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This paper proposes a data-driven H∞ approach to simultaneous fault detection and control problem. This problem is formulated as a time domain H∞ optimization problem and its solution produces a data-driven H∞ controller/detector unit of modest complexity which is capable of achieving some control and fault detection objectives. The mathematical model is assumed to be unknown and only input/output data are used for controller/detector designing. The tradeoff between these objectives is established by tuning a scalar parameter and some weighting matrices. An easily implementable algorithm summarizes the methodology presented in the paper. The proposed algorithm is applied to a numerical example in order to illustrate its effectiveness. [ABSTRACT FROM AUTHOR]

This paper studies Bounded Model Checking (BMC) of invariant properties on compositional systems. To alleviate the path explosion problem resulting from interleaving, an ideal approach is to let the system execute in true-concurrency. However, since it is difficult for the true-concurrency execution manner to obtain all reachable global states, this technique has been rarely employed to verify those properties requiring to check all reachable global states-such as invariant properties. Verification of such properties still adheres to the interleaving semantics. Observed that even for properties such as invariants, it is possible to verify them via checking only a fraction of the global states, this paper presents a true-concurrency encoding for invariant property verification of compositional systems. The crucial innovation is a macro-step technique, which executes a sequence of consecutive transitions in true-concurrency. With this technique, we are able to (1) significantly reduce the exponential number of paths due to interleaving and (2) greatly cut down the number of SAT calls required for BMC to verify the property. Experimental results of real problems show speed increases from 4.8 to 2957 times that of the standard verification method. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, we introduce the so-called symplectic discrete singular convolution differentiator (SDSCD) method for structure-preserving modelling of elastic waves. In the method presented, physical space is discretized by the DSCD, whereas an explicit third-order symplectic scheme is used for the time discretization. This approach uses optimization and truncation to form a localized operator. This preserves the fine structure of the wavefield in complex media and avoids non-causal interaction when parameter discontinuities are present in the medium. Theoretically, the approach presented is a structure-preserving algorithm. Also, some numerical experiments are shown in this paper. Elastic wavefield modelling experiments on a laterally heterogeneous medium with high parameter contrasts demonstrate the superior performance of the SDSCD for suppression of numerical dispersion. Long-term computational experiments exhibit the remarkable capability of the approach presented for long-time simulations. Promising numerical results suggest the SDSCD is suitable for high-precision and long-time numerical simulations, as it has structure-preserving property and it can suppress effectively numerical dispersion when coarse grids are used. [ABSTRACT FROM AUTHOR]

In this paper, we show why the modified Gram--Schmidt algorithm generates a well- conditioned set of vectors. This result holds under the assumption that the initial matrix is not 'too ill-conditioned' in a way that is quantified. As a consequence we show that if two iterations of the algorithm are performed, the resulting algorithm produces a matrix whose columns are orthogonal up to machine precision. Finally, we illustrate through a numerical experiment the sharpness of our result. [ABSTRACT FROM AUTHOR]

Recent contributions to the financial econometrics literature exploit high-frequency (HF) data to improve models for daily asset returns. This paper proposes a new class of dynamic extreme value models that profit from HF data when estimating the tails of daily asset returns. Our realized peaks-over-threshold approach provides estimates for the tails of the time-varying conditional return distribution. An in-sample fit to the S&P 500 index returns suggests that HF data convey information on daily extreme returns beyond that included in low frequency (LF) data. Finally, out-of-sample forecasts of conditional risk measures obtained with HF measures outperform those obtained with LF measures. [ABSTRACT FROM AUTHOR]

Various graph products and operations have been widely used to construct complex networks with common properties of real-life systems. However, current works mainly focus on designing models of binary networks, in spite of the fact that many real networks can be better mimicked by heterogeneous weighted networks. In this paper, we develop a corona product of two weighted graphs, based on which and an observed updating mechanism of edge weight in real networks, we propose a minimal generative model for inhomogeneous weighted networks. We derive analytically relevant properties of the weighted network model, including strength, weight and degree distributions, clustering coefficient, degree correlations and diameter. These properties are in good agreement with those observed in diverse real-world weighted networks. We then determine all the eigenvalues and their corresponding multiplicities of the transition probability matrix for random walks on the weighted networks. Finally, we apply the obtained spectra to derive explicit expressions for mean hitting time of random walks and weighted counting of spanning trees on the weighted networks. Our model is an exactly solvable one, allowing us to analytically treat its structural and dynamical properties, which is thus a good test-bed and an ideal substrate network for studying different dynamical processes, in order to explore the impacts of heterogeneous weight distribution on these processes. [ABSTRACT FROM AUTHOR]

