2020 Department of Mathematics Events

PhD Dissertation Defense 

Speaker: Sunil Giri

Title: Infection Age Structured Vector Borne Disease Model with Direct Transmission

Advisor: Dr. Necibe Tuncer

Abstract:

Mathematical modeling is a powerful tool to study and analyze the disease dynamics prevalent in the community. This thesis studies the dynamics of two time since infection structured vector borne models with the direct transmission. We have included disease induced death rate in the first model to from the second model. The aim of this thesis is to analyze whether these two models have same or different disease dynamics. An explicit expression for the reproduction number denoted by R₀ is derived. Dynamical analysis reveals the forward bifurcation in the first model. That is when the threshold value R₀ < 1, disease free equilibrium is stable both locally and globally implying disease dies out from the population. When R₀ > 1 existence of unique endemic equilibrium is locally asymptotically stable.

For the second model, analysis of the existence and stability of equilibria reveals the existence of backward bifurcation i.e. where the disease-free equilibrium coexists with the endemic equilibrium when the reproduction number R₀₂ is less than unity. This aspect shows that in order to control vector borne disease, it is not sufficient to have reproduction number less than unity although necessary. Thus, the infection can persist in the population even if the reproduction number is less than unity. Numerical simulation is presented to see the bifurcation behavior in the model. By taking the reproduction number as the bifurcation parameter, we find the system undergoes backward bifurcation at R₀₂ = 1. Thus, the model has backward bifurcation and have two positive endemic equilibrium when R₀₂ < 1 and unique positive endemic equilibrium whenever R₀₂ > 1. Stability analysis shows that disease free equilibrium is locally asymptotically stable when R₀₂ < 1 and unstable when R₀₂ > 1. When R₀₂ < 1, lower endemic equilibrium in backward bifurcation is locally stable

Please contact Dr. Hongwei Long <hlong@fau.edu>  for an electronic copy of the dissertation. A hard copy of the dissertation is not displayed in the departmental office in order to avoid multiple people touching the same hard copy at this pandemic time.

Webex meeting information:

https://fau.webex.com/fau/j.php?MTID=m5c244037c6465aa0f9789775ac9c4d88

Meeting number (access code): 1200818367

Meeting password: yHreM67pMn3

Monday, July 20, 2020; 4:00 p.m.

All are cordially invited.

Wed., July 15, 2020
10:00 a.m.

Speaker: Amir Alipour Yengejeh 

Title: Survival Analysis with Cox Proportional Hazard Deep Learning Neural Networks

Abstract: Survival models are used to explore and understand the relationship between individuals’ covariates (e.g. clinical and genetic features) and the effectiveness of various treatment options. There are two types of models:

1. Standard survival models: Cox proportional hazards model.

2. Nonlinear survival models: Neural network and survival forest.

The main problem of standard models is that they need extensive feature engineering, prior (medical) knowledge, or pre-assumptions to model treatment interaction at individual level, while nonlinear can inherently model these high-level interaction terms. One of the conspicuous nonlinear models is DeepSurv: A Cox proportional hazards deep neural network.

In this work, through the results of training DeepSurv on the simulated and real survival data, we will show that the performance of DeepSurv in modeling highly complex relationships between an individual’s covariates and their risk of failure is as well as or better than others. The capabilities of DeepSurv in the prediction and modeling can enable researchers to use deep neural network as a tool in their exploration, understanding, and prediction of the effects of a individuals' characteristics on their risk of failure. 

Meeting information:

• Link:
  https://fau.webex.com/fau/j.php?MTID=me009a97ad5b6079c6f2cf5650e2ae008
• Meeting ID: 120 869 2790
• Password: SAyVZGuw633

All are cordially invited.

MS Presentation:

Speaker: Leila Mirsaleh Kohan (via WebEx):

Title: DYNAMIC AND CONTROL OF AUTOIMMUNE DISORDER UNDER RADIATION

Abstract:  Autoimmune diseases can be developed by exposure to radiation. Ionizing radiation modifies the immune system and diminishing its normal ability to fight diseases.  The extents of the modifications depend on the dose rate and duration of radiation exposure.  This work employs mathematical simulations of autoimmune process dynamics under irradiation. The mathematical model employed in this work consists of four non-linear differential equations.  The variables used in the modeling are the concentration of target cells of the tissue, concentration of cytotoxic T-lymphocytes, the concentration of tissue-specific antigen, and the concentration of T-suppressor cortical thymus.

