Smooth Component Research Articles

Stochastic Proximal Gradient Consensus Over Random Networks

We consider solving a convex, possibly stochastic optimization problem over a randomly time-varying multi-agent network. Each agent has access to some local objective function, and it only has unbiased estimates of the gradients of the smooth component. We develop a dynamic stochastic proximal-gradient consensus (DySPGC) algorithm, with the following key features: i) it works for both the static and certain randomly time-varying networks, ii) it allows the agents to utilize either the exact or stochastic gradient information, iii) it is convergent with provable rate. In particular, we show that the proposed algorithm converges to a global optimal solution, with a rate of $\mathcal{O}(1/r)$ [resp. $\mathcal{O}(1/\sqrt{r})$] when the exact (resp. stochastic) gradient is available, where r is the iteration counter. Interestingly, the developed algorithm bridges a number of (seemingly unrelated) distributed optimization algorithms, such as the EXTRA (Shi et al. 2014), the PG-EXTRA (Shi et al. 2015), the IC/IDC-ADMM (Chang et al. 2014), and the DLM (Ling et al. 2015) and the classical distributed subgradient method. Identifying such relationship allows for significant generalization of these methods. We also discuss one such generalization which accelerates the DySPGC (hence accelerating EXTRA, PG-EXTRA, IC-ADMM).

The computational modeling of problems on domains with small holes

The modeling challenges arising when the problem domain has small supported holes in it are considered through a representative membrane problem. Such problems are sometimes modeled intuitively in engineering practice by taking the limiting case of holes with zero radius. This intuitive model is incorrect, since it has no mathematical solution. It is demonstrated, however, that finite element approximations based on it can still satisfy verification tests and appear to converge, leading to erroneous recovery of quantities of interest. This points to the need for an alternate approach where the holes of finite radius are properly incorporated in the modeling, and robustness with respect to the radius is maintained. To this end, a computational method is presented which combines analytic knowledge of the solution singularities with finite element approximation of its smooth components. Theoretical and numerical results are provided, establishing the efficacy and robustness of the method in extracting quantities of interest. The method converges both with respect to the size of the holes and the mesh discretization parameter, and provides a more accurate alternative to using the asymptotic limit.

Geophysical flows under location uncertainty, Part I Random transport and general models

A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time. Subsequently, the material derivative is modified and leads to a stochastic version of the material derivative to include a drift correction, an inhomogeneous and anisotropic diffusion, and a multiplicative noise. As derived, this stochastic transport exhibits a remarkable energy conservation property for any realizations. As demonstrated, this pivotal operator further provides elegant means to derive stochastic formulations of classical representations of geophysical flow dynamics.

Ultrashort pulsed multibeam processing head for parallel ultrafast micromachining

In recent years, one trend in surface processing can be ascertained in ultrashort pulsed lasers with high pulse repetition rates, e.g., nearly cold ablation for gravure printing. Short pulse width leads to very high peak power (on a megawatt scale). Such a high peak fluence results in multiphoton absorption and enables precise micro- and sub-micro-structuring of surfaces. Additionally, ultrafast processing is compatible with a wide range of materials: besides metals, functional surfaces can be provided to several high-bandgap materials such as glass and ceramics. One challenge of ultrafast micromachining is process velocity. The operational capacity of these processes can be maximized by increasing the scan rate or by increasing the number of beams—subject parallelism. This contribution focuses on parallelism using ultrashort pulsed lasers with a high repetition rate and an individually addressable acousto-optic beam deflector. The core of the multibeam generation is a smooth diffractive beam splitter component with high spot uniformity and negligible power loss and a prismatic array compressor to match the beam pitch according to the beamlet spot size. The optical design and the practical implementation of an eight-beam processing head in combination with a high average power single-mode ultrashort pulsed laser source are presented, as is promising laboratory research currently underway along with the shortly projected micromachining results. Finally, we assess the prospects for scaling the optical system to several tens of beamlets. This contribution will address challenges such as the power of available ultrashort pulsed lasers which can be overcome by beam combining, parallelism using optical modulation components, and optomechanical integration.

Ultrastructure of pheochromocytoma: undescribed morphologic features.

