歷史演講 PAST TALKS

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Abstract： In this talk, we shall discuss some recent results on Stirling permutations, simsun permutations and the cycle descent statistic.

Abstract： As an efficient information aggregation technique, group testing has been widely applied in many areas such as epidemiology, quality control, human genetics, and food safety. Motivated by a chlamydia study in the USA, we develop the optimal design for estimating prevalence with uncertain testing error rates. Our method utilizes the complete class approach and the generalized equivalence theorem. We show that the optimal design has exactly three group sizes and it allocates most trials at the intermediate size. A simulation study indicates that our design is more efficient than the competing designs, even when the prespecified values of the parameters are moderately misspecified. Some extensions of our theory to deal with further practical issues are also addressed. Keywords: Ds-optimality; group testing; sensitivity; specificity Work done jointly with M.-N. L. Huang, K. Shedden, and W. K. Wong.

Abstract： The control of aerodynamic interactions among drops in inkjet printing is critical to drop placement accuracy. The motion of small spherical drops of unequal sizes is based on low- Reynolds number approximation. We employ the Stokesian dynamics formulation to compute the interactions between drops. The comparison of Stokesian dynamics and the Singularity Method of computing drop-drop interaction is presented. Examples of applications to inkjet printing are also presented.

Abstract： We demonstrate recent progress in the nonlocal inverse problems, especially for the nonlocal type Calderón problem, where one tries to determine an unknown coefficient in an anisotropic Schrödinger equation from exterior measurements of solutions. This equation enjoys remarkable uniqueness and approximation properties, which turn out to yield strong results in related inverse problems.

Abstract: Deep learning has been a hot topic since the dominant performance by AlphaGo. Convolution Neural Network (CNN) is one famous model for deep learning especially in image processing. In this talk, I will start with the idea of Neural Network followed by CNN and its application. I will also discuss an interesting idea of “Contrastive Divergence” for estimating the parameters of CNN. Contrastive divergence approach is MCMC with very few iterations (even only one). I will give an example to show why this will work.

Abstract： In software development and maintenance, a software system may frequently be updated to meet rapidly changing user requirements. New test cases will be designed to ensure the correctness of new or modified functions, thus gradually increasing the test suite’s size. Test suite reduction techniques aim to decrease the cost of regression testing by removing the redundant test cases from the test suite and then obtaining a representative set of test cases that still yield a high level of code coverage. Most of the existing reduction algorithms focus on decreasing the test suite’s size. Yet, the differences in execution costs among test cases are usually significant and it may take a lot of execution time to run a test suite consisting of a few long-running test cases. This work presents and empirically evaluates cost-aware algorithms that can produce the representative sets with lower execution costs. We first use a cost-aware test case metric, called Irreplaceability, and its enhanced version, called EIrreplaceability, to evaluate the possibility that each test case can be replaced by others during test suite reduction. Furthermore, we construct a cost-aware framework that incorporates the concept of test irreplaceability into some well-known test suite reduction algorithms. The effectiveness of the cost-aware framework is evaluated via the subject programs and test suites collected from the Software-artifact Infrastructure Repository – frequently chosen benchmarks for experimentally evaluating test suite reduction methods. The empirical results reveal that the presented algorithms produce representative sets that normally incur a low cost to yield a high level of test coverage. The presented techniques indeed enhance the capability of the traditional reduction algorithms to reduce the execution cost of a test suite. Especially for the additional Greedy algorithm, the presented techniques decrease the costs of the representative sets by 8.10% to 46.57%.

Abstract: Hidden Markov models (HMM) has been widely adopted by scientists from various fields for modeling stochastic processes with Markovian structures, i.e. the underlying process is a discrete Markov chain and the observations are noisy realizations of the underlying process. Determining the number of hidden states for an HMM is a model selection problem which has yet to be satisfactorily solved, especially for the highly used Gaussian HMM with heterogenous covariance. In this paper, we propose an asymptotically consistent method for determining the number of hidden states of HMM based on the marginal likelihood, which is obtained by integrating out both the parameters and hidden states. We give a rigorous proof of the asymptotic consistency of the proposed method and provide simulation studies and real data examples to compare the proposed method with the currently mostly adopted method, the Bayesian information criterion (BIC). We have also developed an R package ‘HMMselect’ based on the proposed algorithm. Lin, Jason, Cheng-Hsin gives a brief introduction for HMM in the beginning of the talk. Joint work with Y. Chen, C. L. Kao, and S. C. Kou

Abstract： I will talk about various combinatorics problems which can be tackled by semidefinite programming (SDP) method. In particular, phase retrieval and compressive sensing problems can be discussed by SDP. Especially, I will discuss details about using symbolic semidefinite programming method to prove Musin Conjecture which is a classical problem in discrete geometry. Almost every dimension about maximum spherical two-distance sets problems is solved.

