Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Department Colloquium

Special Colloquium - Qian Qin (University of Florida)

Qian Qin (University of Florida)

Friday, January 25th, 2019

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Qian Qin (University of Florida)

Title: Convergence complexity analysis of MCMC.

Abstract: Convergence complexity analysis is the study of how Markov chain Monte Carlo (MCMC) algorithms used in Bayesian statistics scale with the size of the underlying data set. To conduct this type of analysis, one needs tools to construct convergence bounds for high-dimensional Markov chains. I will review a few classical techniques of Markov chain convergence analysis (in particular, drift and minorization), and discuss their applicability and limitations in high-dimensional settings. I will then present a result concerning the convergence complexity of Albert and Chib's algorithm for Bayesian probit regression.

Qian Qin is a Ph.D. Candidate in Statistics at the University of Florida. His research interests include Markov chain Monte Carlo, Bayesian statistics, and high-dimensional statistics.

Special Colloquium - Michelle Miranda (University of Texas)

Michelle Miranda (University of Texas)

Monday, January 21st, 2019

Time: 4:30 p.m.  Place: Jeffery Hall 234

Speaker: Michelle Miranda (University of Texas)

Title: Modeling Modern Data Objects: Statistical Methods for Ultra-high Dimensionality and Intricate Correlation Structures.

Abstract: Advances in technology have been generating data with increased complexity. Modern data objects are often high-dimensional and can also lay in 2D, 3D and even 4D Euclidean and sometimes non-Euclidean planes. One example are data generated from large-scale multi-site studies such as the Human Connectome Project and the Alzheimer's Disease Neuroimaging Initiative. In these scenarios, complexity comes in the form of brain images such as functional magnetic resonance imaging (fMRI), a 4D object that is high-dimensional (number of voxels is around 100K for each time point and each subject), with measurements that are correlated both in time and in space. Another example are data coming from an instrument specifically designed to measure scleral strain in donor eyes. The device generates functional data with functions defined on a non-Euclidean 2D partial spherical domain. Associating these complex data with clinical, environmental, and genetic variables can be challenging and classical statistical tools need to evolve to keep up with the complexity of these new data types. In this talk I address some of the challenges brought by modern data objects and show a few solutions to some important statistical questions in this context.

Michelle Miranda obtained her Ph.D. degree at the University of North Carolina at Chapel Hill in 2014. She is currently a Postdoctoral Fellow in Biostatistics at The University of Texas MD Anderson Cancer Center. Her research interests include Bayesian analysis with focus on high-dimensional settings, functional data analysis, and methods for correlated data objects.

Department Colloquium - Lee Mosher (Rutgers University)

Lee Mosher (Rutgers University)

Friday, January 18th, 2019

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Lee Mosher (Rutgers University)

Title: The automorphism group of a rank 2 free group, and other matters.

Abstract: As a lead up to discussing current research into the geometry of the automorphism and outer automorphisms groups of finite rank free groups, I’ll examine in some detail the geometry of the automorphism group of a rank 2 free group.

Professor Lee Mosher completed his PhD in Princeton in 1983 under the direction of Bill Thurston. He then went on to Harvard, and was a member of the IAS, before accepting a position at Rutgers University, where he is now a Distinguished Professor. Although trained as a topologist, Prof.~Mosher's broad research interests also cover geometry, geometric group theory and dynamical systems. His work has been published in the top mathematical journals, including Annals of Mathematics, Acta Mathematica and Inventiones, and has been continuously supported by the NSF since 1990.

Special Colloquium - Long Feng (Yale)

Long Feng (Yale)

Wednesday, January 16th, 2019

Time: 3:30 p.m.  Place: Jeffery Hall 234

Speaker: Long Feng (Yale)

Title: Sorted Concave Penalized Regression.

