer behavior. For a general model of consumer choice, we model this multi-product dynamic pricing problem as a stochastic dynamic program and characterize its optimal prices. In addition, since consumer behavior depends on the nature of product differentiation, we specialize the general choice model to capture vertical and horizontal differentiation. When products are vertically differentiated, our results show monotonicity properties of the optimal prices and reveal that the optimal prices can be determined by considering aggregate inventories of products rather than their individual inventory levels. Accordingly, we develop a polynomial-time exact algorithm for determining the optimal prices. When products are horizontally differentiated, we find that analogous structural properties do not hold and the behavior of optimal prices is substantially different. To solve this problem, we develop a variant of the backward induction algorithm that uses cubic spline interpolation to construct the value functions at each stage. We demonstrate that this interpolation-based algorithm has low memory requirements and is very effective in generating near-optimal solutions that result in an average error of less than 0.15%.

报告人简介：
Dr. Xu received her Ph.D degree in Operations Research and Statistics from Rensselaer Polytechnic Institute in 1987, and joined the Faculty of Smeal College of Business at Pennsylvia State University in 1987. Currently, Dr. Xu is Professor of Management Science and Supply Chain Management at Penn State. She had served as the Chair of the Intercollege Dual-Title Degree Graduate Program in Operations Research at Penn State University from 1998-2007. Dr. Xu's primary research interests are centered on design, performance evaluation, simulation and optimization of stochastic operating systems and their applications in supply chain management and service systems, telecommunication, information technology, and reliability. In particular, she is interested in production and inventory systems, queueing theory, Markov decision processes, reliability systems, and stochastic ordering. Dr. Xu serves as Associate Editor of Operations Research, IEEE Trans on Reliability and Probability in Engineering and Informational Sciences. She also serves as Senior Editor of Journal of Flexible Services and Manufacturing.

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I will talk about three recent papers, which are joint work with my students Anat Kopzon and Yoni Nazarathy, in which we use the ideas of fluid approximation and of infinite virtual queues for the control of multi-class queueing networks.In the first paper we describe an asymptotically optimal method for the control of a multi-class queueing network over a finite time horizon. The method works in three steps: We approximate the discrete stochastic queueing network by a continuous deterministic fluid network and formulate a fluid control problem. We solve it using an algorithm for the solution of separated continuous linear programs. The fluid solution consists of piecewise constant flow rates, and in each interval there are some empty and some non-empty fluid queues. We next model each interval as a queuing network with infinite virtual queues, where the empty fluid queues are modeled by non-negative standard queues and the non-empty fluid queues are modeled by infinite virtual queues, which have unlimited supply of work, and which have a nominal out flow rate given by the fluid solution. Finally we use an adaptation of the maximum pressure policy of Dai and Lin to schedule the stochastic discrete queueing network so as to track the fluid solution. This method is asymptotically optimal: if we scale up the number of jobs and speed up the processing rates accordingly, the solution will converge to optimal. We will illustrate this method through an example of finite horizon control of a simple re-entrant line. In papers 2,3 we consider a Push Pull queueing network which is an infininite supply of work version of the Kumar-Seidman Rybko-Stolyar network. Because each server has in nite supply of work, the servers need never idle, so the system works at the service intensity one. We describe policies which can achieve this full utilization, and yet be stable. We obtain detailed steady state behavior for some of these policies in the memoryless processing case. We also obtain fluid and diffusion approximations and prove Harris recurrence in the general renewal processing case. We contrast the behavior of this system with the behavior of the KSRS system, which becomes congested in heavy traffic.

We consider financial markets where asset prices are modeled by piecewise deterministic Markov processes which form a general class of non-diffusion processes. Using an embedding procedure, it is shown how portfolio optimization problems can be solved by looking at discrete-time contracting Markov decision processes. The aim of the talk is to demonstrate that this point of view has a number of advantages, in particular as far as computational aspects are concerned.

In this talk, we present efficient and stable numerical methods to compute ground states and dynamics of Bose-Einstein condensates (BEC) in a rotational frame. As preparatory steps, we take the 3D Gross-Pitaevskii equation (GPE) with an angular momentum rotation, scale it to obtain a four-parameter model and show how to reduce it to 2D GPE in certain limiting regimes. Then we study numerically and asymptotically the ground states, excited states and quantized vortex states as well as their energy and chemical potential diagram in rotating BEC. Some very interesting numerical results are observed. Finally, we study numerically stability and interaction of quantized vortices in rotating BEC. Some interesting interaction patterns will be reported. This talk is based on joint work with Qiang Du, Peter Markowich, Hanquan Wang and Yanzhi Zhang. .