WebEx information:

Meeting number (access code):472 769 468
Meeting password: May20
JOIN BY PHONE +1-415-655-0003 US Toll

All are cordially invited. 

Thurs., May 21, 2020
10:50 am-12:30 pm

FAU SIAM Student Chapter Presents

Speaker: Dr. Christopher Tralie, Ursinus College
Title: TDALabs: (Some of) TDA's Greatest Hits in Interactive Python
Abstract: Abstract: TDA software is becoming more mainstream and accessible to both mathematicians in the field and to data scientists at large. Recently, I worked as part of a small team of open source software developers to create a Python library known as scikit-tda (https://scikit-tda.org/). In addition to using this library in myriad research applications, I have also been developing a compendium of examples for pedagogical purposes, some of which are in a repository I call "TDALabs" (https://github.com/ctralie/TDALabs). In this talk, I will interactively go through a number of these examples, including a demo of the stability theorem, sliding windows in time series and video, the natural space of image patches, diffusion maps and TDA, lower star image filtrations for cell segmentation in images, mesh reconstruction via alpha shapes, and isometry blind 3D shape clustering. It is the hope that people will be inspired to use these materials in their own courses and workshops, and it is also the hope that some will help me build on them and contribute additional concise examples that showcase their work. Pull requests are welcome!

WebEx meeting information:
Meeting number (access code): 476386156
Password: SIAM
Join Meeting

 January 24 - 25, 2020
 8:00 am - 4:30 pm

 Thurs, January 30, 2020
 1:00 pm

Saturday, February 1, 2020

 Weds, February 5, 2020
 2:00 pm

Wed, February 12, 2020                                   
4:00 pm; SE 215  

Algebra Seminar: Dr. Warren McGovern: Possible Theorem About Semi-Clean Group Rings

Thurs, February 13, 2020
11:00 am; SE-215

Dr. Jason Mireles-James, Florida Atlantic University

Title: Collision dynamics in some gravitational N-body problems
Abstract: The equations of motion for gravitating bodies have singularities when any two of the bodies occupy the same point in space, i.e. when there is a collision.  It is well known, but still quite interesting, that one can make sense of orbits that ``go through'' collisions by a process called regularization.  I'll introduce the idea of regularization and illustrate its use in some numerical calculations

Mon, February 17, 2020
11:00 am; SE-215

Algebra Seminar with Dr. Zvi Rose, Department of Mathematical Sciences, Florida Atlantic University

Title: Oriented Matroids and Combinatorial Neural Codes.
Abstract: A combinatorial neural code is convex if it arises as the intersection pattern of convex open subsets of Euclidean space. We relate the emerging theory of convex neural codes to the established theory of oriented matroids, in both a category-theoretic sense and with respect to feasibility and complexity. By way of this connection, we prove that all convex codes are related to some representable oriented matroid, and we show that deciding whether a neural code is convex is NP-hard.

Thurs, February 20, 2020
11:00 am; SE 215

Dr. Yang Li: Modeling Spatial and Spatio-temporal Process on the Sphere with Convolution

Mon, February 24, 2020
4:00 pm; SE-215

Crypto Café with Floyd Johnson, Florida Atlantic University

Title: An Introduction to Quantum Key Distribution
Abstract: Quantum mechanics was one of the greatest scientific breakthroughs of the last century with applications still being found.  Since the 1970’s mathematicians and physicists have been exploring how quantum mechanics can be used in cryptography to achieve previously thought impossible results.  In this talk, we will give an overview of the problem of key establishment and how quantum phenomena can be used to achieve secure key establishment

Wed, February 26, 2020
4 pm; SE-216

Algebra Seminar with Zvi Rose, Florida Atlantic University

Title: Oriented Matroids and Combinatorial Neural Codes
Abstract: A combinatorial neural code is convex if it arises as to the intersection pattern of convex open subsets of Euclidean space. We relate the emerging theory of convex neural codes to the established theory of oriented matroids, in both a category-theoretic sense and with respect to feasibility and complexity. By way of this connection, we prove that all convex codes are related to some representable oriented matroid, and we show that deciding whether a neural code is convex is NP-hard.

