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Links : UCR Interdisciplinary Center for Quantitative Modeling in Biology

UCR Math Department seminar

PDE and Applied Math Seminar

Please contact the organizer (jia.gou@ucr.edu) if you are interested in attending this seminar.

Both virtual and in-person talks will provide hybrid options for seminar participants. One might join the seminars in the designated room or online through Zoom.

Fall 2022 Schedule

Sep. 27th Organization meeting

Oct. 4th

Oct. 11th Dr. Yangyang Wang (University of Iowa) (virtual)

Oct. 18th Dr. Jun Allard (UC Irvine). (in-person)

Oct. 25th Dr. Alexandra Jilkine (University of Notre Dame). (virtual)

Nov. 1st Dr. Yiwei Wang (UC Riverside). (in-person)

Nov 8th Dr. Maria Abou Chakra (University of Toronto). (virtual)

Nov 15th Dr. Lifeng Han (FDA). (virtual)

Nov 22nd Dr. Zhe Fei (UC Riverside). (in-person)

Nov 29th Dr. Yihan Sun (UC Riverside). (in-person)

Future Talk Titles & Abstracts:

Speaker: Dr. Yihan Sun, UC Riverside

Date: Nov 29th, 2pm - 3:20pm (PT)

Title: A Work-Efficient Parallel Algorithm for Longest Increasing Subsequence

Abstract: This work studies parallel algorithms for the longest increasing subsequence (LIS) problem. Let n be the input size and k be the LIS length of the input. Sequentially, LIS is a simple textbook problem that can be solved using dynamic programming (DP) in $O(n\logn)$ work. However, parallelizing LIS is a long-standing challenge. We are unaware of any parallel LIS algorithm that has optimal $n\log n$ work and non-trivial parallelism (i.e., $o(n)$ or $\tilde{O}(k)$ span). Here, the work of a parallel algorithm is the total number of operations, and the span is the longest dependent instructions.

This paper proposes a parallel LIS algorithm that costs $O(n\log k)$ work, ˜$\tilde{O}(k)$ span, and $O(n)$ space, and is much simpler than the previous parallel LIS algorithms. We also generalize the algorithm to a weighted version of LIS, which maximizes the weighted sum for all objects in an increasing subsequence. Our weighted LIS algorithm has $O(n\log^2 n) work and $\tilde{O}(k)$ span.

We also implemented our parallel LIS algorithms. Due to simplicity, our implementation is lightweight, efficient, and scalable. On input size $10^9$, our LIS algorithm outperforms a highly-optimized sequential algorithm (with $O(n\log k)$ cost) on inputs with k<10^6. Our algorithm is also much faster than the best existing parallel implementation by Shen et al. on all input instances.

Bio: Yihan Sun is an Assistant Professor in the Computer Science and Engineering (CSE) Department at the University of California, Riverside (UCR). She received her Bachelor’s degree in Computer Science from Tsinghua University in 2014, and her Ph.D. degree from Carnegie Mellon University in 2019. Her research interests include broad topics in the theory and practice of parallel computing, including algorithms, data structures, frameworks, implementations, programming tools, and their applications. My work involves both designing algorithms with improved asymptotic bounds and developing efficient solutions to large-scale real-world problems.

Past Talk Titles & Abstracts:

Speaker: Dr. Zhe Fei, UC Riverside

Date: Nov 22nd, 2pm - 3:20pm (PT)

Title: Simultaneous Estimation and Inference Based on High Dimensional Regression Models

Abstract: When modeling big data with a large number of predictors, it is crucial to provide statistical inferences to the estimates or predictions, which would give the significance levels and confidence to the findings from the models. In other words, statistical inferences refer to the uncertainty measures of the model parameters of interest, including confidence intervals and p-values. I will introduce a resampling-based approach for high dimensional inference with generalized linear models and show the advantages both in practice and in theory.