We examined samples of human pheochromocytoma from 11 patients aged 30-70years including one case of malignant pheochromocytoma with a view to identifying previously unreported ultrastructural details.We identified two types of nuclear inclusions consisting of irregularly shaped singular or multiple granulofibrillar formations with a typical concentric halo, on the one hand, and accumulations of egg-shaped structures consisting of granules and microfilaments, on the other. In some of the tumor cells, membrane-covered inclusions containing parallel laminar elements arranged in a paracrystalline, periodic fashion, or mega-mitrochondriae characterized by increased electrodensity of their matrix, and fibrillary material in the spaces between the cristae were present. A frequent finding consisted of typical ciliary formations, while rough/smooth tubular aggregates of different size occurred less frequently. Finally, we were able to demonstrate the uptake of norepinephrine by smooth muscle fibers in the periphery of arterial vessels as evidenced by linear accumulations of membrane-covered granules separating bands of contractile smooth muscle components in the peripheral layers of arterial vessels close to norepinephrine producing neoplastic cells.These findings represent ultrastructural features that contribute to further elucidating the ultrastructural characteristics of the human pheochromocytoma.

Renal tumors with low signal intensities on T2-weighted MR image: radiologic-pathologic correlation.

Accurate characterization of renal masses is essential for ensuring appropriate management. Low T2 signal intensity is a common feature of papillary renal cell carcinoma and fat-poor angiomyolipoma. Nonetheless, other types of renal cell carcinoma, oncocytoma, hemangioma, lymphoma, leiomyoma, and urothelial cell carcinoma also can show low signal intensities on T2-weighted imaging (T2WI). Histopathologic features that can lead to low T2 signal intensities in renal tumors include smooth muscle component, papillary architecture, a high nucleus-to-cytoplasm ratio, and hemorrhage. To establish an appropriate differential diagnosis for renal tumors on MRI, it is necessary to understand the relationship between the MR signal intensities and the histopathologic and morphologic features, in addition to contrast enhancement patterns and diffusion characteristics of the tumors.

A Variational Model for Staircase Reduction in Image Denoising

We propose a new variational model to reduce the staircase that often appears in Total variation (TV) based models in image denoising. The model uses BV-seminorm and Besov-seminorm to measure the piecewise constant component and piecewise smooth component of the image, respectively. We discuss the nontrivial property of the proposed model and introduce an alternating iteration algorithm that combines the dual projection algorithm with Wavelet soft thresholding (WST) algorithm to solve the model numerically. The experimental results show that the proposed model is effective for noise removal and staircase reduction, while the contour can be preserved in the denoised images. Furthermore, compared with two classical staircase reduction models, CEP2 and TGV, the proposed model is much faster than these two models.

A new image watermarking technique based on periodic plus smooth decomposition (PPSD)

Robustness against geometric distortion is one of the crucial important issues in watermarking. The discrete Fourier transform (DFT)-based watermarking methods have been proposed to address this issue. However, the effect of the well-known “periodization artifact” caused by the DFT transform limits their application. In this paper, a novel watermarking scheme is proposed. This scheme is based on the periodic plus smooth image decomposition (PPSD). The PPSD is a simple and efficient way to deal with periodization artifacts arising from the use of the DFT transform on 2-D images. It consists in the decomposition of the discrete image into a periodic component that gathers most of the image information but avoids periodization artifacts, and a smooth (harmonic) component that presents very slow variations inside the image. The algorithm is evaluated in terms of imperceptibility and robustness. The experiments indicate that our developed PPSD technique can achieve high imperceptibility while showing good robustness to various kinds of attacks, including geometrical distortions.

A Framework of Mixed Sparse Representations for Remote Sensing Images

In this paper, a new framework of mixed sparse representations (MSRs) is proposed for solving ill-conditioned problems with remote sensing images. In general, it is very difficult to find a common sparse representation for remote sensing images because of complicated ground features. Here we regard a remote sensing image as a combination of subimage of smooth, edges, and point-like components, respectively. Since each domain transformation method is capable of representing only a particular kind of ground object or texture, a group of domain transformations are used to sparsely represent each subimage. To demonstrate the effect of the framework of MSR for remote sensing images, MSR is regarded as a prior for maximum a posteriori when solving ill-conditioned problems such as classification and super resolution (SR), respectively. The experimental results show that not only the new framework of MSR can improve classification accuracy but also it can construct a much better high-resolution image than other common SR methods. The proposed framework MSR is a competitive candidate for solving other remote sensing images-related ill-conditioned problems.

