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A Matrix Splitting Method for Composite Function Minimization(arXiv, 20161207)Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes and analyzes a new Matrix Splitting Method (MSM) for minimizing composite functions. It can be viewed as a generalization of the classical GaussSeidel method and the Successive OverRelaxation method for solving linear systems in the literature. Incorporating a new Gaussian elimination procedure, the matrix splitting method achieves stateoftheart performance. For convex problems, we establish the global convergence, convergence rate, and iteration complexity of MSM, while for nonconvex problems, we prove its global convergence. Finally, we validate the performance of our matrix splitting method on two particular applications: nonnegative matrix factorization and cardinality regularized sparse coding. Extensive experiments show that our method outperforms existing composite function minimization techniques in term of both efficiency and efficacy.

Measurement of the surface susceptibility and the surface conductivity of atomically thin by spectroscopic ellipsometry(arXiv, 20171001)We show how to correctly extract from the ellipsometric data the surface susceptibility and the surface conductivity that describe the optical properties of monolayer $\rm MoS_2$. Theoretically, these parameters stem from modelling a singlelayer twodimensional crystal as a surface current, a truly twodimensional model. Currently experimental practice is to consider this model equivalent to a homogeneous slab with an effective thickness given by the interlayer spacing of the exfoliating bulk material. We prove that the error in the evaluation of the surface susceptibility of monolayer $\rm MoS_2$, owing to the use of the slab model, is at least 10% or greater, a significant discrepancy in the determination of the optical properties of this material.

Metaanalysis reveals hostdependent nitrogen recycling as a mechanism of symbiont control in Aiptasia(Cold Spring Harbor Laboratory, 20180222)The metabolic symbiosis with photosynthetic algae of the genus Symbiodinium allows corals to thrive in the oligotrophic environments of tropical seas. Many aspects of this relationship have been investigated using transcriptomic analyses in the emerging model organism Aiptasia. However, previous studies identified thousands of putatively symbiosisrelated genes, making it difficult to disentangle symbiosisinduced responses from undesired experimental parameters. Using a metaanalysis approach, we identified a core set of 731 highconfidence symbiosisassociated genes that reveal hostdependent recycling of waste ammonium and amino acid synthesis as central processes in this relationship. Combining transcriptomic and metabolomic analyses, we show that symbiontderived carbon enables host recycling of ammonium into nonessential amino acids. We propose that this provides a regulatory mechanism to control symbiont growth through a carbondependent negative feedback of nitrogen availability to the symbiont. The dependence of this mechanism on symbiontderived carbon highlights the susceptibility of this symbiosis to changes in carbon translocation, as imposed by environmental stress.

Microscopic Origin of Interfacial DzyaloshinskiiMoriya Interaction(arXiv, 20170410)Chiral spin textures at the interface between ferromagnetic and heavy nonmagnetic metals, such as Neeltype domain walls and skyrmions, have been studied intensively because of their great potential for future nanomagnetic devices. The DyzaloshinskiiMoriya interaction (DMI) is an essential phenomenon for the formation of such chiral spin textures. In spite of recent theoretical progress aiming at understanding the microscopic origin of the DMI, an experimental investigation unravelling the physics at stake is still required. Here, we experimentally demonstrate the close correlation of the DMI with the anisotropy of the orbital magnetic moment and with the magnetic dipole moment of the ferromagnetic metal. The density functional theory and the tightbinding model calculations reveal that asymmetric electron occupation in orbitals gives rise to this correlation.

Modelbased Quantile Regression for Discrete Data(arXiv, 20180410)Quantile regression is a class of methods voted to the modelling of conditional quantiles. In a Bayesian framework quantile regression has typically been carried out exploiting the Asymmetric Laplace Distribution as a working likelihood. Despite the fact that this leads to a proper posterior for the regression coefficients, the resulting posterior variance is however affected by an unidentifiable parameter, hence any inferential procedure beside point estimation is unreliable. We propose a modelbased approach for quantile regression that considers quantiles of the generating distribution directly, and thus allows for a proper uncertainty quantification. We then create a link between quantile regression and generalised linear models by mapping the quantiles to the parameter of the response variable, and we exploit it to fit the model with RINLA. We extend it also in the case of discrete responses, where there is no 1to1 relationship between quantiles and distribution's parameter, by introducing continuous generalisations of the most common discrete variables (Poisson, Binomial and Negative Binomial) to be exploited in the fitting.