Bio: Dr. Zhe Fei received his doctoral degree in Biostatistics from University of Michigan, Ann Arbor in 2019. He was a faculty member in the Biostatistics Department at UCLA before coming to UCR this summer. His research interests include statistical modeling for big data, with applications in genetics, epigenetics, medical images, etc; high dimensional inference, machine learning methods in public health and medical problems, among others.

Speaker: Dr. Lifeng Han, FDA

Date: Nov 15th, 2pm - 3:20pm (PT)

Title: Mathematical Modeling of Cancer Vaccines

Abstract: Cancer neoantigen vaccines have emerged as a promising approach to stimulate the immune system to fight cancer. We propose a simple model including key elements of cancer-immune interactions and conduct a phase plane analysis to understand immunological mechanisms of cancer neoantigen vaccines. Analytical results are obtained for two widely used functional forms that represent killing rate of tumor cells by immune cells: the law of mass action (LMA) and the dePillis-Radunskaya Law (LPR). We found that a slowly growing tumor can escape the immune surveillance when the LMA is used. The use of LPR makes tumor elimination possible, which lends support for using cancer vaccine as an adjuvant therapy. The implications of the model for vaccine dose schedule will be also discussed.

Bio: Lifeng Han is a postdoctoral fellow at the US Food and Drug Administration working on mathematical modeling of cancer immunotherapy. He obtained his PhD in applied math from Arizona State University. For his PhD research, he worked in the field of mathematical biology. His research interests are in mathematical modeling of cancer and its treatment with a focus on temporal and spatial dynamics that arises from time delay and stochasticity.

Speaker: Dr. Maria Abou Chakra, University of Toronto

Date: Nov 08th, 2pm - 3:20pm (PT)

Title: Control of tissue development and cell diversity by cell cycle dependent transcriptional filtering

Abstract: Cell cycle duration changes dramatically during development, starting out fast to generate cells quickly and slowing down over time as the organism matures. The cell cycle can also act as a transcriptional filter to control the expression of long gene transcripts which are partially transcribed in short cycles. Using mathematical simulations of cell proliferation, we identify an emergent property, that this filter can act as a tuning knob to control gene transcript expression, cell diversity and the number and proportion of different cell types in a tissue. Our predictions are supported by comparison to single-cell RNA-seq data captured over embryonic development. Additionally, evolutionary genome analysis shows that fast developing organisms have a narrow genomic distribution of gene lengths while slower developers have an expanded number of long genes. Our results support the idea that cell cycle dynamics may be important across multicellular animals for controlling gene transcript expression and cell fate.

Bio: Dr. Maria Abou Chakra is a Senior Research Associate at the University of Toronto. She is a theoretical biologist with a focus on complex biological phenomena. She has broad expertise in developing multiscale mathematical and computational models in the fields of evolutionary biology, behavioural ecology, theoretical morphology, and cell development. During her graduate degree she developed a mathematical model that predicted both growth and form of sea urchin skeletons. After graduating she worked at the Max Planck Institute for Evolutionary Biology, where she gained expertise in evolutionary game theory and developed various models that capture behaviors in complex social dilemmas such as Climate Change negotiations and Host parasite interactions. Currently she has applied her expertise to cell development and produced a 3D model that can explore and predict cell diversification in a developing tissue.

Speaker: Dr. Yiwei Wang, University of California, Riverside

Date: Nov 01st, 2pm - 3:20pm (PT)

Title: Energetic Variational Approach to Reaction Kinetics and Beyond

Abstract: In this talk, we will present an energetic variational formulation of the generalized mass-action kinetics for chemical reactions by building an analogy between chemical reactions and classical mechanics. Our general framework describes a reaction kinetics by an energy dissipation law, in which the choice of free energy determines an equilibrium, and the choice of dissipation (entropy production) determines the dynamics. Moreover, the conservation of species is embodied in the formulation. The variational framework enables us to couple chemical effects with other mechanical and thermal effects in a thermodynamically consistent way. If time permits, we will also discuss the structure-preserving numerical discretization to reaction-diffusion equation based on this variational formulation and several applications, in particle, a variational model of a reactive complex fluid, wormlike micellar solutions. The talk is mainly based on several joint works with Prof. Bob Eisenberg, Prof. Chun Liu, and Prof. Cheng Wang.