Early GRB Afterglows from Reverse Shocks in Ultra-relativistic, Long-lasting Winds

Abstract We develop a model of early Gamma-Ray Burst (GRB) afterglows with dominant X-ray contribution from the reverse shock (RS) propagating in highly relativistic (Lorentz factor γ w ∼ 106) magnetized wind of a long-lasting central engine. The model reproduces, in a fairly natural way, the overall trends and yet allows for variations in the temporal and spectral evolution of early optical and X-ray afterglows. The high energy and the optical synchrotron emission from the RS particles occurs in the fast cooling regime; the resulting synchrotron power L s is a large fraction of the wind luminosity, (L w and σ w are wind power and magnetization). Thus, plateaus—parts of afterglow light curves that show slowly decreasing spectral power—are a natural consequence of the RS emission. Contribution from the forward shock (FS) is negligible in the X-rays, but in the optical both FS and RS contribute similarly: FS optical emission is in the slow cooling regime, producing smooth components, while RS optical emission is in the fast cooling regime, and thus can both produce optical plateaus and account for fast optical variability correlated with the X-rays, e.g., due to changes in the wind properties. We discuss how the RS emission in the X-rays and combined FS and RS emission in the optical can explain many puzzling properties of early GRB afterglows.

Accelerated bregman operator splitting with backtracking

This paper develops two accelerated Bregman Operator Splitting (BOS) algorithms with backtracking for solving regularized large-scale linear inverse problems, where the regularization term may not be smooth. The first algorithm improves the rate of convergence for BOSVS [ 5 ] in terms of the smooth component in the objective function by incorporating Nesterov's multi-step acceleration scheme under the assumption that the feasible set is bounded. The second algorithm is capable of dealing with the case where the feasible set is unbounded. Moreover, it allows more aggressive stepsize than that in the first scheme by properly selecting the penalty parameter and jointly updating the acceleration parameter and stepsize. Both algorithms exhibit better practical performance than BOSVS and AADMM [ 21 ], while preserve the same accelerated rate of convergence as that for AADMM. The numerical results on total-variation based image reconstruction problems indicate the effectiveness of the proposed algorithms.

A Randomized Nonmonotone Block Proximal Gradient Method for a Class of Structured Nonlinear Programming

We propose a randomized nonmonotone block proximal gradient (RNBPG) method for minimizing the sum of a smooth (possibly nonconvex) function and a block-separable (possibly nonconvex nonsmooth) function. At each iteration, this method randomly picks a block according to any prescribed probability distribution and solves typically several associated proximal subproblems that usually have a closed-form solution, until a certain progress on objective value is achieved. In contrast to the usual randomized block coordinate descent method [P. Richtárik and M. Takáč, Math. Program., 144 (2014), pp. 1--38; A. Patrascu and I. Necoara, J. Global Optim., 61 (2015), pp. 19--46], our method has a nonmonotone flavor and uses variable stepsizes that can partially utilize the local curvature information of the smooth component of objective function. We show that any accumulation point of the solution sequence of the method is a stationary point of the problem almost surely and the method is capable of finding an approximate stationary point with high probability. We also establish a sublinear rate of convergence for the method in terms of the minimal expected squared norm of certain proximal gradients over the iterations. When the problem under consideration is convex, we show that the expected objective values generated by RNBPG converge to the optimal value of the problem. Under some assumptions, we further establish a sublinear and linear rate of convergence on the expected objective values generated by a monotone version of RNBPG. Finally, we conduct some preliminary experiments to test the performance of RNBPG on the $\ell_1$-regularized least-squares problem, a dual support vector machine problem in machine learning, the $\ell_0$-regularized least-squares problem, and a regularized matrix completion model. The computational results demonstrate that our method substantially outperforms the randomized block coordinate descent method with fixed or variable stepsizes.

Stable exponential random graph models with non-parametric components for large dense networks

Exponential random graph models (ERGM) behave peculiar in large networks with thousand(s) of actors (nodes). Standard models containing 2-star or triangle counts as statistics are often unstable leading to completely full or empty networks. Moreover, numerical methods break down which makes it complicated to apply ERGMs to large networks. In this paper we propose two strategies to circumvent these obstacles. First, we use a subsampling scheme to obtain (conditionally) independent observations for model fitting and secondly, we show how linear statistics (like 2-stars etc.) can be replaced by smooth functional components. These two steps in combination allow to fit stable models to large network data, which is illustrated by a data example including a residual analysis.