參考： Deep Learning Ian Goodfellow, Yoshua Bengio, Aaron Courville

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Abstract: In this talk, we give a brief introduction to finite element methods for solving partial differential equations. For simplicity, we focus on theories for elliptic type equations only but the methods can be applied to other type of equations. We will go over the basic ideas of the methods and demonstrate the error analysis. This talk aims to audiences who have not known the finite element methods. Some materials are from "The mathematical theory of finite element methods" by Brenner and Scott. Detail implementation and practical issues may be discussed in the future talks.

Abstract： Search is an essential technology for various robotic applications and it is also central to human daily activities. Searching for targets efficiently consists of NP-hard problems, but young children can search for targets very efficiently. How humans search for targets efficiently is still a mystery. Hence, two central questions are as follows: First, how do humans search for targets efficiently? Second, how can robots learn to search like humans? The central goal of this talk is to answer these two questions. This talk is organized in three parts–human search analysis, learning in robot search, and other potential applications. The key concepts of this talk are subgoal, submodularity, and sparsity. First, the human search analysis shows that humans' search motion can be represented by a few subgoals. Second, since the motion is divided into discrete subgoals and the objective functions have submodularity, the greedy algorithms generate near-optimal subgoals. Third, although learning submodular functions is a challenge, the sparsity in the Fourier domain makes it feasible. Hence, a robot can learn how to search for a target via these properties. The proposed algorithms generate near-optimal subgoals for both human and robot search experiments. Human experiments showed that the human search performance is improvedwith the assistance of subgoals. Robot experiments demonstrated that the robot can search for the target faster than any existing approaches. To the best of our knowledge, this is the first work that theorems and experiments prove that humans cannot outperform robots on search problems.

Abstract： Markov process is a stochastic process that satisfies the Markov property (sometimes characterized as "memorylessness"). In this section, we discuss several version of definition of Markov property, and prove that Brownian motion is a Markov process.

Abstract: 金融科技是一個新興領域，它所涵蓋的服務內容，相較於我們所知道的「數理金融」或「財務工程」更為廣泛。從世界經濟論壇所描述之「破壞式的創新」、「未來的金融服務」，金融科技的潛力可見一斑。我們將簡介這個領域，強調跨領域整合的重要性，以及我們的一些工作，以及與新創團隊的合作經驗分享。

Abstract： I will show the students how to guess and compute intuitively the fundamental solutions of D.E. by dimensional analysis.

Abstract： The deployment of network infrastructure lies the foundation of many networking services as it decides how the clients are served. Currently, the majority of network infrastructure is built on physical facilities like base stations and Wi-Fi access points. When deploying such facilities, we must take the nature of wireless communication into account. The nature of wireless communication, however, poses many challenges. In the first part of the talk, I will talk about wireless network deployment and present some research results. Wireless networks are solutions for last mile networks, which provide Internet access for end users. To fully meet the requests of end users, e.g., HTTP requests, we must further consider the network deployment problem that takes place in the cloud, i.e., data center networks. This kind of network deployment involves facilities like load balancers and firewalls. Recently, due to the emergence of Network Function Virtualization (NFV), there is a trend of transforming from physical facilities to software middleboxes. As a result, we instead deploy virtual facilities on virtual machines in data centers. In the second part of the talk, I will present the challenges and solutions for such network deployment problems.

Abstract：
In the previous two sections we have obtained results about the almost sure behavior of a Brownian motion without drift. In this section we ask whether these results hold as well for a Brownian motion with drift, or, more generally, for which time-dependent drift functions F the process
            {B(t)+F(t):t≥0}
has the same behavior as a Brownian motion path.

