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Digital pulse shape discrimination (PSD) systems are widely used to extract various kinds of information from the shape of output pulses of radiation detectors. Such systems replace the traditional analog PSD circuits with numerical algorithms running on a digital processor, which makes them more flexible for implementing various PSD methods. However, the available digital PSD algorithms have been generally tailored to the characteristics of the concerned detectors, which limit their general use. Here, for the purpose of building a general-purpose digital PSD module, we present a PSD algorithm that, with minimum alterations, can be used with a wide range of radiation detectors. Our approach is based on using the cosine similarity measure to quantify the variations in the shape of detectors’ pulses with respect to the shape of a unit step pulse. The method is described in detail, and the results of the test experiments with different types of radiation detectors, including a boron tetrafluoride (BF3) proportional counter, a liquid scintillation detector, and high purity germanium (HPGe) detector are shown. The performance of the algorithm is also compared to that of the common rise time discrimination method. [ABSTRACT FROM AUTHOR]

Highlights • We propose a linear classifier design method in the weight space based on the observation that a training sample represents a plane in the weight space. • We proposed search algorithms to find the optimal subspace, though the optimal solution may not be guaranteed since the full search cannot be used. • Experimental results show that the proposed classifier performed better than or equivalent to existing linear classifiers (linear SVM, LDA). Abstract In this paper, we propose a linear classifier design method in the weight space. A linear classifier is completely determined by a weight vector. To design a linear classifier is equivalent to finding a weight vector. When there are a number of training samples, each training sample represents a plane in the weight space. On one side of the plane, the training sample is correctly classified while it is incorrectly classified on the other side. Thus, finding the optimal linear classifier can be formulated as finding a subspace that provides the best classification accuracy. In this paper, we have developed an algorithm to find such optimal subspaces in the weight space. Although we could not find the optimal linear classifier due to prohibitive computational complexity, the proposed design method produced noticeable improvements in some cases. Experimental results show that the proposed linear classifier performed better than or equivalent to existing linear classifiers. [ABSTRACT FROM AUTHOR]

The Korkine–Zolotareff (KZ) reduction is one of the often used reduction strategies for lattice decoding. In this paper, we first investigate some important properties of KZ reduced matrices. Specifically, we present a linear upper bound on the Hermit constant which is around 7/8 times of the existing sharpest linear upper bound, and an upper bound on the KZ constant which is polynomially smaller than the existing sharpest one. We also propose upper bounds on the lengths of the columns of KZ reduced matrices, and an upper bound on the orthogonality defect of KZ reduced matrices which are even polynomially and exponentially smaller than those of boosted KZ reduced matrices, respectively. Then, we derive upper bounds on the magnitudes of the entries of any solution of a shortest vector problem (SVP) when its basis matrix is LLL reduced. These upper bounds are useful for analyzing the complexity and understanding numerical stability of the basis expansion in a KZ reduction algorithm. Finally, we propose a new KZ reduction algorithm by modifying the commonly used Schnorr–Euchner search strategy for solving SVPs and the basis expansion method proposed by Zhang et al. Simulation results show that the new KZ reduction algorithm is much faster and more numerically reliable than the KZ reduction algorithm proposed by Zhang et al., especially when the basis matrix is ill conditioned. [ABSTRACT FROM AUTHOR]

Highlights • A weighted reverse joint sparse model, considering the spatio-temporal characteristic of multiple templates, is proposed. • A binary indicator vector is employed to suppress the inaccurate results generated by the corrupted local image blocks. • An efficient solver, which is based on the smooth l 0, 2 norm, is proposed to solve the weighted joint sparse model. • The experimental results on OTB-100 show the proposed method outperforms other state-of-the-art tracking methods. Abstract In the particle filter framework, the sparse representation method models object tracking by predicting the likelihood of particles with respect to target templates. However, in most tracking methods, the spatio-temporal relationships of different templates have been neglected. This method applies the reverse sparse representation in multi-task learning, thus takes advantage of the temporal information and spatial continuity of a series of templates. Adding a predesigned weight matrix can reflect the temporal information, and make the new entrant templates have a greater influence on atoms' selection. To solve the locally weighted reverse joint sparse model (LWRJM), we design a modified smooth l 0, 2 algorithm which requires only a few iterations. The obtained sparse coding coefficients are mapped to a binary indicator vector by a statistic strategy, which is helpful to eliminate the contributions of the corrupted blocks and preserve the uncorrupted ones. Comparing with other state-of-the-art tracking methods on 100 challenging benchmark image sequences, the proposed tracker (LWRJM) outperforms other methods in both qualitative and quantitative evaluations. [ABSTRACT FROM AUTHOR]

Since the descriptors based on Three-Dimensional (3D) Zernike moments are robust to geometric transformations and noise, they have been proposed for terrain matching. However, terrain matching algorithms based on 3D Zernike Moments (3DZMs) are often difficult to implement in practice since they are computationally intensive. This paper presents a more efficient real-time terrain matching algorithm based on 3DZMs for land applications. Two efficient methods based on coordinate transformation and symmetry are proposed to compute the geometric moments. The impact of the sample difference on the matching result due to heading angle is investigated to prove the feasibility of using a circular template. Consequently, the terrain feature vectors of the reference map can be computed off-line with the circular template to significantly reduce on-line computation. Numerical experiments on a real digital elevation model demonstrate that the proposed algorithm is robust to the heading angle and can be implemented for real-time terrain matching operations. [ABSTRACT FROM AUTHOR]

