We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media, with online parallel complexity that scales optimally as @math , where @math is the number of volume unknowns, and @math is the number of processors, as long as @math grows at most like a small fractional power of @math . The solver decomposes the domain into layers, and uses transmission conditions in boundary integral form to explicitly define "polarized traces", i.e., up- and down-going waves sampled at interfaces. Local direct solvers are used in each layer to precompute traces of local Green's functions in an embarrassingly parallel way (the offline part), and incomplete Green's formulas are used to propagate interface data in a sweeping fashion, as a preconditioner inside a GMRES loop (the online part). Adaptive low-rank partitioning of the integral kernels is used to speed up their application to interface data. The method uses second-order finite differences. The complexity scalings are empirical but motivated by an analysis of ranks of off-diagonal blocks of oscillatory integrals. They continue to hold in the context of standard geophysical community models such as BP and Marmousi 2, where convergence occurs in 5 to 10 GMRES iterations.
Finally, an earlier version of the work presented in this paper can be found in @cite_20 , in which the notion of polarized traces using Green's representation formula was first introduced, obtaining favorable scalings;
@cite_20
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Convolutional neural networks (CNNs) are inherently equivariant to translation. Efforts to embed other forms of equivariance have concentrated solely on rotation. We expand the notion of equivariance in CNNs through the Polar Transformer Network (PTN). PTN combines ideas from the Spatial Transformer Network (STN) and canonical coordinate representations. The result is a network invariant to translation and equivariant to both rotation and scale. PTN is trained end-to-end and composed of three distinct stages: a polar origin predictor, the newly introduced polar transformer module and a classifier. PTN achieves state-of-the-art on rotated MNIST and the newly introduced SIM2MNIST dataset, an MNIST variation obtained by adding clutter and perturbing digits with translation, rotation and scaling. The ideas of PTN are extensible to 3D which we demonstrate through the Cylindrical Transformer Network We introduce a family of kernels on graphs based on the notion of regularization operators. This generalizes in a natural way the notion of regularization and Greens functions, as commonly used for real valued functions, to graphs. It turns out that diffusion kernels can be found as a special case of our reasoning. We show that the class of positive, monotonically decreasing functions on the unit interval leads to kernels and corresponding regularization operators. SUMMARY We present a domain decomposition solver for the 2D Helmholtz equation, with a special choice of integral transmission condition that involves polarizing the waves into oneway components. This refinement of the transmission condition is the key to combining local direct solves into an efficient iterative scheme, which can then be deployed in a highperformance computing environment. The method involves an expensive, but embarrassingly parallel precomputation of local Green’s functions, and a fast online computation of layer potentials in partitioned low-rank form. The online part has sequential complexity that scales sublinearly with respect to the number of volume unknowns, even in the high-frequency regime. The favorable complexity scaling continues to hold in the context of low-order finite difference schemes for standard community models such as BP and Marmousi2, where convergence occurs in 5 to 10 GMRES iterations. Spectrum-based fault localization refers to the process of identifying program units that are buggy from two sets of execution traces: normal traces and faulty traces. These approaches use statistical formulas to measure the suspiciousness of program units based on the execution traces. There have been many spectrum-based fault localization approaches proposing various formulas in the literature. Two of the best performing and well-known ones are Tarantula and Ochiai. Recently, find that theoretically, under certain assumptions, two families of spectrum-based fault localization formulas outperform all other formulas including those of Tarantula and Ochiai. In this work, we empirically validate 's findings by comparing the performance of the theoretically best formulas against popular approaches on a dataset containing 199 buggy versions of 10 programs. Our empirical study finds that Ochiai and Tarantula statistically significantly outperforms 3 out of 5 theoretically best fault localization techniques. For the remaining two, Ochiai also outperforms them, albeit not statistically significantly. This happens because an assumption in 's work is not satisfied in many fault localization settings. Unmanned aerial vehicles (UAVs) have the potential to significantly impact early detection and monitoring of plant diseases. In this paper, we present preliminary work in developing a UAV-mounted sensor suite for detection of citrus greening disease, a major threat to Florida citrus production. We propose a depth-invariant sensing methodology for measuring reflectance of polarized amber light, a metric which has been found to measure starch accumulation in greening-infected leaves. We describe the implications of adding depth information to this method, including the use of machine learning models to discriminate between healthy and infected leaves with validation accuracies up to 93 . Additionally, we discuss stipulations and challenges of use of the system with UAV platforms. This sensing system has the potential to allow for rapid scanning of groves to determine the spread of the disease, especially in areas where infection is still in early