A mismatch between resource supply and demand in cloud computing leads to inefficient utilization of resources or performance degradation. Therefore, this paper establishes a runtime model to evaluate the available capacity of computing resources on the basis of similar tasks. This model takes advantage of a characteristic of cloud workload; that is, similar tasks in cloud computing have a similar execution logic. The model evaluates the available resource capacity according to task similarity, thus avoiding any impact on the resource consumption of existing benchmarks. We apply the model to propose a resource capacity evaluation method called Caipan, which considers numerous factors according to resource type. This method obtains accurate results in a timely manner at little cost. We use the results of Caipan to develop some algorithms that aim to match resource supply and demand and improve cloud platform performance. We test the Caipan method and the Caipan-based algorithms in both dedicated and real-world cloud environments. The test results show that the Caipan method obtains the available resource capacity both accurately and in a timely manner and effectively supports the optimization of both algorithms and platforms. Moreover, algorithms based on Caipan reduce the mismatch between resource supply and demand and significantly improve cloud platform performance. [ABSTRACT FROM AUTHOR]

While mining the association rules in distributed database, overhead increases at each site because of linkage and dependency with other sites. Each site scans database not only for itself but for the neighboring sites also. In the most popular Count Distribution (CD) and Fast Distributed Mining (FDM) algorithms, sites generate and scan the identical candidate itemsets. In the CD algorithm, sites generate candidate k + 1 itemsets using global frequent k-itemsets and in the FDM algorithm, sites generate using its own and neighboring sites heavy frequent k-itemsets. Most of the itemsets scanned by the CD algorithm are infrequent. These infrequent itemsets are not scanned in the FDM algorithm. Anyhow, in the FDM algorithm, some of the itemsets may be found frequent on neither of the sites but scanned on all the sites. In this paper, an efficient framework and an algorithm have been proposed for mining association rules in the distributed database. In the proposed framework, initially, overhead of each site for generating and scanning candidate itemsets for the neighboring sites is reduced. Later, a site either does not scan candidate k-itemset of neighboring site or postpone till its k + 1 itemsets are scanned. [ABSTRACT FROM AUTHOR]

Biological sequence comparison algorithms that compute the optimal local and global alignments calculate a dynamic programming (DP) matrix with quadratic time complexity. The DP matrix H is calculated with a recurrence relation in which the value of each cell Hi,j is the result of a maximum operation on the cell's values Hi-1, j-1, Hi-1, j and Hi,j-1 added or subtracted by a constant value. Therefore, it can be noticed that the difference between the value of cell Hi,j being calculated and the values of direct neighbor cells previously computed respect well-defined upper and lower bounds. Using these bounds, we can show that it is possible to determine the maximum and the minimum value of every cell in H, for a given reference cell. We use this result to define a generic pruning method which determines the cells that can pruned (i.e. no need to be computed since they will not contribute to the final solution), accelerating the computation but keeping the guarantee that the optimal result will be produced. The goal of this paper is thus to investigate and formalize properties of the DP matrix in order to estimate and increase the pruning method efficiency. We also show that the pruning efficiency depends mainly on three characteristics: (a) the order in which the cells of H are calculated, (b) the values of the parameters used in the recurrence relation and (c) the contents of the sequences compared. [ABSTRACT FROM AUTHOR]

Symmetric level-index arithmetic was introduced to overcome the problems of overflow and underflow in the floating-point system. The purpose of this paper is to improve the algorithm performance of SLI arithmetic by introducing an approximation scheme using Taylor's expansion. Following a brief summary of the SLI system and its algorithm for addition/subtraction, the deduction and analysis of Taylor approximation are presented. Also some results from numerical experiments and timing comparisons on possible implementations show the advantage of the approximation method. [ABSTRACT FROM PUBLISHER]

This paper presents a heterogeneous finite element method for a fluid–solid interaction problem. The method, which combines a standard finite element discretization in the fluid region and a mixed finite element discretization in the solid region, allows the use of different meshes in fluid and solid regions. Both semi‐discrete and fully discrete approximations are formulated and analysed. Optimal order a priori error estimates in the energy norm are shown. The main difficulty in the analysis is caused by the two interface conditions which describe the interaction between the fluid and the solid. This is overcome by explicitly building one of the interface conditions into the finite element spaces. Iterative substructuring algorithms are also proposed for effectively solving the discrete finite element equations. [ABSTRACT FROM PUBLISHER]

This paper is devoted to developing a complete algorithm for solving a class of 3D elliptic equations with discontinuous coefficients (so‐called interface problems). The algorithm is based on a more accurate discretization of the problem, as well as on an efficient solution of the discretized equations. A new seven‐point finite volume discretization on cell‐centred grids is derived. It is proved that this discretization is second‐order accurate in the discrete W12 norm. A multigrid algorithm exploiting pointwise a Jacobi smoother is used to solve the ill‐conditioned system of linear algebraic equations arising after the discretization of the above problem. It is demonstrated that the choice of the stopping criterion plays a significant role for the efficiency of the iterative solver. The discretization and the iterative solver are tested in solving an eight‐corner problem (i.e. with different diffusivity coefficients in eight subregions). Second‐order convergence for both the solution and the flux is observed in numerical experiments. Numerical experiments also demonstrate that the algorithm developed for solving 3D interface problems is robust and fast. [ABSTRACT FROM PUBLISHER]

