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We describe mechanical metamaterials created by folding flat sheets in the tradition of origami, the art of paper folding, and study them in terms of their basic geometric and stiffness properties, as well as load bearing capability. A periodic Miura-ori pattern and a non-periodic Ron Resch pattern were studied. Unexceptional coexistence of positive and negative Poisson's ratio was reported for Miura-ori pattern, which are consistent with the interesting shear behavior and infinity bulk modulus of the same pattern. Unusually strong load bearing capability of the Ron Resch pattern was found and attributed to the unique way of folding. This work paves the way to the study of intriguing properties of origami structures as mechanical metamaterials.

Abstract. We have created a large diverse set of cars from overhead images 1 , which are useful for training a deep learner to binary classify, detect and count them. The dataset and all related material will be made publically available. The set contains contextual matter to aid in identification of difficult targets. We demonstrate classification and detection on this dataset using a neural network we call ResCeption. This network combines residual learning with Inception-style layers and is used to count cars in one look. This is a new way to count objects rather than by localization or density estimation. It is fairly accurate, fast and easy to implement. Additionally, the counting method is not car or scene specific. It would be easy to train this method to count other kinds of objects and counting over new scenes requires no extra set up or assumptions about object locations.

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The covering Steiner problem is a generalization of both the k‐MST and the group Steiner problems: given an edge‐weighted graph, with subsets of vertices called the groups, and a nonnegative integer value (called the requirement) for each group, the problem is to find a minimum‐weight tree spanning at least the required number of vertices of every group. When all requirements are equal to 1, this becomes the group Steiner problem, while if there is only one group which contains all vertices of the graph the problem reduces to k‐MST with k equal to the requirement of this unique group. We discuss two different (but equivalent) linear relaxations of the problem for the case when the given graph is a tree and construct polylogarithmic approximation algorithms based on randomized LP rounding of these relaxations. By using a probabilistic approximation of general metrics by tree metrics due to Bartal, our algorithms also solve the covering Steiner problem on general graphs with a further polylogarithmic worsening in the approximation ratio. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 20:465–483, 2002

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We study ways to restrict or prevent the damage that can be caused in a peer-to-peer network by corrupt entities creating multiple pseudonyms. We show that it is possible to remotely issue certificates that can be used to test the distinctness of identities. Our certification protocols are based on geometric techniques that establish location information in a fault-tolerant and distributed fashion. They do not rely on a centralized certifying authority or infrastructure that has direct knowledge of entities in the system, and work in Euclidean or spherical geometry of arbitrary dimension. They tolerate corrupt entities, including corrupt certifiers, collusion by either certification applicants or certifiers, and either a broadcast or point-to-point message model.