Hyperbolicity of Closed Orbits Determined by One Function

Forme normale de perturbation de champs de vecteurs quasi-homogènes

We analyze a massive vector field with a non-canonical kinetic term in the action, minimally coupled to gravity, where the mass and kinetic function of the vector field vary as functions of time during inflation. The vector field is introduced following the same idea of a scalar curvaton, which must not affect the inflationary dynamics since its energy density during inflation is negligible compared to the total energy density in the Universe. Using this hypothesis, the vector curvaton will be solely responsible for generating the primordial curvature perturbation ζ. We have found that the spectra of the vector field perturbations are scale-invariant in superhorizon scales due to the suitable choice of the time dependence of the kinetic function and the effective mass during inflation. The preferred direction, generated by the vector field, makes the spectrum of ζ depend on the wavevector, i.e. there exists statistical anisotropy in ζ . This is discussed principally in the case where the mass of the vector field increases with time during inflation, where it is possible to find a heavy field (M ≫ H) at the end of inflation, making the particle production be practically isotropic; thus, the longitudinal and transverse spectra are nearly the same order which in turn causes that the statistical anisotropy generated by the vector field is within the observational bounds.

We investigate the perturbation theory of a fixed-norm, timelike\nLorentz-violating vector field. After consistently quantizing the vector field\nto put constraints on its parameters, we compute the primordial spectra of\nperturbations generated by inflation in the presence of this vector field. We\nfind that its perturbations are sourced by the perturbations of the inflaton;\nwithout the inflaton perturbation the vector field perturbations decay away\nleaving no primordial spectra of perturbations. Since the inflaton perturbation\ndoes not have a spin-1 component, the vector field generically does not\ngenerate any spin-1 ``vector-type'' perturbations. Nevertheless, it will modify\nthe amplitude of both the spin-0 ``scalar-type'' and spin-2 ``tensor-type''\nperturbation spectra, leading to violations of the inflationary consistency\nrelationship.\n

Criteria for Cr Robust Permanence

A nonstandard approach to averaging theory for ordinary differential equations and functional differential equations is developed. We define a notion of perturbation and we obtain averaging results under weaker conditions than the results in the literature. The classical averaging theorems approximate the solutions of the system by the solutions of the averaged system, for Lipschitz continuous vector fields, and when the solutions exist on the same interval as the solutions of the averaged system. We extend these results to perturbations of vector fields which are uniformly continuous in the spatial variable with respect to the time variable and without any restriction on the interval of existence of the solution.

Systems that operate in different modes with quick transition are usually studied through discontinuous systems. We give a model of a smoothing of the transition between two vector fields along a separation line, allowing perturbations of the vector fields and of the separation line. In this model there appears a canard phenomenon in certain macroscopically indeterminate situations. This phenomenon gives a new point of view on some situations usually studied through discontinuous bifurcations. We also study the dynamics near the transition line through an associated slow-fast system and compare the slow dynamics with the classical theory, namely, sliding mode dynamics in variable structure systems and equivalent control. Le raccordement des trajectoires de deux champs de vecteurs donnés de part et d’autre d’une courbe dans le plan, est fait d’habitude à travers des champs discontinues. On donne un modèle de lissage de ce raccordement, qui fait apparaître des phénomènes canard, dans certaines situations macroscopiquement indeterminés. On utilise un champ lent-rapide associé au modèle de raccordement, pour étudier les dynamiques dans un voisinage infinitésimal de la ligne de transition et on fait un étude comparative avec la théorie classique, notamment: mouvements glissants dans les systèmes de structure variable et contrôle équivalent.

Model-based analytical FOE determination

In this paper, we present a generative sketch model for human hair analysis and synthesis. We treat hair images as2D piecewise smooth vector (flow) fields and, thus, our representation is view-based in contrast to the physically-based 3D hair models in graphics. The generative model has three levels. The bottom level is the high-frequency band of the hair image. The middle level is a piecewise smooth vector field for the hair orientation, gradient strength, and growth directions. The top level is an attribute sketch graph for representing the discontinuities in the vector field.Asketch graph typically has a number of sketch curves which are divided into 11 types of directed primitives. Each primitive is a small window (say 5 _ 7 pixels) where the orientations and growth directions are defined in parametric forms, for example, hair boundaries, occluding lines between hair strands, dividing lines on top of the hair, etc. In addition to the three level representation, we model the shading effects, i.e., the low-frequency band of the hair image, by a linear superposition of some Gaussian image bases andwe encode the hair color by a color map. The inference algorithm is divided into two stages: 1) We compute the undirected orientation field and sketch graph from an input image and 2) we compute the hair growth direction for the sketch curves and the orientation field using a Swendsen-Wang cut algorithm. Both steps maximize a joint Bayesian posterior probability. The generative model provides a straightforward way for synthesizing realistic hair images and stylistic drawings (rendering) from a sketch graph and a few Gaussian bases. The latter can be either inferred from a real hair image or input(edited) manually using a simple sketching interface. We test our algorithm on a large data set of hair images with diverse hair styles.

