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Organizing Committee
Cleveland Clinic Lerner Institute
McGill University
Cleveland State University
University of Manitoba
Virginia Tech
Regis University
Smith College
Abstract
The Queer in Computational and Applied Mathematics (QCAM) workshop will be the first workshop to celebrate research advances and foster stronger research networks of LGBTQIA+ mathematicians specializing in computational and applied mathematics. Goals of QCAM are to support LGBTQIA+ academics through mentoring and research opportunities, as well as providing a safe space for researchers across the subfields of computational and applied mathematics to connect, collaborate, and build support networks within the field. In addition, QCAM intends to address issues of diversity, equity, and inclusion in mathematics pertaining to LGBTQIA+ people, especially those with intersectional identities. This conference will be open to all and will ideally engage the wider mathematical audience of LGBTQIA+ allies to develop a community of support.
The scientific program will have invited speakers and contributed sessions that span the field of computational mathematics, with a planned focus on research in computational methods which may include the following fields:
- Mathematical Biology, Ecology, Epidemiology, and/or Oncology;
- Fluids, Materials, and/or Mathematical Physics;
- Data Science;
- Numerical Analysis and Computational Science; and
- Applied Algebra, Discrete Mathematics, Geometry, and/or Topology.
These general frameworks will be the basis for the creation of working groups during the conference. In these working groups, QCAM participants will be invited to develop supportive and collaborative research networks with other participants of differing career stages. Furthermore, QCAM will include programming that is dedicated within the LGBTQIA+ community and at the intersection with other underrepresented groups, as well issues pertaining to the leaky STEM pipeline for LGBTQIA+ individuals.
The scientific program will have invited speakers and contributed sessions that span the field of computational mathematics, with a planned focus on research in computational methods which may include the following fields:
- Mathematical Biology, Ecology, Epidemiology, and/or Oncology;
- Fluids, Materials, and/or Mathematical Physics;
- Data Science;
- Numerical Analysis and Computational Science; and
- Applied Algebra, Discrete Mathematics, Geometry, and/or Topology.
These general frameworks will be the basis for the creation of working groups during the conference. In these working groups, QCAM participants will be invited to develop supportive and collaborative research networks with other participants of differing career stages. Furthermore, QCAM will include programming that is dedicated within the LGBTQIA+ community and at the intersection with other underrepresented groups, as well issues pertaining to the leaky STEM pipeline for LGBTQIA+ individuals.
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Workshop Schedule
Monday, June 24, 2024
1:00 - 1:30 PM EDT
Welcome
11th Floor Lecture Hall
1:30 - 2:15 PM EDT
From Dynamics to Algorithms for Optimization and Sampling
11th Floor Lecture Hall
Speaker
Andre Wibisono, Yale University
Session Chair
Rustum Choksi, McGill University
Abstract
Optimization and sampling are fundamental algorithmic tasks in machine learning and in many applications. In this talk, we will survey recent results in the design and analysis of algorithms for optimization and sampling via a continuous-time perspective, and via the perspective of sampling as optimization in the space of distributions. Many algorithms in discrete time can be derived as discretization of continuous-time dynamics; for example, gradient descent is a discretization of gradient flow, and momentum method is a discretization of accelerated gradient flow. This perspective provides a systematic way to design algorithms via discretizing continuous-time dynamics, and to derive convergence guarantees via translating the continuous-time properties. In sampling, many random walks or Markov chain methods can be viewed as optimization algorithms in the space of probability distributions; for example, the Langevin dynamics is implementing the gradient flow for minimizing relative entropy. This perspective provides a systematic way to analyze the mixing times of Markov chains via translating the optimization techniques, and to design new sampling algorithms via translating the optimization principles to the space of distributions.
2:30 - 2:45 PM EDT
Computing Barycenters and Applications in Data Science
Contributed Talk - 11th Floor Lecture Hall
Speaker
Stephan Patterson, Louisiana State University in Shreveport
Session Chair
Rustum Choksi, McGill University
Abstract
A barycenter is, informally, a weighted average of a set of probability measures. Finding barycenters is of interest in a variety of fields; however, the barycenter problem has recently been shown to be NP-hard. Barycenters can be computed using linear programming, but designing practical exact and approximate algorithms remains an active area of research. In this talk, I will describe the linear programming models that form the basis of the computations and highlight their uses in data science, such as image and natural language processing.
2:45 - 3:00 PM EDT
Strong Data Processing Inequalities and Langevin Dynamics
Contributed Talk - 11th Floor Lecture Hall
Speaker
Siddharth Mitra, Yale University
Session Chair
Rustum Choksi, McGill University
Abstract
The data processing inequality is a fundamental concept in information theory that states that relative entropy, mutual information, and other important quantities are non-increasing along Markov chains. Strong data processing inequalities check if these quantities are strictly decreasing, and if so, quantify the decrease. In this talk, we will review these information theoretic concepts and present a way to show strong data processing inequalities for some important Markov chains, such as the Langevin dynamics. As an application, by studying the strong data processing inequality in mutual information, we’ll be able to quantify the rate at which we get independent samples along these Markov chains.
3:00 - 3:15 PM EDT
Using projected multi-reference alignment to study challenges in cryo-EM
Contributed Talk - 11th Floor Lecture Hall
Speaker
Tait Weicht, University of California, Davis
Session Chair
Rustum Choksi, McGill University
Abstract
Cryogenic electron microscopy (cryo-EM) is one particular imaging technique used to determine the structure of a molecule. One goal has been to develop an algorithm based on the method of moments that can recover such structure. We will explain some of the advantages of such an approach; however, an efficient and robust algebraic algorithm that can determine multiple molecular structures from cryogenic electron micrographs remains elusive.
