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  1. Geometric graph models of systems as diverse as proteins, DNA assemblies, architected materials and robot swarms are useful abstract representations of these objects that also unify ways to study their properties and control them in space and time. While much work has been done in the context of characterizing the behaviour of these networks close to critical points associated with bond and rigidity percolation, isostaticity, etc., much less is known about floppy, underconstrained networks that are far more common in nature and technology. Here, we combine geometric rigidity and algebraic sparsity to provide a framework for identifying the zero energy floppy modes via a representation that illuminates the underlying hierarchy and modularity of the network and thence the control of its nestedness and locality. Our framework allows us to demonstrate a range of applications of this approach that include robotic reaching tasks with motion primitives, and predicting the linear and nonlinear response of elastic networks based solely on infinitesimal rigidity and sparsity, which we test using physical experiments. Our approach is thus likely to be of use broadly in dissecting the geometrical properties of floppy networks using algebraic sparsity to optimize their function and performance.

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  2. The ability to estimate the 3D human shape and pose from images can be useful in many contexts. Recent approaches have explored using graph convolutional networks and achieved promising results. The fact that the 3D shape is represented by a mesh, an undirected graph, makes graph convolutional networks a natural fit for this problem. However, graph convolutional networks have limited representation power Information from nodes in the graph is passed to connected neighbors, and propagation of information requires successive graph convolutions. To overcome this limitation, we propose a dual-scale graph approach. We use a coarse graph, derived from a dense graph, to estimate the human’s 3D pose, and the dense graph to estimate the 3D shape. Information in coarse graphs can be propagated over longer distances compared to dense graphs. In addition, information about pose can guide to recover local shape detail and vice versa. We recognize that the connection between coarse and dense is itself a graph, and introduce graph fusion blocks to exchange information between graphs with different scales. We train our model end-to-end and show that we can achieve state-of-the-art results for several evaluation datasets. The code is available at the following link, 
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    How can we manipulate the topological connectivity of a three-dimensional prismatic assembly to control the number of internal degrees of freedom and the number of connected components in it? To answer this question in a deterministic setting, we use ideas from elementary number theory to provide a hierarchical deterministic protocol for the control of rigidity and connectivity. We then show that it is possible to also use a stochastic protocol to achieve the same results via a percolation transition. Together, these approaches provide scale-independent algorithms for the cutting or gluing of three-dimensional prismatic assemblies to control their overall connectivity and rigidity. 
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  5. Kirigami, the creative art of paper cutting, is a promising paradigm for mechanical metamaterials. However, to make kirigami-inspired structures a reality requires controlling the topology of kirigami to achieve connectivity and rigidity. We address this question by deriving the maximum number of cuts (minimum number of links) that still allow us to preserve global rigidity and connectivity of the kirigami. A deterministic hierarchical construction method yields an efficient topological way to control both the number of connected pieces and the total degrees of freedom. A statistical approach to the control of rigidity and connectivity in kirigami with random cuts complements the deterministic pathway, and shows that both the number of connected pieces and the degrees of freedom show percolation transitions as a function of the density of cuts (links). Together, this provides a general framework for the control of rigidity and connectivity in planar kirigami.

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  6. Origami structures with a large number of excess folds are capable of storing distinguishable geometric states that are energetically equivalent. As the number of excess folds is reduced, the system has fewer equivalent states and can eventually become rigid. We quantify this transition from a floppy to a rigid state as a function of the presence of folding constraints in a classic origami tessellation, Miura-ori. We show that in a fully triangulated Miura-ori that is maximally floppy, adding constraints via the elimination of diagonal folds in the quads decreases the number of degrees of freedom in the system, first linearly and then nonlinearly. In the nonlinear regime, mechanical cooperativity sets in via a redundancy in the assignment of constraints, and the degrees of freedom depend on constraint density in a scale-invariant manner. A percolation transition in the redundancy in the constraints as a function of constraint density suggests how excess folds in an origami structure can be used to store geometric information in a scale-invariant way.

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  7. Abstract

    We present DR-Train, the first long-term open-access dataset recording dynamic responses from in-service light rail vehicles. Specifically, the dataset contains measurements from multiple sensor channels mounted on two in-service light rail vehicles that run on a 42.2-km light rail network in the city of Pittsburgh, Pennsylvania. This dataset provides dynamic responses of in-service trains via vibration data collected by accelerometers, which enables a low-cost way of monitoring rail tracks more frequently. Such an approach will result in more reliable and economical ways to monitor rail infrastructure. The dataset also includes corresponding GPS positions of the trains, environmental conditions (including temperature, wind, weather, and precipitation), and track maintenance logs. The data, which is stored in a MAT-file format, can be conveniently loaded for various potential uses, such as validating anomaly detection and data fusion as well as investigating environmental influences on train responses.

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