歷史演講 PAST TALKS

簡介： 1. 張家銘 Designing Algorithms to Increase Fairness in Artificial Intelligence 2. 李謦伊 The Functions of Deep Learning 3. 陳靖玟 Interpreting deep learning: The Machine Learning Rorschach Test? 4. 陳忠謙 Differentiation With(out) a Difference 5. 黃耀平 Designers Fine-tune the Aerodynamics of World Cup Soccer Balls

簡介： 1. 粱長雯 Modelling Drug Dynamics in the Brain 2. 蘇逸鎮 Clinically Useful Computational Models for Personalized Treatment Planning in Cardiovascular Disease. 3. 阮毓庭 Detection of Epilepsy in Children Using Neural Network Methods 4. 邱繼賢 Game Theory and Uncertainty Quantification for Cyber Defense Applications 5. 柯智傑 Slings, Bullets, Blow-up, and Linearity.

“ 工業 4.0 時代，大數據分析透過 AI 機器學習演算法，在各產業領域的應用愈來愈廣泛。其中，在商業決策與分析應用方面，從企業正確的 KPI 選取與策略制定 [例如：魔球 (Moneyball) 如何逆轉勝的案例]、商品定價，乃至於金融市場分析與程式交易等等，都可見到 大數據分析的成功案例。 此次演講將透過案例分析方式，介紹 R & Python 大數據分析如何應用於商業決策與資料分析。”

Wang and Tchetgen (2017) studied identification and estimation of the average treatment effect when some confounders are unmeasured. Under their identification condition, they showed that the semiparametric efficient influence function depends on five unknown functionals. They proposed to parameterize all functionals and estimate the average treatment effect from the efficient influence function by replacing the unknown functionals with estimated functionals. They established that their estimator is consistent when certain functionals are correctly specified and attains the semiparametric efficiency bound when all functionals are correctly specified. In applications, it is likely that those functionals could all be misspecified. Consequently, their estimator could be inconsistent or consistent but not efficient. This paper presents an alternative estimator that does not require parameterization of any of the functionals. We establish that the proposed estimator is always consistent and always attains the semiparametric efficiency bound. A simple and intuitive estimator of the asymptotic variance is presented, and a small scale simulation study reveals that the proposed estimation outperforms the existing alternatives in finite samples.

Abstract： The main goal of this talk is to understand the quantitative spatial decay of the solution to the Boltzmann equation with hard potentials for both linear and nonlinear problems. For the nonlinear study, we get the spatial behavior by using the nonlinear weighted energy estimate. For the linear study, we get the quantitative space-time behavior under some slow velocity decay assumption, but without regularity assumption on the initial data. Both results reveal that hard sphere and hard potential models differ in their spatial behaviors. This is a joint work with Yu-Chu Lin and Haitao Wang.

Abstract： In this talk, we will introduce an extension of Toeplitz index theorem to complex manifold with isolated singularities following the relative K-homology theory of Baum, Douglas, and Taylor for manifold with boundary. As an application, we will use this index theorem to study the Arveson-Douglas conjecture. This is joint work with R. Douglas, M. Jabbari and G. Yu.

Abstract： Dehn function, motivated by the isoperimetric function in Riemannian geometry, is a tool to study finitely presented groups. Dehn functions can detect various properties of groups, in particular, they provide upper bounds on the complexity of the word problem for finitely presented groups. In this talk, I will give a survey on Dehn functions and discuss some classical results. Then I will focus on my currnet work about the Dehn functions of subgroups of right-angled Artin groups, especially on Bestvina-Brady groups. This talk is accessible to graduate students.