Time permitting we, will explore a toy model, projected multi-reference alignment, developed to capture some of the fundamental challenges in developing such an algorithm. We will present a method to recursively decompose the problem into sub-problems and the larger implications for solving these types of problems.
3:15 - 3:30 PM EDT
Vertex clustering in diverse dynamic networks
Contributed Talk - 11th Floor Lecture Hall
Speaker
Devavrat Dabke, Level Ventures
Session Chair
Rustum Choksi, McGill University
3:30 - 3:45 PM EDT
Multiscale perspectives on the self-assembly of bicontinuous networks from computational geometry
Contributed Talk - 11th Floor Lecture Hall
Speaker
Michael Dimitriyev, Texas A&M University
Session Chair
Rustum Choksi, McGill University
Abstract
Under conditions of thermodynamic equilibrium, amphiphilic molecules often arrange into a variety of nanoscale structures, including complex "bicontinuous network" phases, consisting of pairs of intercatenated domains that can span large, well-ordered domains. Despite the complex morphologies of these network phases, they possess robust formation pathways in biological systems and synthetic versions, mainly formed from block copolymers, have attracted interest for use in emerging technologies. However, theoretical and computational efforts to understand network phases have long struggled due to the large number of molecules involved in the assembly of a single repeat unit under strong space-filling constraints. We found that the geometry of so-called "terminal boundaries" play a previously-unrecognized role in determining the stability of these phases, resolving a long-standing question about the asymptotic stability of these phases. Our approach relies on the medial axis transform of computational geometry to generate close approximations to these terminal boundaries, in the process yielding space-filling tessellations that serve as coarse-grained molecular environments that are consistent with packing constraints. The result is a multiscale picture of network phases that bridges molecular details with interface and domain geometry, pointing towards a way to relate large-scale structure and structural changes to alterations in molecular packing.
3:45 - 4:00 PM EDT
The Winning Pursuit-Evasion Strategies in Dynamic Systems
Contributed Talk - 11th Floor Lecture Hall
Speaker
Mehdi Salimi, Kwantlen Polytechnic University
Session Chair
Rustum Choksi, McGill University
Abstract
This research focuses on a pursuit-evasion differential game set in a two-dimensional space, incorporating a hybrid system of dynamics. The game involves a pursuer with non-inertial characteristics and an evader with inertial properties, with both players' controls constrained integrally. The duration of the game, denoted as T, remains constant, and the evader's position at time T adheres to a phase constraint. We delineate the attainability domains for both players and devise a winning strategy for the pursuer, ensuring the capture of the evader. Additionally, we demonstrate the validity of our devised strategy.
4:00 - 5:00 PM EDT
Working Groups
Group Work - 11th Floor Collaborative Space
Tuesday, June 25, 2024
9:00 - 9:45 AM EDT
From Bytes to Rights: The Fight for Justice in the Era of Data
11th Floor Lecture Hall
Speaker
Chad Topaz, Institute for the Quantitative Study of Inclusion, Diversity, and Equity
Session Chair
Hermie Monterde, University of Manitoba
Abstract
Tens of millions of people in the United States have been directly impacted by the criminal justice system, with nearly half the population affected through close familial or social ties. Alongside the direct harm inflicted by the system, an insidious challenge arises: the system's opaque nature makes pinpointing the specific loci of harm complex and elusive. Echoing the words of civil rights pioneer Ida B. Wells, who stated that "the way to right wrongs is to turn the light of truth upon them," this talk will showcase how data science can be harnessed to expose racial injustice. It will feature case studies spanning various scales and stages of the criminal justice system, including policing in the small municipality of Williamstown, Massachusetts; sentencing across all 94 federal district courts; and the use of criminal risk algorithms in Florida. These examples underscore the pivotal role of data science tools in fostering transparency and advancing justice.
10:00 - 10:30 AM EDT
Coffee Break
11th Floor Collaborative Space
10:30 - 10:45 AM EDT
Agent-Based and Continuous Models of Locust Swarms
Contributed Talk - 11th Floor Lecture Hall
Speaker
Andrew Bernoff, Harvey Mudd College
Session Chair
Hermie Monterde, University of Manitoba
Abstract
Locust swarms pose a major threat to agriculture, notably in northern Africa, the Middle East, and Australia. In the early stages of aggregation, juvenile locusts form hopper bands. These are coordinated groups that march in columnar structures that are often kilometers long and may contain millions of individuals. In later stages locust swarms become airborne and can decimate crops over hundreds of kilometers potentially leading to famine and widespread ecological disruption. In this talk I will describe two strategies for modeling locust swarms. Agent-based models (ABMs) yield ordinary differential equations for groups of interacting individuals and are easy to implement but challenging to analyze. Homogenizing these models replaces the individuals with population densities that are governed by partial differential equations (PDEs) which are more difficult to simulate but which can be analyzed via dynamical system methods. Finally I'll discuss the challenges of tuning these models with experimental observations.