Abstract: The Lasso is biased. Concave penalized lease squares estimation (PLSE) takes advantage of signal strength to reduce this bias, leading to sharper error bounds in prediction, coefficient estimation and variable selection. For prediction and estimation, the bias of the Lasso can be also reduced by taking a smaller penalty level than what selection consistency requires, but such smaller penalty level depends on the sparsity of the true coefficient vector. The sorted L1 penalized estimation (Slope) was proposed for adaptation to such smaller penalty levels. However, the advantages of concave PLSE and Slope do not subsume each other. We propose sorted concave penalized estimation to combine the advantages of concave and sorted penalizations. We prove that sorted concave penalties adaptively choose the smaller penalty level and at the same time benefits from signal strength, especially when a significant proportion of signals are stronger than the corresponding adaptively selected penalty levels. A local convex approximation, which extends the local linear and quadratic approximations to sorted concave penalties, is developed to facilitate the computation of sorted concave PLSE and proven to possess desired prediction and estimation error bounds. We carry out a unified treatment of penalty functions in a general optimization setting, including the penalty levels and concavity of the above mentioned sorted penalties and mixed penalties motivated by Bayesian considerations. Our analysis of prediction and estimation errors requires the restricted eigenvalue condition on the design, not beyond, and provides selection consistency under a required minimum signal strength condition in addition. Thus, our results also sharpens existing results on concave PLSE by removing the upper sparse eigenvalue component of the sparse Riesz condition.

Long Feng obtained his Ph.D. degree at the Department of Statistics and Biostatistics, Rutgers University, in 2017. He is currently a Postdoctoral Associate at Yale University. His research interests include high-dimensional statistics, variable selection, empirical Bayes methods, tensor regression, imaging data analysis, and convex/non-convex optimizations.

Department Colloquium - Kexue Zhang (Queen's University)

Kexue Zhang (Queen's University)

Friday, November 30th, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Kexue Zhang (Queen's University)

Title: Input-to-State Stability of Impulsive Systems with Time-Delay

Abstract: Impulsive systems are dynamical systems subject to state jumps at a sequence of discrete-time moments. These systems are often modelled by impulsive differential equations, and have applications in a wide variety of areas, including network synchronization and epidemic dynamics. Time-delay is an essential part of most practical scenarios of impulsive systems. For instance, time-delay is unavoidable in sampling and transmission of the impulse information. In this talk, I will given an overview of the fundamental theory of impulsive functional differential equations, which provide the mathematical building blocks for studying impulsive time-delay systems. I then discuss the stability of the evolution of these systems, where I will focus on the input-to-state stability problem. As an application, impulsive synchronization of time-delay systems will be studied. This is joint work with Xinzhi Liu (Waterloo).

Kexue Zhang obtained his Ph.D. degree in the Department of Applied Mathematics, University of Waterloo,Canada in 2017. He is currently a Coleman Postdoctoral Fellow at Queen's University. His research interests include hybrid systems and control, differential equations on time scales, and their various applications on complex dynamical networks.

Lorne Campbell Lectureship - Frank R. Kschischang (U of T)

Frank R. Kschischang

Friday, November 23rd, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 126

Speaker: Frank R. Kschischang
(Distinguished Professor of Digital Communication, University of Toronto)

Title: The Mathematics of Modems

Abstract: Virtually all practical digital communications systems in use today include some form of error-control coding scheme. In this talk, I will review the theory and development of error-correcting schemes that can achieve, with practical decoding complexity, a performance approaching the fundamental information-theoretic limits established by Claude E. Shannon over seven decades ago

Frank R. Kschischang received the B.A.Sc. degree (with honours) from the University of British Columbia in 1985 and the M.A.Sc. and Ph.D. degrees from the University of Toronto in 1988 and 1991, respectively, all in electrical engineering. He holds the title of Distinguished Professor of Digital Communication in the Department of Electrical and Computer Engineering at the University of Toronto, where he has been a faculty member since 1991. During 1997-98, he was a visiting scientist at MIT, Cambridge, MA; in 2005 he was a visiting professor at the ETH, Zurich, and in 2011 and again in 2012-13 he was a visiting Hans Fischer Senior Fellow at the Institute for Advanced Study at the Technical University of Munich.

