We study the problem of visibility-based exploration, reconstruction and surveillance in the context of supervised learning. Using a level set representation of data and information, we train a convolutional neural network to determine vantage points that maximize visibility. We show that this method drastically reduces the on-line computational cost and determines a small set of vantage points that solve the problem. This enables us to efficiently produce highly-resolved and topologically accurate maps of complex 3D environments. We present realistic simulations on 2D and 3D urban environments.
propose an alternating minimization scheme for optimizing the visibility of @math observers @cite_25 . use a system of differential equations to optimize the location and orientation of @math sensors to maximize surveillance @cite_6 . Both works assume the number of sensors is given.
@cite_25 @cite_6
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We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . We propose a computational method to optimally position a sensor system. Each sensor has limited range and viewing angle, and it may fail with a certain failure rate. The goal is to find the optimal locations as well as the viewing directions of all the sensors and achieve the maximal surveillance of the known environment. We set up the problem using the level set framework. Both the environment and the viewing range of the sensors are represented by level set functions. Then we solve a system of ordinary differential equations (ODEs) to find the optimal viewing directions and locations of all sensors together. Furthermore, we use the intermittent diffusion, which converts the ODEs into stochastic differential equations, to find the global maximum of the total surveillance area. The numerical examples include various failure rates of sensors, different rates of importance of the surveillance region, and 3-dimensional setups. They show the effectiveness of the proposed method. Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ... We consider an interval coverage problem. Given @math intervals of the same length on a line @math and a line segment @math on @math , we want to move the intervals along @math such that every point of @math is covered by at least one interval and the sum of the moving distances of all intervals is minimized. As a basic geometry problem, it has applications in mobile sensor barrier coverage in wireless sensor networks. The previous work solved the problem in @math time. In this paper, by discovering many interesting observations and developing new algorithmic techniques, we present an @math time algorithm. We also show an @math time lower bound for this problem, which implies the optimality of our algorithm. This paper addresses the maximal lifetime scheduling for sensor surveillance systems with K sensors to 1 target. Given a set of sensors and targets in an Euclidean plane, a sensor can watch only one target at a time and a target should be watched by k, k 1, sensors at any time. Our task is to schedule sensors to watch targets and pass data to the base station, such that the lifetime of the surveillance system is maximized, where the lifetime is the duration up to the time when there exists one target that cannot be watched by k sensors or data cannot be forwarded to the base station due to the depletion of energy of the sensor nodes. We propose an optimal solution to find the target watching schedule for sensors that achieves the maximal lifetime. Our solution consists of three steps: 1) computing the maximal lifetime of the surveillance system and a workload matrix by using linear programming techniques, 2) decomposing the workload matrix into a sequence of schedule matrices that can achieve the maximal lifetime, and 3) determining the sensor surveillance trees based on the above obtained schedule matrices, which specify the active sensors and the routes to pass sensed data to the base station. This is the first time in the literature that this scheduling problem of sensor surveillance systems has been formulated and the optimal solution has been found. We illustrate our optimal method by a numeric example and experiments in the end. Consider a set of @math agents seeking to solve distributively the minimization problem @math where the convex functions @math are local to the agents. The popular Alternating Direction Method of Multipliers has the potential to handle distributed optimization problems of this kind. We provide a general reformulation of the problem and obtain a class of distributed algorithms which encompass various network architectures. The rate of convergence of our method is considered. It is assumed that the infimum of the problem is reached at a point @math , the functions @math are twice differentiable at this point and @math in the positive definite ordering of symmetric matrices. With these assumptions, it is shown that the convergence to the consensus @math is linear and the exact rate is provided. Application examples where this rate can be optimized with respect to the ADMM free parameter @math are also given. A new algorithm is presented for computing a canonical rank- @math tensor approximation that has minimal distance to a given tensor in the Frobenius norm, where the canonical rank- @math tensor consists of the sum of @math rank-one tensors. Each iteration of the