10:45 - 11:00 AM EDT
Adaptive Stimulations in a Biophysical Network Model of Parkinson's Disease
Contributed Talk - 11th Floor Lecture Hall
Speaker
Tom Stojsavljevic, Beloit College
Session Chair
Hermie Monterde, University of Manitoba
Abstract
Deep brain stimulation (DBS)—through a surgically implanted electrode to the subthalamic
nucleus (STN)—has become a widely used therapeutic option for the treatment of Parkinson’s disease and other neurological disorders. The standard conventional high-frequency stimulation (HF) that is currently used has several drawbacks. To overcome the limitations of HF, researchers have been developing closed-loop and demand-controlled, adaptive stimulation protocols wherein the amount of current that is delivered is turned on and off in real-time in accordance with a biophysical signal. Computational modeling of DBS in neural network models is an increasingly important tool in the development of new protocols that aid researchers in animal and clinical studies. In this computational study, we seek to implement a novel technique of DBS where we stimulate the STN in an adaptive fashion using the interspike time of the neurons to control stimulation. Our results show that our protocol eliminates bursts in the synchronized bursting neuronal activity of the STN, which is hypothesized to cause the failure of thalamocortical neurons (TC) to respond properly to excitatory cortical inputs. Further, we are able to significantly decrease the TC relay errors, representing potential therapeutics for Parkinson’s disease.
11:00 - 11:15 AM EDT
Modeling and simulation of the cytoskeleton: the role of friction
Contributed Talk - 11th Floor Lecture Hall
Speaker
Mariya Savinov, New York University
Session Chair
Hermie Monterde, University of Manitoba
Abstract
Many essential cellular processes depend on subcellular structures capable of generating active forces. In particular, actomyosin networks and their contraction are central for cell organization, shape, and motility. However, the relative importance of active local stresses, network deformation, external friction, and geometry is still not well understood.
In vitro experiments with reconstituted actomyosin networks on micropatterned surfaces have shown a robust contraction bias to higher friction surfaces, while an insensitivity to the myosin motor distribution driving the dynamics. We model the actomyosin network as a 2D deformable viscoelastic cable-network material with active contractile stresses generated by myosin motors advected by the deforming network. The internal network forces are then balanced by external drag forces. Through analysis and simulation, we find that our model reproduces key experimental results. Notably, the model explains why the friction, not myosin, pattern determines the compaction point. Our findings shed light on the importance of mechanical effects over biochemical ones. Though contraction is local and randomly initialized, the external friction pattern and network connectedness lead to robust global behaviors on the cellular level.
11:15 - 11:30 AM EDT
Gut Instincts: Understanding Spontaneous Contractions in the Colon
Contributed Talk - 11th Floor Lecture Hall
Speaker
Andrea Welsh, University of Pittsburgh
Session Chair
Hermie Monterde, University of Manitoba
Abstract
Colon motility, the spontaneous self-generated movement and motion of the colon muscle and its cells, is produced by activity in different types of cells such as myenteric neurons of the enteric nervous system (ENS), neurons of the autonomic nervous system (ANS) and interstitial cells of Cajal (ICC). Two colon motor patterns measured experimentally are colonic motor complexes (CMC) often associated with the propulsion of fecal contents, and ripple contractions which are involved in mixing and absorption. How ICC and neurons of the ENS and ANS interact to initiate and influence colon motility is still not completely understood. This makes it difficult to develop new therapies to restore function in pathological conditions. We aim to create a model that reproduces the global dynamics observed in optogenetic and calcium measurements of mouse colons. In particular, we focus on how certain coupling parameters affect the speed and frequency of the observed CMC and ICC waves and how other parameters affect the robustness of the model.
11:30 - 11:45 AM EDT
The role of feature heterogeneities on optimal management strategies
Contributed Talk - 11th Floor Lecture Hall
Speaker
Michael Kelly, Transylvania University
Session Chair
Hermie Monterde, University of Manitoba
Abstract
Spatial fishery models are discussed with an emphasis on optimal management strategies. The models incorporate nonlinear, parabolic partial differential equations with density-dependence in the growth rate of the fish stock on a spatial domain. The role of feature heterogeneities such as habitat properties, spatial boundaries, and destructive fishing practices will be presented. The objective is to find the dynamic distribution of harvest effort that maximizes the discounted net present value of stock while minimizing costs. Optimal management strategies are found numerically.
11:45 AM - 12:00 PM EDT
Transcriptional trajectory inference of image-localized high-grade glioma biopsies reveals distinct population ecologies and associated enriched pathways
Contributed Talk - 11th Floor Lecture Hall
Speaker
Lee Curtin, Mayo Clinic
Session Chair
Hermie Monterde, University of Manitoba
Abstract
The intra- and inter-patient heterogeneity in high-grade glioma (HGG) continues to contribute to its poor prognosis. Clinical biopsies are often harvested from limited regions and typically are not image localized. Thus, they fail to capture the diversity within tumor regions, immune expression or normal cell abundances that play key roles in tumor development. It is important to gain an understanding of these subpopulation ecologies, their spatial resolution, and interactions between them that may then be exploited for future therapeutic benefit. Further, these may differ by patient characteristics such as sex, age at diagnosis and treatment status. Using an ongoing image-localized biopsy collection protocol, we have so far evaluated the bulk transcriptomics of 202 multi-regional biopsies from 58 patients to characterize HGG heterogeneity. These samples were processed through Monocle, a reverse graph embedding algorithm that groups samples into states and orders them along developmental trajectories. Deconvolution methods were previously used to predict relative abundances of 7 normal, 6 glioma, and 5 immune cell subpopulations for each sample, which we have now overlaid on the Monocle graph. Monocle classified HGG into 4 main states along a three-pronged trajectory. These states reveal distinct population ecologies with associated enriched gene pathways. We also note significant immune pathway enrichments that differ between state and patient-reported sex. Together, these algorithms reveal a simple transcriptomic trajectory that helps us understand the development and evolution of HGG. Characterizing the in vivo diversity within and between high grade gliomas is important for understanding prognosis, stratifying future treatments and ultimately improving patient outcome.