SimRank is a well-known similarity measure between graph vertices. This measure relies on a graph topology and is built on the intuition that 'two objects are similar if they are related to similar objects'. Formalization of this intuition leads to a system of linear equations, so large that even the solution vector will not fit in the RAM for many real-world graphs. To solve this issue we propose a new method based on a low-rank approximation of the linear system solution. This approach requires less memory and provides a significant calculation speed-up. The experiments show that the proposed method provides an accurate SimRank approximation. [ABSTRACT FROM AUTHOR]

This paper addresses the task of locating and identifying an unknown number of objects of different types in an image. Baddeley & Van Lieshout (1993) advocate marked point processes as object priors, whereas Grenander & Miller (1994) use deformable template models. In this paper elements of both approaches are combined to handle scenes containing variable numbers of objects of different types, using reversible jump Markov chain Monte Carlo methods for inference (Green, 1995). The naive application of these methods here leads to slow mixing and we adapt the model and algorithm in tandem in proposing three strategies to deal with this. The first two expand the model space by introducing an additional 'unknown' object type and the idea of a variable resolution template. The third strategy, utilising the first two, augments the algorithm with classes of updates which provide intuitive transitions between realisations containing different numbers of cells by splitting or merging nearby objects. [ABSTRACT FROM PUBLISHER]

A new class of complex nonsymmetric algebraic Riccati equations has been studied by Liu & Xue (2012. Complex nonsymmetric algebraic Riccati equations arising in Markov modulated fluid flows. SIAM J. Matrix Anal. Appl., 33, 569–596), which is related to the M-matrix algebraic Riccati equations. Doubling algorithms, with properly chosen parameters, are used there for equations in this new class. It is pointed out that the number of iterations for the doubling algorithms may be relatively large in some situations. In this paper, we show that the performance of the doubling algorithms can often be improved significantly if a proper preprocessing procedure is used on the given Riccati equation. There are some difficult cases for which the preprocessing procedure does not help much by itself. We then propose new strategies for choosing parameters for doubling algorithms after using the preprocessing procedure. Numerical experiments show that our preprocessing procedure and the new parameter strategies are very effective. [ABSTRACT FROM AUTHOR]

This paper introduces the paradigm of optimization under uncertainty for modelling and solving matrix nearness problems. In particular, it considers the concrete problem of recovering correlation matrices from uncertain observations by introducing two different approaches to tackling uncertainty. The first approach invokes the framework of robust optimization to construct low error solutions that are immune to worst-case uncertainty in the input. The second approach takes a less pessimistic view on uncertainty, and considers a situation where instead of the worst one, it suffices to use any matrix in the uncertainty set. We formulate both our approaches as convex (possibly nonsmooth) optimization problems. Thereafter, we show how to exploit problem structure to obtain efficient iterative first-order algorithms. We present several numerical results on both nearness and completion versions of the optimization problem; our results highlight the effectiveness of our proposed algorithmic techniques. [ABSTRACT FROM AUTHOR]

As long as a square non-negative matrix A has total support then it can be balanced, that is, we can find a diagonal scaling of A that has row and column sums equal to one. A number of algorithms have been proposed to achieve the balancing, the most well known of these being Sinkhorn–Knopp. In this paper, we derive new algorithms based on inner–outer iteration schemes. We show that Sinkhorn–Knopp belongs to this family, but other members can converge much more quickly. In particular, we show that while stationary iterative methods offer little or no improvement in many cases, a scheme using a preconditioned conjugate gradient method as the inner iteration converges at much lower cost (in terms of matrix–vector products) for a broad range of matrices; and succeeds in cases where the Sinkhorn–Knopp algorithm fails. [ABSTRACT FROM AUTHOR]

We study stationary discretionary equilibria in dynamic linear-quadratic rational expectations models. Past papers have assumed that this is uniquely determined; we show that such models can have multiple equilibria in some situations. We demonstrate the existence of multiple discretionary equilibria using a number of examples of increasing complexity and discuss their potential to explain interesting economic phenomena. We investigate the general properties of discretionary equilibria and discuss the design implications for the numerical algorithms needed to find them. [ABSTRACT FROM AUTHOR]

Relative risks (RRs) are generally considered preferable to odds ratios in prospective studies. However, unlike logistic regression for odds ratios, the standard log-binomial model for RR regression does not respect the natural parameter constraints and is therefore often subject to numerical instability. In this paper, we develop a reliable and flexible method for fitting log-binomial models. We use an Expectation–Maximization (EM) algorithm where the multiplicative event probability is viewed as the joint probability for a collection of latent binary outcomes. This gives a simple iterative scheme that provides stable convergence to the maximum likelihood estimate. In addition to reliability, the method offers some flexible generalizations, including models with unspecified isotonic regression functions. We examine the method's performance using simulations and data analyses of the age-specific RR of mortality following heart attack. These analyses demonstrate the potential for numerical instability in RR regression and show how this can be overcome using the proposed approach. Source code to implement the method in R is provided as supplementary material available at Biostatistics online. [ABSTRACT FROM PUBLISHER]

