January 24
Speaker: Bo Deng (University of Nebraska, Lincoln)
Title: Error-free Training for Artificial Neural Networks
Abstract: If we define intelligence as not making the same mistake twice, then a system achieves this artificial intelligence if and only if it can learn from its mistakes every time. For a feedforward neural network under supervised training, this means that it can be trained error-free for every data set. This problem is known as the discreet classification problem in mathematics. Its solution was obtained more than thirty years ago by what is now known as the Universal Approximation Theorem. In this talk, I will present a numerical algorithm to fulfill the UAT. I will illustrate the algorithm by both abstract and practical classification problems.
January 31
Speaker: Mingchao Cai (Morgan State)
Title: Models and Simulations for Lung Ventilation
Abstract: This talk explores mechanical models for lung ventilation and highlights recent advancements in numerical simulation. Two key models will be presented: (1) a 3D fluid airway tree model incorporating elastic boundary conditions to capture the effects of lung elastance and resistance. These boundary conditions are implemented using an inverse problem approach, and simulation results for the upper airway tree demonstrate the model's validity and consistency. (2) A hyperelastic-poroelastic model describing lung parenchyma deformation, with simulations based on porcine data illustrating biophysically consistent outcomes. These models and techniques provide valuable insights into lung mechanics and their numerical representation.
February 7
Speaker: Claus Kadelka (Iowa State University)
Title: Including human behavior in infectious disease models
Abstract: The COVID-19 pandemic has revealed the good and the bad of infectious disease models. While a well-developed model provides invaluable insights needed to understand and combat the pandemic, many models suffer from imperfect or simplistic assumptions that result in inaccurate or even completely wrong predictions.
In this talk, I will present several infectious disease models my group has developed since the beginning of the COVID-19 pandemic, using both classical differential equations as well as individual-based network models. All presented models incorporate certain aspects of human behavior (e.g., rates of mask wearing or vaccine uptake that depend on age, education, etc.) and social processes (e.g., homophily in social interaction patterns). A particular focus will be on heterogeneous mixing patterns. People with similar characteristics are more likely to interact, a phenomenon called assortative mixing or homophily. Empirical age-stratified social contact matrices have been derived by extensive survey work. We lack however similar empirical studies that provide social contact matrices for a population stratified by attributes beyond age, such as gender, sexual orientation, or ethnicity. Accounting for heterogeneities with respect to these attributes can have a profound effect on infectious disease model dynamics. I will present a new method, which uses linear algebra and non-linear optimization, to expand a given contact matrix to populations stratified by binary attributes with a known level of homophily and a known population-wide prevalence. As an example, I will show how accounting for ethnic homophily in the United States can give rise to interesting and non-trivial trade-offs that should be taken into consideration when developing prioritization strategies for future mass vaccine rollouts.
February 14
Speaker: Peter Hinow (University of Wisconsin - Milwaukee)
Title: Conversations on space debris
Abstract: Since the beginning of the era of space exploration in 1957, artificial objects have been left behind in the near-Earth environment. At velocities of 10 km s$^{-1}$, even small objects pose a significant risk to human activity in outer space. This debris population continues to grow due to ground launches, loss of external parts from spaceships, and uncontrollable collisions between objects. There is a surprising similarity to the mathematical modeling of spatially structured biological populations that are subject to birth and death processes, diffusion, as well as inter-species interactions. In the first part, we propose a diffusion-collision model for the evolution of debris density in Low-Earth Orbit (LEO, 200 - 2000 km altitude) and its dependence on ground-launch policy. We parametrize this model and test it against data from publicly available object catalogs to examine timescales for uncontrolled growth. In the second part, we will report on ongoing work to elucidate the somewhat cryptic title.
February 21
Speaker: Chengcheng Huang (University of Pittsburgh)
Title: State modulation in spatial networks of multiple interneuron subtypes
Abstract: Neuronal responses to sensory stimuli can be strongly modulated by animal's brain state. Three distinct subtypes of inhibitory interneurons, parvalbumin (PV), somatostatin (SOM), and vasoactive intestinal peptide (VIP) expressing cells, have been identified as key players in flexibly modulating network activity. The three interneuron populations have specialized local microcircuit motifs and are targeted differentially by neuromodulators and top-down inputs from higher-order cortical areas. However, the specific contribution of each interneuron subtype remains unclear. In this work, we study the function of each interneuron cell type in a spatially ordered spiking neuron network. We find that the firing rates of the SOM neurons align closely with the level of network synchrony irrespective of the target of modulatory input. Further analysis reveals that inhibition from SOM to PV interneurons must be limited to allow gradual transitions from asynchrony to synchrony and that the strength of recurrent excitation onto SOM neurons determines the level of synchrony achievable in the network. Overall, our results highlight common dynamic regimes achieved across modulations of different cell populations and identify SOM cells as the main driver of network synchrony.