Smooth Principal Component Analysis over two-dimensional manifolds with an application to neuroimaging

Motivated by the analysis of high-dimensional neuroimaging signals located over the cortical surface, we introduce a novel Principal Component Analysis technique that can handle functional data located over a two-dimensional manifold. For this purpose a regularization approach is adopted, introducing a smoothing penalty coherent with the geodesic distance over the manifold. The model introduced can be applied to any manifold topology, can naturally handle missing data and functional samples evaluated in different grids of points. We approach the discretization task by means of finite element analysis and propose an efficient iterative algorithm for its resolution. We compare the performances of the proposed algorithm with other approaches classically adopted in literature. We finally apply the proposed method to resting state functional magnetic resonance imaging data from the Human Connectome Project, where the method shows substantial differential variations between brain regions that were not apparent with other approaches.

Inexact proximal Newton methods for self-concordant functions

We analyze the proximal Newton method for minimizing a sum of a self-concordant function and a convex function with an inexpensive proximal operator. We present new results on the global and local convergence of the method when inexact search directions are used. The method is illustrated with an application to L1-regularized covariance selection, in which prior constraints on the sparsity pattern of the inverse covariance matrix are imposed. In the numerical experiments the proximal Newton steps are computed by an accelerated proximal gradient method, and multifrontal algorithms for positive definite matrices with chordal sparsity patterns are used to evaluate gradients and matrix-vector products with the Hessian of the smooth component of the objective.

Membranous Support for Eyes of Strepsirrhine Primates and Fruit Bats.

Living primates have relatively large eyes and support orbital tissues with a postorbital bar (POB) and/or septum. Some mammals with large eyes lack a POB, and presumably rely on soft tissues. Here, we examined the orbits of four species of strepsirrhine primates (Galagidae, Cheirogaleidae) and three species of fruit bats (Pteropodidae). Microdissection and light microscopy were employed to identify support structures of the orbit. In bats and primates, there are two layers of fascial sheets that border the eye laterally. The outer membrane is the most superficial layer of deep fascia, and has connections to the POB in primates. In fruit bats, which lacked a POB or analogous ligament, the deep fascia is reinforced by transverse ligaments. Bats and primates have a deeper membrane supporting the eye, identified as the periorbita (PA) based on the presence of elastic fibers and smooth muscle. The PA merges with periostea deep within the orbit, but has no periosteal attachment to the POB of primates. These findings demonstrate that relatively big eyes can be supported primarily with fibrous connective tissues as well as the PA, in absence of a POB or ligament. The well-developed smooth muscle component within the PA of fruit bats likely helps to protrude the eye, maintaining a more convergent eye orientation, with greater overlap of the visual fields. The possibility should be considered that early euprimates, and even stem primates that may have lacked a POB, also had more convergent eyes than indicated by osseous measurements of orbital orientation. Anat Rec, 299:1690-1703, 2016. © 2016 Wiley Periodicals, Inc.

Quadrature Weights on Tensor-Product Nodes for Accurate Integration of Hypersingular Functions over Some Simple 3-D Geometric Shapes

AbstractIn this paper, we present accurate and economic integration quadratures for hypersingular functions over three simple geometric shapes in ℝ3 (spheres, cubes, and cylinders). The quadrature nodes are made of the tensor-product of 1-D Gauss nodes on [–1,1] for non-periodic variables or uniform nodes on [0,2π] or [0,π] for periodic ones. The quadrature weights are converted from a brute-force integration of the hypersingular function through interpolating the smooth component of the integrand. Numerical results are presented to validate the accuracy and efficiency of computing hypersingular integrals, as in the computations of Cauchy principal values, with a minimum number of quadrature nodes. The pre-calculated quadrature tables can be then readily used to implement Nyström collocation methods of hypersingular volume integral equations such as the one for Maxwell equations.