Fri, February 28, 2020
4 pm; SE-215

Title: Combinatorial Game Theory
Abstract: This will be a talk which begins with the game of Nim and Sprague-Grundy numbers. We will then discuss a few newer games and some recent results.  The level of the talk should be suitable for graduate students and even some interested undergraduates.

Wed, March 4, 2020
4 pm; 5:00 p.m.
Jupiter Campus 

Algebra Seminar with Robert Raphael, Department of Mathematics and Statistics at the University of Concordia

Title: The countable lifting problem and the reduced-ring partial order.
Abstract: The origins of the countable lifting problem, the work of Topping and Conrad. The case of C(X) by Hager and the speaker. The RR-order on reduced rings. What it means for Boolean rings and for domains.  The algebraic results. Weakly Baer rings and almost weakly Baer rings. The topological results. RR-good spaces. When are products of rr-good spaces rr-good?

 March 9 - 13, 2020
 8:00 am - 5:00 pm

 Sat, March 14, 2020
 8:00 am - 3:30pm

Wed., April 15, 2020
2:00  p.m.

Master's Presentation with Melissa De Jesus

Title: Stability Analysis of the SIR model
Abstract:  The SIR model is one way that we can analyze how the spread of a disease effects a population overtime.  In this model, the spread of a disease divides our population into 3 non-intersecting classes: susceptible, infected, and recovered.  By studying the dynamics of this system, we are able to predict how the disease will behave in the population. We are interested in the stability of the equilibria points which will help us decide whether a disease will die out, or if it will stabilize itself.

WebEx information:
https://fau.webex.com/fau/j.php?MTID=m1dcefaca5c128b7e0c386ae32644cb6d
Meeting number (access code): 475 541 943 
Meeting password: GEb3G4VfFt3 
JOIN BY PHONE +1-415-655-0003 US Toll

Fri., April 17, 2020
1:00 p.m.

Virtual Student Presentation with Noah Corbett

Title: The Stable Manifold Theorem
Abstract:  In this talk, we set up the necessary framework to state the Stable Manifold Theorem for a hyperbolic fixed point.  We then proceed to prove the theorem in detail.  

WebEx information:
https://fau.webex.com/fau/j.php?MTID=m4a8f4ecf5db9fb87837401224f571ed3
Meeting number (access code): 472 811 477
Meeting password: 20200417-MS
JOIN BY PHONE +1-415-655-0003 US Toll

All are cordially invited. 

Fri., April 17, 2020
3:00 p.m.

Ph.D. Dissertation Defense with Jorge Gonzalez 

https://fau.webex.com/fau/j.php?MTID=m187e82a5cb0e7be96ef8409fd72a0ab0
Meeting number (access code): 478 231 370
Meeting password: 20200417

Tue., May 5, 2020
4:00 p.m.

FAU's Student Chapter of the AWM Care To BEE Event

Dr. Nina Fefferman will be joining us live on Webex for a problem-solving session based on topics from a pre-recorded webinar from NIMBioS,  "The Role of Applied Math in Real-time Pandemic Response How Basic Disease Models Work"

Dr. Nina Fefferman is a mathematical biologist with a long history of work on biosecurity and pandemic preparedness and response. She has consulted in this area for state and federal agencies and departments on threats including TB, Ebola, Zika virus, H1N1 2009, and many others, now including COVID-19. She is a professor in the Departments of Mathematics and Ecology & Evolutionary Biology at the University of Tennessee, Knoxville. Dr. Fefferman directs the Mathematical Modeling Center at the National Institute for Mathematical and Biological Synthesis.

Abstract: It's not normally instantly obvious what mathematicians do. It's also not normal to be able to use middle-school math to help try to save the world. Right now, things are not normal. Join us for "The role of applied math in real-time pandemic response: How basic disease models work" for a presentation about how very simple, middle-school math (and much fancier versions of the same thing) can help us fight COVID-19.

Be sure to register online. This conference is open to anyone interested in mathematics at FAU and neighboring institutions! Please sign up so that we can contact you with relevant information. Also, if you would like to provide a mailing address, we will be sending out promotional items (note this is optional). 

This initiative was made possible by the generous support of Lisa Simonyi, the IAS Women and Mathematics Program, and the FAU Department of Mathematical Sciences.

Mon, May 11, 2020
CANCELED