stages, including citrus farms in California. Although presented in the context of citrus greening disease, the methods can be applied to a variety of plant pathology studies, enabling timely monitoring of plant health—impacting scientists, growers, and policymakers. An arithmetic read-once formula (ROF for short) is a formula (a circuit whose underlying graph is a tree) in which the operations are + ,× and such that every input variable labels at most one leaf. In this paper we study the problems of giving deterministic identity testing and reconstruction algorithms for ROFs. Our main result is an @math time deterministic algorithm for checking whether a black box holding the sum of k n -variate ROFs computes the zero polynomial. In other words, we provide a hitting set of size @math for the sum of k ROFs. This result greatly improves [27] where an @math algorithm was given for the problem. Using our new results we obtain a deterministic reconstruction algorithms for read-once formulas that runs in time @math . In fact, our results also hold for the more general model of preprocessed read-once formulas that we define in this paper. In this model we are allowed to replace each variable x i with a polynomial T i (x i ). Our techniques are very close to the techniques in [27]. The main difference is that we obtain several tighter versions of the tools first used there. In particular we obtain a better version of the hardness of representation approach which was first used in [27]. This technique can be thought of as a very explicit way of transforming (mild) hardness of a very structured polynomial to an identity testing algorithm. We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the denotation of a unique cut-free proof net. A key role is played by the notion of history-free strategy: strong connections are made between history-free strategies and the Geometry of Interaction. Our semantics incorporates a natural notion of polarity, leading to a refined treatment of the additives. We make comparisons with related work by Joyal, Blass, et al GENERAL MEASURE THEORY Measures and Measurable Functions Lusin's and Egoroff's Theorems Integrals and Limit Theorems Product Measures, Fubini's Theorem, Lebesgue Measure Covering Theorems Differentiation of Radon Measures Lebesgue Points Approximate continuity Riesz Representation Theorem Weak Convergence and Compactness for Radon Measures HAUSDORFF MEASURE Definitions and Elementary Properties Hausdorff Dimension Isodiametric Inequality Densities Hausdorff Measure and Elementary Properties of Functions AREA AND COAREA FORMULAS Lipschitz Functions, Rademacher's Theorem Linear Maps and Jacobians The Area Formula The Coarea Formula SOBOLEV FUNCTIONS. Definitions And Elementary Properties. Approximation Traces. Extensions. Sobolev Inequalities Compactness. Capacity Quasicontinuity Precise Representations of Sobolev Functions. Differentiability on Lines BV FUNCTIONS AND SETS OF FINITE PERIMETER Definitions and Structure Theorem Approximation and Compactness Traces. Extensions. Coarea Formula for BV Functions. Isoperimetric Inequalities. The Reduced Boundary The Measure Theoretic Boundary Gauss-Green Theorem. Pointwise Properties of BV Functions Essential Variation on Lines A Criterion for Finite Perimeter. DIFFERENTIABILITY AND APPROXIMATION BY C1 FUNCTIONS. Lp Differentiability a.e. Approximate Differentiability Differentiability A.E. for W1,P (P > N). Convex Functions Second Derivatives a.e. for convex functions Whitney's Extension Theorem Approximation by C1 Functions NOTATION REFERENCES We extend the trace semantics for labeled transition systems to a randomized model of concurrent computation. The main objective is to obtain a compositional semantics. The role of a trace in the randomized model is played by a probability distribution over traces, called a trace distribution. We show that the preorder based on trace distribution inclusion is not a precongruence, and we build an elementary context, called the principal context, that is sufficiently powerful to characterize the coarsest precongruence that is contained in the trace distribution preorder. Finally, we introduce a notion of a probabilistic forward simulation and we prove that it is sound for the trace distribution precongruence. An important characteristic of probabilistic forward simulations is that they relate states to probability distributions over states. Previous research indicates that during the past 20 years, the highest-quality work has been published in an increasingly diverse and larger group of journals. In this article, we examine whether this diversification has also affected the handful of elite journals that are traditionally considered to be the best. We examine citation patterns during the past 40 years of seven long-standing traditionally elite journals and six journals that have been increasing in importance during the past 20 years. To be among the top 5 or 1 cited papers, papers now need about twice as many citations as they did 40 years ago. Since the late 1980s and early 1990s, elite journals have been publishing a decreasing proportion of these top-cited papers. This also applies to the two journals that are typically considered as the top venues and often used as bibliometric indicators of "excellence": Science and Nature. On the other hand, several new and established journals are publishing an increasing proportion of the most-cited papers. These changes bring new challenges and opportunities for all parties. Journals can enact policies to increase or maintain their relative position in the journal hierarchy. Researchers now have the option to publish in more diverse venues knowing that their work can still reach the same audiences. Finally, evaluators and administrators need to know that although there will always be a certain prestige associated with publishing in "elite" journals, journal hierarchies are in constant flux. We introduce Elephant Tracks (ET), a dynamic program analysis tool for producing traces of garbage collection events, including object allocations, object deaths, and pointer updates. Like prior work, our tracing tool is based on the Merlin algorithm [2002], but offers several substantial new capabilities. First, it is much more precise than previous tools: it measures time in terms of method entries and exits, allowing it to place events precisely in the context of the program structure. Furthermore, we exploit this notion of time to actually reduce the amount of work required to compute precise object death times. Second, it is implemented using a combination of JVM Tool Interface (JVMTI) Microsystems [2004] callbacks and bytecode rewriting, and works with any standard JVM. Finally, it properly handles Java Reference objects, including weak references, finalization, and multithreaded programs. The paper presents a connectionist framework that is capable of representing and learning propositional knowledge. An extended version of propositional calculus is developed and is demonstrated to be useful for nonmonotonic reasoning, dealing with conflicting beliefs and for coping with inconsistency generated by unreliable knowledge sources. Formulas of the extended calculus are proved to be equivalent in a very strong sense to symmetric networks (like Hopfield networks and Boltzmann machines), and efficient algorithms are given for translating back and forth between the two forms of knowledge representation. A fast learning procedure is presented that allows symmetric networks to learn representations of unknown logic formulas by looking at examples. A connectionist inference engine is then sketched whose knowledge is either compiled from a symbolic representation or learned inductively from training examples. Experiments with large scale randomly generated formulas suggest that the parallel local search that is executed by the networks is extremely fast on average. Finally, it is shown that the extended logic can be used as a high-level specification language for connectionist networks, into which several recent symbolic systems may be mapped. The paper demonstrates how a rigorous bridge can be constructed that ties together the (sometimes opposing) connectionist and symbolic approaches. The authors propose models for both temporal and spatial locality of reference in streams of requests arriving at Web servers. They show that simple models based on document popularity alone are insufficient for capturing either temporal or spatial locality. Instead, they rely on an equivalent, but numerical, representation of a reference stream: a stack distance trace. They show that temporal locality can be characterized by the marginal distribution of the stack distance trace, and propose models for typical distributions and compare their cache performance to the traces. They also show that spatial locality in a reference stream can be characterized using the notion of self-similarity. Self-similarity describes long-range correlations in the data set, which is a property that previous researchers have found hard to incorporate into synthetic reference strings. They show that stack distance strings appear to be strongly self-similar, and provide measurements of the degree of self-similarity in the traces. Finally, they discuss methods for generating synthetic Web traces that exhibit the properties of temporal and spatial locality measured in the data. Causal exponentials play a fundamental role in classical system theory. Starting from those elementary building blocks, we propose a complete and self-contained signal processing formulation of exponential splines defined on a uniform grid. We specify the corresponding B-spline basis functions and investigate their reproduction properties (Green function and exponential polynomials); we also characterize their stability (Riesz bounds). We show that the exponential B-spline framework allows an exact implementation of continuous-time signal processing operators including convolution, differential operators, and modulation, by simple processing in the discrete B-spline domain. We derive efficient filtering algorithms for multiresolution signal extrapolation and approximation, extending earlier results for polynomial splines. Finally, we present a new asymptotic error formula that predicts the magnitude and the Nth-order decay of the L sub 2 -approximation error as a function of the knot spacing T. The increasing availability of large-scale location traces creates unprecedent opportunities to change the paradigm for knowledge discovery in transportation systems. A particularly promising area is to extract energy-efficient transportation patterns (green knowledge), which can be used as guidance for reducing inefficiencies in energy consumption of transportation sectors. However, extracting green knowledge from location traces is not a trivial task. Conventional data analysis tools are usually not customized for handling the massive quantity, complex, dynamic, and distributed nature of location traces. To that end, in this paper, we provide a focused study of extracting energy-efficient transportation patterns from location traces. Specifically, we have the initial focus on a sequence of mobile recommendations. As a case study, we develop a mobile recommender system which has the ability in recommending a sequence of pick-up points for taxi drivers or a sequence of potential parking positions. The goal of this mobile recommendation system is to maximize the probability of business success. Along this line, we provide a Potential Travel Distance (PTD) function for evaluating each candidate sequence. This PTD function possesses a monotone property which can be used to effectively prune the search space. Based on this PTD function, we develop two algorithms, LCP and SkyRoute, for finding the recommended routes. Finally, experimental results show that the proposed system can provide effective