Difference between revisions of "SIAM Student Chapter Seminar"

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__NOTOC__
 
__NOTOC__
  
 
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*'''When:''' 3:30 pm
 
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*'''Where:''' Zoom
*'''When:''' Most Friday at 11:30 am (see e-mail)
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*'''Organizers:''' [http://www.math.wisc.edu/~xshen/ Xiao Shen]
*'''Where:''' 901 Van Vleck Hall
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*'''Faculty advisers:''' [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault], [http://pages.cs.wisc.edu/~swright/ Steve Wright]  
*'''Organizers:''' [http://www.math.wisc.edu/~xshen/ Xiao Shen]  
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*'''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 [join-siam-chapter@lists.wisc.edu].
 
  
 
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== Fall 2020 ==
== Fall 2019 ==
 
  
 
{| cellpadding="8"
 
{| cellpadding="8"
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!align="left" | title
 
!align="left" | title
 
|-
 
|-
|Sept. 27, Oct. 4
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|9/29
|[http://www.math.wisc.edu/~xshen/ Xiao Shen] (Math)
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|Yu Feng (Math)
|''[[#Sep 27, Oct 4: Xiao Shen (Math)|The corner growth model]]''
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|''[[#9/29, Yu Feng (Math)|Phase separation in the advective Cahn--Hilliard equation]]''
 
|-
 
|-
|Oct. 11
 
|''no seminar''
 
|
 
 
|-
 
|-
 +
|10/14
 +
|Dongyu Chen (WPI)
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|''[[#10/14, Yuchen Dong (WPI)|A Half-order Numerical Scheme for Nonlinear SDEs with one-sided Lipschitz Drift and H\:{o}lder Continuous Diffusion Coefficients]]''
 
|-
 
|-
|Oct. 18
 
|[https://scholar.google.com/citations?user=7cVl9IkAAAAJ&hl=en Bhumesh Kumar] (EE)
 
|''[[#Oct 18: Bhumesh Kumar (EE)|Non-stationary Stochastic Approximation]]''
 
|
 
 
|-
 
|-
 +
|10/28
 +
|Evan Sorenson (math)
 +
|''[[#10/28, Evan Sorenson (math)|Unsupervised data classification via Bayesian inference]]''
 
|-
 
|-
|Oct. 25
 
|Max Bacharach
 
|''[[#Oct 25:|Coalescent with Recombination]]''
 
 
|-
 
|-
|-
 
|Nov. 1
 
|''no seminar''
 
|
 
|-
 
|-
 
|Nov. 8
 
|
 
 
|
 
|
 
|}
 
|}
  
== Abstract ==
+
== Abstracts ==
 +
 
 +
=== 9/29, Yu Feng (Math) ===
 +
'''Phase separation in the advective Cahn--Hilliard equation'''
  
=== Sep 27, Oct 4: Xiao Shen (Math) ===
+
The Cahn--Hilliard equation is a classic model of phase separation in binary mixtures that exhibits spontaneous coarsening of the phases. We study the Cahn--Hilliard equation with an imposed advection term in order to model the stirring and eventual mixing of the phases. The main result is that if the imposed advection is sufficiently mixing then no phase separation occurs, and the solution instead converges exponentially to a homogeneous mixed state. The mixing effectiveness of the imposed drift is quantified in terms of the dissipation time of the associated advection-hyperdiffusion equation, and we produce examples of velocity fields with a small dissipation time. We also study the relationship between this quantity and the dissipation time of the standard advection-diffusion equation.
'''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.
 
  
 +
=== 10/14, Yuchen Dong (WPI) ===
 +
'''A Half-order Numerical Scheme for Nonlinear SDEs with one-sided Lipschitz Drift and Hölder Continuous Diffusion Coefficients'''
  
=== Oct 18: Bhumesh Kumar (EE) ===
+
We consider positivity-preserving explicit schemes for one-dimensional nonlinear stochastic differential
'''Non-stationary Stochastic Approximation'''
+
equations. The drift coefficients satisfy the one-sided Lipschitz condition, and the diffusion coefficients
 +
are Hölder continuous. To control the fast growth of moments of solutions, we introduce several explicit
 +
schemes including the tamed and truncated Euler schemes. The fundamental idea is to guarantee the
 +
non-negativity of solutions. The proofs rely on the boundedness for negative moments and exponential of
 +
negative moments. We present several numerical schemes for a modified Cox-Ingersoll-Ross model and a
 +
two-factor Heston model and demonstrate their half-order convergence rate.
  
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.
 
  
Reference: https://arxiv.org/abs/1802.07759 (To appear in Mathematics of Control, Signals and Systems)
+
=== 10/28, Evan Sorenson (math) ===
 +
''' Unsupervised data classification via Bayesian inference'''
 +
 
 +
Bayesian inference is a way of “updating” our current state of knowledge given some data. In this talk, I will discuss how one can use Bayesian inference to classify data into separate groups. Particularly, I will discuss an application of this to outlier detection in contamination control within semiconductor manufacturing. Time permitting, I will talk about some computational tools for these models.
  
=== Oct 25: Max Bacharach (Math) ===
 
'''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.
 
  
 
<br>
 
<br>
 +
 +
== Past Semesters ==
 +
*[[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 10:02, 28 October 2020



Fall 2020

date speaker title
9/29 Yu Feng (Math) Phase separation in the advective Cahn--Hilliard equation
10/14 Dongyu Chen (WPI) A Half-order Numerical Scheme for Nonlinear SDEs with one-sided Lipschitz Drift and H\:{o}lder Continuous Diffusion Coefficients
10/28 Evan Sorenson (math) Unsupervised data classification via Bayesian inference

Abstracts

9/29, Yu Feng (Math)

Phase separation in the advective Cahn--Hilliard equation

The Cahn--Hilliard equation is a classic model of phase separation in binary mixtures that exhibits spontaneous coarsening of the phases. We study the Cahn--Hilliard equation with an imposed advection term in order to model the stirring and eventual mixing of the phases. The main result is that if the imposed advection is sufficiently mixing then no phase separation occurs, and the solution instead converges exponentially to a homogeneous mixed state. The mixing effectiveness of the imposed drift is quantified in terms of the dissipation time of the associated advection-hyperdiffusion equation, and we produce examples of velocity fields with a small dissipation time. We also study the relationship between this quantity and the dissipation time of the standard advection-diffusion equation.


10/14, Yuchen Dong (WPI)

A Half-order Numerical Scheme for Nonlinear SDEs with one-sided Lipschitz Drift and Hölder Continuous Diffusion Coefficients

We consider positivity-preserving explicit schemes for one-dimensional nonlinear stochastic differential equations. The drift coefficients satisfy the one-sided Lipschitz condition, and the diffusion coefficients are Hölder continuous. To control the fast growth of moments of solutions, we introduce several explicit schemes including the tamed and truncated Euler schemes. The fundamental idea is to guarantee the non-negativity of solutions. The proofs rely on the boundedness for negative moments and exponential of negative moments. We present several numerical schemes for a modified Cox-Ingersoll-Ross model and a two-factor Heston model and demonstrate their half-order convergence rate.


10/28, Evan Sorenson (math)

Unsupervised data classification via Bayesian inference

Bayesian inference is a way of “updating” our current state of knowledge given some data. In this talk, I will discuss how one can use Bayesian inference to classify data into separate groups. Particularly, I will discuss an application of this to outlier detection in contamination control within semiconductor manufacturing. Time permitting, I will talk about some computational tools for these models.



Past Semesters