12:00 - 12:10 PM EDT
Group Photo (Immediately After Talk)
11th Floor Lecture Hall
12:10 - 1:30 PM EDT
Lunch/Free Time
1:30 - 2:15 PM EDT
Every Patient Deserves their own Equation
11th Floor Lecture Hall
Virtual Speaker
Kristin Swanson, Mayo Clinic
Session Chair
Rowan Barker-Clarke, Cleveland Clinic Lerner Institute
2:30 - 3:00 PM EDT
Coffee Break
11th Floor Collaborative Space
3:00 - 5:00 PM EDT
Working Groups
Group Work - 11th Floor Lecture Hall
5:00 - 6:30 PM EDT
Reception
11th Floor Collaborative Space
Wednesday, June 26, 2024
9:00 - 9:45 AM EDT
Discrete statistics of permutations and their generalizations
11th Floor Lecture Hall
Speaker
Pamela E. Harris, University of Wisconsin Milwaukee
Session Chair
Alexander Hoover, Cleveland State University
Abstract
The study of discrete statistics has a long history and many connections to numerous areas of mathematics. In this talk, we introduce discrete statistics such as descents, ascents, peaks, and pinnacles of permutations and provide a sample of known results. We then focus on a superset of permutations called parking functions, give a summary of what is known about their discrete statistics, and provide open problems for us to explore.
10:00 - 10:30 AM EDT
Coffee Break
11th Floor Collaborative Space
10:30 - 10:45 AM EDT
Probabilistic Computing? Bet on Dice.
Contributed Talk - 11th Floor Lecture Hall
Speaker
J. Darby Smith, Sandia National Laboratories
Session Chair
Alexander Hoover, Cleveland State University
Abstract
Operations in biological brains are probabilistic and hence stochasticity has become intertwined with brain-inspired hardware, algorithms, and devices. Within this sea of stochasticity, we find a growing trend of new probabilistic computing devices for generating true random numbers. The ability to quickly and efficiently generate true random numbers at a device level suggests a future where stochastic elements are ubiquitous in computing. That same trend of new computing devices is focused largely on binary or two-state devices, i.e. coin flips. However, we find that there are inherent benefits to multi-state random draws, i.e. dice rolls. In this talk, we will revisit classic distribution results for distributions induced by Bernoulli random variables and extend them to the multi-state dice roll case, providing a proof of a ‘folk theorem.’ We analyze the benefits of dice compared to coins through simulation of a sampling neural network. Additionally, we showcase benefits from a real two-state stochastic tunnel diode device interpreted as a die roll.
10:45 - 11:00 AM EDT
Adaptive optimized Schwarz methods
Contributed Talk - 11th Floor Lecture Hall
Speaker
Conor McCoid, Université Laval
Session Chair
Alexander Hoover, Cleveland State University
Abstract
Optimized Schwarz methods use Fourier analysis or similar to find transmission conditions between subdomains that provide faster convergence over standard Schwarz methods. However, this requires significant upfront analysis of the operator, and may not be straightforward for all problems. This work presents black box methods for adaptively optimizing the transmission conditions, which is equivalent to a Krylov subspace method.
11:00 - 11:15 AM EDT
Row-aware Randomized SVD with applications
Contributed Talk - 11th Floor Lecture Hall
Speaker
Davide Palitta, Alma Mater Studiorum, Universita' di Bologna
Session Chair
Alexander Hoover, Cleveland State University
Abstract
After briefly recalling state-of-the-art procedures, either deterministic or randomized, for computing an SVD-type approximation of a tall matrix A, I will introduce a novel randomization-based algorithm that improves the standard Randomized Singular Value Decomposition (RSVD). Most significantly, this new approach, the Row-aware RSVD (R-RSVD), explicitly constructs information from the row space of A. This leads to better approximations to Range(A) while maintaining the same computational cost of RSVD. The efficacy of the R-RSVD scheme is supported by both robust theoretical results and extensive numerical experiments. Furthermore, I present an alternative algorithm inspired by R-RSVD, capable of achieving comparable accuracy despite utilizing only a subsample of the rows of A, resulting in a significantly reduced computational cost. This method, named the Subsample Row-aware RSVD (Rsub-RSVD), is supported by a weaker error bound compared to the ones derived for R-RSVD, but still meaningful as it ensures that the error remains under control. Additionally, numerous experiments demonstrate that the Rsub-RSVD trend is akin to the one attained by RSVD when the subsampling parameter is on the order of n, for a m×n A, with m >> n. Finally, I will consider the application of these schemes in the computation of DEIM-induced CUR decompositions.
This talk is based on a joint work with Sascha Portaro (University of Bologna).
11:15 - 11:30 AM EDT
Graph ‘texture’ features, using image analysis methods to derive new summary statistics for complex graphs.