February 28 (Special Time: 1pm Central Time / 2pm Eastern Time)
Speaker: Veronica Ciocanel (Duke University)
Title: Modeling Mechanisms of Length and Polarity Regulation in Neuronal Microtubules
Zoom Link: https://illinois.zoom.us/j/82616248519?pwd=CAR0v0aaIpTnIVwxJDa59wFvusobot.1
Abstract: Microtubules are protein polymers which are known to be stable and to have specific orientations in neurons. This is crucial, since key proteins get transported along these polarized microtubules, which ensures long-term survival of neurons. However, microtubules also need to be dynamic and reorganize in response to injury events. How this balance is achieved remains an open question. Using information from experimental measurements, we seek to understand mechanisms that control microtubule length and numbers in dendrites of fruit fly neurons. We consider both stochastic and reduced continuous models that incorporate restrictions on filament growth, such as limited tubulin availability and the dependence of shrinking events on microtubule length. More recently, we have been interested in understanding how nucleation impacts the number of filaments in these cells, given that neuronal injury is known to regulate the formation of new microtubules. Ongoing work is focused on how these dynamics microtubule filaments collectively organize into polarized structures in neurons.
March 7
Speaker: Adrian Lam (Ohio State University)
Title: What is the ideal free distribution in time-periodic environment?
Zoom Link: https://illinois.zoom.us/j/82616248519?pwd=CAR0v0aaIpTnIVwxJDa59wFvusobot.1
Abstract: A population is said to have an ideal free distribution in a spatially heterogeneous but temporally constant environment if each of its members have chosen a fixed spatial location in a way that optimizes its individual fitness, allowing for the effects of crowding. In this paper, we extend the idea of individual fitness associated with a specific location in space to account for the full path that an individual organism takes in space and time over a periodic cycle, and extend the mathematical formulation of an ideal free distribution to general time periodic environments. We show that such generalized ideal freedistribution enables a population to be evolutionarily stable. A sharp criterion on the environmental functions is found to be necessary and sufficient for such ideal free distribution to be feasible. In the case the criterion is met, we showed that there exist dispersal strategies that can be identified as producing a time-periodic version of an ideal freedistribution, and such strategies are evolutionarily steady and are neighborhood invaders from the viewpoint of adaptive dynamics. Our results extend previous works in which the environments are either temporally constant, or temporally periodic but the total carrying capacity is temporally constant. This is joint work with R.S. Cantrell and C. Cosner of Univ. Miami, and Hua Zhang of Shanghai Jiaotong Univ.
March 14
Speaker: Sabrina Streipert (University of Pittsburgh)
Title: An evolutionary epidemic model to study the impact of tolerance on disease-induced recoveries
Zoom Link: https://illinois.zoom.us/j/82616248519?pwd=CAR0v0aaIpTnIVwxJDa59wFvusobot.1
Abstract: Recoveries of populations that have suffered severe disease-induced declines are being observed across disparate taxa. Yet, we lack theoretical understanding of the drivers and dynamics of recovery in host populations. Motivated by diseaseinduced declines and nascent recoveries in amphibians, we developed a model to ask: how does the rapid evolution of different host defense strategies affect the transient recovery trajectories of hosts following pathogen invasion and disease-induced declines? Our model, based on a moment closure approximation, provided key insights into the transient effects of different defense mechanisms. Furthermore, populations evolving tolerance recovered on average four times slower than populations evolving resistance. This motivated the long-term study of a tolerance evolving host species. We found that in the presence of a trade-off, where a higher tolerance comes at the expense of a lower reproductive rate, the set of pandemic equilibria increases in richness to contain equilibria where different tolerance classes are present, contrasting the results obtained in the absence of such trade-off.