method consists of three steps. In the first step, a tentative new iterate is generated by a stand-alone one-step process, for which we use alternating least squares (ALS). In the second step, an accelerated iterate is generated by a nonlinear generalized minimal residual (GMRES) approach, recombining previous iterates in an optimal way, and essentially using the stand-alone one-step process as a preconditioner. In particular, the nonlinear extension of GMRES we use that was proposed by Washio and Oosterlee in [Electron. Trans. Numer. Anal., 15 (2003), pp. 165--185] for nonlinear partial differential equation problems (which is itself related to other existing acceleration methods for nonlinear equation systems). In the third step, a line search is perfor... Distributed algorithms for (re)configuring mobile sensors to cover a given area are important for autonomous multi-robot operations in application areas such as surveillance and environmental monitoring. Depending on the assumptions about the choice of the environment, the sensor models, the coverage metric, and the motion models of sensor nodes, there are different versions of the problem that have been formulated and studied. In this paper, we consider a system of holonomic mobile robots equipped with anisotropic sensors (e.g., limited field of view cameras) that are required to cover a polygonal region with polygonal obstacles to detect interesting events. We assume a given probability distribution of the events over a region. Motivated by scenarios where the sensing performance not only depends on the resolution of sensing but also on the relative orientation between the sensing axis and the event, we assume that the probability of detection of an event depends on both sensing parameters and the orientation of observation. We present a distributed gradient-ascent algorithm for reconfiguring the system of mobile robots so that the joint probability of detection of events over the whole region is maximized (i.e., positioning the mobile robots and determining their sensor parameters). As an example case study, we use a system of mobile robots equipped with limited field of view cameras with pan and zoom capabilities. We present simulation results demonstrating the performance of our algorithm. Unmanned Aerial Vehicle (UAV) networks have emerged as a promising technique to rapidly provide wireless coverage to a geographical area out of the reach or capacity of existing core networks, where a flying UAV can be fast deployed to serve as a base station. Existing work on UAV overlook the emergency deployment problem and only the recent research on sensor networks study the deployment problems the assumed in one-dimensional (1D) ground. However, UAVs should be deployed to the air (beyond one-dimension) by considering their different flying speeds during deployment and deployment altitudes, this paper studies this novel emergency UAV deployment to minimize the UAV deployment delay till covering the whole target area. When a number @math of diverse UAVs are dispatched from the same location (e.g., the closest UAV station) to the target area, we present an optimal deployment algorithm by balancing UAVs' diverse flying speeds and coverage radii, and this algorithm has low computation complexity @math . When UAVs are generally dispatched from different locations, we first prove that the emergency UAV deployment problem is NP-complete. By preserving UAVs' location order, we then successfully design a fully polynomial time approximation scheme (FPTAS) of computation complexity @math to arbitrarily approach the global optimum. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. We consider the following fundamental Mutual Visibility problem: Given a set of n identical autonomous point robots in arbitrary distinct positions in the Euclidean plane, find a schedule to move them such that within finite time they reach, without collisions, a configuration in which they all see each other. The robots operate following Look-Compute-Move cycles and a robot @math can not see other robot @math if there lies a third robot @math in the line segment connecting the positions of @math and @math . Moreover, n is not assumed to be known to the robots. We study this problem in the robots with lights model, where each robot has an externally visible persistent light which can assume colors from a fixed set of colors and the color set is identical to all the robots. This model corresponds to the classical model of oblivious robots when the number of colors @math in the color set. Therefore, we focus here on the objective of minimizing the number of colors required to successfully solve Mutual Visibility. Di [16] presented two algorithms and showed that Mutual Visibility can always be solved without collisions with @math colors for both semi-synchronous and asynchronous robots under both rigid and non-rigid moves. In this paper, we present and analyze an improved algorithm which requires only @math colors and works for both semi-synchronous and asynchronous robots under both rigid and non-rigid moves; this is optimal since any algorithm for Mutual Visibility needs at least 2 colors in the robots with lights model, when n is not known. We employ a non-trivial technique which moves all the interior robots first to the boundary of the initial convex hull and then the robots in the boundary of the hull except