Contributed Talk - 11th Floor Lecture Hall
Speaker
Rowan Barker-Clarke, Cleveland Clinic Lerner Institute
Session Chair
Alexander Hoover, Cleveland State University
Abstract
Image texture features, such as those derived by Haralick et al, are widely used for image classification across fields including cancer research. We demonstrate how analogous texture features can be derived for graphs and networks. We also illustrate how these new metrics summarize graph-structured data and may aid comparative graph studies including evaluating dysregulation in gene expression networks. Node weight co-occurrence matrices for graphs are generated by summing frequencies of pairs of neighboring nodes in the graph. These texture features form novel second-order summary features for networks or graphs with ordered node labels. Our novel graph 'texture' features are shown to correspond to different graph structure and node label distributions. Just like equivalent image textures, the metrics are sensitive to discretization parameters and noise in node labels. In the complex cancer informatics setting, evolutionary analyses and drug response prediction are two examples where new network science approaches like this may prove fruitful.
11:30 - 11:45 AM EDT
Quantum state transfer on graphs
Contributed Talk - 11th Floor Lecture Hall
Speaker
Hermie Monterde, University of Manitoba
Session Chair
Alexander Hoover, Cleveland State University
Abstract
Quantum states carry information, and in order to construct an operational quantum computer, it is important to understand how quantum states travel across a network. In this talk, we survey old and new results in the study of quantum state transfer that are of interest to both physicists and mathematicians. Our focus is to highlight the role of spectral and algebraic graph theory in this study. We also discuss some open problems.
11:45 AM - 12:00 PM EDT
Guiding Stress : From Pentamodes to Cable Webs to Masonry Structures
Contributed Talk - 11th Floor Lecture Hall
Speaker
John Patton, University of Utah
Session Chair
Alexander Hoover, Cleveland State University
Abstract
Pentamode materials are a class of materials that are useful for guiding stress. In particular, they have been proposed for acoustic cloaking by guiding stress around objects, and have been physically constructed. A key feature of pentamode materials is that each vertex in the material is the junction of 4 double cone elements. Thus the tension in one element determines the tension in the other elements, and by extension uniquely determines the stress in the entire metamaterial. Here we show how this key feature can be extended to discrete wire networks, supporting forces at the terminal nodes and which may have internal nodes where no forces are applied. In usual wire or cable networks, such as in a bridge or bicycle wheel, one distributes the forces by adjusting the tension in the wires. Here our discrete networks provide an alternative way of distributing the forces through the geometry of the network. In particular the network can be chosen so it is uniloadable, i.e. supports only one set of forces at the terminal nodes. Such uniloadable networks provide the natural generalization of pentamode materials to discrete networks. We extend such a problem to compression-only 'strut nets' subjected to fixed and variable nodal loads. These systems provide discrete element models of masonry bodies, which lie inside the polygon/polyhedron with vertices at the points of application of the given forces ('underlying masonry structures'). In particular, we solve the two-dimensional problem where one wants the strut net to avoid a given set of obstacles, and also allow some of the forces to be reactive ones. This is joint work with Ada Amendola, Guy Bouchitt{\'e}, Andrej Cherkaev, Antonio Fortunato, Fernando Fraternali, Ornella Mattei, and Pierre Seppecher.
12:00 - 1:30 PM EDT
EDI Theme
Working Lunch - 11th Floor Collaborative Space
1:30 - 2:30 PM EDT
Working Groups
Group Work - 11th Floor Collaborative Space
2:30 - 3:00 PM EDT
Coffee Break
11th Floor Collaborative Space
3:00 - 5:00 PM EDT
EDI Panel
Panel Discussion - 11th Floor Lecture Hall
Session Chair
Rustum Choksi, McGill University
Session Chair
Hermie Monterde, University of Manitoba
Thursday, June 27, 2024
9:00 - 9:45 AM EDT
Key Factors and Parameter Ranges for Immune Control of Equine Infectious Anemia Virus Infection
11th Floor Lecture Hall
Speaker
Stacey Smith?, University of Ottowa
Session Chair
Michael Robert, Virginia Tech
Abstract
Equine Infectious Anemia Virus (EIAV) is an important infection in equids, and its similarity to HIV creates hope for a potential vaccine. We analyze a within-host model of EIAV infection with antibody and cytotoxic T lymphocyte (CTL) responses. In this model, the stability of the biologically relevant endemic equilibrium, characterized by the coexistence of long-term antibody and CTL levels, relies upon a balance between CTL and antibody growth rates, which is needed to ensure persistent CTL levels. We determine the model parameter ranges at which CTL and antibody proliferation rates are simultaneously most influential in leading the system towards coexistence and can be used to derive a mathematical relationship between CTL and antibody production rates to explore the bifurcation curve that leads to coexistence. We employ Latin hypercube sampling and least squares to find the parameter ranges that equally divide the endemic and boundary equilibria. We then examine this relationship numerically via a local sensitivity analysis of the parameters. Our analysis is consistent with previous results showing that an intervention (such as a vaccine) intended to control a persistent viral infection with both immune responses should moderate the antibody response to allow for stimulation of the CTL response. Finally, we show that the CTL production rate can entirely determine the long-term outcome, regardless of the effect of other parameters, and we provide the conditions for this result in terms of the identified ranges for all model parameters.