The problem of maximizing non-negative monotone submodular functions under a certain constraint has been intensively studied in the last decade. In this paper, we address the problem for functions defined over the integer lattice. Suppose that a non-negative monotone submodular function f:Z+n→R+ is given via an evaluation oracle. Assume further that f satisfies the diminishing return property, which is not an immediate consequence of submodularity when the domain is the integer lattice. Given this, we design polynomial-time (1-1/e-ϵ)-approximation algorithms for a cardinality constraint, a polymatroid constraint, and a knapsack constraint. For a cardinality constraint, we also provide a (1-1/e-ϵ)-approximation algorithm with slightly worse time complexity that does not rely on the diminishing return property. [ABSTRACT FROM AUTHOR]

The problem of reconstructing a sparse signal vector from magnitude-only measurements (a.k.a. compressive phase retrieval) emerges in diverse applications, but it is NP-hard in general. Building on recent advances in nonconvex optimization, this paper puts forth a new algorithm that is termed compressive reweighted amplitude flow (CRAF) and abbreviated as CRAF, for compressive phase retrieval. Specifically, CRAF operates in two stages. The first stage seeks a sparse initial guess via a new spectral procedure. In the second stage, CRAF implements a few hard thresholding based iterations using reweighted gradients. When there are sufficient measurements, CRAF provably recovers the underlying signal vector exactly with high probability under suitable conditions. Moreover, its sample complexity coincides with that of state-of-the-art procedures. Finally, numerical tests showcase improved performance of the new spectral initialization, as well as improved exact recovery relative to competing alternatives. Empirically, the number of measurements required for exact recovery by CRAF is about 40% less than those of competing alternatives in our experiments using real images. [ABSTRACT FROM AUTHOR]

Abstract Different semantic interpretation tasks such as text entailment and question answering require the classification of semantic relations between terms or entities within text. However, in most cases, it is not possible to assign a direct semantic relation between entities/terms. This paper proposes an approach for composite semantic relation classification using one or more relations between entities/term mentions, extending the traditional semantic relation classification task. The proposed model is different from existing approaches which typically use machine learning models built over lexical and distributional word vector features in that is uses a combination of a large commonsense knowledge base of binary relations, a distributional navigational algorithm and sequence classification to provide a solution for the composite semantic relation classification problem. The proposed approach outperformed existing baselines with regard to F1-score, Accuracy, Precision and Recall. [ABSTRACT FROM AUTHOR]

This paper considers online robust principal component analysis (RPCA) in time-varying decomposition problems such as video foreground-background separation. We propose a compressive online RPCA algorithm that decomposes recursively a sequence of data vectors (e.g., frames) into sparse and low-rank components. Different from conventional batch RPCA, which processes all the data directly, our approach considers a small set of measurements taken per data vector (frame). Moreover, our algorithm can incorporate multiple prior information from previous decomposed vectors via proposing an $n$ - $\ell _{1}$ minimization method. At each time instance, the algorithm recovers the sparse vector by solving the $n$ - $\ell _{1}$ minimization problem—which promotes not only the sparsity of the vector but also its correlation with multiple previously recovered sparse vectors—and, subsequently, updates the low-rank component using incremental singular value decomposition. We also establish theoretical bounds on the number of measurements required to guarantee successful compressive separation under the assumptions of static or slowly changing low-rank components. We evaluate the proposed algorithm using numerical experiments and online video foreground-background separation experiments. The experimental results show that the proposed method outperforms the existing methods. [ABSTRACT FROM AUTHOR]

The Quantum Query Model is a framework that allows us to express most known quantum algorithms. Algorithms represented by this model consist of a set of unitary operators acting over a finite Hilbert space, and a final measurement step consisting of a set of projectors. In this work, we prove that the application of these unitary operators before the measurement step is equivalent to decomposing a unit vector into a sum of vectors and then inverting some of their relative phases. We also prove that the vectors of that sum must fulfill a list of properties and we call such vectors a Block Set . If we define the measurement step for the Block Set Formulation similarly to the Quantum Query Model, then we prove that both formulations give the same Gram matrix of output states, although the Block Set Formulation allows a much more explicit form. Therefore, the Block Set reformulation of the Quantum Query Model gives us an alternative interpretation of how quantum algorithms work. Finally, we apply our approach to the analysis and complexity of quantum exact algorithms. [ABSTRACT FROM AUTHOR]

Anomaly detection has been known to be a challenging problem due to the uncertainty of anomaly and the interference of noise. In this paper, we focus on anomaly detection in hyperspectral images (HSIs) and propose a novel detection algorithm based on spectral unmixing and dictionary-based low-rank decomposition. The innovation is threefold. First, due to the highly mixed nature of pixels in HSI data, instead of using the raw pixel directly for anomaly detection, the proposed algorithm applies spectral unmixing to obtain the abundance vectors and uses these vectors for anomaly detection. We show that the abundance vectors possess more distinctive features to identify anomaly from background. Second, to better represent the highly correlated background and the sparse anomaly, we construct a dictionary based on the mean shift clustering of the abundance vectors to improve both the discriminative and representative powers of the algorithm. Finally, a low-rank matrix decomposition method based on the constructed dictionary is proposed to encourage the coefficients of the dictionary, instead of the background itself, to be low rank, and the residual matrix to be sparse. Anomalies can then be extracted by summing up the columns of the residual matrix. The proposed algorithm is evaluated on both synthetic and real data sets. Experimental results show that the proposed approach constantly achieves high detection rate, while maintaining low false alarm rate regardless of the type of images tested. [ABSTRACT FROM AUTHOR]