March 21
Speaker: Merlin Pelz (University of Minnesota)
Title: The Emergence of Spatial Patterns and Synchronization with Diffusion-Coupled Compartments with Activator-Inhibitor Kinetics
Zoom Link: https://illinois.zoom.us/j/82616248519?pwd=CAR0v0aaIpTnIVwxJDa59wFvusobot.1
Abstract: Since Alan Turing’s pioneering publication on morphogenetic pattern formation obtained with reaction-diffusion (RD) systems, it has been the prevailing belief that two-component reaction diffusion systems have to include a fast diffusing inhibiting component (inhibitor) and a much slower diffusing activating component (activator) in order to break symmetry from a uniform steady-state. This time-scale separation is often unbiological for cell signal transduction pathways. We modify the traditional RD paradigm by considering nonlinear reaction kinetics only inside compartments with reactive boundary conditions to the extra-compartmental space which diffusively couples the compartments via two species. The construction of a nonlinear algebraic system for all existing steady-states enables us to derive a globally coupled matrix eigenvalue problem for the growth rates of eigenperturbations from the symmetric steady-state in 1-D, 2-D, and 3-D. We show that the membrane permeability ratio of inhibitor permeability to activator permeability is a key bifurcation parameter leading to robust symmetry-breaking of the compartments. Illustrated with Gierer-Meinhardt, FitzHugh-Nagumo and Rauch-Millonas intra-compartmental kinetics, our compartmental-reaction diffusion system does not require diffusion of inhibitor and activator on vastly different time scales. Further, our system can be viewed as a Kuramoto coupled oscillator system in which continuous diffusion constitutes the coupling. Through a similar but now time-dependent asymptotic reduction, we are deriving precise coupling terms guiding the oscillator dynamics that are then described by an integro-differential system, and we are illustrating various synchronization behaviors with Sel'kov glycolysis intracellular kinetics using an efficient sum-of-exponential numerical marching scheme. Our results reveal possible simple mechanisms of the ubiquitous biological steady and oscillatory cell group specialization observed in nature.
March 28
Speaker: Meghan Ferall-Fairbanks (University of Florida)
Title: Engineering cancer solutions using big data and evolutionary medicine
Zoom link: https://zoom.us/j/93292678117?pwd=koxG6VOuFfYbP9KCR769XbaGoPrQ4T.1
Abstract: Current clinical trials often fail to account for comorbid conditions and complex patient environments, resulting in findings that do not translate well to broader populations. Biomedical research has traditionally used a reductionist approach, focusing on isolated molecules, which overlooks the complexity of human organisms with multiple concurrent health issues. Our approaches aim to understand how the host conditioning affects cellular interactions within individuals and leverage the extensive information available in patients' electronic health records and disease status to tailor therapeutic options. We use multi-modal data, machine learning, mathematical modeling, and in vitro culture systems to explore the impact of host conditioning on cancer progression and response to therapy. Our long-term goal is to employ multidisciplinary approaches to elucidate the physical and molecular changes in cellular phenotypes as they adapt to various environments and exposures, ultimately personalizing treatments and improving human health. Our recent findings on the adaptability of cellular phenotypes in response to different environments and interactions underscore the potential of these approaches.
April 4
Speaker: Zixuan Cang (North Carolina State)
Title: Analyzing Single-cell and Spatial Transcriptomics Data Using Optimal Transport
Zoom link: https://illinois.zoom.us/j/82616248519?pwd=CAR0v0aaIpTnIVwxJDa59wFvusobot.1
Abstract: Single-cell and spatial transcriptomics data examines high-throughput gene expression profiles at fine resolutions providing an unprecedented opportunity to elucidate the underlying complex biological processes. Optimal transport has proven to be an effective tool for various applications with such data, such as multi-omics integration. In this talk, we will discuss several optimal transport variants motivated by the biological applications, where there are detailed application-specific constraints, multiple distribution species, and multiple embedding spaces of the same system. We will illustrate the applications of these tools for addressing multi-compatible molecular species in cell-cell communication analysis and devising coherent trajectories of the same biological system from multi-omics datasets.
April 18
Speaker: Stephanie Dodson (Colby College)
Title: Curvature dependent onset of oscillations in excitable tissue
Zoom link: https://illinois.zoom.us/j/82616248519?pwd=CAR0v0aaIpTnIVwxJDa59wFvusobot.1
Abstract: In cardiac tissue, the sinoatrial node (SAN) is responsible for initiating the periodic electrical pulses underlying heart beats. However, other regions of local heterogeneous tissue can act as rogue pacemakers and produce ectopic oscillations in neighboring tissue that compete with the natural pacemaking of the SAN and cause potentially life-threatening arrhythmias. Thus, it is important to understand the physiological conditions that enable the SAN to robustly act as the cardiac pacemaker and for local depolarized regions of tissue to form pathological rhythms. It is well known that small heterogeneities (sources) should not be able to easily activate a large area of excitable tissue (sink). On a local level, this source-sink balance implies that positive curvature of a pacemaking region reduces the ability to drive the neighboring tissue. However, while numerous studies provide evidence that supports the source-sink balance relationship in which high curvature deters oscillations, other studies have shown that for some depolarized heterogeneities, oscillations tend to emerge from corners and other areas of high curvature. In this research, we use an idealized two-domain reaction-diffusion system and corresponding two-cell model to bridge the gap between these seemingly opposing viewpoints. In doing so, we identify the conditions for which curvature of a pacemaking region promotes or obstructs the production of oscillations in the neighboring tissue. This work is a joint collaboration with Tim Lewis (UC Davis) and Emily Meyer (University of Colorado Anschutz Medical Campus).
