Wednesday 10:00 -10:50 am, https://ucr.zoom.us/j/97606227247
Organizers : Weitao Chen / Heyrim Cho / Yat Tin Chow / Qixuan Wang / Jia Guo / Mykhailo Potomkin
Past Organizers : Mark Alber / James Kelliher / Amir Moradifam
In Spring 2023, the PDE & Applied math seminar will be held both through zoom and in person. Specific information about format of each talk will be provided in the email announcement and posted below. If you're interested in attending the seminar, please contact Dr. Jia Gou (jgao@ucr.edu) and Dr. Mykhailo Potomkin (mykhailp@ucr.edu).
Spring 2023 Schedule
April 5 10:00 AM (Wed) Organizational meeting
April 12 4:00 PM (Wed) Benedetto Piccoli (University Rutgers Camden) [jointly with Departmental Colloquium]
April 19 10:00 AM (Wed) Roger Temam (Indiana University) [jointly with Departmental Colloquium]
April 26 4:00 PM (Wed) Kelin Xia (Nanyang Technological University, Singapore)
May 3 10:00 AM (Wed) Daley Thomale (University of California, Riverside)
May 10 10:00 AM (Wed) Heather Zinn-Brooks (Harvey Mudd College)
May 17 10:00 AM (Wed) Hye-Won Kang (University of Maryland at Baltimore County)
May 24 10:00 AM (Wed) Benjamin Walker (University of Bath, United Kingdom)
June 7 10:00 AM (Wed) Qixuan Wang (University of California, Riverside)
Upcoming Talk:
Title and Abstracts:
April 26, 2023, 4:00 PM - 4:50 PM PT
Dr. Kelin Xia, Nanyang Technological University, Singapore
Title: Mathematical AI for molecular data analysis
Abstract: Artificial intelligence (AI) based molecular data analysis has begun to gain momentum due to the great advancement in experimental data, computational power and learning models. However, a major issue that remains for all AI-based learning models is the efficient molecular representations and featurization (or feature engineering). Here we propose advanced mathematics-based molecular representations and featurization. Molecular structures and their interactions are represented as various simplicial complexes (Rips complex, Neighborhood complex, Dowker complex, and Hom-complex), hypergraphs, and Tor-algebra-based models. Molecular descriptors are systematically generated from various persistent invariants, including persistent homology, persistent Ricci curvature, persistent spectral, and persistent Tor-algebra. These features are combined with machine learning and deep learning models, including GBT, CNN, RNN, Transformer, BERT, and others. They have demonstrated great advantage over traditional models in drug design and material informatics.
May 3, 2023, 10:00 AM - 10:50 AM PT
Daley Thomale, University of California, Riverside
Title: Introducing Acute Myeloid Leukemia Modeling through ODE and PDE Models
Abstract: Hematopoietic stem cells (HSCs) are characterized by their ability of self-renewal to replenish the stem cell pool and differentiation to more mature cells. The subsequent stages of progenitor cells also share some of this dual ability. It is yet unknown whether external signals modulate proliferation rate or rather the fraction of self-renewal. Three multicompartment models, which rely on a single external feedback mechanism, have been recently proposed. I compare these multi-compartment models with our updated multi-lineage ODE model. I will then expand from the ODE model and introduce a PDE advection diffusion reaction model for Acute Myeloid Leukemia.