The well-known Jahn-Graef-Younes algorithm, proposed by Jahn in 2006, generates all minimal elements of a finite set with respect to an ordering cone. It consists of two Graef-Younes procedures, namely the forward iteration, which eliminates a part of the non-minimal elements, followed by the backward iteration, which is applied to the reduced set generated by the previous iteration. Without using the backward iteration, we develop new algorithms that also compute all minimal elements of the initial set, by combining the forward iteration with certain sorting procedures based on cone-monotone functions. In particular, when the ordering cone is polyhedral, computational results obtained in MATLAB allow us to compare our algorithms with the Jahn-Graef-Younes algorithm, within a bi-objective optimization problem. [ABSTRACT FROM AUTHOR]

Abstract: This paper concerns the problem of quantifying the observability of different states in linear (or linearized) time‐varying systems with focus on the usability to integrated navigation. The main goal is the derivation of a novel scalar method to measure the degree of observability in order to quantitatively analyze the observability of each state variable of a system. The new proposed observability analysis method is easily employed in practice with less computer memory and clearer physical meanings. The application to integrated navigation systems was illustrated to analyze the observability properties of navigation error‐states. According to the simulation results, the degree of observability can help us to quantitatively compare the observability of each state variable and further function as an indicator to analyze the influence of physical model parameters on the observability and estimability of navigation errors. Copyright © 2018 Institute of Navigation [ABSTRACT FROM AUTHOR]

For a class of matrices connected with Cauchon diagrams, Cauchon matrices, and the Cauchon algorithm, a method for determining the rank, and for checking a set of consecutive row (or column) vectors for linear independence is presented. Cauchon diagrams are also linked to the elementary bidiagonal factorization of a matrix and to certain types of rank conditions associated with submatrices called descending rank conditions. [ABSTRACT FROM AUTHOR]

New approaches to the construction of intervals of analogous behavior of the parameters of an object from time series are considered. The intervals are constructed in the form of certain sets of sequential values of the parameters (coordinates of neighbor vectors) that are close to the set of their final values which are used in the prediction. It is shown that through the use of the newly constructed technique it is possible to increase the number of neighbor vectors for the purpose of finding statistical characteristics. A unified algorithm for finding a set of neighbor vectors in each of the variants considered is proposed. An algorithm for one step ahead prediction based on an analysis of the coordinates of the neighbor vectors is constructed. [ABSTRACT FROM AUTHOR]

Diffuse optical tomography (DOT) is a noninvasive imaging modality that reconstructs the optical parameters of a highly scattering medium. However, the inverse problem of DOT is ill-posed and highly nonlinear due to the zig-zag propagation of photons that diffuses through the cross section of tissue. The conventional DOT imaging methods iteratively compute the solution of forward diffusion equation solver which makes the problem computationally expensive. Also, these methods fail when the geometry is complex. Recently, the theory of compressive sensing (CS) has received considerable attention because of its efficient use in biomedical imaging applications. The objective of this paper is to solve a given DOT inverse problem by using compressive sensing framework and various Greedy algorithms such as orthogonal matching pursuit (OMP), compressive sampling matching pursuit (CoSaMP), and stagewise orthogonal matching pursuit (StOMP), regularized orthogonal matching pursuit (ROMP) and simultaneous orthogonal matching pursuit (S-OMP) have been studied to reconstruct the change in the absorption parameter i.e, Δ α from the boundary data. Also, the Greedy algorithms have been validated experimentally on a paraffin wax rectangular phantom through a well designed experimental set up. We also have studied the conventional DOT methods like least square method and truncated singular value decomposition (TSVD) for comparison. One of the main features of this work is the usage of less number of source–detector pairs, which can facilitate the use of DOT in routine applications of screening. The performance metrics such as mean square error (MSE), normalized mean square error (NMSE), structural similarity index (SSIM), and peak signal to noise ratio (PSNR) have been used to evaluate the performance of the algorithms mentioned in this paper. Extensive simulation results confirm that CS based DOT reconstruction outperforms the conventional DOT imaging methods in terms of computational efficiency. The main advantage of this study is that the forward diffusion equation solver need not be repeatedly solved. [ABSTRACT FROM AUTHOR]

In this paper, an improved set-membership proportionate normalized least mean square (SM-PNLMS) algorithm is proposed for block-sparse systems. The proposed algorithm, which is named the block-sparse SM-PNLMS (BS-SMPNLMS), is implemented by inserting a penalty of a mixed l2,1 norm of weight-taps into the cost function of the SM-PNLMS. Furthermore, an improved BS-SMPNLMS algorithm (the (BS-SMIPNLMS algorithm) is also derived and analyzed. The proposed algorithms are well investigated in the framework of network echo cancellation. The results of simulations indicate that the devised BS-SMPNLMS and BS-SMIPNLMS algorithms converge faster and have smaller estimation errors compared with related algorithms. [ABSTRACT FROM AUTHOR]