10:00 - 10:30 AM EDT
Coffee Break
11th Floor Collaborative Space
10:30 - 10:45 AM EDT
A first-principles geometric model for dynamics of motor-driven centrosomal asters
Contributed Talk - 11th Floor Lecture Hall
Speaker
Yuan Young, New Jersey institute of technology
Session Chair
Michael Robert, Virginia Tech
Abstract
The centrosomal aster is a mobile and adaptable cellular organelle that exerts and transmits forces necessary for tasks such as nuclear migration and spindle positioning. Recent experimental and theoretical studies of nematode and human cells demonstrate that pulling forces on asters by cortically anchored force generators are dominant during such processes. Here we present a comprehensive investigation of a first-principles model of aster dynamics, the S-model (S for stoichiometry), based solely on such forces. The model evolves the astral centrosome position, a probability field of cell-surface motor occupancy by centrosomal microtubules (under an assumption of stoichiometric binding), and free boundaries of unattached, growing microtubules. We show how cell shape affects the stability of centering of the aster, and its transition to oscillations with increasing motor number. Seeking to understand observations in single-cell embryos, we use highly accurate simulations to examine the nonlinear structure of the bifurcations, and demonstrate the importance of binding domain overlap to interpreting genetic perturbation experiments. More generally, we find a rich dynamical landscape, dependent upon cell shape, including internal aster orbits that arise as traveling waves. Finally, we explore the interactions of multiple asters, unveiling novel phenomena such as centrosome relaxation to the vertices of platonic solids. Our findings align with experimental observations, providing insights into the mechanisms governing spindle positioning and cell division dynamics.
10:45 - 11:00 AM EDT
Using evolutionary methods to bridge data science and clinical research to describe and subvert cancer progression and therapeutic resistance.
Contributed Talk - 11th Floor Lecture Hall
Speaker
NIc Fisk, University of Rhode Island
Session Chair
Michael Robert, Virginia Tech
Abstract
Cancer is a complex family of diseases with high stakes and is on track to overtake heart disease as the leading cause of death in the United States in the next decade. The majority of these moralities are due to metastatic progression and spread of tumors which are often resistant to first-line therapy. Due to the complexity and urgency for better understanding and subverting this evolving scourge, researchers have approached the study of cancer origination, progression, and acquisition of resistance using myriad techniques developed across the diverse biological, medical, and physical sciences alongside advancement in mathematical, informatic, and computational methods to make sense of the results of these experiments. However, like all tools of research, these informatics tools must be fit-for-purpose to maximize their utility in the shared endeavor of understanding and undermining cancer progression. In this work, we demonstrate that explicit inclusion of evolutionary theory in informatics approaches to the study of cancer improves the predictive power of models, generates more interpretable and actionable findings, and—due to the fundamental nature of the theory of evolution to biology—can be used pan-cancer, across scales (i.e., individual to catchment), and especially thru time. We further demonstrate the translational utility of bridging cancer biology and informatics by identifying orthogonal immunotherapuetic targets.
11:00 - 11:15 AM EDT
Uniform Boundedness and Long-time Behavior of Solutions to SI Models with Intermittent Treatment
Contributed Talk - 11th Floor Lecture Hall
Speaker
Haseeb Ansari, University of Houston
Session Chair
Michael Robert, Virginia Tech
Abstract
We study a dynamic SI (Susceptible-Infected) model with an intermittent treatment term. Results are given for the cases when no components diffuse, and all components diffuse. In each case, we prove uniform boundedness of solutions and investigate their long-time behavior.
11:15 - 11:30 AM EDT
Analytical Predictions of Epidemic Dynamics on Sparse Locally Tree-Like Networks
Contributed Talk - 11th Floor Lecture Hall
Speaker
Juniper Cocomello, Brown University
Session Chair
Michael Robert, Virginia Tech
Abstract
Formulating and analyzing tractable models of infectious disease spreading is a public health priority, with applications that extend to a variety of phenomena characterized by the spreading of information, such as the propagation of blackouts, computer viruses and rumors. We study compartmental models of epidemics with non-fading immunity, such as the SIR and SEIR models, with possibly time-varying rates, on a class of networks that are locally tree-like, which includes sparse Erdős-Rènyi random graphs, random regular graphs, and other configuration models. We identify tractable systems of ODEs that exactly describe the dynamics of such process in a suitable asymptotic regime in which the population size goes to infinity. We characterize the outbreak size of the SIR and SEIR models as the unique zero of an explicit functional. We also demonstrate via simulations the efficacy of our approximations for populations of moderate size.
11:30 - 11:45 AM EDT
Magnetic skyrmions under confinement
Contributed Talk - 11th Floor Lecture Hall
Speaker
Theresa Simon, University of Münster
Session Chair
Michael Robert, Virginia Tech
Abstract
In extremely thin ferromagnetic films, an additional interaction, the so-called Dzyaloshinskii-Moriya interaction (DMI), arises in the micromagnetic energy. In such materials, topoligically nontrivial, point-like configurations of the magnetization called magnetic skyrmions are observed, which are of great interest in the physics community due to possible applications in high-density data storage.
We characterize skyrmions as minimizers of a micromagnetic energy augmented by DMI on bounded domains with Dirichlet data and describe their asymptotics in the regime of dominating exchange (or Dirichlet) energy. As in this limit skyrmions collapse into a point, we rely on a quantitative rigidity result for degree 1 harmonic maps into the two-dimensional sphere.
11:45 AM - 12:00 PM EDT
A Geometric Perspective on Computational Mechanics
Contributed Talk - 11th Floor Lecture Hall
Speaker
Eitan Grinspun, University of Toronto
Session Chair
Michael Robert, Virginia Tech
Abstract
The connection between geometry and mechanics has been explored for centuries. How this connection shapes computation is a question we are just beginning to explore.
If computers can predict how materials move and deform, they can help us to understand, predict, and manipulate the physical world. Our group develops models and algorithms that capture the characteristic behavior of a mechanical system. We focus on the geometry behind the physics. We build a discrete geometric picture from the ground up, mimicking the axioms, structures, and symmetries of the smooth setting. The result is a readily computable model that preserves invariants and conservation laws. With applications spanning flagellar propulsion to robotics, we are learning that this geometric approach can impact consumer product design, medical research, engineering design and basic scientific research.