May 10, 2023, 10:00 AM - 10:50 AM PT
Dr. Heather Zinn-Brooks, Harvey Mudd College
Title: Emergence of polarization in a sigmoidal bounded-confidence model of opinion dynamics
Abstract: We propose a nonlinear bounded-confidence model (BCM) of continuous time opinion dynamics on networks with both persuadable individuals and zealots. The model is parameterized by a scalar γ, which controls the steepness of a smooth influence function that encodes the relative weights that nodes place on the opinions of other nodes. When γ = 0, this influence function exactly recovers Taylor’s averaging model; when γ→∞, the influence function converges to that of a modified Hegselmann–Krause (HK) BCM. Unlike the classical HK model, however, our sigmoidal bounded-confidence model (SBCM) is smooth for any finite γ. We show that the set of steady states of our SBCM is qualitatively similar to that of the Taylor model when γ is small and that the set of steady states approaches a subset of the set of steady states of a modified HK model as γ →∞. For several special graph topologies, we give analytical descriptions of important features of the space of steady states. A notable result is a closed-form relationship between the stability of a polarized state and the graph topology in a simple model of echo chambers in social networks. Because the influence function of our BCM is smooth, we are able to study it with linear stability analysis, which is difficult to employ with the usual discontinuous influence functions in BCMs. This is joint work with Phil Chodrow and Mason Porter.
May 17, 2023, 10:00 AM - 10:50 AM PT
Dr. Hye-Won Kang, University of Maryland at Baltimore County
Title: Stochastic Modeling of Chemical Reactions in Biology
Abstract: Inherent fluctuations may play an important role in biological or biophysical systems when the system involves some species with low copy numbers. In this talk, I will present my recent work on stochastic modeling of chemical reaction networks. In the first part of the talk, I will show two examples of enzyme kinetics and glucose metabolism, where we use a continuous-time Markov chain model to describe the temporal evolution of the system dynamics with different time scales. We apply a multiscale approximation method to reduce the models with some key features.
In the second part of the talk, I will show another example of glucose metabolism where we see different-sized enzyme complexes. We hypothesize that the size of enzyme complexes is related to their functional roles and model how glucose flux can be regulated under different scenarios using differential equations. We will also see a microscopic model using the Langevin dynamics describing the movement and interactions of enzyme complexes.
May 24, 2023, 10:00 AM - 10:50 AM PT
Dr. Benjamin Walker, University of Bath, United Kingdom
Title: Multiscale methods and microswimmer models
Abstract: Swimming on the microscale has long been the subject of intense research efforts, from experimental studies of bacteria, sperm, and algae through to varied theoretical questions of low-Reynolds-number fluid mechanics. The biological and biophysical settings that drive this ongoing research are often confoundingly complex, a fact that has driven the development and use of simple models of microswimmers. In this talk, we'll motivate and explore some of these models, building up our intuition for Stokesian fluid dynamics and the behaviours of microscale swimmers. Using these models, we will showcase how we can often exploit separated scales present in these problems to reveal surprisingly simple emergent dynamics, ranging from coarse-grained flow profiles to predictions of globally attracting, long-term behaviours. In doing so, we'll also uncover a surprising cautionary tale, the root of which is captured by a single, elementary statement that nevertheless calls into question much of the intuition gained from commonplace models of microswimming. In particular, we'll see that a wave-of-the-hands, which I have been guilty of before, can drastically and qualitatively change the dynamics that simple models predict, and we'll see how such missteps can be addressed through systematic multiscale methods.
June 7, 2023, 10:00 AM - 10:50 AM PT
Professor Qixuan Wang, University of California, Riverside
Title: Cell fate regulation in hair follicles and wound healing
Abstract: Skin is the largest organ by surface area in the human body, and it is critical in shielding internal tissues. In addition, skin also hosts a large population of hair follicles, which produce hairs that serve as further protections to the body. To maintain the well-functioning of skin and its appendages, it requires proper regulations of skin cell fate decisions. In this talk, I will share my recent research results in cell fate regulations in hair follicles and wound healing. In hair follicles, we first develop a probabilistic Boolean model, developed from literature and then refined from single cell RNA sequencing data. Using this model, we investigate hair follicle matrix cells’ decisions when responding to various signals. Next, we develop a cell lineage population model and use it to investigate the hair follicle regenerative dynamics in response to ionizing radiation, exploring the key factors in the apoptosis pathways that may lead to either regeneration or degeneration in the hair follicle epithelium. Finally, I will share my recent research progress in agent-based models on two types of scars wound healing: keloid scars and hypertrophic scars.