Aircraft and spacecraft navigation precision is dependent on the measurement system for position and attitude determination. Rotation of an aircraft can be determined measuring two vectors in two different reference systems. Velocity vector can be determined in the inertial reference frame from a GNSS-based sensor and by integrating the acceleration measurements in the body reference frame. Estimating gravity vector in both reference frames, and combining with velocity vector, determines rotation of the body. A new approach for gravity vector estimations is presented and employed in an attitude determination algorithm. Nonlinear simulations demonstrate that using directly the positioning and velocity outputs of GNSS sensors and strap-down accelerometers, aircraft attitude determination is precise, especially in ballistic projectiles, to substitute precise attitude determination devices, usually expensive and forced to bear high solicitations as for instance G forces. [ABSTRACT FROM AUTHOR]

Inherent to state-of-the-art dimension reduction algorithms is the assumption that global distances between observations are Euclidean, despite the potential for altogether non-Euclidean data manifolds. We demonstrate that a non-Euclidean manifold chart can be approximated by implementing a universal approximator over a dictionary of dissimilarity measures, building on recent developments in the field. This approach is transferable across domains such that observations can be vectors, distributions, graphs and time series for instance. Our novel dissimilarity learning method is illustrated with four standard visualisation datasets showing the benefits over the linear dissimilarity learning approach. [ABSTRACT FROM AUTHOR]

This article concerns finite element approximations of a quasi-static poroelasticity model in displacementpressure formulation, which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To better describe the multiphysics process of deformation and diffusion for poroelastic materials, we first present a reformulation of the original model by introducing two pseudo-pressures. We then propose a time-stepping algorithm that decouples the reformulated partial differential equation (PDE) problem at each time step into two sub-problems: one of which is a generalized Stokes problem for the displacement vector field (of the solid network of the poroelastic material) along with one pseudopressure field, and the other is a diffusion problem for the other pseudo-pressure field (of the solvent of the material). To make this multiphysics approach feasible numerically, two critical issues must be resolved: the first one is the uniqueness of the generalized Stokes problem and the other is to find a good boundary condition for the diffusion equation, so that it also becomes uniquely solvable. To address the first issue, we discover certain conserved quantities for the PDE solution that provide ideal candidates for a needed boundary condition for the pseudo-pressure field. The solution to the second issue is to use the generalized Stokes problem to generate a boundary condition for the diffusion problem. A practical advantage of the time-stepping algorithm allows one to use any convergent Stokes solver (and its code) together with any convergent diffusion equation solver (and its code) to solve the poroelasticity model. In this article, the Taylor-Hood mixed finite element method combined with the P1 -conforming finite element method is used as an example to demonstrate the viability of the proposed multiphysics approach. It is proved that the solutions of the fully discrete finite element methods fulfill a discrete energy law, which mimics the differential energy law satisfied by the PDE solution and converges optimally in the energy norm. Moreover, it is showed that the proposed formulation also has a built-in mechanism to overcome so-called 'locking phenomenon' associated with the numerical approximations of the poroelasticity model. Numerical experiments are presented to show the performance of the proposed approach and methods, and to demonstrate the absence of 'locking phenomenon' in our numerical experiments. This article also presents a detailed PDE analysis for the poroelasticity model, especially it is proved that this model converges to the well-known Biot's consolidation model from soil mechanics as the constrained specific storage coefficient tends to zero. As a result, the proposed approach and methods are robust under such a limit process. [ABSTRACT FROM AUTHOR]

The match-count problem on strings is the basic problem of counting the matches of characters between two strings for every possible alignment. The problem is classically computed in O( σ n log m) time using a fast Fourier transform (FFT) for two strings of lengths m and n ( m ≤ n) over an alphabet of size σ. This paper extends the target of this FFT-based algorithm to a weighted version of the problem, which computes the sum of similarities between characters instead of the number of matches. The algorithm extended in this paper can solve the weighted match-count problem in O( dn log m) time by mapping characters to numerical vectors of dimensionality d. This paper also evaluates the usefulness of the extended algorithm by applying it to plagiarism detection in documents. The experimental results show that the proposed algorithm is applicable to general vector representation of words and that the obtained plagiarism detection method can extremely reduce the processing time with a slight decrease of accuracy from the method based on the normal match-count problem. [ABSTRACT FROM AUTHOR]

We design a control algorithm for objects under parametric uncertainty, external bounded disturbances, and saturation of the controlled signal. We assume that the object model is described by a linear dynamical system with arbitrary relative degree and several inputs and outputs. The developed algorithm provides approximate tracking of the output of the control object for a reference signal. We obtain sufficient stability conditions for the closed system that depend on object parameters, reference model, and the controller. We show modeling results that illustrate the operation of the developed scheme. [ABSTRACT FROM AUTHOR]