SUMMARY The rapid melting of the Earth's ice reservoirs will produce geographically distinct patterns of sea level change that have come to be known as sea level fingerprints. A basic, gravitationally self-consistent theory for computing these patterns appeared in the 1970s; however, recent, highly discrepant fingerprint calculations have led to suggestions that the algorithms and/or theoretical implementation adopted in many previous predictions is not robust. We present a suite of numerical predictions, including benchmark comparisons with analytic results, that counter this argument and demonstrate the accuracy of most published predictions. Moreover, we show that small differences apparent in calculations published by some groups can be accounted for by subtle differences in the underlying physics. The paper concludes with two sensitivity analyses: (1) we present the first-ever calculation of sea level fingerprints on earth models with 3-D variations in elastic structure and density, and conclude that this added complexity has a negligible effect on the predictions; (2) we compare fingerprints of polar ice sheet mass flux computed under the (very common) assumption of a uniform melt distribution to fingerprints calculated using melt geometries constrained by analysing recent trends in GRACE gravity data. Predictions in the near field of the ice sheets are sensitive to the assumed melt geometry; however, this sensitivity also extends to the far field, particularly in the case of Antarctic mass changes, because of the strong dependence of the rotational feedback signal on the melt geometry. We conclude that inferences of ice sheet mass flux based on modern sea level constraints should consider these more realistic melt geometries. [ABSTRACT FROM AUTHOR]

A commonly used algorithm for generating adaptive meshes for a given adaptation function in one dimension is due to de Boor. In its original form the algorithm produces a sequence of meshes upon using piecewise constant interpolation for the adaptation function on the current mesh and generating a new mesh that exactly equidistributes the interpolant. In this paper we present a proof for the existence of a limit mesh and for the convergence of de Boor's algorithm. Numerical results are given to illustrate the theoretical findings, and stopping criteria necessary for the implementation of the algorithm are examined. [ABSTRACT FROM PUBLISHER]

Rather than viewing receiver operating characteristic (ROC) curves directly to compare the performances of diagnostic methods, the whole and the partial areas under the ROC curve (area under the ROC curve [AUC] and partial area under the ROC curve [pAUC]) are 2 of the most popularly used summaries of the curve. Moreover, when high specificity is a prerequisite, as in some medical diagnostics, pAUC is preferable. In this paper, we propose a wrapper-type algorithm to select the best linear combination of markers that has high sensitivity within a confined specificity range. The markers selected by the proposed algorithm are different from those selected by AUC-based algorithms and therefore provide different information for further studies. Most notably, for example, within the given range of specificity, the markers selected by the proposed algorithm always have higher individual sensitivities than those selected by other AUC-based methods. This characteristic makes the proposed method a good addition to existing methods. Without assuming the underlying distributions of markers, we prove that the pAUC obtained with the proposed algorithm is a strongly consistent estimate of the true pAUC and then illustrate its performance with numerical studies using synthesized data and 2 real examples. The results are compared with those obtained by its AUC-based counterpart. We found that the classification performance of the final classifier based on the selected markers is very competitive. [ABSTRACT FROM AUTHOR]

The Fast Marching Method is an efficient numerical algorithm for propagating interfaces such as first-arrival seismic wave fronts travelling through a velocity distribution. Fast Marching solutions have been developed for use on rectilinear grids in 2-D and 3-D. We are interested in unstructured grids as they provide some computational advantages when dealing with complicated shapes that are difficult to represent with rectilinear grids. Fast Marching solutions have also been developed for unstructured 2-D triangular grids but this has yet to be extended to unstructured 3-D tetrahedral grids. In this paper, we extend the Fast Marching Method to unstructured 3-D tetrahedral grids using a derivation that follows the 2-D case. The resulting equations are discussed in intuitive terms and an error analysis is performed. Our method is applied to a simple synthetic example and to a more complicated model based on the Voisey's Bay massive sulphide deposit in Labrador, Canada. [ABSTRACT FROM AUTHOR]

We address in this paper a parabolic equation used to model the phase mass balance in two-phase flows, which differs from the mass balance for chemical species in compressible multicomponent flows by the addition of a nonlinear term of the form ∇·ρϕ(y)ur, where y is the unknown mass fraction, ρ stands for the density, ϕ is a regular function such that ϕ(0) = ϕ(1) = 0 and ur is a (not necessarily divergence free) velocity field. We propose a finite-volume scheme for the numerical approximation of this equation, with a discretization of the nonlinear term based on monotone flux functions. Under the classical assumption that the discretization of the convection operator must be such that it vanishes for a constant y, we prove the existence and uniqueness of the solution, together with the fact that it remains within its physical bounds, i.e., within the interval [0, 1]. Then this scheme is combined with a pressure correction method to obtain a semi-implicit fractional step scheme for the so-called drift-flux model. To satisfy the above-mentioned assumption a specific time stepping algorithm with particular approximations for the density terms is developed. Numerical tests are performed to assess the convergence and stability properties of this scheme. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the numerical analysis of a dynamic problem which models the temperature evolution in a thermoviscoelastic body. The variational problem is formulated as a coupled system of evolutionary nonlinear variational equations. An existence and uniqueness result is recalled. Then, a fully discrete numerical scheme is introduced by using the finite-element method to approximate the spatial variable and an Euler scheme to discretise the time derivatives. Error estimates are derived and, under suitable regularity assumptions, the linear convergence of the numerical scheme is obtained. Finally, the results of simulations of some two-dimensional numerical examples are presented to demonstrate the accuracy of the algorithm and the behaviour of the solution. [ABSTRACT FROM PUBLISHER]