Modeling DzyaloshinskiiMoriya Interaction at Transition Metal Interfaces: Constrained Moment versus Generalized Bloch Theorem(arXiv, 20171029)DzyaloshinskiiMoriya interaction (DMI) at Pt/Co interfaces is investigated theoretically using two different first principles methods. The first one uses the constrained moment method to build a spin spiral in real space, while the second method uses the generalized Bloch theorem approach to construct a spin spiral in reciprocal space. We show that although the two methods produce an overall similar total DMI energy, the dependence of DMI as a function of the spin spiral wavelength is dramatically different. We suggest that longrange magnetic interactions, that determine itinerant magnetism in transition metals, are responsible for this discrepancy. We conclude that the generalized Bloch theorem approach is more adapted to model DMI in transition metal systems, where magnetism is delocalized, while the constrained moment approach is mostly applicable to weak or insulating magnets, where magnetism is localized.

Modeling high dimensional multichannel brain signals(arXiv, 20170327)In this paper, our goal is to model functional and effective (directional) connectivity in network of multichannel brain physiological signals (e.g., electroencephalograms, local field potentials). The primary challenges here are twofold: first, there are major statistical and computational difficulties for modeling and analyzing high dimensional multichannel brain signals; second, there is no set of universallyagreed measures for characterizing connectivity. To model multichannel brain signals, our approach is to fit a vector autoregressive (VAR) model with sufficiently high order so that complex leadlag temporal dynamics between the channels can be accurately characterized. However, such a model contains a large number of parameters. Thus, we will estimate the high dimensional VAR parameter space by our proposed hybrid LASSLE method (LASSO+LSE) which is imposes regularization on the first step (to control for sparsity) and constrained least squares estimation on the second step (to improve bias and meansquared error of the estimator). Then to characterize connectivity between channels in a brain network, we will use various measures but put an emphasis on partial directed coherence (PDC) in order to capture directional connectivity between channels. PDC is a directed frequencyspecific measure that explains the extent to which the present oscillatory activity in a sender channel influences the future oscillatory activity in a specific receiver channel relative all possible receivers in the network. Using the proposed modeling approach, we have achieved some insights on learning in a rat engaged in a nonspatial memory task.

Modeling of Viral Aerosol Transmission and Detection(2018)The objective of this work is to investigate the spread mechanism of diseases in the atmosphere as an engineering problem. Among the viral transmission mechanisms that do not include physical contact, aerosol transmission is the most significant mode of transmission where virusladen droplets are carried over long distances by wind. In this work, we focus on aerosol transmission of virus and introduce the idea of viewing virus transmission through aerosols and their transport as a molecular communication problem, where one has no control over transmission source but a robust receiver can be designed using nanobiosensors. To investigate this idea, a complete system is presented and endtoend mathematical model for the aerosol transmission channel is derived under certain constraints and boundary conditions. In addition to transmitter and channel, a receiver architecture composed of air sampler and Silicon Nanowire field effect transistor is also discussed. Furthermore, a detection problem is formulated for which maximum likelihood decision rule and the corresponding missed detection probability is discussed. At the end, simulation results are presented to investigate the parameters that affect the performance and justify the feasibility of proposed setup in related applications.

Modeling soil organic carbon with Quantile Regression: Dissecting predictors' effects on carbon stocks(arXiv, 20170813)Soil Organic Carbon (SOC) estimation is crucial to manage both natural and anthropic ecosystems and has recently been put under the magnifying glass after the Paris agreement 2016 due to its relationship with greenhouse gas. Statistical applications have dominated the SOC stock mapping at regional scale so far. However, the community has hardly ever attempted to implement Quantile Regression (QR) to spatially predict the SOC distribution. In this contribution, we test QR to estimate SOC stock (030 $cm$ depth) in the agricultural areas of a highly variable semiarid region (Sicily, Italy, around 25,000 $km2$) by using topographic and remotely sensed predictors. We also compare the results with those from available SOC stock measurement. The QR models produced robust performances and allowed to recognize dominant effects among the predictors with respect to the considered quantile. This information, currently lacking, suggests that QR can discern predictor influences on SOC stock at specific subdomains of each predictors. In this work, the predictive map generated at the median shows lower errors than those of the Joint Research Centre and International Soil Reference, and Information Centre benchmarks. The results suggest the use of QR as a comprehensive and effective method to map SOC using legacy data in agroecosystems. The R code scripted in this study for QR is included.