This paper presents a novel saliency detection method via updating initial labels from spectral graph in a semi-supervised learning (SSL) framework. For updating labels efficiently with graph-based SSL, two principles generally should be considered. The first one is that the updated labels should not change too much from their initial assignment. The second one is that the updated labels should not change too much between similar samples. To follow the first principle, the biggest eigenvector of Laplacian matrix, which contains rich contrast between background regions and salient regions, is employed to obtain the initial label vector. To follow the second principle, a new graph construction scheme, in which only boundary samples with similar features can be connected with each other, is proposed to reduce the geodesic distance in graph. Then a graph-based manifold regularization framework is exploited to update the label vector for separating salient samples from non-salient samples. A refinement function cooperating with an activation function is further presented for saliency optimization. Experimental results show that the proposed method achieves competitive performance against some recent state-of-the-art algorithms for saliency detection. [ABSTRACT FROM AUTHOR]

Fixman's work in 1974 and the follow-up studies have developed a method that can factorize the inverse of mass matrix into an arithmetic combination of three sparse matrices—one of them is positive definite and needs to be further factorized by using the Cholesky decomposition or similar methods. When the molecule subjected to study is of serial chain structure, this method can achieve O ( n ) time complexity. However, for molecules with long branches, Cholesky decomposition about the corresponding positive definite matrix will introduce massive fill-in due to its nonzero structure. Although there are several methods can be used to reduce the number of fill-in, none of them could strictly guarantee for zero fill-in for all molecules according to our test, and thus cannot obtain O ( n ) time complexity by using these traditional methods. In this paper we present a new method that can guarantee for no fill-in in doing the Cholesky decomposition, which was developed based on the correlations between the mass matrix and the geometrical structure of molecules. As a result, the inverting of mass matrix will remain the O ( n ) time complexity, no matter the molecule structure has long branches or not. [ABSTRACT FROM AUTHOR]

This paper introduces a new algorithm for Boolean operations on rasterized geometric shapes that are represented with chain codes. The algorithm works in three steps. Firstly, the chain code symbols are transformed in the Hilbert space, where the overlaid chain code symbols are recognised. After that, a suitable starting cell is determined. Finally, the walk-about through the sequence of the initial chain code symbols is performed to obtain the sequence of chain code symbols representing the shape of the required Boolean operation. The algorithm is demonstrated on Freeman chain code in four directions. The time and space complexity of the proposed algorithm is linear, which was proven theoretically and confirmed by experiments. [ABSTRACT FROM AUTHOR]

Based on the symbol-flipping algorithm with multiple-votes (MV-SF), this paper presents two simplified algorithms, symbol flipping with truncated and multiple votes (T-MV-SF) and symbol flipping with simplified and multiple votes (S-MV-SF), for nonbinary low-density parity-check(NB-LDPC) codes. Unlike previous symbol-flipping based algorithms (SFBAs), the T(S)-MV-SF uses the truncated voting information in each check and variable node update. The proposed algorithms also approximate the sorting function in each check update. Therefore, their complexity and memory consumption are remarkably reduced as compared with existing SFBAs. Furthermore, we introduce several parameters to compensate the information loss caused by the truncated voting information. After optimizing all the parameters, the proposed algorithms even have better performance than the MV-SF. As compared with the MV-SF, the maximum performance gain among all numerical examples is about 0.11 dB for the S-MV-SF on the (63, 37) code. The T-MV-SF has the largest reduction of the computational complexity on the (255, 175) code, which is about 80% of the complexity of the MV-SF. Moreover, the performance of the T-MV-SF is better than the MV-SF on the (255, 175) code. As a result, the proposed algorithms can effectively balance the error performance and complexity for decoding of NB-LDPCs. [ABSTRACT FROM PUBLISHER]

Ridge regression is an important approach in many applications, such as healthcare system of smart wearable equipments. Due to the limited resources of wearable devices, outsourcing is a promising computation paradigm. Nevertheless, it also suffers from some privacy challenges, as outsourced computation probably involves some sensitive data. In this paper, we propose a ridge regression outsourcing scheme, which can securely utilize the cloud to analyse large-scale wearable device dataset and dramatically reduce the computation cost of the resource-limited clients. Technically, we use random vectors and dense matrices to perturb input dataset and regression output, such that both input privacy and output privacy can be efficiently protected. Then, we present a highly-efficient verification algorithm to robustly check the correctness of cloud’s answer against a dishonest/lazy cloud server. Finally, we evaluate our scheme through theoretical analysis and extensive experiments. The results show we can achieve input/output privacy, correctness, robust checkability and practical efficiency. [ABSTRACT FROM AUTHOR]

In this paper, a novel crowd descriptor, termed as bilinear CD (Curl and Divergence) descriptor, is proposed based on the bilinear interaction of curl and divergence. Specifically, the curl and divergence activation maps are computed from the normalized average flow. A local curl patch and the corresponding divergence patch are cropped respectively from the activation maps. The outer product of the two local patches is defined as the bilinear CD vector. Through sliding a window on the activation maps, we can get hundreds to thousands local bilinear CD vectors. To encode them into a compact representation, fisher vector pooling and PCA algorithms are applied on the local descriptors. Experiments on the CUHK crowd dataset show that the proposed bilinear dynamics can improve the performance of video classification and retrieval by a noticeable margin when compared with the existing crowd features. [ABSTRACT FROM AUTHOR]