Markov chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of Markov chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to build efficient high dimensional proposal distributions by using sequential Monte Carlo methods. This allows us not only to improve over standard Markov chain Monte Carlo schemes but also to make Bayesian inference feasible for a large class of statistical models where this was not previously so. We demonstrate these algorithms on a non-linear state space model and a Lévy-driven stochastic volatility model. [ABSTRACT FROM AUTHOR]

In this paper, we consider Smolyak algorithms based on quasi-Monte Carlo rules for high-dimensional numerical integration. The quasi-Monte Carlo rules employed here use digital (t, α, β, σ, d)-sequences as quadrature points. We consider the worst-case error for multivariate integration in certain Sobolev spaces and show that our quadrature rules achieve the optimal rate of convergence. By randomizing the underlying digital sequences, we can also obtain a randomized Smolyak algorithm. The bound on the worst-case error holds also for the randomized algorithm in a statistical sense. Further, we also show that the randomized algorithm is unbiased and that the integration error can be approximated as well. [ABSTRACT FROM PUBLISHER]

This paper deals with perturbed linear fixed point methods in the presence of round-off errors. Successive approximations as well as the more general asynchronous iterations are treated. Forward and backward error estimates are presented, and these are used to propose theoretical stopping criteria for these methods. In the case of asynchronous iterations, macro-iterations are used as a tool in order to obtain estimates. [ABSTRACT FROM PUBLISHER]

In this paper, an iterative algorithm based on the Landweber method in combination with the boundary element method is developed for solving the Cauchy problem in isotropic linear elasticity. An efficient regularizing stopping criterion is also employed. The numerical results obtained confirm that the iterative method produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data, respectively. [ABSTRACT FROM PUBLISHER]

Nuisance parameters do not pose any problems in Bayesian inference as marginalisation allows for study of the posterior distribution solely in terms of the parameter of interest. However, no general solution is available for removing nuisance parameters under the frequentist paradigm. In this paper, we merge the two approaches to construct a general procedure for frequentist elimination of nuisance parameters through the use of matching priors. In particular, we perform Bayesian marginalisation with respect to a prior distribution under which posterior inferences have approximate frequentist validity. Matching priors are constructed as solutions to a partial differential equation. Unfortunately, except in simple cases, these partial differential equations do not yield to analytical nor even standard numerical methods of solution. We present a numerical/Monte Carlo algorithm for obtaining the matching prior, in general, as a solution to the appropriate partial differential equation and draw posterior inferences. To be specific, we develop an automated routine through an implementation of the Metropolis–Hastings algorithm for deriving frequentist valid inferences via the matching prior. We illustrate our results in the contexts of fitting random effects models, fitting logistic regression models and fitting teratological data by beta‐binomial models. [ABSTRACT FROM PUBLISHER]

Motivation: Analysis of millions of pyro-sequences is currently playing a crucial role in the advance of environmental microbiology. Taxonomy-independent, i.e. unsupervised, clustering of these sequences is essential for the definition of Operational Taxonomic Units. For this application, reproducibility and robustness should be the most sought after qualities, but have thus far largely been overlooked.Results: More than 1 million hyper-variable internal transcribed spacer 1 (ITS1) sequences of fungal origin have been analyzed. The ITS1 sequences were first properly extracted from 454 reads using generalized profiles. Then, otupipe, cd-hit-454, ESPRIT-Tree and DBC454, a new algorithm presented here, were used to analyze the sequences. A numerical assay was developed to measure the reproducibility and robustness of these algorithms. DBC454 was the most robust, closely followed by ESPRIT-Tree. DBC454 features density-based hierarchical clustering, which complements the other methods by providing insights into the structure of the data.Availability: An executable is freely available for non-commercial users at ftp://ftp.vital-it.ch/tools/dbc454. It is designed to run under MPI on a cluster of 64-bit Linux machines running Red Hat 4.x, or on a multi-core OSX system.Contact: dbc454@vital-it.ch or nicolas.guex@isb-sib.ch [ABSTRACT FROM AUTHOR]

