SIAM Student Chapter Seminar: Difference between revisions

From UW-Math Wiki
Jump to navigation Jump to search
 
(62 intermediate revisions by 7 users not shown)
Line 3: Line 3:
*'''When:''' Fridays at 1 PM unless noted otherwise
*'''When:''' Fridays at 1 PM unless noted otherwise
*'''Where:''' 9th floor lounge (we will also broadcast the virtual talks on the 9th floor lounge with refreshments)
*'''Where:''' 9th floor lounge (we will also broadcast the virtual talks on the 9th floor lounge with refreshments)
*'''Organizers:''' [https://sites.google.com/wisc.edu/evan-sorensen Evan Sorensen], Jordan Radke, Peiyi Chen, and Yahui Qu
*'''Organizers:''' Yahui Qu, Peiyi Chen, Shi Chen and Zaidan Wu
*'''Faculty advisers:''' [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault], [http://pages.cs.wisc.edu/~swright/ Steve Wright]  
*'''Faculty advisers:''' [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault], [http://pages.cs.wisc.edu/~swright/ Steve Wright]  
*'''To join the SIAM Chapter mailing list:''' email [mailto:siam-chapter+join@g-groups.wisc.edu siam-chapter+join@g-groups.wisc.edu].
*'''To join the SIAM Chapter mailing list:''' email [mailto:siam-chapter+join@g-groups.wisc.edu siam-chapter+join@g-groups.wisc.edu].
*'''Zoom link:''' https://uwmadison.zoom.us/j/99844791267?pwd=eUFwM25Hc2Roc1kvSzR3N2tVVlpLQT09
*'''Zoom link:''' https://uwmadison.zoom.us/j/97976615799?pwd=U2xFSERIcnR6M1Y1czRmTjQ1bTFJQT09
*'''Passcode: 641156'''
*'''Passcode: 281031'''
 
== Spring 2024 ==


<br>
==Fall 2022==
{| class="wikitable"
{| class="wikitable"
!Date (1 PM unless otherwise noted)
|+
!Date
!Location
!Location
!Speaker
!Speaker
!Title
!Title
|-
|-
|9/23
|2/2
|[https://uwmadison.zoom.us/j/99844791267?pwd=eUFwM25Hc2Roc1kvSzR3N2tVVlpLQT09 Virtual] and 911 Van Vleck                         
|VV911
|[http://www-personal.umich.edu/~tganders/ Thomas Anderson] (University of Michigan)                        
|Thomas Chandler (UW-Madison)
|A few words on potential theory in modern applied math
|Fluid–body interactions in anisotropic fluids
|-
|-
|9/30 ('''11 AM''')
|3/8
|[https://uwmadison.zoom.us/j/99844791267?pwd=eUFwM25Hc2Roc1kvSzR3N2tVVlpLQT09 Virtual] and 911 Van Vleck
|Ingraham 214
|[https://jeffhammond.github.io/ Jeff Hammond] (Principal Engineer at [https://www.nvidia.com/en-us/ NVIDIA])
|Danyun He (Harvard)
|Industry talk
|Energy-positive soaring using transient turbulent fluctuations
|-
|-
|10/7
|3/15
|[https://uwmadison.zoom.us/j/99844791267?pwd=eUFwM25Hc2Roc1kvSzR3N2tVVlpLQT09 Virtual] and 911 Van Vleck
|VV911&Zoom
|[https://walterbabyrudin.github.io/ Jie Wang] (Georgia Institute of Technology)
|Xiaoyu Dong (UMich)
|Sinkhorn Distributionally Robust Optimization
|Approximately Hadamard matrices and Riesz bases in frames
|-
|-
|10/14
|3/22
|[https://uwmadison.zoom.us/j/99844791267?pwd=eUFwM25Hc2Roc1kvSzR3N2tVVlpLQT09 Virtual] and 911 Van Vleck
|VV911&Zoom
|[https://you.stonybrook.edu/reutergroup/ Matt Reuter] (Stony Brook University)
|Mengjin Dong (UPenn)
|Becoming a Ghost Buster
|Advancing Alzheimer's Disease Research: Insights and Innovations in MRI-Based Progression Tracking
|-
|-
|10/19 ('''Wednesday at 4 PM)'''
|4/5
|[https://uwmadison.zoom.us/j/99844791267?pwd=eUFwM25Hc2Roc1kvSzR3N2tVVlpLQT09 Virtual] and 911 Van Vleck
|VV911
|Ying Li  
|Sixu Li (UW-Madison)
|Industry talk
|TBD
|-
|-
|10/28
|4/12
|911 Van Vleck
|VV911&Zoom
|[https://ylzhang2447.github.io/ Yinling Zhang] (UW-Madison)
|Anjali Nair (UChicago)
|A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterization
|TBD
|-
|-
|11/4
|4/19
|911 Van Vleck
|VV911
|Haley Kottler (UW-Madison)
|Jingyi Li (UW-Madison)
|Gaussian Mixture Model Parameter Recovery
|TBD
|-
|-
|11/11
|5/3
|911 Van Vleck
|[https://sites.google.com/wisc.edu/zinanwang/ Zinan Wang] (UW-Madison)
|Encountering Singularities of a Serial Robot Along Continuous Paths at High Precision
|-
|11/18
|911 Van Vleck
|Parvathi Kooloth (UW-Madison)
|
|
|-
|Bella Finkel (UW-Madison)
|11/25
|TBD
|NO TALK
|THANKSGIVING WEEK
|
|-
|12/2
|[https://uwmadison.zoom.us/j/99844791267?pwd=eUFwM25Hc2Roc1kvSzR3N2tVVlpLQT09 Virtual] and 911 Van Vleck
|Jenny Yeon (Applied Scientist at Amazon)
|Industry talk
|}
|}