Modeling spatial processes with unknown extremal dependence class(arXiv, 20170317)Many environmental processes exhibit weakening spatial dependence as events become more extreme. Wellknown limiting models, such as maxstable or generalized Pareto processes, cannot capture this, which can lead to a preference for models that exhibit a property known as asymptotic independence. However, weakening dependence does not automatically imply asymptotic independence, and whether the process is truly asymptotically (in)dependent is usually far from clear. The distinction is key as it can have a large impact upon extrapolation, i.e., the estimated probabilities of events more extreme than those observed. In this work, we present a single spatial model that is able to capture both dependence classes in a parsimonious manner, and with a smooth transition between the two cases. The model covers a wide range of possibilities from asymptotic independence through to complete dependence, and permits weakening dependence of extremes even under asymptotic dependence. Censored likelihoodbased inference for the implied copula is feasible in moderate dimensions due to closedform margins. The model is applied to oceanographic datasets with ambiguous true limiting dependence structure.

Momentum and Stochastic Momentum for Stochastic Gradient, Newton, Proximal Point and Subspace Descent Methods(arXiv, 20171227)In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these methods are studied. We choose to perform our analysis in a setting in which all of the above methods are equivalent. We prove global nonassymptotic linear convergence rates for all methods and various measures of success, including primal function values, primal iterates (in L2 sense), and dual function values. We also show that the primal iterates converge at an accelerated linear rate in the L1 sense. This is the first time a linear rate is shown for the stochastic heavy ball method (i.e., stochastic gradient descent method with momentum). Under somewhat weaker conditions, we establish a sublinear convergence rate for Cesaro averages of primal iterates. Moreover, we propose a novel concept, which we call stochastic momentum, aimed at decreasing the cost of performing the momentum step. We prove linear convergence of several stochastic methods with stochastic momentum, and show that in some sparse data regimes and for sufficiently small momentum parameters, these methods enjoy better overall complexity than methods with deterministic momentum. Finally, we perform extensive numerical testing on artificial and real datasets, including data coming from average consensus problems.

Monotone numerical methods for finitestate meanfield games(arXiv, 20170429)Here, we develop numerical methods for finitestate meanfield games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These nonstandard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and timedependent problems. We illustrate our methods in a MFG modeling the paradigmshift problem.

Motif signatures of transcribed enhancers(Cold Spring Harbor Laboratory, 20170914)In mammalian cells, transcribed enhancers (TrEn) play important roles in the initiation of gene expression and maintenance of gene expression levels in spatiotemporal manner. One of the most challenging questions in biology today is how the genomic characteristics of enhancers relate to enhancer activities. This is particularly critical, as several recent studies have linked enhancer sequence motifs to specific functional roles. To date, only a limited number of enhancer sequence characteristics have been investigated, leaving space for exploring the enhancers genomic code in a more systematic way. To address this problem, we developed a novel computational method, TELS, aimed at identifying predictive cell type/tissue specific motif signatures. We used TELS to compile a comprehensive catalog of motif signatures for all known TrEn identified by the FANTOM5 consortium across 112 human primary cells and tissues. Our results confirm that distinct cell type/tissue specific motif signatures characterize TrEn. These signatures allow discriminating successfully a) TrEn from random controls, proxy of nonenhancer activity, and b) cell type/tissue specific TrEn from enhancers expressed and transcribed in different cell types/tissues. TELS codes and datasets are publicly available at http://www.cbrc.kaust.edu.sa/TELS.

MultiBranch Fully Convolutional Network for Face Detection(arXiv, 20170720)Face detection is a fundamental problem in computer vision. It is still a challenging task in unconstrained conditions due to significant variations in scale, pose, expressions, and occlusion. In this paper, we propose a multibranch fully convolutional network (MBFCN) for face detection, which considers both efficiency and effectiveness in the design process. Our MBFCN detector can deal with faces at all scale ranges with only a single pass through the backbone network. As such, our MBFCN model saves computation and thus is more efficient, compared to previous methods that make multiple passes. For each branch, the specific skip connections of the convolutional feature maps at different layers are exploited to represent faces in specific scale ranges. Specifically, small faces can be represented with both shallow finegrained and deep powerful coarse features. With this representation, superior improvement in performance is registered for the task of detecting small faces. We test our MBFCN detector on two public face detection benchmarks, including FDDB and WIDER FACE. Extensive experiments show that our detector outperforms stateoftheart methods on all these datasets in general and by a substantial margin on the most challenging among them (e.g. WIDER FACE Hard subset). Also, MBFCN runs at 15 FPS on a GPU for images of size 640 x 480 with no assumption on the minimum detectable face size.