ABSTRACT For analysing maps of the cosmic microwave background sky, it is necessary to mask out the region around the Galactic equator where the parasitic foreground emission is strongest as well as the brightest compact sources. Since many of the analyses of the data, particularly those searching for non-Gaussianity of a primordial origin, are most straightforwardly carried out on full-sky maps, it is of great interest to develop efficient algorithms for filling in the missing information in a plausible way. In this paper, we explore algorithms for filling in based on constrained Gaussian realizations. The non-trivial step in such a filling-in procedure is to find the maximum likelihood configuration for the masked pixels given the data for the unmasked pixels. We reformulate the problem in terms of an integral equation involving a short-range kernel and show that in the far interior of a masked region the maximum likelihood configuration very nearly obeys the Laplace equation. Although carrying out constrained Gaussian realizations is in principle straightforward, for finely pixelized maps as will be required for the Planck analysis, a direct brute force method is not numerically tractable. Here we present some concrete solutions to this problem, both on a spatially flat sky with periodic boundary conditions and on the pixelized sphere. One approach is to solve the linear system using an appropriately preconditioned conjugate gradient method. While this approach was successfully implemented on a rectangular domain with periodic boundary conditions and converged rapidly even for very wide masked regions, we found that the method failed on the pixelized sphere for reasons that we explain here. We present an approach that works for full-sky pixelized maps on the sphere involving a kernel-based multiresolution Laplace solver followed by a series of conjugate gradient corrections near the boundary of the mask. [ABSTRACT FROM AUTHOR]

Perhaps, the most astonishing idea in eigenvalue computation is Rutishauser's idea of applying the LR transform to a matrix for generating a sequence of similar matrices that become more and more triangular. The same idea is the foundation of the ubiquitous QR algorithm. It is well known that this idea originated in Rutishauser's qd algorithm, which precedes the LR algorithm and can be understood as applying LR to a tridiagonal matrix. But how did Rutishauser discover qd and when did he find the qd–LR connection? We checked some of the early sources and have come up with an explanation. [ABSTRACT FROM PUBLISHER]

We have developed a massively parallel, simple and fast hydrodynamics code for multidimensional, self-gravitating and adiabatic flows. Our primary motivation is the study of the non-linear development of white dwarf oscillations excited via tidal resonances, typically over hundreds of stellar dynamical times. Consequently, we require long-term stability, low diffusivity and high-numerical efficiency. This is accomplished by an Eulerian finite-difference scheme on a regular Cartesian grid. This choice of coordinates provides uniform resolution throughout the flow as well as simplifying the computation of the self-gravitational potential, which is done via spectral methods. In this paper, we describe the numerical scheme and present the results of some common diagnostic problems. We also demonstrate the stability of a cold white dwarf in three dimensions over hundreds of dynamical times. Finally, we compare the results of the numerical scheme to the linear theory of adiabatic oscillations, finding numerical quality factors on the order of 6000 and excellent agreement with the oscillation frequency obtained by the linear analysis. [ABSTRACT FROM AUTHOR]

Evaluating the log-sum-exp function or the softmax function is a key step in many modern data science algorithms, notably in inference and classification. Because of the exponentials that these functions contain, the evaluation is prone to overflow and underflow, especially in low-precision arithmetic. Software implementations commonly use alternative formulas that avoid overflow and reduce the chance of harmful underflow, employing a shift or another rewriting. Although mathematically equivalent, these variants behave differently in floating-point arithmetic and shifting can introduce subtractive cancellation. We give rounding error analyses of different evaluation algorithms and interpret the error bounds using condition numbers for the functions. We conclude, based on the analysis and numerical experiments, that the shifted formulas are of similar accuracy to the unshifted ones, so can safely be used, but that a division-free variant of softmax can suffer from loss of accuracy. [ABSTRACT FROM AUTHOR]

Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data and can outperform analytical models. In particular, alternating optimization algorithms have been popular for learning such models. In this work, we focus on alternating minimization for a specific structured unitary sparsifying operator learning problem and provide a convergence analysis. While the algorithm converges to the critical points of the problem generally, our analysis establishes under mild assumptions, the local linear convergence of the algorithm to the underlying sparsifying model of the data. Analysis and numerical simulations show that our assumptions hold for standard probabilistic data models. In practice, the algorithm is robust to initialization. [ABSTRACT FROM AUTHOR]

Motivation Full-order partial correlation, a fundamental approach for network reconstruction, e.g. in the context of gene regulation, relies on the precision matrix (the inverse of the covariance matrix) as an indicator of which variables are directly associated. The precision matrix assumes Gaussian linear data and its entries are zero for pairs of variables that are independent given all other variables. However, there is still very little theory on network reconstruction under the assumption of non-linear interactions among variables. Results We propose Distance Precision Matrix, a network reconstruction method aimed at both linear and non-linear data. Like partial distance correlation, it builds on distance covariance, a measure of possibly non-linear association, and on the idea of full-order partial correlation, which allows to discard indirect associations. We provide evidence that the Distance Precision Matrix method can successfully compute networks from linear and non-linear data, and consistently so across different datasets, even if sample size is low. The method is fast enough to compute networks on hundreds of nodes. Availability and implementation An R package DPM is available at https://github.molgen.mpg.de/ghanbari/DPM. Supplementary information Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