==Abstracts==
==Abstracts==
'''February 2, Thomas Chandler (UW-Madison):''' Fluid anisotropy, or direction-dependent response to deformation, can be observed in biofluids like mucus or, at a larger scale, self-aligning swarms of active bacteria. A model fluid used to investigate such environments is a nematic liquid crystal. In this talk, we will use complex variables to analytically solve for the interaction between bodies immersed in liquid crystalline environments. This approach allows for the solution of a wide range of problems, opening the door to studying the role of body geometry, liquid crystal anchoring conditions, and deformability. Shape-dependent forces between bodies, surface tractions, and analogues to classical results in fluid dynamics will also be discussed.


'''9/23 Thomas Anderson:''' I'll talk a bit about potential theory as it is used today in the solution, via boundary integral equations / the boundary element method, of linear PDEs. These aren't only a numerical approach: I'll say a few words too about how they can be used to do analysis on problems. Then I may say a few things about volumetric potential theory: what are the problems there I've been thinking about, and application studies in mixing, for example, that they enable. Finally, I'll be happy to talk a bit about my experience so far in academia.
'''March 8, Danyun He (Harvard University):''' The ability of birds to soar in the atmosphere is a fascinating scientific problem. It relies on an interplay between the physical processes governing atmospheric flows, and the capacity of birds to process cues from their environment and learn complex navigational strategies. Previous models for soaring have primarily taken advantage of thermals of ascending hot air to gain energy. Yet, it remains unclear whether energy loss due to drag can be overcome by extracting work from transient turbulent fluctuations. In this talk, I will present a recent work that we look at the alternative scenario of a glider navigating in an idealized model of a turbulent fluid where no thermals are present. First, I will show the numerical simulations of gliders navigating in a kinematic model that captures the spatio-temporal correlations of atmospheric turbulence. Energy extraction is enabled by an adaptive algorithm based on Monte Carlo tree search that dynamically filters acquired information about the flow to plan future paths. Then, I will demonstrate that for realistic parameter choices, a glider can navigate to gain height and extract energy from flow. Glider paths reflect patterns of foraging, where exploration of the flow is interspersed with bouts of energy extraction through localized spirals. As such, this work broadens our understanding of soaring, and extends the range of scenarios where soaring is known to be possible.
 
'''9/30 Jeff Hammond:''' Jeff Hammond is a principal engineer with NVIDIA based in Helsinki, Finland, where his focus is developing better ways to write software for numerical algorithms. From 2014 to 2021, Jeff worked for Intel in Portland, Oregon; he started in the research organization and moved to the data center business group. Prior to that he worked for Argonne National Laboratory, first as a postdoc and then as a scientist in the supercomputing facility. Jeff was a graduate student at the University of Chicago and focused on developing open-source chemistry simulation software with Karol Kowalski at Pacific Northwest National Laboratory.  He majored in chemistry and mathematics at the University of Washington.  Details can be found on Jeff's home page: <nowiki>https://jeffhammond.github.io/</nowiki>. 
 
'''10/7 Jie Wang:''' We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive convex programming dual reformulations when the nominal distribution is an empirical distribution and a general distribution, respectively. Compared with Wasserstein DRO, it is computationally tractable for a larger class of loss functions, and its worst-case distribution is more reasonable. We propose an efficient stochastic mirror descent algorithm to solve the dual reformulation with provable convergence guarantees. Finally, we provide various numerical examples using both synthetic and real data to demonstrate its competitive performance and light computation cost. 
 