Abstract： 本次演講的內容會著重於介紹在倫敦金融圈，例如投資銀行、避險基金、金融科技或新創公司 ，實際上在面對或解決那些問題。演講的第一部分會介紹在分析這些實務問題時，所使用的方法與數學語言及工具，例如傳統的PDE, Monte Carlo到近期的Machine Learning, 並且簡介如何利用平行計算，例如GPU Computing, 去加速運算來降低研究時間。演講的第二部分會針對數學系背景的學生提供建議，例如若有興趣成為Quant, 有哪些知識及技能是必須提早準備以及資源可以利用。實際的例子像是Python的學習以及財務商品的認識，以及Kaggle的競賽等等都會在這個部分介紹。

Abstract Let {S_(θ,n), n ≥ 1} be a sequence of perturbed random walks indexed by θ, in thesense that the increments and drift depend on a small random noise. In this paper, we first consider a first passage time problem of S_(θ,n) crossing a constant boundary, and present a limiting distribution of the overshoot. Next we investigate the joint limiting distribution between the first passage time and the overshoot of the perturbed random walk. The asymptotic result for the boundary crossing problem is taken as θ↓0 simultaneously with the boundary goes to infinity. To this end, we present a uniform renewal theory for the perturbed random walk. In addition, we provide an interesting application. Numerical examples are also given. keywords: Boundary crossing; uniform renewal theory; perturbed random walk; small random noise; overshoot; asymptotic independent.

Abstract： 在下雨天如果我們觀察窗台上的欄杆，會發現欄杆下會懸掛著一顆顆的水珠。在這講題裡，我會以此現象起介紹一些液體介面的不穩定現象，並且介紹一數學建模的一些基本思想以及數學在這些問題中所扮演的角色。 歡迎大學生及研究生踴躍參加！

Abstract： Bell nonlocality and Einstein-Podolsky-Rosen (EPR) steering are very important quantum correlations of a composite quantum system. Bell nonlocality of a bipartite state is a kind of quantum correlations demonstrated by some local quantum measurements, while EPR steering is another form of quantum correlations, observed firstly by Schrödinger in the context of famous EPR paradox. In this talk, we introduce Bell nonlocality and EPR steering of bipartite states, including mathematical definitions and characterizations of these two quantum correlations, the convexity and compactness of the sets of all Bell local states and all EPR unsteerable states, respectively. We also derive some sufficient conditions for a state to be steerable, which imply that whenever Alice has two POV measurements such that the sets of Bob's normalized conditional states become two disjoint sets of pure states, or whenever she has one POV measurement such that Bob's normalized conditional states become a linearly independent set of pure states, Alice can steer Bob's state.

Abstract： 「在品牌行銷的世界裡，投放廣告的目的在於長時間慢慢累積觀眾對品牌的印象，因此廣告商最在乎各個不同性別與年齡層中的觀看次數(impressions)和觀看人數(people)。若先不論性別年齡，觀看次數可以由廣告伺服器中的紀錄獲得，然而估計觀看人數卻是一個極為困難的問題。 在這場演說中我們將簡介Google團隊為了估計觀看人數而推導建立的數學模型，該模型可適用於現今多重平台與多重裝置的社會。這些成果可同時展示數學系學生紮實的數學背景在資訊業界擁有無限的可能性！」

Abstract： The automatic synthesis of facial sketches has attracted growing interest in the computer vision field in recent years. In large part, this interest can be attributed to emerging law enforcement requirements for automatic facial recognition and subject detection, and the needs of social media and the digital entertainment industry to caricature facial images in a humorous and/or exaggerated way. However, manually producing facial sketches which accurately portray the unique characteristics of an individual’s face is difficult and requires an innate artistic ability or years of dedicated practice and training. In this talk, I will present approaches that we have developed to teach machine to draw facial sketches by learning from examples. The proposed scheme aims to synthesize sketches, which reproduce the unique drawing style of a particular artist. In particular, the proposed approach is capable of synthesizing facial sketches from input images with a wide variety of facial poses, gaze directions, and facial expressions even when such images are not included within the original training data set.

Abstract We consider large classes of symmetric pure jump Markov processes. The first processes are dominated by isotropic unimodal Levy processes with weak scaling conditions, and we establish sharp two-sided heat kernel estimates for these in $C^{1,1}$ open sets. The second processes are anisotropic Markov processes, and we establish sharp two-sided heat kernel estimates for these in $R^d$. These are joint works with Tomasz Grzywny, Panki Kim and Moritz Kassmann, Takashi Kumagai.