Constraining the Galactic structure parameters with the XSTPS-GAC and SDSS photometric surveys

Photometric data from the Xuyi Schmidt Telescope Photometric Survey of the Galactic Anticentre (XSTPS-GAC) and the Sloan Digital Sky Survey (SDSS) are used to derive the global structure parameters of the smooth components of the Milky Way. The data, which cover nearly 11,000 deg$^2$ sky area and the full range of Galactic latitude, allow us to construct a globally representative Galactic model. The number density distribution of Galactic halo stars is fitted with an oblate spheroid that decays by power law. The best-fit yields an axis ratio and a power law index $\kappa=0.65$ and $p=2.79$, respectively. The $r$-band differential star counts of three dwarf samples are then fitted with a Galactic model. The best-fit model yielded by a Markov Chain Monte Carlo analysis has thin and thick disk scale heights and lengths of $H_{1}=$ 322\,pc and $L_{1}=$2343\,pc, $H_{2}=$794\,pc and $L_{2}=$3638\,pc, a local thick-to-thin disk density ratio of $f_2=$11\,per\,cent, and a local density ratio of the oblate halo to the thin disk of $f_h=$0.16\,per\,cent. The measured star count distribution, which is in good agreement with the above model for most of the sky area, shows a number of statistically significant large scale overdensities, including some of the previously known substructures, such as the Virgo overdensity and the so-called "north near structure", and a new feature between 150\degr $< l < $ 240\degr~and $-1$5\degr $< b < $ $-$5\degr, at an estimated distance between 1.0 and 1.5\,kpc. The Galactic North-South asymmetry in the anticentre is even stronger than previously thought.

An Unusual Etiology of Lower Gastrointestinal Bleeding, Small Intestinal Adenomyoma

Introduction: Intestinal adenomyomas, also known as myoepithelial hamartomas, are benign lesions characterized by glandular structures lined by cuboidal or tall columnar epithelium and surrounded by smooth muscle bundles. Reported cases of adenomyoma of the gastrointestinal tract have been largely confined to the stomach and duodenum mainly involving the peri-ampullary region, with lesions distal to the duodenum occurring less frequently The majority of these cases were found incidentally on surgery or autopsy. Here we report a case of adenomyoma of the jejunum that presented with anemia. Case summary: A 62 year old woman with heartburn & cholecystectomy presented to an outside hospital for bronchial thermoplasty for treatment of asthma and was incidentally found to have anemia. EGD and colonoscopy were negative for a source of bleeding. Capsule endoscopy revealed a pedunculated polyp in the distal jejunum. Endoscopic removal of the polyp in the distal jejunum was completed by double balloon enteroscopy. Grossly (Figure 1), the lesion was a polypoid shaped mass measuring 0.9 x 0.8 x 0.6cm. Microscopically, it was a well circumscribed submucosal lesion composed of variably sized glandular structures surrounded by smooth muscle bundles. The glandular structures showed pyloric morphology and were lined by cuboidal or columnar epithelium with interspersed goblet cells and occasional Paneth cells (Figure 2). Immunostains were performed with appropriate controls (Figure 3). The lesions epithelial component was strongly and diffusely positive for CK7 and CK19 and weakly positive for CDX2, but negative for CK20. The smooth muscle component was positive for desmin and alpha-SMA. Ki-67/MIB-1 highlighted rare lymphocytes in the lesion and basal cells of the small intestinal mucosal epithelium (Figure 4). All features supportied a final diagnosis of adenomyoma.Figure 1Figure 2Figure 3Discussion: Adenomyoma of the small intestine is an extremely rare tumor largely unknown to most clinicians. While typically asymptomatic, symptoms of intestinal adenomyoma vary depending on size, location, and patient age. In our patient this lesion was likely the source of chronic GI bleeding manifesting as anemia. The prognosis of adenomyoma is excellent, with no evidence of recurrence or metastatic transformation in reported cases. Treatment of asymptomatic or bleeding adenomyomas is simple resection.

Screen Content Image Segmentation Using Robust Regression and Sparse Decomposition

This paper considers how to separate text and/or graphics from smooth background in screen content and mixed document images and proposes two approaches to perform this segmentation task. The proposed methods make use of the fact that the background in each block is usually smoothly varying and can be modeled well by a linear combination of a few smoothly varying basis functions, while the foreground text and graphics create sharp discontinuity. The algorithms separate the background and foreground pixels by trying to fit background pixel values in the block into a smooth function using two different schemes. One is based on robust regression, where the inlier pixels will be considered as background, while remaining outlier pixels will be considered foreground. The second approach uses a sparse decomposition framework where the background and foreground layers are modeled with a smooth and sparse components respectively. These algorithms have been tested on images extracted from HEVC standard test sequences for screen content coding, and are shown to have superior performance over previous approaches. The proposed methods can be used in different applications such as text extraction, separate coding of background and foreground for compression of screen content, and medical image segmentation.