There exist two issues among popular lattice reduction algorithms that should cause our concern. The first one is Korkine–Zolotarev (KZ) and Lenstra–Lenstra–Lovász (LLL) algorithms may increase the lengths of basis vectors. The other is KZ reduction suffers worse performance than Minkowski reduction in terms of providing short basis vectors, despite its superior theoretical upper bounds. To address these limitations, we improve the size reduction steps in KZ and LLL to set up two new efficient algorithms, referred to as boosted KZ and LLL, for solving the shortest basis problem with exponential and polynomial complexity, respectively. Both of them offer better actual performance than their classic counterparts, and the performance bounds for KZ are also improved. We apply them to designing integer-forcing (IF) linear receivers for multi-input multioutput communications. Our simulations confirm their rate and complexity advantages. [ABSTRACT FROM PUBLISHER]

A monotone drawing of a graph G is a straight-line drawing of G such that, for every pair of vertices u,w in G, there exists a path Puw in G that is monotone in some direction luw. (Namely, the order of the orthogonal projections of the vertices of Puw on luw is the same as the order in which they appear in Puw.) The problem of finding monotone drawings for trees has been studied in several recent papers. The main focus is to reduce the size of the drawing. Currently, the smallest drawing size is O(n log n) × O(n log n). In this paper, we present an algorithm for constructing monotone drawings of trees on a grid of size at most 12n × 12n. The smaller drawing size is achieved by a procedure that carefully assigns primitive vectors to the paths of the input tree T. We also show that there exists a tree T0 such that any monotone drawing of T0 must use a grid of size at least n/9 × n/9. So the size of our monotone drawings is asymptotically optimal. [ABSTRACT FROM AUTHOR]

This paper proposes a new measure for recommendation through integrating Triangle and Jaccard similarities. The Triangle similarity considers both the length and the angle of rating vectors between them, while the Jaccard similarity considers non co-rating users. We compare the new similarity measure with eight state-of-the-art ones on four popular datasets under the leave-one-out scenario. Results show that the new measure outperforms all the counterparts in terms of the mean absolute error and the root mean square error. [ABSTRACT FROM AUTHOR]

In recent years, eyetracking has begun to be used to study the dynamics of analogy making. Numerous scanpath-comparison algorithms and machine-learning techniques are available that can be applied to the raw eyetracking data. We show how scanpath-comparison algorithms, combined with multidimensional scaling and a classification algorithm, can be used to resolve an outstanding question in analogy making-namely, whether or not children's and adults' strategies in solving analogy problems are different. (They are.) We show which of these scanpath-comparison algorithms is best suited to the kinds of analogy problems that have formed the basis of much analogy-making research over the years. Furthermore, we use machine-learning classification algorithms to examine the item-to-item saccade vectors making up these scanpaths. We show which of these algorithms best predicts, from very early on in a trial, on the basis of the frequency of various item-to-item saccades, whether a child or an adult is doing the problem. This type of analysis can also be used to predict, on the basis of the item-to-item saccade dynamics in the first third of a trial, whether or not a problem will be solved correctly. [ABSTRACT FROM AUTHOR]

We study the complexity of algorithmic problems for matrices that are represented by multi-terminal decision diagrams (MTDD). These are a variant of ordered decision diagrams, where the terminal nodes are labeled with arbitrary elements of a semiring (instead of 0 and 1). A simple example shows that the product of two MTDD-represented matrices cannot be represented by an MTDD of polynomial size. To overcome this deficiency, we extended MTDDs to + MTDDs by allowing componentwise symbolic addition of variables (of the same dimension) in rules. It is shown that accessing an entry, equality checking, matrix multiplication, and other basic matrix operations can be solved in polynomial time for + MTDD-represented matrices. On the other hand, testing whether the determinant of a MTDD-represented matrix vanishes is P S P A C E-complete, and the same problem is N P-complete for + MTDD-represented diagonal matrices. Computing a specific entry in a product of MTDD-represented matrices is # P-complete. [ABSTRACT FROM AUTHOR]

Limited-memory BFGS (L-BFGS; Liu and Nocedal, 1989) is often considered to be the method of choice for continuous optimization when first- or second-order information is available. However, the use of L-BFGS can be complicated in a black box scenario where gradient information is not available and therefore should be numerically estimated. The accuracy of this estimation, obtained by finite difference methods, is often problem-dependent and may lead to premature convergence of the algorithm. This article demonstrates an alternative to L-BFGS, the limited memory covariance matrix adaptation evolution strategy (LM-CMA) proposed by Loshchilov (2014). LM-CMA is a stochastic derivative-free algorithm for numerical optimization of nonlinear, nonconvex optimization problems. Inspired by L-BFGS, LM-CMA samples candidate solutions according to a covariance matrix reproduced from m direction vectors selected during the optimization process. The decomposition of the covariance matrix into Cholesky factors allows reducing the memory complexity to O(mn), where n is the number of decision variables. The time complexity of sampling one candidate solution is also O(mn) but scales as only about 25 scalar-vector multiplications in practice. The algorithm has an important property of invariance with respect to strictly increasing transformations of the objective function; such transformations do not compromise its ability to approach the optimum. LM-CMA outperforms the original CMA-ES and its large-scale versions on nonseparable ill-conditioned problems with a factor increasing with problem dimension. Invariance properties of the algorithm do not prevent it from demonstrating a comparable performance to L-BFGS on nontrivial large-scale smooth and nonsmooth optimization problems. [ABSTRACT FROM AUTHOR]