In this talk, we present efficient and stable numerical methods to compute ground states and dynamics of Bose-Einstein condensates (BEC) in a rotational frame. As preparatory steps, we take the 3D Gross-Pitaevskii equation (GPE) with an angular momentum rotation, scale it to obtain a four-parameter model and show how to reduce it to 2D GPE in certain limiting regimes. Then we study numerically and asymptotically the ground states, excited states and quantized vortex states as well as their energy and chemical potential diagram in rotating BEC. Some very interesting numerical results are observed. Finally, we study numerically stability and interaction of quantized vortices in rotating BEC. Some interesting interaction patterns will be reported. This talk is based on joint work with Qiang Du, Peter Markowich, Hanquan Wang and Yanzhi Zhang. .

A real valued function defined on R is called g–convex if it satisfies the following “generalized Jensen’s inequality” under a given g-expectation, i.e., h(Eg[X]) ≤ Eg[h(X)], for all random variables X such that both sides of the inequality are meaningful. We will give a necessary and sufficient condition for a C2-function being g-convex. We also studied some more general situations. We also studied g-concave and g-affine functions.

In this talk, we present efficient and stable numerical methods to compute ground states and dynamics of Bose-Einstein condensates (BEC) in a rotational frame. As preparatory steps, we take the 3D Gross-Pitaevskii equation (GPE) with an angular momentum rotation, scale it to obtain a four-parameter model and show how to reduce it to 2D GPE in certain limiting regimes. Then we study numerically and asymptotically the ground states, excited states and quantized vortex states as well as their energy and chemical potential diagram in rotating BEC. Some very interesting numerical results are observed. Finally, we study numerically stability and interaction of quantized vortices in rotating BEC. Some interesting interaction patterns will be reported. This talk is based on joint work with Qiang Du, Peter Markowich, Hanquan Wang and Yanzhi Zhang. .

In this talk, we present efficient and stable numerical methods to compute ground states and dynamics of Bose-Einstein condensates (BEC) in a rotational frame. As preparatory steps, we take the 3D Gross-Pitaevskii equation (GPE) with an angular momentum rotation, scale it to obtain a four-parameter model and show how to reduce it to 2D GPE in certain limiting regimes. Then we study numerically and asymptotically the ground states, excited states and quantized vortex states as well as their energy and chemical potential diagram in rotating BEC. Some very interesting numerical results are observed. Finally, we study numerically stability and interaction of quantized vortices in rotating BEC. Some interesting interaction patterns will be reported. This talk is based on joint work with Qiang Du, Peter Markowich, Hanquan Wang and Yanzhi Zhang. .

In this talk, we introduce various necessary and sufficient conditions for Markov chains of GI/G/1 type with finite blocks. We also provide an iff condition for the Markov chain to be geometric ergodic, which is equivalent to the condition for the stationary distribution to be light-tailed. Furthermore, we provide a necessary and sufficient condition for doubly M/G/1 type Markov chains with infinite blocks to be ergodic.

We consider continuous-review, multiproduct assemble-to-order (ATO) systems with positive replenishment lead times under base-stock replenishment policies. Specifically, we focus on the effectiveness of a class of dynamic component allocation rules, termed no-holdback (NHB) rules. Under these rules, a product demand is backordered if and only if at least one of its required components is out of stock. We show that under certain product and cost structures, the NHB rules outperform all possible allocation rules at minimizing system-wide average inventory and backorder cost. We also develop tools to evaluate key system performance measures under NHB rules. For systems that exhibit certain material-flow topologies, we obtain exact performance expressions. For general systems, we obtain performance bounds and approximations. Finally, we show that while NHB rules always outperform the commonly used FIFO allocation rule on the immediate fill rates, it may underperform FIFO on fill rates within a specific time window.

简历：
Dr. Yao Zhao is an associate professor of Supply Chain Management and Marketing Sciences at Rutgers Business School, Rutgers University - the State University of New Jersey. He holds a Ph.D. degree in Industrial Engineering and Management Sciences from Northwestern University, Evanston. He was a visiting professor at Fuqua School of Business, Duke University, and a visiting scholar at MIT Operations Research Center.

Dr. Zhao's current research interests lie in supply chain management with a focus on control, design and integration of stochastic production-inventory systems. He has published papers in journals like Operations Research, Manufacturing & Service Operations Management, IEEE Transactions of Automatic Control and Naval Research Logistics. He is the recipient of Honorable Mention of the 2001 student paper competition in Manufacturing & Service Operations Management. In 2008, he receives an National Science Foundation (NSF) CAREER Award on a project that integrates supply chain management and project management.