'''10/12 Matt Reuter:''' As children, most of us didn't know what we wanted to be "when we grew up," and, when asked, might have said, "an astronaut" or "a firefighter." I wanted to be a Ghost Buster and, pragmatically, wound up in computational chemistry and applied mathematics. In this talk, I'll discuss the winding path of my career from school to the national laboratory system to tenure-track faculty to teaching-line faculty. Along the way I’ll discuss my work exorcising (1) numerical ghosts from nanoscience research and (2) psychological ghosts from students when teaching mathematics. 
 
'''10/19 Ying Li:''' I will talk about my math background and my current role as a quantitative analytics specialist at Wells Fargo. Different types of quantitative analytics specialist at banking field will be generally introduced along with my opinions of the pros and cons for quantitative analytics jobs in financial area as a math student. I will also share my experience from academia to industry and the desired skill sets to be developed for looking for industry jobs.


'''10/28 Yinling Zhang''': Discovering the underlying dynamics of complex systems from data is an important practical topic. In this paper, a new iterative learning algorithm for complex turbulent systems with partial observations is developed that alternates between identifying model structures, recovering unobserved variables, and estimating parameters. First, a causality-based learning approach is utilized for the sparse identification of model structures, which takes into account certain physics knowledge that is pre-learned from data. Next, a systematic nonlinear stochastic parameterization is built to characterize the time evolution of the unobserved variables. Furthermore, the localization of the state variable dependence and the physics constraints are incorporated into the learning procedure. Numerical experiments show that the new algorithm succeeds in identifying the model structure and providing suitable stochastic parameterizations for many complex nonlinear systems.  
'''March 15, Xiaoyu Dong (University of Michigan, Ann Arbor):''' An $n \times n$ matrix with $\pm 1$ entries which acts on $\R^n$ as a scaled isometry is called Hadamard. Such matrices exist in some, but not all dimensions. Combining number-theoretic and probabilistic tools we construct matrices with $\pm 1$ entries which act as approximate scaled isometries in $\R^n$ for all $n \in \N$. More precisely, the matrices we construct have condition numbers bounded by a constant independent of $n$.


'''11/4 Haley Kottler:''' Gaussian mixture models are an important class of models that arise in many applications.  This talk will introduce these models, and talk about one method of parameter recovery from samples - the method of moments.  I will also discuss some of the challenges that arise in implementation of this method in the multivariate case.  
Using this construction, we establish a phase transition for the probability that a random frame contains a Riesz basis. Namely, we show that a random frame in $\R^n$ formed by $N$ vectors with  independent identically distributed coordinate having a non-degenerate symmetric distribution contains many Riesz bases with high probability provided that $N \ge \exp(Cn)$. On the other hand, we prove that if the entries are subgaussian, then a random frame fails to contain a Riesz basis with probability close to $1$ whenever $N \le \exp(cn)$, where $c<C$ are constants depending on the distribution of the entries.


'''11/11 Zinan Wang:''' In this talk, I will first introduce how to describe motions of a spatial serial robot and its singularities. Then I will talk about a new variable step method which rapidly calculates continuous kinematic paths that encounter singularities of a serial robot, especially how to control the step length. 


'''11/18 Parvathi Kooloth:''' One of the most important conservation laws in atmospheric and oceanic science is conservation of potential vorticity. The original derivation is approximately a century old, in the work of Rossby and Ertel, and it is related to the celebrated circulation theorems of Kelvin and Bjerknes. However, the laws apply to idealized fluids, and extensions to more realistic scenarios such as an atmosphere with moisture and phase changes have been problematic. In the talk, I'll describe a systematic approach based on Noether's theorem to arrive at the conservation principles for moist PV. 
'''March 22, Mengjin Dong (University of  Pennsylvania)''': Alzheimer’s disease (AD) is a progressive neurodegenerative disorder characterized by memory loss, cognitive decline, and behavioral changes primarily in the elderly population. As the most prevalent form of dementia, it impacts millions of families globally. The pathological hallmarks of AD, such as abnormal protein build-up in the brain, can manifest decades before the onset of clinical symptoms. Neuroimaging modalities such as positron emission tomography (PET) and magnetic resonance imaging (MRI) play pivotal roles in studying disease progression and elucidating its underlying mechanisms.


'''12/6 Jenny Yeon:''' Finding a job is perhaps the most stressful part of the graduate school journey - at least this was the case for me. Magically, I ended up with multiple industry offers - from an engineering role to a scientist role. A huge success? Not really. The hiring managers placed me into the "entry-level," which means less salary plus many other things. This talk is about how I would have prepared differently so that I would have avoided a bunch of "entry-level" jobs. How can we make our time at "phd" also count toward the years of experience?
In this presentation, I will commence with an overview of AD fundamentals and recent research advancements. Subsequently, I will delve into my research, which utilizes deep learning techniques to longitudinally monitor and localize AD progression using MRI data.