April 25
Speaker: Montie Avery
Title: Predicting front invasion speeds via marginal stability
Zoom link: https://illinois.zoom.us/j/82616248519?pwd=CAR0v0aaIpTnIVwxJDa59wFvusobot.1
Abstract: Front propagation into unstable states often mediates state transitions in spatially extended systems, in biological models and across the sciences. Classical examples include the Fisher-KPP equation for population genetics, Lotka-Volterra models for competing species, and Keller-Segel models for bacterial motion in the presence of chemotaxis. A fundamental question is to predict the speed of the propagating front as well as which new state is selected in its wake. In some cases, the propagation speed in a full nonlinear PDE model agrees with that predicted by its linearization about the unstable state, in which case we say the speed is linearly determined, and the fronts are pulled. If the nonlinear speed is faster than the linear spreading speed, we say the fronts are pushed. The marginal stability conjecture asserts that front invasion speeds are determined by the spectrum of the linearization about traveling wave solutions of the PDE model. We present a formulation and proof of the marginal stability conjecture, together with complementary results which allow one to efficiently detect the transition between pushed and pulled front propagation as system parameters vary. We illustrate the utility of our theory by applying it to Lotka-Volterra systems, Keller-Segel models with repulsive chemotaxis, a model for growth of cancer stem cell driven tumors, and a FitzHugh-Nagumo model for signal propagation in nerve fibers.
May 2
Speaker: Bo Zhang (Oklahoma State University)
Title: Movement Dynamics: Responses and Consequences in Changing Environments
Abstract: Anthropogenic actions and climate change are fragmenting the environment and putting more emphasis on the role of organism movement to favorable habitats, which sustains population survivorship and biodiversity. The main focus of the presentation is to incorporate movement into modeling to develop more accurate and realistic ecological dynamics models. For instance, habitat loss and fragmentation, when taken together, can negatively impact biodiversity. However, clarification is required to determine the relative importance of the latter, due to the challenges of conducting field studies that distinguish the relative independent impacts of habitat loss and fragmentation. Moreover, species with different locomotion rates respond differently to fragmentation, complicating any direct comparison across differing taxa and landscape patterns. To overcome these challenges, we combined mechanistic mathematical modeling and laboratory experiments to disentangle the impacts of habitat fragmentation and locomotion. We applied the Caenorhabditis elegans (C. elegans) experimental system to engineer mutants with different movement behaviors and performed competition experiments to identify consequences of movement strategies in spatially and temporally heterogeneous/fragmentation environments. Our theoretical and empirical results found that species with a relatively low motility rate maintained a moderate growth rate and high population abundance in fragmented habitat. Alternatively, fragmentation harmed fast-moving populations through a decrease in the populations’ growth rate by creating a mismatch between the population distribution and the resource distribution. Our findings shed new light on the role of locomotion in determining the effects of habitat fragmentation.
May 9
Speaker: Mario Gómez Flores(Florida State University)
Title: Vietoris-Rips Complexes of Split-Decomposable Spaces
Abstract: Split-metric decompositions are an important tool in the theory of phylogenetics, particularly because of the link between the tight span and the class of totally decomposable spaces, a generalization of metric trees whose decomposition does not have a "prime" component. Their close relationship with trees makes totally decomposable spaces attractive in the search for spaces whose persistent homology can be computed efficiently. We study the subclass of circular decomposable spaces, finite metrics that resemble subsets of $\mathbb{S}^1$ and can be recognized in quadratic time. We give an $O(n^2)$ characterization of the circular decomposable spaces whose Vietoris-Rips (VR) complexes are cyclic for all distance parameters, and compute their homotopy type using well-known results on $\mathbb{S}^1$. We extend this result to a recursive formula that computes the homology of certain circular decomposable spaces that fail the previous characterization. Going beyond totally decomposable spaces, we identify an $O(n^3)$ decomposition of the VR complex of $X$ induced by the blocks of the tight span of $X$ and use it to induce a direct-sum decomposition of the homology of the VR complex.