the corners to outside of the hull until all the robots eventually become corners, without the need of any third color. Our result is interesting in the sense that asynchronicity and non-rigidity of robot movements have no effect on Mutual Visibility with respect to the number of colors needed to successfully solve it. We also provide an improved solution to the Circle Formation problem. Wireless sensor networks (WSNs) are prone to propagating malware because of special characteristics of sensor nodes. Considering the fact that sensor nodes periodically enter sleep mode to save energy, we develop traditional epidemic theory and construct a malware propagation model consisting of seven states. We formulate differential equations to represent the dynamics between states. We view the decision-making problem between system and malware as an optimal control problem; therefore, we formulate a malware-defense differential game in which the system can dynamically choose its strategies to minimize the overall cost whereas the malware intelligently varies its strategies over time to maximize this cost. We prove the existence of the saddle-point in the game. Further, we attain optimal dynamic strategies for the system and malware, which are bang–bang controls that can be conveniently operated and are suitable for sensor nodes. Experiments identify factors that influence the propagation of malware. We also determine that optimal dynamic strategies can reduce the overall cost to a certain extent and can suppress the malware propagation. These results support a theoretical foundation to limit malware in WSNs. This paper addresses the problem of driving robotic sensors for an energy-constrained mobile wireless network in efficiently monitoring and predicting spatial phenomena, under data locational errors. The paper first discusses how errors of mobile sensor locations affect estimating and predicting the spatial physical processes, given that spatial field to be monitored is modeled by a Gaussian process. It then proposes an optimality criterion for designing optimal sampling paths for the mobile robotic sensors given the localization uncertainties. Although the optimization problem is optimally intractable, it can be resolved by a polynomial approximation algorithm, which is proved to be practically feasible in an energy-constrained mobile sensor network. More importantly, near-optimal solutions of this navigation problem are guaranteed by a lower bound within @math of the optimum. The performance of the proposed approach is evaluated on simulated and real-world data sets, where impact of sensor location errors on the results is demonstrated by comparing the results with those obtained by using noise-less data locations. We introduce a new random key predistribution scheme for securing heterogeneous wireless sensor networks. Each of the @math sensors in the network is classified into @math classes according to some probability distribution @math . Before deployment, a class- @math sensor is assigned @math cryptographic keys that are selected uniformly at random from a common pool of @math keys. Once deployed, a pair of sensors can communicate securely if and only if they have a key in common. We model the communication topology of this network by a newly defined inhomogeneous random key graph. We establish scaling conditions on the parameters @math and @math so that this graph: 1) has no isolated nodes and 2) is connected, both with high probability. The results are given in the form of zero-one laws with the number of sensors @math growing unboundedly large; critical scalings are identified and shown to coincide for both graph properties. Our results are shown to complement and improve those given by and for the same model, therein referred to as the general random intersection graph. Phase retrieval problems involve solving linear equations, but with missing sign (or phase, for complex numbers) information. More than four decades after it was first proposed, the seminal error reduction algorithm of (Gerchberg and Saxton 1972) and (Fienup 1982) is still the popular choice for solving many variants of this problem. The algorithm is based on alternating minimization; i.e. it alternates between estimating the missing phase information, and the candidate solution. Despite its wide usage in practice, no global convergence guarantees for this algorithm are known. In this paper, we show that a (resampling) variant of this approach converges geometrically to the solution of one such problem -- finding a vector @math from @math , where @math and @math denotes a vector of element-wise magnitudes of @math -- under the assumption that @math is Gaussian. Empirically, we demonstrate that alternating minimization performs similar to recently proposed convex techniques for this problem (which are based on "lifting" to a convex matrix problem) in sample complexity and robustness to noise. However, it is much more efficient and can scale to large problems. Analytically, for a resampling version of alternating minimization, we show geometric convergence to the solution, and sample complexity that is off by log factors from obvious lower bounds. We also establish close to optimal scaling for the case when the unknown vector is sparse. Our work represents the first theoretical guarantee for alternating minimization (albeit with resampling) for any