His research interests are focused primarily on the area of channel coding techniques, applied to wireline, wireless and optical communication systems and networks. In 1999 he was a recipient of the Ontario Premier’s Excellence Research Award and in 2001 (renewed in 2008) he was awarded the Tier I Canada Research Chair in Communication Algorithms at the University of Toronto.

Received the 2010 Communications Society and Information Theory Society Joint Paper Award. He is a recipient of the 2012 Canadian Award in Telecommunications Research. He is a Fellow of IEEE, of the Engineering Institute of Canada, and of the Royal Society of Canada.

During 1997-2000, he served as an Associate Editor for Coding Theory for the IEEE Transactions on Information Theory, and from 2014 to 2016, he served as this journal’s Editor-in-Chief. In 2016, he received the Aaron D. Wyner Distinguished Service Award of the IEEE Information Theory Society.

Images from Dr. Frank Kschischang's Lecture - Nov. 23rd, 2018

Lorne Campbell Lectureship - Dr. Frank Kschischang
Lorne Campbell Lectureship - Dr. Frank Kschischang
Lorne Campbell Lectureship - Dr. Frank Kschischang
Lorne Campbell Lectureship - Dr. Frank Kschischang

Department Colloquium - Anne Broadbent (University of Ottawa)

Anne Broadbent (University of Ottawa)

Friday, November 16th, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Anne Broadbent (University of Ottawa)

Title: How to Verify a Quantum Computation?

Abstract: Experimental implementations of quantum computers are in their infancy, but already we are faced with the following conundrum: if quantum computers are exponentially more powerful than their classical counterparts, how can we verify the outcome of a quantum computation? In this context, the scientific method of "predict and verify" appears to fail dramatically: these computations are so complex that they are impossible to predict. For a solution to this problem, we turn to theoretical computer science, where it is well established that interaction dramatically increases the power of a verification process.

Dr. Anne Broadbent is an Associate Professor in the Department of Mathematics and Statistics at the University of Ottawa, where she holds the University Research Chair in Quantum Information Processing. Her research focuses on quantum complexity and cryptography and she is perhaps best known for her 2009 paper on 'Blind Quantum Computing'. Dr. Broadbent was awarded the NSERC Doctoral Prize (2009), the John Charles Polanyi Prize in Physics (2010), the Ontario Early Researcher Award (2016) and the Andre Aisenstadt Mathematics Prize of the Centre de Recherches Mathematiques (2016). She is also a CIFAR Global Scholar Alumni and an affiliate member of the Perimeter Institute for Theoretical Physics, the Institute for Quantum Computing, and the Institut Transdiscliplinaire d'Informatique Quantique.

Department Colloquium - Dennis K. J. Lin (Penn State University)

Dennis K. J. Lin (Penn State University)

Friday, November 9th, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Dennis K. J. Lin (Penn State University)

Title: Ghost Data.

Abstract: As natural as the real data, ghost data is everywhere -- it is just data that you cannot see. We need to learn how to handle it, how to model with it, and how to put it to work. Some examples of ghost data are (see, Sall, 2017):
a) Virtual data -- it isn't there until you look at it;
b) Missing data -- there is a slot to hold a value, but the slot is empty;
c) Pretend data -- data that is made up;
d) Highly Sparse Data -- whose absence implies a near zero, and
e) Simulation data -- data to answer ``what if.''
For example, absence of evidence/data is not evidence of absence. In fact, it can be evidence of something. More Ghost Data can be extended to other existing areas: Hidden Markov Chain, Two-stage Least Square Estimate, Optimization via Simulation, Partition Model, Topological Data, just to name a few. Three movies will be discussed in this talk: (1) ``The Sixth Sense'' (Bruce Willis) -- I can see things that you cannot see; (2) ``Sherlock Holmes'' (Robert Downey) -- absence of expected facts; and (3) ``Edge of Tomorrow'' (Tom Cruise) -- how to speed up your learning (AlphaGo-Zero will also be discussed). It will be helpful, if you watch these movies before coming to my talk. This is an early stage of my research in this area--any feedback from you is deeply appreciated. Much of the basic idea is highly influenced via Mr. John Sall (JMP-SAS).