A MultiResolution Spatial Model for Large Datasets Based on the Skewt Distribution(arXiv, 20171206)Large, nonGaussian spatial datasets pose a considerable modeling challenge as the dependence structure implied by the model needs to be captured at different scales, while retaining feasible inference. Skewnormal and skewt distributions have only recently begun to appear in the spatial statistics literature, without much consideration, however, for the ability to capture dependence at multiple resolutions, and simultaneously achieve feasible inference for increasingly large data sets. This article presents the first multiresolution spatial model inspired by the skewt distribution, where a largescale effect follows a multivariate normal distribution and the finescale effects follow a multivariate skewnormal distributions. The resulting marginal distribution for each region is skewt, thereby allowing for greater flexibility in capturing skewness and heavy tails characterizing many environmental datasets. Likelihoodbased inference is performed using a Monte Carlo EM algorithm. The model is applied as a stochastic generator of daily wind speeds over Saudi Arabia.

MultiScale Factor Analysis of HighDimensional Brain Signals(arXiv, 20170518)In this paper, we develop an approach to modeling highdimensional networks with a large number of nodes arranged in a hierarchical and modular structure. We propose a novel multiscale factor analysis (MSFA) model which partitions the massive spatiotemporal data defined over the complex networks into a finite set of regional clusters. To achieve further dimension reduction, we represent the signals in each cluster by a small number of latent factors. The correlation matrix for all nodes in the network are approximated by lowerdimensional substructures derived from the clusterspecific factors. To estimate regional connectivity between numerous nodes (within each cluster), we apply principal components analysis (PCA) to produce factors which are derived as the optimal reconstruction of the observed signals under the squared loss. Then, we estimate global connectivity (between clusters or subnetworks) based on the factors across regions using the RVcoefficient as the crossdependence measure. This gives a reliable and computationally efficient multiscale analysis of both regional and global dependencies of the large networks. The proposed novel approach is applied to estimate brain connectivity networks using functional magnetic resonance imaging (fMRI) data. Results on restingstate fMRI reveal interesting modular and hierarchical organization of human brain networks during rest.

Multilevel Monte Carlo in Approximate Bayesian Computation(arXiv, 20170213)In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.

Multilevel weighted least squares polynomial approximation(arXiv, 20170630)Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasioptimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of singlelevel approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.

Mutual Information of BufferAided FullDuplex Relay Channels(arXiv, 20170409)We derive closedform expressions for the achievable rates of a bufferaided fullduplex (FD) multipleinput multipleoutput (MIMO) Gaussian relay channel. The FD relay still suffers from residual selfinterference (RSI) after the application of selfinterference mitigation techniques. We investigate both cases of a slowRSI channel where the RSI is fixed over the entire codeword, and a fastRSI channel where the RSI changes from one symbol duration to another within the codeword. We show that the RSI can be completely eliminated in the slowRSI case when the FD relay is equipped with a buffer while the fast RSI cannot be eliminated. For the fixedrate data transmission scenario, we derive the optimal transmission strategy that should be adopted by the source node and relay node to maximize the system throughput. We verify our analytical findings through simulations.

Nested and Hierarchical Archimax copulas(arXiv, 20170703)The class of Archimax copulas is generalized to nested and hierarchical Archimax copulas in several ways. First, nested extremevalue copulas or nested stable tail dependence functions are introduced to construct nested Archimax copulas based on a single frailty variable. Second, a hierarchical construction of dnorm generators is presented to construct hierarchical stable tail dependence functions and thus hierarchical extremevalue copulas. Moreover, one can, by itself or additionally, introduce nested frailties to extend Archimax copulas to nested Archimax copulas in a similar way as nested Archimedean copulas extend Archimedean copulas. Further results include a general formula for the density of Archimax copulas.