June 23, 2024

There are no events currently scheduled for June 23rd.

June 24, 2024

• 8:30 - 9:00 am EDT

  Arrival Time / Sign In

  Arrival Time / Sign In - 11th Floor Collaborative Space
• 9:00 - 9:30 am EDT

  Check in with TAs

  - 10th Floor Collaborative Space
• 9:30 - 10:30 am EDT

  Group Work

  Assigned Group Work Space
• 10:30 - 11:00 am EDT

  Break

  Coffee Break
• 11:00 - 11:15 am EDT

  Question of the Day

  - 10th Floor Collaborative Space
• 11:15 am - 12:00 pm EDT

  Group Work

  Assigned Group Work Space
• 12:00 - 1:30 pm EDT

  Lunch/Free Time
• 1:30 - 3:00 pm EDT

  Group Work

  Assigned Group Work Space
• 3:00 - 3:30 pm EDT

  Coffee Break

  10th Floor Collaborative Space
• 3:30 - 4:30 pm EDT

  Group Work / Writing Time

  Group Work - Assigned Group Work Space

• 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.

  • Video Available Soon
• 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

June 25, 2024

• 8:30 - 9:00 am EDT

  Arrival Time / Sign In

  Arrival Time / Sign In - 11th Floor Collaborative Space
• 9:00 - 9:30 am EDT

  Check in with TAs

  Check in with TAs - 10th Floor Collaborative Space
• 9:30 - 10:30 am EDT

  Group Work

  Assigned Group Work Space
• 10:30 - 11:00 am EDT

  Break

  Coffee Break
• 11:00 - 11:15 am EDT

  Question of the Day

  - 10th Floor Collaborative Space
• 11:15 am - 12:00 pm EDT

  Group Work

  Assigned Group Work Space
• 12:00 - 1:30 pm EDT

  Lunch/Free Time
• 1:30 - 3:00 pm EDT

  Group Work

  Assigned Group Work Space
• 3:00 - 3:30 pm EDT

  Coffee Break

  10th Floor Collaborative Space
• 3:30 - 4:30 pm EDT

  Group Work / Writing Time

  Group Work - Assigned Group Work Space

• 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

  • Video Available Soon
• 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

June 27, 2024

• 8:30 - 9:00 am EDT

  Arrival Time / Sign In

  Arrival Time / Sign In - 11th Floor Collaborative Space
• 9:00 - 9:30 am EDT

  Check in with TAs

  - 10th Floor Collaborative Space
• 9:30 - 10:30 am EDT

  Group Work

  10th Floor Collaborative Space
• 10:30 - 11:00 am EDT

  Break

  Coffee Break
• 11:00 - 11:15 am EDT

  Question of the Day

  - 10th Floor Collaborative Space
• 11:15 am - 12:00 pm EDT

  Group Work

  Assigned Group Work Space
• 12:00 - 1:30 pm EDT

  Lunch/Free Time
• 1:30 - 3:00 pm EDT

  Group Work

  Assigned Group Work Space
• 3:00 - 3:30 pm EDT

  Coffee Break

  10th Floor Collaborative Space
• 3:30 - 4:30 pm EDT

  Group Work / Writing Time

  Group Work - Assigned Group Work Space
• 8:00 - 10:00 pm EDT

  Movie Night

  - 11th Floor Lecture Hall

• 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

June 28, 2024

• 8:30 - 9:00 am EDT

  Arrival Time / Sign In

  Arrival Time / Sign In - 11th Floor Collaborative Space
• 8:30 - 9:00 am EDT

  Check in with TAs

  Check in with TAs - 10th Floor Collaborative Space
• 9:30 - 10:30 am EDT

  Group Work

  Assigned Group Work Space
• 10:30 - 11:00 am EDT

  Break

  Coffee Break
• 11:00 - 11:15 am EDT

  Question of the Day

  - 10th Floor Collaborative Space
• 11:15 am - 12:00 pm EDT

  Group Work

  Assigned Group Work Space
• 12:00 - 1:30 pm EDT

  Lunch/Free Time
• 1:30 - 3:00 pm EDT

  Group Work

  Assigned Group Work Space
• 3:00 - 3:30 pm EDT

  Coffee Break

  10th Floor Collaborative Space
• 3:30 - 4:30 pm EDT

  Group Work/ Writing Time

  Group Work - Assigned Group Work Space

• 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

  - 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

June 29, 2024

There are no events currently scheduled for June 29th.