mobile sequential recommendation and the knowledge extracted from location traces can be used for coaching drivers and leading to the efficient use of energy. Counting the number of leaves in plants is important for plant phenotyping, since it can be used to assess plant growth stages. We propose a learning-based approach for counting leaves in rosette (model) plants. We relate image-based descriptors learned in an unsupervised fashion to leaf counts using a supervised regression model. To take advantage of the circular and coplanar arrangement of leaves and also to introduce scale and rotation invariance, we learn features in a log-polar representation. Image patches extracted in this log-polar domain are provided to K-means, which builds a codebook in a unsupervised manner. Feature codes are obtained by projecting patches on the codebook using the triangle encoding, introducing both sparsity and specifically designed representation. A global, per-plant image descriptor is obtained by pooling local features in specific regions of the image. Finally, we provide the global descriptors to a support vector regression framework to estimate the number of leaves in a plant. We evaluate our method on datasets of the (LCC), containing images of Arabidopsis and tobacco plants. Experimental results show that on average we reduce absolute counting error by 40 w.r.t. the winner of the 2014 edition of the challenge -a counting via segmentation method. When compared to state-of-the-art density-based approaches to counting, on Arabidopsis image data 75 less counting errors are observed. Our findings suggest that it is possible to treat leaf counting as a regression problem, requiring as input only the total leaf count per training image. We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform way. We define Equation found, the infinitary extension of a given equational theory =R, and →∞, the standard notion of infinitary rewriting associated to a reduction relation →R, as follows: (Formula Presented) Equation found Here μ and ν are the least and greatest fixed-point operators, respectively, and (Formula Presented) Equation found The setup captures rewrite sequences of arbitrary ordinal length, but it has neither the need for ordinals nor for metric convergence. This makes the framework especially suitable for formalizations in theorem provers. The theme of this work is an "inside-out" approach to the enumeration of graphs. It is based on a well-known decomposition of a graph into its 2-core, i.e. the largest subgraph of minimum degree 2 or more, and a forest of trees attached. Using our earlier (asymptotic) formulae for the total number of 2-cores with a given number of vertices and edges, we solve the corresponding enumeration problem for the connected 2-cores. For a subrange of the parameters, we also enumerate those 2-cores by using a deeper inside-out notion of a kernel of a connected 2-core.Using this enumeration result in combination with Caley's formula for forests, we obtain an alternative and simpler proof of the asymptotic formula of Bender, Canfield and McKay for the number of connected graphs with n vertices and m edges, with improved error estimate for a range of m values.As another application, we study the limit joint distribution of three parameters of the giant component of a random graph with n vertices in the supercritical phase, when the difference between average vertex degree and 1 far exceeds n-1 3. The three parameters are defined in terms of the 2-core of the giant component, i.e. its largest subgraph of minimum degree 2 or more. They are the number of vertices in the 2-core, the excess (#edges - #vertices) of the 2-core, and the number of vertices not in the 2-core. We show that the limit distribution is jointly Gaussian throughout the whole supercritical phase. In particular, for the first time, the 2-core size is shown to be asymptotically normal, in the widest possible range of the average vertex degree. The aim of Green Cloud Computing is to achieve a balance between the resource consumption and quality of service. In order to achieve this objective and to maintain the flexibility of the cloud, dynamic provisioning and allocation strategies are needed to regulate the internal settings of the cloud to address oscillatory peaks of workload. In this context, we propose strategies to optimize the use of the cloud resources without decreasing the availability. This work introduces two hybrid strategies based on a distributed system management model, describes the base strategies, operation principles, tests, and presents the results. We combine existing strategies to search their benefits. To test them, we extended CloudSim to simulate the organization model upon which we were based and to implement the strategies, using this improved version to validate our solution. Achieving a consumption reduction up to 87 comparing Standard Clouds with Green Clouds, and up to 52 comparing the proposed strategy with other Green Cloud Strategy. GPS-equipped taxis can be viewed as pervasive sensors and the large-scale digital traces produced allow us to reveal many hidden "facts" about the city dynamics and human behaviors. In this paper, we aim to discover anomalous driving patterns from taxi's GPS traces, targeting applications like automatically detecting taxi driving frauds or road network change in modern cites. To achieve the objective, firstly we group all the taxi trajectories crossing the same source destination cell-pair and represent each taxi trajectory as a sequence of symbols. Secondly, we propose an Isolation-Based Anomalous Trajectory (iBAT) detection method and verify with large scale taxi data that iBAT achieves remarkable performance (AUC>0.99, over 90 detection rate at false alarm rate of less than 2 ). Finally, we demonstrate the potential of iBAT in enabling innovative applications by using it for taxi driving fraud detection and road network change detection.