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  1. We study how to optimize the latent space of neural shape generators that map latent codes to 3D deformable shapes. The key focus is to look at a deformable shape generator from a differential geometry perspective. We define a Riemannian metric based on as-rigid-as-possible and as-conformal-as-possible deformation energies. Under this metric, we study two desired properties of the latent space: 1) straight-line interpolations in latent codes follow geodesic curves; 2) latent codes disentangle pose and shape variations at different scales. Strictly enforcing the geometric interpolation property, however, only applies if the metric matrix is a constant. We show how to achieve this property approximately by enforcing that geodesic interpolations are axis-aligned, i.e., interpolations along coordinate axis follow geodesic curves. In addition, we introduce a novel approach that decouples pose and shape variations via generalized eigendecomposition. We also study efficient regularization terms for learning deformable shape generators, e.g., that promote smooth interpolations. Experimental results on benchmark datasets show that our approach leads to interpretable latent codes, improves the generalizability of synthetic shapes, and enhances performance in geodesic interpolation and geodesic shooting.

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    Free, publicly-accessible full text available December 5, 2024
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  4. Altered tissue mechanics is an important signature of invasive solid tumors. While the phenomena have been extensively studied by measuring the bulk rheology of the extracellular matrix (ECM) surrounding tumors, micromechanical remodeling at the cellular scale remains poorly understood. By combining holographic optical tweezers and confocal microscopy on in vitro tumor models, we show that the micromechanics of collagen ECM surrounding an invading tumor demonstrate directional anisotropy, spatial heterogeneity and significant variations in time as tumors invade. To test the cellular mechanisms of ECM micromechanical remodeling, we construct a simple computational model and verify its predictions with experiments. We find that collective force generation of a tumor stiffens the ECM and leads to anisotropic local mechanics such that the extension direction is more rigid than the compression direction. ECM degradation by cell-secreted matrix metalloproteinase softens the ECM, and active traction forces from individual disseminated cells re-stiffen the matrix. Together, these results identify plausible biophysical mechanisms responsible for the remodeled ECM micromechanics surrounding an invading tumor. 
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  5. The online knapsack problem is a classic online resource allocation problem in networking and operations research. Its basic version studies how to pack online arriving items of different sizes and values into a capacity-limited knapsack. In this paper, we study a general version that includes item departures, while also considering multiple knapsacks and multi-dimensional item sizes. We design a threshold-based online algorithm and prove that the algorithm can achieve order-optimal competitive ratios. Beyond worst-case performance guarantees, we also aim to achieve near-optimal average performance under typical instances. Towards this goal, we propose a data-driven online algorithm that learns within a policy-class that guarantees a worst-case performance bound. In trace-driven experiments, we show that our data-driven algorithm outperforms other benchmark algorithms in an application of online knapsack to job scheduling for cloud computing. 
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  6. Coordinated responses to environmental stimuli are critical for multicellular organisms. To overcome the obstacles of cell-to-cell heterogeneity and noisy signaling dynamics within individual cells, cells must effectively exchange information with peers. However, the dynamics and mechanisms of collective information transfer driven by external signals are poorly understood. Here we investigate the calcium dynamics of neuronal cells that form confluent monolayers and respond to cyclic ATP stimuli in microfluidic devices. Using Granger inference to reconstruct the underlying causal relations between the cells, we find that the cells self-organize into spatially decentralized and temporally stationary networks to support information transfer via gap junction channels. The connectivity of the causal networks depends on the temporal profile of the external stimuli, where short periods, or long periods with small duty fractions, lead to reduced connectivity and fractured network topology. We build a theoretical model based on communicating excitable units that reproduces our observations. The model further predicts that connectivity of the causal network is maximal at an optimal communication strength, which is confirmed by the experiments. Together, our results show that information transfer between neuronal cells is externally regulated by the temporal profile of the stimuli and internally regulated by cell–cell communication. 
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  7. Abstract. The discovery of Antarctica's deepest subglacial troughbeneath the Denman Glacier, combined with high rates of basal melt at thegrounding line, has caused significant concern over its vulnerability toretreat. Recent attention has therefore been focusing on understanding thecontrols driving Denman Glacier's dynamic evolution. Here we consider theShackleton system, comprised of the Shackleton Ice Shelf, Denman Glacier,and the adjacent Scott, Northcliff, Roscoe and Apfel glaciers, about whichalmost nothing is known. We widen the context of previously observed dynamicchanges in the Denman Glacier to the wider region of the Shackleton system,with a multi-decadal time frame and an improved biannual temporal frequencyof observations in the last 7 years (2015–2022). We integrate newsatellite observations of ice structure and airborne radar data with changesin ice front position and ice flow velocities to investigate changes in thesystem. Over the 60-year period of observation we find significant riftpropagation on the Shackleton Ice Shelf and Scott Glacier and notablestructural changes in the floating shear margins between the ice shelf andthe outlet glaciers, as well as features indicative of ice with elevatedsalt concentration and brine infiltration in regions of the system. Over theperiod 2017–2022 we observe a significant increase in ice flow speed (up to50 %) on the floating part of Scott Glacier, coincident with small-scalecalving and rift propagation close to the ice front. We do not observe anyseasonal variation or significant change in ice flow speed across the restof the Shackleton system. Given the potential vulnerability of the system toaccelerating retreat into the overdeepened, potentially sediment-filledbedrock trough, an improved understanding of the glaciological,oceanographic and geological conditions in the Shackleton system arerequired to improve the certainty of numerical model predictions, and weidentify a number of priorities for future research. With access to theseremote coastal regions a major challenge, coordinated internationallycollaborative efforts are required to quantify how much the Shackletonregion is likely to contribute to sea level rise in the coming centuries. 
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