We consider a causal effect that is confounded by an unobserved variable, but for which observed proxy variables of the confounder are available. We show that with at least two independent proxy variables satisfying a certain rank condition, the causal effect can be nonparametrically identified, even if the measurement error mechanism, i.e. the conditional distribution of the proxies given the confounder, may not be identified. Our result generalizes the identification strategy of Kuroki & Pearl (2014), which rests on identification of the measurement error mechanism. When only one proxy for the confounder is available, or when the required rank condition is not met, we develop a strategy for testing the null hypothesis of no causal effect. [ABSTRACT FROM AUTHOR]

Summary: Motivated by a cutting edge problem related to the shape of α‐helices in proteins, we formulate a parametric statistical model, which incorporates the cylindrical nature of the helix. Our focus is to detect a “kink,” which is a drastic change in the axial direction of the helix. We propose a statistical model for the straight α‐helix and derive the maximum likelihood estimation procedure. The cylinder is an accepted geometric model for α‐helices, but our statistical formulation, for the first time, quantifies the uncertainty in atom positions around the cylinder. We propose a change point technique “Kink‐Detector” to detect a kink location along the helix. Unlike classical change point problems, the change in direction of a helix depends on a simultaneous shift of multiple data points rather than a single data point, and is less straightforward. Our biological building block is crowdsourced data on straight and kinked helices; which has set a gold standard. We use this data to identify salient features to construct Kink‐detector, test its performance and gain some insights. We find the performance of Kink‐detector comparable to its computational competitor called “Kink‐Finder.” We highlight that identification of kinks by visual assessment can have limitations and Kink‐detector may help in such cases. Further, an analysis of crowdsourced curved α‐helices finds that Kink‐detector is also effective in detecting moderate changes in axial directions. [ABSTRACT FROM AUTHOR]

For the moduli stacks of α-stable curves introduced in [4], we prove nefness of natural log canonical divisors, thus generalizing a well-known result of Cornalba and Harris for the moduli stack of Deligne-Mumford stable curves. We then deduce the projectivity of the good moduli spaces of α-stable curves and identify these moduli spaces with the log canonical models of Mg,n appearing in the Hassett-Keel program. [ABSTRACT FROM AUTHOR]

We consider the partial least squares algorithm for dependent data and study the consequences of ignoring the dependence both theoretically and numerically. Ignoring nonstationary dependence structures can lead to inconsistent estimation, but a simple modification yields consistent estimation. A protein dynamics example illustrates the superior predictive power of the proposed method. [ABSTRACT FROM AUTHOR]

The dynamic response of a coated inclusion is considered in the context of active cloaking. The active cloak is achieved for a coated inclusion in the presence of flexural and membrane waves. In this article, we investigate the design of an active cloak for a coated inclusion in three frequency regimes: the low-frequency range, the intermediate range and the higher frequency range in which scattering resonances occur. In the first of these ranges, we extend previous work, which resulted in a simple mass-compensation design for the monopole scatterer, while in the second and third ranges, a combination of the use of an appropriate coating and the appropriate choice of the amplitudes of the active cloaking sources is necessary.We show that such cloaking can indeed be effective in the region of strong scattering resonances. We give closed form analytic expressions for the required amplitudes of the active cloaking sources in the three frequency regions and provide asymptotic estimates and numerical illustrations. [ABSTRACT FROM AUTHOR]

Tensors admitting an expression as the sum of at most s rank 1 tensors can be considered points of the sth order secant variety of a Segre variety, yet the most basic invariant of this variety—its dimension—is not yet fully understood. A conjecture was nevertheless proposed by Abo et al. (2009, Induction for secant varieties of Segre varieties. Trans. Amer. Math. Soc., 361, 767–792), which was proved to be correct for s≤6. We propose a numerical randomized algorithm for testing whether a mathematically exact and structured matrix is singular, requiring only the availability of an approximate matrix–vector product. Using this method, we test whether the aforementioned conjecture is true. The proposed method requires several orders of magnitude less memory than approaches based on symbolic arithmetic, thus greatly increasing the number of varieties that can be handled. Our experiments establish that the Segre varieties embedded in with expected generic rank s≤55 obey the conjecture; the probability that a defective variety is incorrectly classified as nondefective is less than <10−55. [ABSTRACT FROM AUTHOR]

The aim of this work is to consider multiscale algorithms for solving partial differential equations (PDEs) with Galerkin methods on bounded domains. We provide results on convergence and condition numbers. We show how to handle PDEs with Dirichlet boundary conditions. We also investigate convergence in terms of the mesh norms and the angles between subspaces to better understand the differences between the algorithms and the observed results. We also consider the issue of the supports of the radial basis funtions overlapping the boundary in our stability analysis, which has not been considered in the literature to the best of our knowledge. [ABSTRACT FROM AUTHOR]

