SIAM Student Chapter Seminar: Difference between revisions

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*'''When:''' Most Friday at 11:30am
*'''When:''' Fridays at 1 PM unless noted otherwise
*'''Where:''' 901 Van Vleck Hall
*'''Where:''' 9th floor lounge (we will also broadcast the virtual talks on the 9th floor lounge with refreshments)
*'''Organizers:''' [http://www.math.wisc.edu/~xshen/ Xiao Shen]
*'''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 [join-siam-chapter@lists.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/97976615799?pwd=U2xFSERIcnR6M1Y1czRmTjQ1bTFJQT09
*'''Passcode:  281031'''


<br>
== Spring 2024 ==


== Fall 2019  ==
{| class="wikitable"
 
|+
{| cellpadding="8"
!Date
!align="left" | date
!Location
!align="left" | speaker
!Speaker
!align="left" | title
!Title
|-
|Sept. 27, Oct. 4
|[http://www.math.wisc.edu/~xshen/ Xiao Shen] (Math)
|''[[#Sep 27, Oct 4: Xiao Shen (Math)|The corner growth model]]''
|-
|Oct. 11
|''no seminar''
|
|-
|-
|2/2
|VV911
|Thomas Chandler (UW-Madison)
|Fluid–body interactions in anisotropic fluids
|-
|-
|Oct. 18
|3/8
|[https://scholar.google.com/citations?user=7cVl9IkAAAAJ&hl=en Bhumesh Kumar] (EE)
|Ingraham 214
|''[[#Oct 18: Bhumesh Kumar (EE)|Non-stationary Stochastic Approximation]]''
|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
|-
|-
|Oct. 25
|3/22
|Max Bacharach (Math)
|VV911&Zoom
|''[[#Oct 25:|Coalescent with Recombination]]''
|Mengjin Dong (UPenn)
|Advancing Alzheimer's Disease Research: Insights and Innovations in MRI-Based Progression Tracking
|-
|-
|4/5
|VV911
|Sixu Li (UW-Madison)
|TBD
|-
|-
|Nov. 1
|4/12
|''no seminar''
|VV911&Zoom
|
|Anjali Nair (UChicago)
|TBD
|-
|-
|4/19
|VV911
|Jingyi Li (UW-Madison)
|TBD
|-
|-
|Nov. 8
|5/3
|
|
|
|Bella Finkel (UW-Madison)
|TBD
|}
|}


== 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.
=== Sep 27, Oct 4: Xiao Shen (Math) ===
'''The corner growth model'''


Imagine there is an arbitrary amount of donuts attached to the integer points of Z^2. The goal is to pick an optimal up-right path which allows you to eat as much donuts as possible along the way. We will look at some basic combinatorial observations, and how specific probability distribution would help us to study this model.
'''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.


=== Oct 18: Bhumesh Kumar (EE) ===
'''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 $n$.
'''Non-stationary Stochastic Approximation'''


Abstract: Robbins–Monro pioneered a general framework for stochastic approximation to find roots of a function with just noisy evaluations.With applications in optimization, signal processing and control theory there is resurged interest in time-varying aka non-stationary functions. This works addresses that premise by providing explicit, all time, non-asymptotic tracking error bounds via Alekseev's nonlinear variations of constant formula.  
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.


Reference: https://arxiv.org/abs/1802.07759 (To appear in Mathematics of Control, Signals and Systems)


=== Oct 25: Max Bacharach (Math) ===
'''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.
'''Coalescent with Recombination'''


I will talk about the continuous time coalescent with mutation and recombination, with a focus on introducing key concepts related to genetic distance and evolutionary relatedness. The talk will be informal and accessible.
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.


<br>
==Past Semesters==
*[[SIAM Fall 2023]]
*[[SIAM Spring 2023]]
*[[SIAM Seminar Fall 2022|Fall 2022]]
*[[Spring 2022 SIAM|Spring 2022]]
*[[SIAM Student Chapter Seminar/Fall2021|Fall 2021]]
*[[SIAM_Student_Chapter_Seminar/Fall2020|Fall 2020]]
*[[SIAM_Student_Chapter_Seminar/Spring2020|Spring 2020]]
*[[SIAM_Student_Chapter_Seminar/Fall2019|Fall 2019]]
*[[SIAM_Student_Chapter_Seminar/Fall2018|Fall 2018]]
*[[SIAM_Student_Chapter_Seminar/Spring2017|Spring 2017]]

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