Speaker: Dr. Alexandra Jilkine, University of Notre Dame

Date: Oct 25th, 2pm - 3:20pm (PT)

Title: Modeling Diffusion-Coupled Oscillations in Cell Polarity

Abstract: One of the major tasks that a cell faces during its lifecycle is how to spatially localize its components. Correct spatial organization of various proteins (cellular polarity) is fundamental not only for the correct cell shape, but also to carry out essential cellular functions, such as the spatial coordination of cell division.We present a mathematical model of the core mechanism responsible for the regulation of polarized growth dynamics in the model organism, fission yeast. The model is based on the competition of growth zones of polarity protein Cdc42 localized at the cell tips for a common substrate (inactive Cdc42) that diffuses in the cytosol.

To explore the underlying mechanism for oscillations and the effect of diffusion and noise, we consider three model frameworks including a 1D deterministic model, a 2D deterministic model, and a stochastic model. We simulate and analyze these models using numerical bifurcation tools, PDEs, and stochastic simulation algorithms.

Speaker: Dr. Jun Allard, UC Irvine

Date: Oct 18th, 2pm - 3:20pm (PT)

Title: Optimal curvature in long-range cell-cell communication

Abstract: Cells in tissue can communicate long-range via diffusive signals. In addition, another class of cell-cell communication is by long, thin cellular protrusions that are ~100 microns (many cell-lengths) in length and ~100 nanometers (below traditional microscope resolution) in width. These protrusions have been recently discovered in many organisms, including nanotubes humans and airinemes in zebrafish. But, before establishing communication, these protrusions must find their target cell. Here we demonstrate airinemes in zebrafish are consistent with a finite persistent random walk model. We study this model by stochastic simulation, and by numerically solving the survival probability equation using Strang splitting. The probability of contacting the target cell is maximized for a balance between ballistic search (straight) and diffusive (highly curved, random) search. We find that the curvature of airinemes in zebrafish, extracted from live cell microscopy, is approximately the same value as the optimum in the simple persistent random walk model. We also explore the ability of the target cell to infer direction of the airineme’s source, finding the experimentally observed parameters to be at a Pareto optimum balancing directional sensing with contact initiation.

Collaborators: Sohyeon Park, Hyunjoong Kim, Yoichiro Mori, Dae Seok Eom

Speaker: Dr. Yangyang Wang, University of Iowa

Date: Oct 11th, 2pm - 3:20pm (PT)

Title: Mathematical analysis and models for understanding neural dynamics

Abstract: Central pattern generators (CPGs) are neural networks that are intrinsically capable of producing rhythmic patterns of neural activity and are adaptable to sensory feedback to produce robust motor behaviors such as breathing and swallowing. In this talk, I will discuss mathematical tools we developed for understanding intrinsic multiple-time-scale bursting dynamics in CPG neurons as well as robust responses of motor systems to external perturbations. Applications related to respiratory rhythms and motor control in the Aplysia feeding system will be highlighted.

Bio: Yangyang Wang is an assistant professor in the mathematics department at the University of Iowa, the Interdisciplinary Graduate Program in Neuroscience and the Iowa Neuroscience Institute. She received her PhD from the mathematics department at University of Pittsburgh in 2016. Then she worked as a postdoctoral fellow at the Mathematical Biosciences Institute at the Ohio State University during 2016-2019.

Her research interests include computational neuroscience and dynamical systems, with a focus on modeling and analyzing multiscale neural dynamics in central pattern generators, sensory feedback control in complex adaptive biological systems and network dynamics.