Dennis K. J. Lin (Penn State University): He is a university distinguished professor of supply chain and statistics at Penn State University. His research interests are quality assurance, industrial statistics, data mining, and response surface. He has published more than 200 SCI/SSCI papers in a wide variety of journals. He currently serves or has served as associate editor for more than 10 professional journals and was co-editor for Applied Stochastic Models for Business and Industry. Dr. Lin is an elected fellow of ASA, IMS and ASQ, an elected member of ISI, a lifetime member of ICSA, and a fellow of RSS. He is an honorary chair professor for various universities, including a Chang-Jiang Scholar at Renmin University of China, Fudan University, and National Chengchi University (Taiwan). His recent awards including, the Youden Address (ASQ, 2010), the Shewell Award (ASQ, 2010), the Don Owen Award (ASA, 2011), the Loutit Address (SSC, 2011), the Hunter Award (ASQ, 2014), and the Shewhart Medal (ASQ, 2015). Last year, he was awarded the SPES Award at the 2016 Joint Statistical Meeting.

Department Colloquium - Thomas Koberda (University of Virginia)

Thomas Koberda (University of Virginia)

Friday, November 2nd, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Thomas Koberda (University of Virginia)

Title: Algebra versus regularity for group actions on one-manifolds.

Abstract: I will survey some results concerning the algebraic structure of finitely generated groups which admit faithful actions on compact one-manifolds. I will concentrate on continuous, $C^1$, and $C^2$ actions, and on the various algebraic restrictions imposed by regularity requirements. Of particular interest will be nilpotent groups, right-angled Artin groups, mapping class groups of surface, and Thompson's groups F and T. Time permitting, I will indicate some recent progress.

After obtaining his undergraduate at the University of Chicago, Thomas Koberda got his Ph.D.~from Harvard in 2012, then went to Yale as an NSF and Gibbs assistant professor before joining the University of Virginia in 2015. Thomas achievements have been recognized by a Sloan Research Fellowship and the Kamil Duszenko Prize of 2017.

Department Colloquium - Camille Horbez (CNRS-Universite Paris Sud)

Camille Horbez (CNRS-Universite Paris Sud)

Friday, October 19th, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Camille Horbez (CNRS – Universite Paris Sud)

Title: Mostow-type rigidity and normal subgroups of automorphisms of free groups.

Abstract: The talk is based on a recent joint work with Richard D. Wade. Let Out(Fn) be the outer automorphism group of a finitely generated free group. In 2007, Farb and Handel proved that when n is at least 4, every isomorphism between two finite-index subgroups of Out(Fn) extends to an inner automorphism of Out(Fn). This rigidity statement, asserting that Out(Fn) has no more symmetries than the obvious ones, can be viewed as an analogue of the Mostow rigidity theorem for lattices in Lie groups, or of a result of Ivanov for mapping class groups of surfaces. We recently gave a new proof of Farb and Handel's theorem, which enabled us to also understand the symmetries of some natural normal subgroups of Out(Fn). In my talk, I will emphasize the analogies between Out(Fn), arithmetic groups and mapping class groups, and will present some general ideas behind these rigidity phenomena.

Camille Horbez obtained his Ph.D in at the Universite de Rennes in 2014, and after a year at the University of Utah, he became a Charge de Recherches for the CNRS at the Universite de Paris Sud (Orsay). In 2017, Camille was selected to give a Cours Peccot, a semester long course given at the College de France by a mathematician less than 30 year old.

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