Schedule for: 22w5062 - Building Networks: Women in Complex & Nonlinear Systems

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

I will talk about research from my lab in which we build networks of various sorts, using granular materials, laser cutters, and additive manufacturing (3D printing). Our past work has focused on understanding how rigidity arises, and sometimes fails, and how disordered materials often contain both rigid and floppy subnetworks. I will talk about 3 frameworks capable of connecting the internal structure of disordered materials to their rigidity and/or failure under loading, and describe how my collaborators and I have applied these frameworks. These are, in order of increasing physics content: (1) centrality within an adjacency matrix describing its connectivity, (2) Maxwell constraint counting on the full network of frictional contact forces, and (3) the vibrational modes of a synthetic dynamical matrix (Hessian). The first two rely primarily on topology, and the second two include more information about the physics. All three methods, while successfully elucidating the origins of rigidity and brittle vs. ductile failure, also provide interesting counterpoints regarding how much information is enough to make predictions. In keeping with the spirit of the conference, I will also talk about the networks of women+ who have made this work possible.

Living matter, such as biological tissue, can be seen as a nonequilibrium hierarchical assembly of assemblies of smaller and smaller active components, where energy is consumed at many scales. The functionality and versatility of such living or "active-matter" systems render it a promising candidate to study and to synthetically design. While many active-matter systems reside in fluids (solution, blood, ocean, air), so far, studies that include hydrodynamic interactions have focussed on microscopic scales in Stokes flows, where the active particles are <100μm and the Reynolds number, Re <<1. At those microscopic scales viscosity dominates and inertia can be neglected. However, what happens as swimmers slightly increase in size (say ~0.1mm-100cm) or as they form larger aggregates and swarms? The system then enters the intermediate Reynolds regime where both inertia and viscosity play a role, and where nonlinearities in the fluid are introduced. In this talk, I will present a simple model swimmer used to understand the transition from Stokes to intermediate Reynolds numbers, first for a single swimmer, then for pairwise interactions and finally for collective behavior. We show that, even for a simple model, inertia can induce hydrodynamic interactions that generate novel phase behavior, steady states and transitions.

Biological systems under the influence of microscale active agents such as proteins are frequently modeled using switching forces as the agents shift between different states, pushing the system out of equilibirium. For example, protein action plays a crucial role in the organization of the DNA inside the cell nucleus, modeled by a bead-spring polymer, in the form of stochastic crosslinking. Despite these rapidly switching forces causing a constant state of disequilibrium, we observed in numerical simulations long-lived stable condensed clusters of beads consistent with experimental results, with the stochastic switching rate acting like an effective temperature. Rapid switching produced low-temperature-like stable clusters, slow switching produced high-temperature-like amorphic arrangements, and intermediate switching times allowed for dynamic clusters with beads exchanging between clusters. To explain the mechanism behind this emergent clustering behavior, we derive an effective thermal equilibrium that captures both the average force and fluctuations induced by the stochastically switching force, accurately predicting the mean transition time between stable configurations.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Meet in the PDC front desk for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Experience shapes our expectations and helps us learn about the structure of our environment, which impacts our cognitive strategies. Learning the environment can be described as a gradual refinement of the observer’s estimate of the environmental prior. For instance, when trying to remember features such as the color of an object, learned priors may bias the estimate in the direction of common feature values. Humans display such biases when retaining color estimates on short time intervals. We propose that these systematic biases emerge from modulation of the connections between networks of neurons, shaping the persistent and collective neural activity that encodes the stimulus estimate. Here, we model the effects of environmental priors on neural circuit models and their low-dimensional reductions, considering both models with network connectivity that is fixed and those shaped by experience. We compare these results to human behavior and find that most subjects exhibit strategies best described by learning models, supporting the hypothesis that long-term representation biases result from learning the environmental structure.

Central to the functioning of self-organizing systems — from ant colonies to human societies — are individual variation and population structure. In this talk, I will discuss two studies on how the interplay between these features influences collective dynamics, and vice versa, in complex social systems. The first study explores the role of opinion diversity in the coupled dynamics of inter-individual cooperation and political polarization. Using a cultural evolution model grounded in evolutionary game theory, we show that increasing interest diversity can improve individual and collective outcomes. But partisanship reduces the dimensionality of opinion space via self-sorting along party lines, potentially yielding greater in-group cooperation at the cost of heightened polarization—an emergent tension between the individual and the collective. The second study examines mechanisms underlying the emergence of enduring hierarchies. Using an adaptive network model, we prove that feedback between social prestige and individual-level decision-making alone can lead to stratification among otherwise equal competitors. Fitting the model to empirical data, such as hiring patterns among mathematicians, reveals that observed social systems may be near the critical threshold between egalitarianism and hierarchy.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