==Past Semesters==
==Past Semesters==
*[[SIAM Fall 2023]]
*[[SIAM Spring 2023]]
*[[SIAM Seminar Fall 2022|Fall 2022]]
*[[SIAM Seminar Fall 2022|Fall 2022]]
*[[Spring 2022 SIAM|Spring 2022]]
*[[Spring 2022 SIAM|Spring 2022]]

Latest revision as of 19:28, 18 March 2024


Spring 2024

Date Location Speaker Title
2/2 VV911 Thomas Chandler (UW-Madison) Fluid–body interactions in anisotropic fluids
3/8 Ingraham 214 Danyun He (Harvard) Energy-positive soaring using transient turbulent fluctuations
3/15 VV911&Zoom Xiaoyu Dong (UMich) Approximately Hadamard matrices and Riesz bases in frames
3/22 VV911&Zoom Mengjin Dong (UPenn) Advancing Alzheimer's Disease Research: Insights and Innovations in MRI-Based Progression Tracking
4/5 VV911 Sixu Li (UW-Madison) TBD
4/12 VV911&Zoom Anjali Nair (UChicago) TBD
4/19 VV911 Jingyi Li (UW-Madison) TBD
5/3 Bella Finkel (UW-Madison) TBD

Abstracts

February 2, Thomas Chandler (UW-Madison): Fluid anisotropy, or direction-dependent response to deformation, can be observed in biofluids like mucus or, at a larger scale, self-aligning swarms of active bacteria. A model fluid used to investigate such environments is a nematic liquid crystal. In this talk, we will use complex variables to analytically solve for the interaction between bodies immersed in liquid crystalline environments. This approach allows for the solution of a wide range of problems, opening the door to studying the role of body geometry, liquid crystal anchoring conditions, and deformability. Shape-dependent forces between bodies, surface tractions, and analogues to classical results in fluid dynamics will also be discussed.

March 8, Danyun He (Harvard University): The ability of birds to soar in the atmosphere is a fascinating scientific problem. It relies on an interplay between the physical processes governing atmospheric flows, and the capacity of birds to process cues from their environment and learn complex navigational strategies. Previous models for soaring have primarily taken advantage of thermals of ascending hot air to gain energy. Yet, it remains unclear whether energy loss due to drag can be overcome by extracting work from transient turbulent fluctuations. In this talk, I will present a recent work that we look at the alternative scenario of a glider navigating in an idealized model of a turbulent fluid where no thermals are present. First, I will show the numerical simulations of gliders navigating in a kinematic model that captures the spatio-temporal correlations of atmospheric turbulence. Energy extraction is enabled by an adaptive algorithm based on Monte Carlo tree search that dynamically filters acquired information about the flow to plan future paths. Then, I will demonstrate that for realistic parameter choices, a glider can navigate to gain height and extract energy from flow. Glider paths reflect patterns of foraging, where exploration of the flow is interspersed with bouts of energy extraction through localized spirals. As such, this work broadens our understanding of soaring, and extends the range of scenarios where soaring is known to be possible.

March 15, Xiaoyu Dong (University of Michigan, Ann Arbor): An $n \times n$ matrix with $\pm 1$ entries which acts on $\R^n$ as a scaled isometry is called Hadamard. Such matrices exist in some, but not all dimensions. Combining number-theoretic and probabilistic tools we construct matrices with $\pm 1$ entries which act as approximate scaled isometries in $\R^n$ for all $n \in \N$. More precisely, the matrices we construct have condition numbers bounded by a constant independent of $n$.

Using this construction, we establish a phase transition for the probability that a random frame contains a Riesz basis. Namely, we show that a random frame in $\R^n$ formed by $N$ vectors with  independent identically distributed coordinate having a non-degenerate symmetric distribution contains many Riesz bases with high probability provided that $N \ge \exp(Cn)$. On the other hand, we prove that if the entries are subgaussian, then a random frame fails to contain a Riesz basis with probability close to $1$ whenever $N \le \exp(cn)$, where $c<C$ are constants depending on the distribution of the entries.


March 22, Mengjin Dong (University of Pennsylvania): Alzheimer’s disease (AD) is a progressive neurodegenerative disorder characterized by memory loss, cognitive decline, and behavioral changes primarily in the elderly population. As the most prevalent form of dementia, it impacts millions of families globally. The pathological hallmarks of AD, such as abnormal protein build-up in the brain, can manifest decades before the onset of clinical symptoms. Neuroimaging modalities such as positron emission tomography (PET) and magnetic resonance imaging (MRI) play pivotal roles in studying disease progression and elucidating its underlying mechanisms.

In this presentation, I will commence with an overview of AD fundamentals and recent research advancements. Subsequently, I will delve into my research, which utilizes deep learning techniques to longitudinally monitor and localize AD progression using MRI data.

Past Semesters