12:00 - 12:15 PM EDT
Active nematic fluids on arbitrary manifolds
Contributed Talk - 11th Floor Lecture Hall
Speaker
David Saintillan, UC San Diego
Session Chair
Michael Robert, Virginia Tech
Abstract
The dynamics of biological surfaces often involves the coupling of internal active processes with in-plane orientational order and hydrodynamic flows. Such active surfaces play a key role in various biological processes, from cytokinesis to tissue morphogenesis. In this talk, we present a novel computational approach for the simulation of active nematic fluids confined to Riemannian manifolds. The fluid velocity and nematic order parameter are represented as the sections of the complex line bundle of a two-manifold. Using a geometric approach based on the Levi-Civita connection, we introduce a coordinate-free discretization method that preserves the continuous local-to-global theorems in differential geometry. Furthermore, we establish a nematic Laplacian on complex functions that can accommodate fractional topological charges through the covariant derivative on the complex nematic representation. Advection of the nematic field is formulated based on the Lie derivative, resulting in a stable geometric semi-Lagrangian discretization scheme for transport by the flow. The proposed surface-based method offers an efficient and stable means to investigate the influence of local curvature and topology on the hydrodynamics of active nematic systems, and we illustrate its capabilities by simulating active flows on a range of surfaces of increasing complexity.
12:15 - 1:30 PM EDT
Lunch/Free Time
1:30 - 2:15 PM EDT
Storm Surge Modeling with Compound Flood Effects
11th Floor Lecture Hall
Speaker
Clint Dawson, University of Texas at Austin
Session Chair
Becca Thomases, Smith College
Abstract
In this talk we will describe mathematics, software, and applications of coastal ocean models to hurricane storm surge and compound flooding. Applications include validation studies, forecasting, and futurecasting. Recent research on compound flood modeling will be highlighted.
2:30 - 3:00 PM EDT
Coffee Break
11th Floor Collaborative Space
3:00 - 5:00 PM EDT
Working Groups
Group Work - 11th Floor Lecture Hall
Friday, June 28, 2024
9:00 - 9:45 AM EDT
Shape optimization and shapeshifting in soft matter
11th Floor Lecture Hall
Speaker
Timothy Atherton, Tufts University
Session Chair
Alexander Hoover, Cleveland State University
Abstract
Soft materials are ubiquitous in biology and are ideal candidates for advanced engineering applications including soft, biomimetic robots, self-building machines, shape-shifters, artificial muscles, and chemical delivery packages. In many of these, the material must make a dramatic change in shape with an accompanying re-ordering of the material; in others changes in the ordering can be used to drive or even interrupt shape change. To optimize the materials and structures, it is necessary to have a detailed understanding of how the microstructure and macroscopic shape co-evolve. In this talk, I will present my group's mathematical modelling work on shape shifting in emulsions, liquid crystals and other soft materials. To develop the description, we draw upon differential geometry, topology, optimization theory and computer simulations. I will also describe a second research direction: Elucidating the climate for LGBTQ+ people in Physics & Astronomy, and present ideas and opportunities for the Applied Math community to better support queer people.
10:00 - 10:30 AM EDT
Coffee Break
11th Floor Collaborative Space
10:30 AM - 12:00 PM EDT
Town Hall
Other - 11th Floor Lecture Hall
Session Chair
Alexander Hoover, Cleveland State University
12:00 - 1:30 PM EDT
Networking Lunch
Working Lunch - 11th Floor Collaborative Space
1:30 - 2:30 PM EDT
Working Groups
Group Work - 11th Floor Collaborative Space
2:30 - 3:00 PM EDT
Coffee Break
11th Floor Collaborative Space
3:00 - 4:30 PM EDT
Working Groups
Group Work - 11th Floor Lecture Hall
Projects
MetaMath: Quantifying the Mathematical Sciences Community
Ron Buckmire (Occidental College)
The MetaMath working group at its heart is a mathematical modeling enterprise and quantitative justice project; MetaMath uses tools, techniques, and topics from the mathematical sciences to analyze the mathematical sciences community itself, in order to enhance social justice. MetaMath builds upon similar work called “the Science of Science” (or SciSci) that uses scientific methods to analyze how science is done. Because MetaMath originated at a data science and social justice workshop (at ICERM in summer 2022 and summer 2023), our initial research projects are generally classified as data science but in the spirit of mathematical modeling, we welcome anyone who wants to ``use math to analyze Math.” Participation in MetaMath is very flexible: (1) propose new MetaMath problems or projects; 2) work on pending MetaMath projects that have been identified but not yet begun; or 3) join work on ongoing MetaMath projects.
Modeling the effects of climate change on equine infectious anemia virus
Stacey Smith? (University of Ottowa)
Equine infectious anemia virus (EIAV) is a vector-borne retrovirus in both wild and domestic horses (it is the analogue of HIV in horses). Climate change is likely to impact EIAV as warmer temperatures will create more favorable temperatures for the vectors, which are various species of biting flies. For example, these vectors are likely to live longer and thus carry the virus longer as temperatures warm. The goals of this working group will be to develop multi-patch mathematical models to study the impacts of climate change on EIAV.