The present study introduces results about unique solvability of Gaussian RBF interpolation with the different data sites and basis centers. For $$ N=2 $$ , we show that the interpolation matrix is singular only when the vector of difference between basis centers and the vector of difference between data sites are perpendicular to each other. For $$N>2$$ , we show certain states that the interpolation matrix is singular, then we provide several mild conditions which guarantee the interpolation matrix to be non-singular. We propose an algorithm to describe how to choose the basis centers and data sites. The results show that if the basis centers are chosen different from the data sites, the interpolation is uniquely solvable under mild conditions. [ABSTRACT FROM AUTHOR]

It is well known that sparse approximation problem is NP-hard under general dictionaries. Several algorithms have been devised and analyzed in the past decade under various assumptions on the coherence μ of the dictionary represented by an M × N matrix from which a subset of k column vectors is selected. All these results assume μ = O ( k − 1 ) . This article is an attempt to bridge the big gap between the negative result of NP-hardness under general dictionaries and the positive results under this restrictive assumption. In particular, it suggests that the aforementioned assumption might be asymptotically the best one can make to arrive at any efficient algorithmic result under well-known conjectures of complexity theory. In establishing the results, we make use of a new simple multilayered PCP which is tailored to give a matrix with small coherence combined with our reduction. [ABSTRACT FROM AUTHOR]

A new technique based on the multiple measurement vectors FOCal Underdetermined System Solver (M-FOCUSS) for synthesis of pattern reconfigurable sparse arrays is presented. The method, based on the MMVs sparse recovery theory, is used for finding the common element positions and individual element excitations for multiple patterns in the guidance of collaborative synthesis strategy. A reasonable tradeoff between the number of active antenna elements and pattern characteristics can be achieved. Numerical examples show the high efficiency and robustness of the proposed method. Furthermore, the M-FOCUSS method is combined with the active element pattern technique so that the mutual coupling between real antennas can be taken into account in the synthesis process. The M-FOCUSS-Active algorithm is used to design an E-plane coupled microstrip antenna array. Measured results validate the effectiveness of this approach. [ABSTRACT FROM PUBLISHER]

The aim of this paper is to compute all the Frenet apparatus of non-transversal intersection curves (hyper-curves) of three implicit hypersurfaces in Euclidean 4-space. The tangential direction at a transversal intersection point can be computed easily, but at a non-transversal intersection point, it is difficult to calculate even the tangent vector. If three normal vectors are parallel at a point, the intersection is “tangential intersection”; and if three normal vectors are not parallel but are linearly dependent at a point, we have “almost tangential” intersection at the intersection point. We give algorithms for each case to find the Frenet vectors ( t , n , b 1 , b 2 ) and the curvatures ( k 1 , k 2 , k 3 ) of the non-transversal intersection curve. [ABSTRACT FROM AUTHOR]

We identify a class of Linear Complementarity Problems (LCPs) that are solvable in strongly polynomial time by Lemke's Algorithm (Scheme 1) or by the Parametric Principal Pivoting Method (PPPM). This algorithmic feature for the class of problems under consideration here is attributable to the proper selection of the covering vector in Scheme 1 or the parametric direction vector in the PPPM which leads to solutions of limited and monotonically increasing support size; such solutions are sparse. These and other LCPs may very well have multiple solutions, many of which are unattainable by either algorithm and thus are said to be elusive. The initial conditions imposed on the new matrix class identified in Sect. 2 are subsequently relaxed in later sections. [ABSTRACT FROM AUTHOR]

We consider a linear pursuit differential game of one pursuer and one evader. Controls of the pursuer and evader are subjected to integral and geometric constraints, respectively. In addition, phase constraint is imposed on the state of evader, whereas pursuer moves throughout the space. We say that pursuit is completed, if inclusion y(t1)-x(t1)∈M is satisfied at some t1>0, where x(t) and y(t) are states of pursuer and evader, respectively, and M is terminal set. Conditions of completion of pursuit in the game from all initial points of players are obtained. Strategy of the pursuer is constructed so that the phase vector of the pursuer first is brought to a given set, and then pursuit is completed. [ABSTRACT FROM AUTHOR]

This paper proposes a new differential evolution (DE) algorithm for unconstrained continuous optimisation problems, termed $$\mu $$ JADE, that uses a small or 'micro' ( $$\mu $$ ) population. The main contribution of the proposed DE is a new mutation operator, 'current-by-rand-to-pbest.' With a population size less than 10, $$\mu $$ JADE is able to solve some classical multimodal benchmark problems of 30 and 100 dimensions as reliably as some state-of-the-art DE algorithms using conventionally sized populations. The algorithm also compares favourably to other small population DE variants and classical DE. [ABSTRACT FROM AUTHOR]

The complexity status of several well-known discrete optimization problems with the direction of optimization switching from maximum to minimum is analyzed. The task is to find a subset of a finite set of Euclidean points (vectors). In these problems, the objective functions depend either only on the norm of the sum of the elements from the subset or on this norm and the cardinality of the subset. It is proved that, if the dimension of the space is a part of the input, then all these problems are strongly NP-hard. Additionally, it is shown that, if the space dimension is fixed, then all the problems are NP-hard even for dimension 2 (on a plane) and there are no approximation algorithms with a guaranteed accuracy bound for them unless P = NP. It is shown that, if the coordinates of the input points are integer, then all the problems can be solved in pseudopolynomial time in the case of a fixed space dimension. [ABSTRACT FROM AUTHOR]

