Difference between revisions of "SIAM Student Chapter Seminar"

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__NOTOC__
 
__NOTOC__
  
*'''When:''' Most Friday at 11:30am
+
*'''When:''' 3:30 pm
*'''Where:''' 901 Van Vleck Hall
+
*'''Where:''' Zoom
 
*'''Organizers:''' [http://www.math.wisc.edu/~xshen/ Xiao Shen]
 
*'''Organizers:''' [http://www.math.wisc.edu/~xshen/ Xiao Shen]
 
*'''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].
  
 
<br>
 
<br>
  
== Fall 2019 ==
+
== Fall 2020 ==
  
 
{| cellpadding="8"
 
{| cellpadding="8"
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!align="left" | title
 
!align="left" | title
 
|-
 
|-
|Sept. 27, Oct. 4
+
|9/29
|[http://www.math.wisc.edu/~xshen/ Xiao Shen] (Math)
+
|Yu Feng (Math)
|''[[#Sep 27, Oct 4: Xiao Shen (Math)|The corner growth model]]''
+
|''[[#9/29, Yu Feng (Math)|Phase separation in the advective Cahn--Hilliard equation]]''
 
|-
 
|-
 
|-
 
|-
|Oct. 18
+
|10/14
|[https://scholar.google.com/citations?user=7cVl9IkAAAAJ&hl=en Bhumesh Kumar] (EE)
+
|Dongyu Chen (WPI)
|''[[#Oct 18: Bhumesh Kumar (EE)|Non-stationary Stochastic Approximation]]''
+
|''[[#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]]''
|
+
|-
 +
|-
 +
|10/28
 +
|Evan Sorenson (math)
 +
|''[[#10/28, Evan Sorenson (math)|Unsupervised data classification via Bayesian inference]]''
 
|-
 
|-
 
|-
 
|-
|Oct. 25
 
|Max (Math)
 
|''[[#Oct 25: Coalescent with Recombination]]''
 
|
 
 
|-
 
|-
 
|-
 
|-
|Nov. 8
+
|11/23
|Hongfei Chen (Math)
+
|Weijie Pang (McMaster University)
|''[[#Nov 15: Brownian swimmers in a channel]]''
+
|''[[#11/23, Weijie Pang (McMaster University)|Pandemic Model with Asymptomatic Viral Carriers and Health Policy]]''
|
 
 
|-
 
|-
 
|-
 
|-
|
 
 
|
 
|
 
|}
 
|}
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== Abstracts ==
 
== Abstracts ==
  
=== Sep 27, Oct 4: Xiao Shen (Math) ===
+
=== 9/29, Yu Feng (Math) ===
'''The corner growth model'''
+
'''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.
  
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.
 
  
=== Oct 18: Bhumesh Kumar (EE) ===
 
'''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.
+
=== 11/23, Weijie Pang (McMaster University) ===
  
Reference: https://arxiv.org/abs/1802.07759 (To appear in Mathematics of Control, Signals and Systems)
+
'''Pandemic Model with Asymptomatic Viral Carriers and Health Policy '''
  
=== Oct 25: Max (Math) ===
+
By October 13, 2020, the total number of COVID-19 confirmed cases had been 37,880,040 with 1,081,857 death in the world. The speed, range and influence of this virus exceed any pandemic in history. To find reasons of this incredible fast spread, we introduce asymptomatic category into a SEIR pandemic model. Based on published data of Italy, we calibrated exposed rates of COVID-19 in this model and then simulated the spread of COVID-19 for different asymptomatic rates. To measure the effects of different types of public health policies on this pandemic, we construct a pandemic model including health policies. By the simulation of this model, we provide feasible suggestions of containment to regulators.
'''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.
 
  
=== Nov 15: Hongfei Chen (Math) ===
 
'''Brownian swimmers in a channel'''
 
  
Abstract: Shape matters! I will talk about how their shapes affect their mean reversal time.
 
 
<br>
 
<br>
  
 
== Past Semesters ==
 
== 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/Fall2018|Fall 2018]]
 
*[[SIAM_Student_Chapter_Seminar/Spring2017|Spring 2017]]
 
*[[SIAM_Student_Chapter_Seminar/Spring2017|Spring 2017]]

Latest revision as of 10:37, 1 February 2021



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
11/23 Weijie Pang (McMaster University) Pandemic Model with Asymptomatic Viral Carriers and Health Policy

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.


11/23, Weijie Pang (McMaster University)

Pandemic Model with Asymptomatic Viral Carriers and Health Policy

By October 13, 2020, the total number of COVID-19 confirmed cases had been 37,880,040 with 1,081,857 death in the world. The speed, range and influence of this virus exceed any pandemic in history. To find reasons of this incredible fast spread, we introduce asymptomatic category into a SEIR pandemic model. Based on published data of Italy, we calibrated exposed rates of COVID-19 in this model and then simulated the spread of COVID-19 for different asymptomatic rates. To measure the effects of different types of public health policies on this pandemic, we construct a pandemic model including health policies. By the simulation of this model, we provide feasible suggestions of containment to regulators.



Past Semesters