The study of emergent behavior of swarms is of great interest for applied sciences. The primary focus of the talk is the stability of a system of $n$-coupled, self-propelled particles, with all-to-all linear coupling: $\ddot r_k = (1-|\dot r_k|^2)\dot r_k - \frac{1}{n}\sum_{m=1}^n(r_k-r_m)$, $r_k\in \mathbb R^2$. Previous numerical experiments have shown that for a large set of initial conditions, after an initial drift, the center of mass of the system converges to a stationary point and each particle eventually rotates with unit angular velocity around the stationary center of mass. Such limit states are dubbed {\it rotating states}. The distribution of the particles on the circle need not be uniform. We prove that all rotating states are stable and we show that every solution that starts near a rotating state asymptotically approaches some rotating state. Characterizing the stability of multi-agent systems is complicated by the inherent large dimensionality of the neutral directions (our central manifold has dimension $n+1$), by the large number of parameters encoding the limiting states ($n-2$), and by the presence of non-isolated periodic orbits or non-isolated fixed points. The talk will illustrate why the usual Taylor polynomial approximations of the central manifold are ineffective {\it in this setting}, and present an alternate approach. Using the non-isolated fixed points as anchoring, we produce an approximation of the center manifold and its flow that is error-free at the fixed points, and that nearby is consistent with the scales of the true flow.

In this talk, I will two present two projects. The first part of my talk focuses on the use of motifs in linear stochastic processes on static networks (Schwarze & Porter, SIAM Journal on Applied Dynamical Systems 20 (4), 2516-2557) to improve methods for network inference from observations of coupled dynamical systems (Schwarze, Ichinaga & Brunton, arXiv preprint arXiv:2208.08871). In the second part, I will present results from the stability analysis of mean-field approximations for a family of models for opinion formation on adaptive networks that I aim to fit to data collected on the alcohol-drinking behavior of college students (work in progress).

Mathematical methods can be used to study evolutionary processes associated with carcinogenesis. Selection, mutation, and drift all play a role in cancer dynamics and cancer treatment. In the first part of my talk, I will present two very general types of evolutionary patterns that occur in the context of many cancers: loss-of-function and gain-of-function mutations. This will be followed by a discussions of different scenarios of cell population dynamics -- including stochastic tunneling and calculating the rate of cancer evolution. In the second part, we will discuss how mathematical tools can be used to connect stochastic evolutionary dynamics in cellular populations with the epidemiological data on the prevalence of colon cancer. Data suggest that aspirin can decrease the risk of developing cancer. We will use experimental (in vitro and in vivo) data and modeling to understand the role of aspirin in prevention of colorectal cancer.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Recent advancements in computational fluid dynamics have enabled researchers to efficiently explore problems that involve moving elastic boundaries immersed in fluids for problems such as cardiac fluid dynamics and animal swimming. These advances have also made modeling both nutrient exchange in a fluid and the muscle driven motion of a flexible organ or organism through a fluid feasible. The work presented here focuses on the development and implementation of such methods and models for the pumping and pulsation of tubular hearts and jellyfish bells. We leverage existing computational algorithms for fluid-structure interactions and extend this technology to “living” boundaries. Muscle models integrate feedback between the conduction of action potentials, the contraction of muscles, the movement of tissues, and fluid motion. These models are then used to resolve pumping mechanisms in tubular hearts and resonant swimming in jellyfish. If time permits, I will present simulations at intermediate Reynolds and Peclet numbers to reveal how the morphology and kinematics of other marine organisms greatly enhance feeding and exchange flows.

We propose a mathematical framework to describe the neurobiology of drug addiction. Substances of abuse are known to activate and disrupt neuronal circuits in the brain reward system To quantify these disruptions, we incorporate the psychiatric concepts of drug-induced incentive salience (IST), reward prediction error (RPE), and opponent process theory (OPT) in a simple and easily interpretable dynamical system model. Drug-induced dopamine releases activate a biphasic reward response with pleasurable, positive ``a-processes" (euphoria, rush) followed by unpleasant, negative "b-processes" (cravings, withdrawal symptoms). Neuroadaptive processes triggered by successive intakes enhance the negative component of the reward response, against which the user compensates by increasing drug dose and/or intake frequency. This positive feedback between physiological changes and drug self-administration eventually leads to full addiction. Our model gives rise to qualitatively different pathways to addiction that allow us to represent a diverse set of user profiles (genetics, age) or drug potencies. Finally, we include possible mechanisms to mitigate withdrawal symptoms, such as through methadone or other auxiliary drugs used in detoxification.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

5-day workshop participants are welcome to use BIRS facilities (TCPL ) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 11AM.