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Sensor placement optimization methods have been studied extensively. They can be applied to a wide range of applications, including surveillance of known environments, optimal locations for 5G towers, and placement of missile defense systems. However, few works explore the robustness and efficiency of the resulting sensor network concerning sensor failure or adversarial attacks. This paper addresses this issue by optimizing for the least number of sensors to achieve multiple coverage of non-simply connected domains by a prescribed number of sensors. We introduce a new objective function for the greedy (next-best-view) algorithm to design efficient and robust sensor networks and derive theoretical bounds on the network's optimality. We further introduce a Deep Learning model to accelerate the algorithm for near real-time computations. The Deep Learning model requires the generation of training examples. Correspondingly, we show that understanding the geometric properties of the training data set provides important insights into the performance and training process of deep learning techniques. Finally, we demonstrate that a simple parallel version of the greedy approach using a simpler objective can be highly competitive.

This paper investigates the impact of multiscale data on machine learning algorithms, particularly in the context of deep learning. A dataset is multiscale if its distribution shows large variations in scale across different directions. This paper reveals multiscale structures in the loss landscape, including its gradients and Hessians inherited from the data. Correspondingly, it introduces a novel gradient descent approach, drawing inspiration from multiscale algorithms used in scientific computing. This approach seeks to transcend empirical learning rate selection, offering a more systematic, data-informed strategy to enhance training efficiency, especially in the later stages., Comment: 28 pages, 4 figures, submitted under review

We address the problem of efficient and unobstructed surveillance or communication in complex environments. On one hand, one wishes to use a minimal number of sensors to cover the environment. On the other hand, it is often important to consider solutions that are robust against sensor failure or adversarial attacks. This paper addresses these challenges of designing minimal sensor sets that achieve multi-coverage constraints -- every point in the environment is covered by a prescribed number of sensors. We propose a greedy algorithm to achieve the objective. Further, we explore deep learning techniques to accelerate the evaluation of the objective function formulated in the greedy algorithm. The training of the neural network reveals that the geometric properties of the data significantly impact the network's performance, particularly at the end stage. By taking into account these properties, we discuss the differences in using greedy and $\epsilon$-greedy algorithms to generate data and their impact on the robustness of the network.

Player performance prediction is a serious problem in every sport since it brings valuable future information for managers to make important decisions. In baseball industries, there already existed variable prediction systems and many types of researches that attempt to provide accurate predictions and help domain users. However, it is a lack of studies about the predicting method or systems based on deep learning. Deep learning models had proven to be the greatest solutions in different fields nowadays, so we believe they could be tried and applied to the prediction problem in baseball. Hence, the predicting abilities of deep learning models are set to be our research problem in this paper. As a beginning, we select numbers of home runs as the target because it is one of the most critical indexes to understand the power and the talent of baseball hitters. Moreover, we use the sequential model Long Short-Term Memory as our main method to solve the home run prediction problem in Major League Baseball. We compare models' ability with several machine learning models and a widely used baseball projection system, sZymborski Projection System. Our results show that Long Short-Term Memory has better performance than others and has the ability to make more exact predictions. We conclude that Long Short-Term Memory is a feasible way for performance prediction problems in baseball and could bring valuable information to fit users' needs., Comment: 25 pages, 1 figures, 18 tables

We consider surveillance-evasion differential games, where a pursuer must try to constantly maintain visibility of a moving evader. The pursuer loses as soon as the evader becomes occluded. Optimal controls for game can be formulated as a Hamilton-Jacobi-Isaac equation. We use an upwind scheme to compute the feedback value function, corresponding to the end-game time of the differential game. Although the value function enables optimal controls, it is prohibitively expensive to compute, even for a single pursuer and single evader on a small grid. We consider a discrete variant of the surveillance-game. We propose two locally optimal strategies based on the static value function for the surveillance-evasion game with multiple pursuers and evaders. We show that Monte Carlo tree search and self-play reinforcement learning can train a deep neural network to generate reasonable strategies for on-line game play. Given enough computational resources and offline training time, the proposed model can continue to improve its policies and efficiently scale to higher resolutions.