Abstract The goal of quickest change detection in hidden Markov models (HMMs) is to utilize the observed values to detect a change from the original HMM into a new one as soon as possible, under a restriction of false alarms. Fuh and Mei (2015) studied the problem of quickest change detetion and Kullback-Leibler divergence (KL divergence) for two-state HMMs. In this short talk, I will first point out several subtle problems appeared in their paper. Next, a more general framework is developed for the multi-state HMMs and major corrections of the subtle problems are presented. Moreover, I will show that the Fredholm integral equation method proposed in Fuh and Mei (2015) is indeed an alternative way to solve random eigensystems of random matrices. To my best knowledge, constrast to the current prevailing studies on the statistical properties of random eigensystems, the integral equation approach offers a numerical approach to solving random eigensystems, which might shed some light on this topic with a better understanding. References [1] Fuh, C. D., & Mei, Y. (2015). Quickest change detection and Kullback-Leibler divergence for two-state hidden Markov models. IEEE Transactions on Signal Processing, 63(18), 4866-4878.

Abstract：
In the previous two sections we have obtained results about the almost sure behavior of a Brownian motion without drift. In this section we ask whether these results hold as well for a Brownian motion with drift, or, more generally, for which time-dependent drift functions F the process
              {B(t)+F(t):t≥0}
has the same behavior as a Brownian motion path.

Abstract： The formerly basic theory of deformable porous media was demonstrated by Biot’s linear constitutive equations, coupled with fluid flow via Darcy’s law, in 1941. During this half-century, poroelasticity theory has been applied to many scientific fields, such as biomedical engineering, and petroleum engineering. In this study, the cerebral poromechanics model that we plan to utilise originates from Zienkiewicz who proposed a version for research purpose in soil liquefaction. Two important recent landmarks in neuroscience; the glymphatic system and its functional dependence on aquaporins will be harnessed. It will be the most sophisticated and up-to-date model available, as it is very close to mimic the cerebral environment (and can naturally incorporate traditional rodent/human experimentally extracted parameters). In exploring the pathophysiology of various neurodegenerative disorders that fall within the spectrum of dementia (such as normal pressure hydrocephalus), the boundary conditions and initial conditions will be provided in order to close the governing equations. We will utilise this model to explore specific pathologies allied to hydrocephalus, via our in-house code (2D and 3D finite element based discretization of the governing equations).

Abstract: The optimal investment and consumption problem is studied in a financial market model governed by a stochastic factor, which lives in a Hilbert space and obeys to a stochastic functional differential equation. Important examples of such stochastic factors are a forward interest rate curve model with delay and a forward/future price curve model with delay. We are lead to solve a stochastic optimal control problem in infinite dimension. Employing a duality method, the dual value function is characterized as a unique strict solution of the associated dual HJB equation. Using it, the primal value function and the feedback-form optimal strategy are constructed. The talk is based on a joint work with Fausto Gozzi and Cecilia Prosdocimi (LUISS, Rome).

Abstract： We survey several simple invariance property included scaling invariance, time inversion and the law of large number for Bownian motion. Also, we survey the simple version of the definition of Markov process.

Abstract： We survey the details of the well-known Theorem which is given by Paul Levy in 1923. In mathematics, Brownian motion is described by the Wiener process; the theorem, also known as Levy’s construction, solved the existence of the standard Brownian motion.

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摘要： 在這次的演講中，我會簡單介紹近年來美國銀行業的市場趨勢與人才需求並分享自身在業界近兩年的工作經驗。其次，我會簡單介紹一些業界常用的統計模型與數學工具。機率與統計是應用數學的重要一個分支並且在銀行中被廣泛的應用，尤其是在建模和模型驗證這一部份。我也會針對這一部分做更深入的探討包含所需要的知識與工具，希望藉由這次的分享讓大家更了解數學和記量分析在美國銀行業中所扮演的角色及其市場生態與需求。

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Abstract： In this talk I will introduce a Liouville type result for a backward global solution to the Navier-Stokes equations in the half plane with the no-slip boundary condition. No assumptions on spatial decay for the vorticity nor the velocity field are imposed. We study the vorticity equations instead of the original Navier-Stokes equations. As an application, we extend the geometric regularity criterion for the Navier-Stokes equations in the three-dimensional half space under the no-slip boundary condition.