Abstract： Convolutional sparse coding (CSC) is a useful tool in many image and audio applications. Maximizing the best performance of CSC requires that the dictionary used to store the features of signals be learned from real data. This so-called convolution dictionary learning (CDL) problem is formulated within a non-convex non-smooth optimization framework. Most existing CDL solvers alternately update the coefficients and dictionary in an iterative manner. However, these approaches are prone to running redundant iterations, and their convergence properties are difficult to analyze. Moreover, most of those methods approximate the original non-convex sparse inducing function using a convex regularizer to promote computational efficiency. This approach to approximation may result in non-sparse representations and thereby hinder the performance of the applications. In this paper, we deal with the non-convex nonsmooth constraints of the original CDL directly using the modified forward-backward splitting approach, in which the coefficients and dictionary are simultaneously updated in each iteration. We also propose a novel parameter adaption scheme to increase the speed of the algorithm used to obtain a usable dictionary and in so doing prove convergence. We also show that the proposed approach is applicable to parallel processing to reduce the computing time required by the algorithm to achieve convergence. Experiment results demonstrate that our method requires less time than existing methods to achieve the convergence point, while using a smaller final functional value. We also applied the dictionaries learned using the proposed and existing methods to an application involving signal separation. The dictionary learned using the proposed approach provides performance superior to that of comparable methods. Keywords：Convolutional Sparse Coding, Dictionary Learning, Machine Learning, Optimization, Signal Separation

Abstract： The Newtonian 2-body problem is also known as the Kepler problem in honor of Johannes Kepler (1571-1630) for his discovery of three laws of planetary motion, based on which Newton deduced in 1687 the celebrated law of universal gravitation. It is commonly considered a well-understood problem, as solving it with given initial data and proving Kepler's three laws require nothing more than tools from elementary calculus. In this talk I will briefly describe its history, and outline recent discoveries from variational perspectives.

Abstract： 典範移轉 - 雲端改變了世界 開源經濟創造的新霸權 企業數位轉型的當務之急 自助分析對專業/非專業人員帶來的衝擊

Abstract： 深度學習是機器學習研究領域的一個分支。深度學習演算法的發展在人工智慧領域取得了巨大的成功，例如機器視覺、臉部及語音辨識、自然語言的處理、甚至玩圍棋。 由於深度學習過程幾乎完全經由數據推導出結論，因此當巨量的數據參與這些過程時，深度學習的表現會更加突出。因此，透過深入研究包括 Fully-connected Deep Networks、卷積神經網路（CNN）和遞歸神經網路（RNN）等等的演算法，將有助於我們有效地理解並能實際操作大數據分析解決方案中的學習過程。

Abstract： In this talk, we will talk about a recent joint work of Chi Hin Chan and Magdalena Czubak in which we proved the existence of a nontrivial Stationary Navier-Stokes flow on an exterior domain of a hyperbolic plane which satisfies both the no slip boundary condition and the finite Dirichlet norm property. This shows that there is no Stokes paradox in the hyperbolic plane setting.

Abstract： 美國工業與應用數學會（Society for Industrial and Aplied Matheamtics，簡稱 SIAM）在2012年發表了一篇報告: 產業中的數學(SIAM Report on Mathematics in Industry)。他們發現不論是在傳統或嶄新產業，數學與科學計算皆有愈來愈多的應用。這些應用會對公司的盈虧造成極大幅的影響。在這個講題裡，我將跟大家分享我個人的經驗裡數學在哪些產業與應用提供了什麼貢獻，並且稍微介紹計算數學的一些核心思想。

Abstract： 我大學念師大數學系，後來到了美國念 Illinois 的數學碩士，就改行作應用數學了。發現念數學的什麼都可以做，什麼都可以試，讓我有信心的接受各種挑戰，也享受到數學（代數、分析、幾何、數論）能力給我的優勢。從數學到數學應用，每一次闖入ㄧ個新的領域，我不只學到新的數學應用，也學到很多人生的道理。從MIT，IBM，資料庫，圖學，供應鏈，需求鏈，電子商務，系統工程，醫院管理，超級電容，石墨烯，散熱，生態系統，風力發電，節能儲能，到我最想做的金融財物模型，諾貝爾經濟學得獎題目的挑戰，我都得到很大的啟示與學習。我將分享我念數學，做應用，碰到的挑戰，及內化後，得到的無窮收穫。我還有很多未解決，想解決的數學問題。