This paper is concerned with the question of reconstructing a vector in a finite-dimensional complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new invertibility results as well as an iterative algorithm that finds the least-square solution, which is robust in the presence of noise. We analyze its numerical performance by comparing it to the Cramer-Rao lower bound. [ABSTRACT FROM AUTHOR]

The efficient computation of matrix function vector products has recently become an important area of research, driven in particular by two important applications: the numerical solution of fractional partial differential equations and the integration of large systems of ordinary differential equations. In this work we consider a problem that combines these two applications in the form of a numerical solution algorithm for fractional reaction-diffusion equations that, after spatial discretization, is advanced in time using the exponential Euler method. We focus on the efficient implementation of the algorithm on graphics processing units (GPUs), as we wish to make use of the increased computational power available with this hardware. We compute the matrix function vector products using the contour integration method in [N. Hale, N. J. Higham, and L. N. Trefethen, SIAM J. Numer. Anal., 46 (2008), pp. 2505-2523]. Multiple levels of preconditioning are applied to reduce the GPU memory footprint and to further accelerate convergence. We also derive an error bound for the convergence of the contour integral method that allows us to predetermine the appropriate number of quadrature points. Results are presented that demonstrate the effectiveness of the method for large two-dimensional problems, showing a speedup of more than an order of magnitude compared to a CPU-only implementation. [ABSTRACT FROM AUTHOR]

We introduce the notion of a resolving sequence of (scalar) operators for a given differential or difference system with coefficients in some differential or difference field K. We propose an algorithm to construct, such a sequence, and give some examples of the use of this sequence as a suitable auxiliary tool for finding certain kinds of solutions of differential and difference systems of arbitrary order. Some experiments with our implementation of the algorithm are reported. [ABSTRACT FROM AUTHOR]

From three interferograms, a novel algorithm for extracting phase shifts based on the vector projection of normalized difference maps is presented. In it, subtraction and vector normalization are operated successively to obtain two normalized interferogram differences without the effect of background component. Then, the phase shift can be estimated based on the analysis and calculation of the vector projection. Without any iteration and complex calculation, this algorithm can be implemented for phase-shift range approximately being well distributed from 0 to 2π, when fringe number of interferograms is more than one. It offers a powerful tool for rapid calibration of phase shifts because of its high efficiency and easy implementation. Numerical simulations and experiments are performed to prove its validity. [ABSTRACT FROM PUBLISHER]

Discriminant analysis is an important and well-studied algorithm in pattern recognition area, and many linear discriminant analysis methods have been proposed over the last few decades. However, in the previous works, the between-scatter matrix is not updated when seeking the discriminant vectors, which causes redundancy for the well separated pairs. In this paper, a between-scatter matrix updating scheme is proposed based on the separable status of the obtained vectors. In our scheme, separable status determination of obtained vectors is decisive. Here, we notice that appropriate separation of a multi-dimensional feature (with homoscedastic Gaussian distribution) may help to find better discriminant vectors, and the separability of a multi-dimensional feature can be deduced from the separability of its elements. To make the discriminant vectors statistically uncorrelated, the algorithm is applied to the S t -orthogonal space of the obtained vectors in an iterative way. We also extend our method to more general cases, like heteroscedastic distributions, by an appropriate kernel function. Experimental results on multiple databases demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper focuses on the identification problem of an input nonlinear state space system with colored noise. Based on the observability canonical form, an identification model is derived and a state observer is designed. By using the hierarchical identification principle, a state observer based hierarchical stochastic gradient algorithm is presented for estimating the parameter vectors and states jointly. Furthermore, by using the multi-innovation identification theory, a state observer based hierarchical multi-innovation stochastic gradient algorithm is proposed for improving the convergence rate. The analysis indicates that the parameter estimates given by the proposed algorithms converge to the true values under persistent excitation conditions. Two numerical examples are offered to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Nonlinear adaptive filtering has been extensively studied in the literature, using, for example, Volterra filters or neural networks. Recently, kernel methods have been offering an interesting alternative because they provide a simple extension of linear algorithms to the nonlinear case. The main drawback of online system identification with kernel methods is that the filter complexity increases with time, a limitation resulting from the representer theorem, which states that all past input vectors are required. To overcome this drawback, a particular subset of these input vectors (called dictionary) must be selected to ensure complexity control and good performance. Up to now, all authors considered that, after being introduced into the dictionary, elements stay unchanged even if, because of nonstationarity, they become useless to predict the system output. The objective of this paper is to present an adaptation scheme of dictionary elements, which are considered here as adjustable model parameters, by deriving a gradient-based method under collinearity constraints. The main interest is to ensure a better tracking performance. To evaluate our approach, dictionary adaptation is introduced into three well-known kernel-based adaptive algorithms: kernel recursive least squares, kernel normalized least mean squares, and kernel affine projection. The performance is evaluated on nonlinear adaptive filtering of simulated and real data sets. As confirmed by experiments, our dictionary adaptation scheme allows either complexity reduction or a decrease of the instantaneous quadratic error, or both simultaneously. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]