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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. 

Abstract Using the concepts of mixed volumes and quermassintegrals of convex geometry, we derive an exact formula for the exclusion volume v ex ( K ) for a general convex body K that applies in any space dimension. While our main interests concern the rotationally-averaged exclusion volume of a convex body with respect to another convex body, we also describe some results for the exclusion volumes for convex bodies with the same orientation. We show that the sphere minimizes the dimensionless exclusion volume v ex ( K )/ v ( K ) among all convex bodies, whether randomly oriented or uniformly oriented, for any d , where v ( K ) is the volume of K . When the bodies have the same orientation, the simplex maximizes the dimensionless exclusion volume for any d with a large- d asymptotic scaling behavior of 2 2 d / d 3/2 , which is to be contrasted with the corresponding scaling of 2 d for the sphere. We present explicit formulas for quermassintegrals W 0 ( K ), …, W d ( K ) for many different nonspherical convex bodies, including cubes, parallelepipeds, regular simplices, cross-polytopes, cylinders, spherocylinders, ellipsoids as well as lower-dimensional bodies, such as hyperplates and line segments. These results are utilized to determine the rotationally-averaged exclusion volume v ex ( K ) for these convex-body shapes for dimensions 2 through 12. While the sphere is the shape possessing the minimal dimensionless exclusion volume, we show that, among the convex bodies considered that are sufficiently compact, the simplex possesses the maximal v ex ( K )/ v ( K ) with a scaling behavior of 2 1.6618… d . Subsequently, we apply these results to determine the corresponding second virial coefficient B 2 ( K ) of the aforementioned hard hyperparticles. Our results are also applied to compute estimates of the continuum percolation threshold η c derived previously by the authors for systems of identical overlapping convex bodies. We conjecture that overlapping spheres possess the maximal value of η c among all identical nonzero-volume convex overlapping bodies for d ⩾ 2, randomly or uniformly oriented, and that, among all identical, oriented nonzero-volume convex bodies, overlapping simplices have the minimal value of η c for d ⩾ 2. 

Although catenanes comprising two ring-shaped components can be made in large quantities by templation, the preparation of three-dimensional (3D) catenanes with cage-shaped components is still in its infancy. Here, we report the design and syntheses of two 3D catenanes by a sequence of S N 2 reactions in one pot. The resulting triply mechanically interlocked molecules were fully characterized in both the solution and solid states. Mechanistic studies have revealed that a suit[3]ane, which contains a threefold symmetric cage component as the suit and a tribromide component as the body, is formed at elevated temperatures. This suit[3]ane was identified as the key reactive intermediate for the selective formation of the two 3D catenanes which do not represent thermodynamic minima. We foresee a future in which this particular synthetic strategy guides the rational design and production of mechanically interlocked molecules under kinetic control. 

Sensor metadata tagging, akin to the named entity recognition task, provides key contextual information (e.g., measurement type and location) about sensors for running smart building applications. Unfortunately, sensor metadata in different buildings often follows dis- tinct naming conventions. Therefore, learning a tagger currently requires extensive annotations on a per building basis. In this work, we propose a novel framework, SeNsER, which learns a sensor metadata tagger for a new building based on its raw metadata and some existing fully annotated building. It leverages the commonality between different buildings: At the character level, it employs bidirectional neural language models to capture the shared underlying patterns between two buildings and thus regularizes the feature learning process; At the word level, it leverages as features the k-mers existing in the fully annotated building. During inference, we further incorporate the information obtained from sources such as Wikipedia as prior knowledge. As a result, SeNsER shows promising results in extensive experiments on multiple real-world buildings.