Physics informed neural networks (PINNs) for PDE on domains with complex geometry
Eitan Grinspun (University of Toronto), Peter Yichen Chen (MIT)
Physics informed neural networks (PINNs), are a type of deep neural network trained to solve PDE in which the training process seeks a field satisfying a given partial differential equation (PDE) or variational principle. This PINNs approach is promising because it forgoes explicit discretization of the domain, in contrast to grid-, mesh-, or point-based methods (e.g., finite differences, finite elements, radial basis functions). These methods are attractive as they are "discretization-free" and thus can avoid some difficulties of complex domains and dimensionality. Despite their promise, PINNs have by and large been demonstrated only for simple domain geometries (squares, discs, etc.). On the other hand, many important problems require consideration of complex domain geometries, e.g., heat flow over real-world machined parts; processing of real-world geometric datasets with the goal of smoothing, interpolation, in-filling and denoising; and even the study of entangled matter. The goals of this working group will combine classical and emergent representations for complex domain geometries with PINNs to develop novel PDE solvers for domains with complex geometry and nontrivial topology. Useful skills include some familiarity with Laplace's equation corresponding to an undergraduate introductory course in partial differential equations or applied physics and some experience programming in python, but no experience is necessary to join. The plan for the workshop includes participants actively working on problems from basic code in Python provided by the organizers and moving towards open research questions by the conclusion of the workshop.
Geospatial Analysis of Pharmacy Prescription Refusals
Chad Topaz (Institute for the Quantitative Study of Inclusion, Diversity, and Equity)
In many states, a pharmacist who has a moral or religious objection to a customer's prescription can legally refuse to fill it. Anecdotally, prescription refusals seem to disproportionately impact marginalized groups, with the relevant medications including hormones for transgender individuals, contraceptives for people who can become pregnant, drugs for terminating pregnancies, and HIV prophylaxis, mainly for men who have sex with men. These incidents underscore a significant social justice issue, yet there is no empirical data to understand the problem's scope. To bridge this gap, our project aims to map the risk of pharmacy prescription refusals across different communities. Integrating geographic and demographic data sources, our research may employ methodologies such as "floating catchment maps" or topological data analysis to develop a nuanced understanding of the populations most vulnerable if a local pharmacy were to refuse to provide specific medications. Our project will likely be the first one to address prescription refusals quantitatively, and it aims to provide a foundation for further academic research and informed activism. It is particularly suited for participants who are interested in applying mathematical and geographical analysis to critical social issues and who are eager to engage with large data sets. Participants do not need prior experience with any of the data modeling methodologies but will benefit from a strong background in coding in R or similar languages.
Computations in permutations and their generalizations
Pamela E. Harris (University of Wisconsin Milwaukee)
We let n ∈ N = {1, 2, 3, . . .}, and [n] = {1, 2, . . . , n}. A permutation of the set [n] is a bijection from the set to itself and we denote the set of all permutations of [n] by Sn. Given a permutation, we will denote it in one-line notation π = π1π2…πn since we will simply think of permutations as an arrangement of the numbers in the set [n]. Thinking of permutations as ways to arrange the elements in [n] in one line, we arrive at the fact that there are n! Permutations. What else could one count in the set of permutations? There are many things we could count! For example, descents and ascents. We recall that if πi > πi+1, then π has a descent at index i; and if πi < πi+1, then π has an ascent at index i. For example, the permutation 54123 has descents at indices 1 and 2 and ascents at indices 3 and 4. Questions we could ponder are: What is the largest number of descents (ascents) a permutation could have? How many permutations have exactly k descents (ascents)? As these examples illustrate, there is a lot of deep mathematics that arises from asking simple counting questions. Here are some possible directions for our working group.
(1) Change the set: We can consider some supersets or subsets of permutations and study descents, ascents, and peaks. (For example, we could take parking functions and Fubini rankings)
(2) Change the statistic: The website https://www.findstat.org is “a database of combinatorial statistics and maps on combinatorial collections” which could motivate us to study or even create new statistics we could study on permutations.
(3) Do both! We could pick new combinatorial sets and new statistics to study.
(1) Change the set: We can consider some supersets or subsets of permutations and study descents, ascents, and peaks. (For example, we could take parking functions and Fubini rankings)
(2) Change the statistic: The website https://www.findstat.org is “a database of combinatorial statistics and maps on combinatorial collections” which could motivate us to study or even create new statistics we could study on permutations.
(3) Do both! We could pick new combinatorial sets and new statistics to study.
Dynamics and Algorithms for Optimization and Sampling in Machine Learning
Andre Wibisono (Yale University)
Machine learning, which is a framework for learning patterns from data, has been tremendously successful and is ubiquitous in modern life and many scientific applications. Many tasks in machine learning can be framed as either Optimization or Sampling problems.
In this working group, we will familiarize the participants with the general area of dynamics and algorithms for optimization and sampling by reviewing the basic results. We will also point to some open questions that can be interesting to explore together.
Prior knowledge of the following are helpful but not required: optimization (convexity, convergence analysis of gradient descent), sampling (mixing time of Markov chains), dynamical systems (ordinary differential equations (ODEs), Brownian motion, stochastic differential equations (SDEs), partial differential equation (PDE) representation of SDEs).
In this working group, we will familiarize the participants with the general area of dynamics and algorithms for optimization and sampling by reviewing the basic results. We will also point to some open questions that can be interesting to explore together.
Prior knowledge of the following are helpful but not required: optimization (convexity, convergence analysis of gradient descent), sampling (mixing time of Markov chains), dynamical systems (ordinary differential equations (ODEs), Brownian motion, stochastic differential equations (SDEs), partial differential equation (PDE) representation of SDEs).