Dr. Zhao teaches core operations management and supply chain management courses for undergraduate, MBA, executive and PhD programs at Rutgers Business School. Prior to joining Rutgers, he taught at Northwestern University School of Engineering.
Dr. Zhao has collaborated with Estee Launder Companies Inc. in the areas of forecasting and inventory control for new product introduction, and with General Motors on spare part operations.

Boundary Harnack principle is one of the most important result in Potential theory. In this talk, we discuss about Boundary Harnack principle for a large class of Levy processes. Even though boundary Harnack principle is not true for some simple Levy processes, it is true for a large class of subordinate Brownian motion, including mixtures of symmetric stable processes, in bounded $\kappa$-fat open set (disconnected analogue of John domains). As an application of the boundary Harnack principle, we identify the Martin boundary and the minimal Martin boundary of bounded $\kappa$-fat open sets with respect to these processes with their Euclidean boundary. This talk is based on a joint work with Renming Song and Zoran Vondracek
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We propose a new mixture model via latent cure rate markers for survival data with a cure fraction. In the proposed model, the latent cure rate markers are modeled via a multinomial logistic regression. The proposed model assumes that the patients may be classified into several risk groups based on their cure fractions. Based on the nature of the proposed model, a posterior predictive algorithm is developed to classify patients into different risk groups. Compared to several existing competing cure rate models, the proposed model fits the data better based on the logarithm of pseudomarginal likelihood (LPML) measure. In addition, we develop efficient Markov Chain Monte Carlo algorithms for carrying out Bayesian computation. A real data set from a prostate cancer clinical trial is analyzed in detail to further demonstrate the proposed methodology.

In this talk, an introductory tour to Bayesian analysis will be given.The history of Bayesian statistics and the current development of Bayesian approaches will be visited. The outline of the talk are given as follows:
1. Introduction
2. Three Types of Statistical Inferences
3. Prior Elicitation
4. Bayesian Model Comparison and Assessment
5. Bayesian Software
6. Bayesian Approaches in FDA
7. Concluding Remarks.

We will extend Kruzkov's idea of entropic solution and ideas from others on Young measures/compensated compactness to a stochastic setting. The uniqueness result applies to any spatial dimension. The existence theory is limited to 1-D only at this point.

For a superprocess under a stochastic flow in one dimension, we prove that it has a density with respect to the Lebesgue measure. A stochastic partial differential equation is derived for the density. The regularity of the solution is then proved by using Krylov's $L_p$-theory for linear SPDE. This talk is based on a joint paper with Mueller and Lee.

In this research, we study waiting line problems at the border-crossings between the U.S. and Canada. To evaluate a practical staffing policy, we develop an analytical model to compute the important performance measures. The policy is called "congestion based staffing" or CBS, because the number of open inspection booths is adjusted according to the queue length during each planning period. Our analysis is based on the matrix-geometric solution, the regeneration cycle, and the fluid approximations. With a certain cost structure, we provide a numerical search approach to determine the best CBS policy for border-crossing stations. Under certain conditions, we can obtain the close-form solution for the optimal policy parameters and prove the convexity of the average cost function. The model also applies to other similar queueing settings with security concerns and the production/inventory systems. The directions of future studies are outlined.

http://www.cbe.wwu.edu/zhang/zhang.htm

The heat kernel for Dirichlet fractional Laplacian $-(-\Delta)^{\alpha/2}|_D$, $\alpha\in (0, 2)$, with zero exterior condition is the transition density of a symmetric $\alpha$-stable process killed upon exiting $D$. In this talk, I will present recent results on sharp two-sided estimates for the heat kernel of the Dirichlet fractional Laplacian in $C^{1, 1}$ open sets. I will also present results on the estimates of transition density of other related processes. This talk is based on two joint papers with Zhen-Qing Chen and Panki Kim.

A mob $(2k+1)$-orientation of a graph $G$ is an orientation $D$ of $G$ such that at each vertex $v$ of $G$, the number of the out going edges minus the number of incoming edges is congruent to zero modulo $(2k+1)$. Graphs with mod 3-orientations are also called graphs with nowhere zero 3-flows. In this talk, we present the motivation of the problem, the main unsolved problems, the developments, and some of our recent progresses made in this direction. We will also present an approach by Barat and Thomassen using generalized claw-decompositions. With our approach, we disprove a conjecture by Barat and Thomassen on claw-decompositions.

See http://jacobi.math.wvu.edu/%7Ehjlai/