Group Meeting

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Deviations from mirror symmetry in multicellular organisms are ubiquitous, yet the molecular mechanisms responsible for the symmetry-breaking remain largely unclear. We investigated the development of a chiral pattern in single cells and groups of cells confined to adhesive islands. Single cells on circular islands had actomyosin stress fibers arranged radially, like spokes on a wheel, tilted counterclockwise. When multiple cells were confined to a rectangular island, they elongated along one preferred diagonal and two long rectangle boundaries, making the Cyrillic letter И. Several knockdowns found to reverse stress fiber tilting clockwise in single cells caused multiple cell patterns to reverse chirality to the Roman letter N. To understand the origin of this chirality, we translated microscopy observations into computational models in which the dynamic stress fibers merge and align along the long axis of the cell, and then tilt relative to this axis in a chiral way; neighboring cells tend to align with each other, and cells align with the adhesive boundary.
Simulations of several variants of this model and comparison with experiments based on model predictions revealed that the collective chirality arises from the cells interacting with the boundary, and not from the cell-cell interactions inside the cell group. The resulting model successfully reproduced all observed experimental patterns on the islands of many shapes and sizes. Lastly, we mixed cells of opposite chirality, which led to intricate patterns dependent on the density ratio between these cell types. Our results suggest a novel pathway of chirality propagation from subcellular to multicellular scale underscored by stress fiber dynamics and geometry of the multicellular environment.

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We show how to obtain improved active learning methods in the agnostic (adversarial noise) setting by combining marginal leverage score sampling with non-independent sampling strategies that promote spatial coverage. In particular, we propose an easily implemented method based on the \emph{pivotal sampling algorithm}, which we test on problems motivated by learning-based methods for parametric PDEs and uncertainty quantification. In comparison to independent sampling, our method reduces the number of samples needed to reach a given target accuracy by up to 50.

We support our findings with two theoretical results. First, we show that any non-independent leverage score sampling method that obeys a weak \emph{one-sided ℓ∞ independence condition} (which includes pivotal sampling) can actively learn d dimensional linear functions with O(d log⁡ d) samples, matching independent sampling. This result extends recent work on matrix Chernoff bounds under ℓ∞ independence, and may be of interest for analyzing other sampling strategies beyond pivotal sampling. Second, we show that, for the important case of polynomial regression, our pivotal method obtains an improved bound of O(d) samples.

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With the promise of computational advantage in memory and speed, quantum computing has emerged as a potential counterpart to classical machines, for numerically solving problems in a wide range of applications, each with a unique computational challenge. We discuss one such unique domain -- fluid dynamics, whose study involves solving well defined, governing partial differential equations, derived from the underlying flow physics. First we give a brief introduction to some fundamental concepts of quantum computing. Then we proceed to an overview of different algorithms developed in this field, while also highlighting the challenges involved in simulating practical nonlinear PDEs. We will then delve into some specific non-linear embedding methods, state-of-the-art quantum algorithms, their computational complexities and the flow simulation results with a hybrid quantum-classical scheme. We will also highlight here, a high-performance, open-source quantum simulator package called QFlowS, that was developed in-house as part of this work. We then give a pragmatic outlook on current quantum hardware capabilities by solving a one-dimensional, linear advection-diffusion problem on a real IBM quantum device. Finally an outline of future directions and bottlenecks that need attention in this area of research will be discussed.

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Following an introduction by Nandan Kulkarni, we will present a model of the mouse cortex(>400,000 biological neurons) and a series of simulations of the model, where different spatiotemporal patterns, such as traveling waves, emerge from different connectivity, connection strength and external stimuli. 

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10 minute introduction to the fluid dynamics of ice by Georg Stadler

Talk by Gonzalo Gonzalez de Diego: A Stokes problem with contact boundary conditions and an evolving free boundary emerges in the study of glaciers when modeling the formation of subglacial cavities and grounding line dynamics. Before describing this contact problem, Gonzalo will first give an introduction to modeling the evolution of glaciers as viscous fluids and how the resulting equations can be solved with the finite element method in Firedrake.

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