We propose a new framework for the sampling, compression, and analysis of distributions of point sets and other geometric objects embedded in Euclidean spaces. Our approach involves constructing a tensor called the RaySense sketch, which captures nearest neighbors from the underlying geometry of points along a set of rays. We explore various operations that can be performed on the RaySense sketch, leading to different properties and potential applications. Statistical information about the data set can be extracted from the sketch, independent of the ray set. Line integrals on point sets can be efficiently computed using the sketch. We also present several examples illustrating applications of the proposed strategy in practical scenarios., Comment: 48 pages, 14 figures, accepted to Communication on Applied Mathematics and Computation (CAMC), Focused Issue in Honor of Prof. Stanley Osher on the Occasion of His 80th Birthday. Fixed typos and improved notations

We consider the exploration problem: an agent equipped with a depth sensor must map out a previously unknown environment using as few sensor measurements as possible. We propose an approach based on supervised learning of a greedy algorithm. We provide a bound on the optimality of the greedy algorithm using submodularity theory. Using a level set representation, 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. Unlike traditional next-best-view and frontier-based strategies, the proposed method accounts for geometric priors while evaluating potential vantage points. While existing deep learning approaches focus on obstacle avoidance and local navigation, our method aims at finding near-optimal solutions to the more global exploration problem. We present realistic simulations on 2D and 3D urban environments.

Bias and heterogeneity in peer assessment can lead to the issue of unfair scoring in the educational field. To deal with this problem, we propose a reference ranking method for an online peer assessment system using HodgeRank. Such a scheme provides instructors with an objective scoring reference based on mathematics., Comment: 7 pages. To appear in MLRec 2018

We propose a new neural network architecture for automatic generation of missing characters in a Chinese font set. We call the neural network architecture the Variational Grid Setting Network which is based on the variational autoencoder (VAE) with some tweaks. The neural network model is able to generate missing characters relatively large in size ($256 \times 256$ pixels). Moreover, we show that one can use very few samples for training data set, and get a satisfied result., Comment: 8 pages, 6 figures

We study analytically and numerical the growth rate of a crystal surface growing by several screw dislocations. To describe several spiral steps we use the revised level set method for spirals by the authors (Journal of Scientific Computing 62, 831-874, 2015). We carefully compare our simulation results on the growth rates with predictions in a classical paper by Burton et al. (Philos Trans R Soc Lond Ser A Math Phys Sci 243,299-358, 1951). Then, we propose improved estimates on the growth rate with several different configurations, which are in agreement with our numerical simulations. The influence of distribution of screw dislocations in a group on a line to the growth rate, and the growth rate by a group including different rotational orientations of spirals are also studied in this paper., Comment: 45 pages

The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging class of problems including problems with sonic points, shocks originating in the interior of the domain, rarefaction waves, and two-dimensional systems. We show that fast sweeping methods can produce higher-order accuracy. Computational results validate the claims of accuracy, sharp shock curves, and optimal computational efficiency.

Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton-Jacobi equations. By adapting the main idea behind these methods, we describe a new approach for computing steady state solutions to systems of conservation laws. By exploiting the flow of information along characteristics, these fast sweeping methods can compute solutions very efficiently. Furthermore, the methods capture shocks sharply by directly imposing the Rankine-Hugoniot shock conditions. We present convergence analysis and numerics for several one- and two-dimensional examples to illustrate the use and advantages of this approach.

Colorectal polyps are important precursors to colon cancer, a major health problem. Colon capsule endoscopy (CCE) is a safe and minimally invasive examination procedure, in which the images of the intestine are obtained via digital cameras on board of a small capsule ingested by a patient. The video sequence is then analyzed for the presence of polyps. We propose an algorithm that relieves the labor of a human operator analyzing the frames in the video sequence. The algorithm acts as a binary classifier, which labels the frame as either containing polyps or not, based on the geometrical analysis and the texture content of the frame. The geometrical analysis is based on a segmentation of an image with the help of a mid-pass filter. The features extracted by the segmentation procedure are classified according to an assumption that the polyps are characterized as protrusions that are mostly round in shape. Thus, we use a best fit ball radius as a decision parameter of a binary classifier. We present a statistical study of the performance of our approach on a data set containing over 18,900 frames from the endoscopic video sequences of five adult patients. The algorithm demonstrates a solid performance, achieving 47% sensitivity per frame and over 81% sensitivity per polyp at a specificity level of 90%. On average, with a video sequence length of 3747 frames, only 367 false positive frames need to be inspected by a human operator., Comment: 16 pages, 9 figures, 4 tables