We show improvements in the precision of the Bayesian infrasound source localization (BISL) method by incorporating semi-empirical model-based prior information. Given a set of backazimuths and delay times at ≥2 arrays, BISL scans a parameter space (that comprises the horizontal coordinates, celerity and origin time) for the most likely solution. A key element of BISL is its flexibility; the method allows the incorporation of prior information to constrain the parameters. Our research focuses on generating model-based propagation catalogues using a comprehensive set of atmospheric scenarios, extracting celerity distributions based on range and azimuth from the catalogues and using these distributions as prior probability density functions to enhance the location solution from BISL. To illustrate the improvements in source location precision, we compare the BISL results computed using uniform celerity distribution priors with those using enhanced priors; as applied to: (1) a set of events recorded across a regional network and (2) a large accidental chemical explosion recorded by six infrasound arrays in Eurasia. Finally, we discuss efforts to improve the numerical implementation of BISL by expanding the parameter space to cover a richer set of parameters that can include station-specific celerity distributions. [ABSTRACT FROM AUTHOR]

We show the existence and uniqueness of a solution for the nonlocal vector-valued Allen–Cahn variational inequality in a formulation involving Lagrange multipliers for local and nonlocal constraints. Furthermore, we propose and analyse a primal–dual active set (PDAS) method for local and nonlocal vector-valued Allen–Cahn variational inequalities. The local convergence behaviour of the PDAS algorithm is studied by interpreting the approach as a semismooth Newton method and numerical simulations are presented demonstrating its efficiency. [ABSTRACT FROM AUTHOR]

We propose a numerical algorithm for solving first arrival transmission traveltime tomography problems where the underlying slowness is piecewise continuous. The idea is based upon our previously efficient approach for smooth slowness inversion (Leung & Qian) using the fast sweeping method and the adjoint state method. In this work, we further incorporate the level set method to implicitly represent the discontinuity in the velocity. One main advantage of such implicit representation is that there is no assumption on the number of disjoint components in the inverted structure. The evolution of the level set function will naturally take care of the change in the topology. Like in the previous work, the gradient of the mismatch functional is derived using the adjoint state method. The forward problem and the adjoint equation are efficiently solved by the fast sweeping method. To further improve the computational efficiency, we also propose a local level set method so that most computer power of updating the level set evolution is spent near the discontinuity in the slowness. Numerical results will be given to demonstrate the robustness of the algorithm. [ABSTRACT FROM AUTHOR]

We derive an algorithm for the adaptive approximation of solutions to parabolic equations. It is based on adaptive finite elements in space and the implicit Euler discretization in time with adaptive time-step sizes. We prove that, given a positive tolerance for the error, the adaptive algorithm reaches the final time with a space-time error between continuous and discrete solution that is below the given tolerance. Numerical experiments reveal a more than competitive performance of our algorithm ASTFEM (adaptive space-time finite element method). [ABSTRACT FROM AUTHOR]

. For high dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due to diverging spectra and accumulation of noise. Therefore, researchers proposed independence rules to circumvent the diverging spectra, and sparse independence rules to mitigate the issue of accumulation of noise. However, in biological applications, often a group of correlated genes are responsible for clinical outcomes, and the use of the covariance information can significantly reduce misclassification rates. In theory the extent of such error rate reductions is unveiled by comparing the misclassification rates of the Fisher discriminant rule and the independence rule. To materialize the gain on the basis of finite samples, a regularized optimal affine discriminant (ROAD) is proposed. The ROAD selects an increasing number of features as the regularization relaxes. Further benefits can be achieved when a screening method is employed to narrow the feature pool before applying the ROAD method. An efficient constrained co-ordinate descent algorithm is also developed to solve the associated optimization problems. Sampling properties of oracle type are established. Simulation studies and real data analysis support our theoretical results and demonstrate the advantages of the new classification procedure under a variety of correlation structures. A delicate result on continuous piecewise linear solution paths for the ROAD optimization problem at the population level justifies the linear interpolation of the constrained co-ordinate descent algorithm. [ABSTRACT FROM AUTHOR]

The full likelihood approach in statistical analysis is regarded as the most efficient means for estimation and inference. For complex length-biased failure time data, computational algorithms and theoretical properties are not readily available, especially when a likelihood function involves infinite-dimensional parameters. Relying on the invariance property of length-biased failure time data under the semiparametric density ratio model, we present two likelihood approaches for the estimation and assessment of the difference between two survival distributions. The most efficient maximum likelihood estimators are obtained by the em algorithm and profile likelihood. We also provide a simple numerical method for estimation and inference based on conditional likelihood, which can be generalized to k-arm settings. Unlike conventional survival data, the mean of the population failure times can be consistently estimated given right-censored length-biased data under mild regularity conditions. To check the semiparametric density ratio model assumption, we use a test statistic based on the area between two survival distributions. Simulation studies confirm that the full likelihood estimators are more efficient than the conditional likelihood estimators. We analyse an epidemiological study to illustrate the proposed methods. [ABSTRACT FROM PUBLISHER]