variant of phase retrieval problems in the non-convex setting. The usual approach to developing and analyzing first-order methods for smooth convex optimization assumes that the gradient of the objective function is uniformly smooth with some Lipschitz constant @math . However, in many settings the differentiable convex function @math is not uniformly smooth---for example, in @math -optimal design where @math and @math , or even the univariate setting with @math . In this paper we develop a notion of “relative smoothness” and relative strong convexity that is determined relative to a user-specified “reference function” @math (that should be computationally tractable for algorithms), and we show that many differentiable convex functions are relatively smooth with respect to a correspondingly fairly simple reference function @math . We extend two standard algorithms---the primal gradient scheme and the dual averaging scheme---to our new setting, with associated computational guarantees. We apply our new a... Given a simplicial complex with weights on its simplices, and a nontrivial cycle on it, we are interested in finding the cycle with minimal weight which is homologous to the given one. Assuming that the homology is defined with integer ( @math ) coefficients, we show the following (Theorem 5.2): For a finite simplicial complex @math of dimension greater than @math , the boundary matrix @math is totally unimodular if and only if @math is torsion-free for all pure subcomplexes @math in @math of dimensions @math and @math , respectively, where @math . Because of the total unimodularity of the boundary matrix, we can solve the optimization problem, which is inherently an integer programming problem, as a linear program and obtain an integer solution. Thus, the problem of finding optimal cycles in a given homology class can be solved in polynomial time. This result is surprising in the backdrop of a recent result which says that the problem is NP-hard under @math coefficients which, being a field, is in general easier to deal with. Our result implies, among other things, that one can compute in polynomial time an optimal @math -cycle in a given homology class for any triangulation of an orientable compact @math -manifold or for any finite simplicial complex embedded in @math . Our optimization approach can also be used for various related problems, such as finding an optimal chain homologous to a given one when these are not cycles. Our result can also be viewed as providing a topological characterization of total unimodularity. Two widely studied models of multiple-node repair in distributed storage systems are centralized repair and cooperative repair. The centralized model assumes that all the failed nodes are recreated in one location, while the cooperative one stipulates that the failed nodes may communicate but are distinct, and the amount of data exchanged between them is included in the repair bandwidth. We show that cooperative model is stronger than the centralized one, in the sense that MDS codes with optimal repair bandwidth under the former model have the same property under the latter one. In this paper we present explicit constructions of MDS codes with optimal cooperative repair for all possible parameters. More precisely, given any @math such that @math we construct explicit @math MDS codes over the field @math of size @math that can optimally repair any @math erasures from any @math helper nodes. The repair scheme of our codes involves two rounds of communication. In the first round, each failed node downloads information from the helper nodes, and in the second one, each failed node downloads additional information from the other failed nodes. This shows that two rounds of communication in cooperative repair always suffice, and that the proposed codes achieve the optimal repair bandwidth using the smallest possible number of rounds. The problem of distributed detection involving N sensors is considered. The configuration of sensors is serial in the sense that the Jth sensor decides using the decision it receives along with its own observation. When each sensor uses the Neyman-Pearson test, the probability of detection is maximized for a given probability of false alarm, at the Nth stage. With two sensors, the serial scheme has a performance better than or equal to the parallel fusion scheme analyzed in the literature. Numerical examples illustrate the global optimization by the selection of operating thresholds at the sensors. > To achieve better performance, we adopt a Heterogeneous Sensor Network (HSN) model. In many applications, the locations of some sensor nodes are controllable. In this paper, first we propose a novel density-varying deployment scheme for high-end sensors (H-sensors) in an HSN. The scheme solves the bottleneck problem in typical many-to-one sensor networks. We then study the optimal placement of H-sensors whose locations are controllable. The goal is to use the minimum number of H-sensors for ensuring successful data delivery, coverage and connectivity in a network for a given lifetime. We present an effective H-sensor placement scheme that can simultaneously achieve coverage, connectivity and data relay requirements while uses a small number of H-sensors. Both theoretical proofs and simulation results demonstrate that the proposed H-sensor placement scheme achieves very good performance.