This paper describes a morphing-based approach for the verification of precipitation forecasts. This approach employs a pyramid matching algorithm to morph the precipitation features in a forecast into features that match the related precipitation features in the verifying analysis (observations) as closely as possible. The algorithm computes an optical flow (vector field) that maps the original forecast features into the morphed forecast features. The optical flow also provides quantitative information about the error in the location of the forecast features. This information, combined with information about the error in the prediction of the total precipitation over the verification domain, is used to quantify the structure error in the precipitation forecast. The proposed approach has three novel aspects compared to the published morphing-based verification strategies. First, it imposes a constraint on the pyramid matching algorithm to prevent overconvergence toward strong precipitation features during morphing. Second, it introduces an objective criterion for the selection of the subsampling parameter to avoid splitting or distorting features due to an arbitrary maximum displacement limit. Third, the proposed definitions of the location and structure errors are new. The behavior of the proposed multivariate verification metrics is investigated by applications to both idealized and numerical forecast examples.

We use a vector field model to formulate flow of information at every point of a dense wireless sensor network. The magnitude of this vector field represents the density of communication activity and its direction is toward the flow of information at each point. We present a general method for flow optimization in a wireless sensor network by minimizing the p-norm of the information flow vector field subject to the basic flow constraints, that is the flow conservation law and boundary constraints. We have called this problem the p-norm flow optimization, and use Sequential Quadratic Programming to solve it. The p-norm flow optimization shows interesting properties for different values of p. For p close to 1, the information routes resemble the geometric shortest paths while as p gets larger, there will be more load balancing effects in the flow. In this work we focus on the numerical analysis of the p-norm flow problem. For this we have to approximate the continuous flow problem by a discrete problem which adds some inaccuracy to the solutions. Therefore, we propose an algorithm to continuously compensate the error in the information flow vector field and avoid error accumulation in the system. We also discuss ways with which we can support different network geometries in the numerical analysis.

We study the perturbations of scalar, vector, and tensor fields in a slowly rotating Kerr-(Anti-)de Sitter black hole spacetime, presenting new and existing Schr\"odinger style master equations for each type of perturbation up to linear order in black hole spin $a$. For each type of field we calculate analytical expressions for the fundamental quasi-normal mode frequencies. These frequencies are compared to existing results for Schwarzschild-de Sitter, slowly rotating Kerr, and slowly rotating Kerr-de Sitter black holes. In all cases good agreement is found between the analytic expressions and those frequencies calculated numerically. In addition, the axial and polar gravitational frequencies are shown to be isospectral to linear order in $a$ for all cases other than for both non-zero $a$ and $\Lambda$.

The changes in flow channel area and convergence-expanding nozzle help to flow rate of natural gas to the sound speed, also increase diameter to accelerate flow velocity and finally reach transonic flow condition. At this point, the temperature drop makes saturated water in natural gas condenses into droplets, generates swirl around the delta-wing, realize gas-water separation. This paper concentrates on Flent6.1 software process gas flow around a delta wing simulation, explains expansion angle and attack angle of delta-wing, determines a reasonable delta-wing attack angle is 10°, pipeline expansion angle is 0.29°, and obtains velocity vector, mach number, total pressure, static temperature and other flow field details of the attack angle and expansion angle, which lay foundation for production and application of the technology.

Automatic and accurate detection of vertebral pose of low resolution x-ray images with different bone structure is essential to diagnose patient condition. Low resolution and incomplete x-ray image is created from low level of irradiating that can avoid radiation over doze. In this research, we propose a novel approach to estimate vertebral pose. There are three main steps including Vertical Projection, Gradient Vector Flow and Feature of Vector Field. Firstly, we segment vertebral zone from full image using Vertical Projection Average with Normal Distribution. Secondly, we introduce Gradient Vector Flow to identify background and foreground of image. Energy calculation helps to divide different objects on image. Then vector field algorithm will help to promote the exact border of the object. Finally, the horizontal field is chosen as the best information to identify the vertebral pose. From the experimental results, we can extract six main bone layouts. There are two normal layouts and four abnormal layouts. For each layout, we deploy different criteria to identify vertebral pose. For the layouts that located between 0–67 index, the separation hyperplane needs to be shifted up, otherwise shifted down. We use 80 low resolution and incomplete x-ray images from a local hospital. The accuracy rate is 79.25% compared with the ground-truth.

Ultrasound (US) breast cancer images is one of the most complicated medical images to extract the desired area of interest. It is often difficult to separate the tumor region from the background tissues. Therefore, tumor segmentation is the challenging problems in the computed aided diagnosis. Among many image segmentation techniques, a generalized gradient vector flow (GGVF) method is one of the popular techniques. It is based on vector transformation of the edge map of the gray scale image. GGVF introduces a non-uniform diffusion to preserve the large gradient of the boundary area and smooth the gradients caused by noise and speckles. However, the improper numerical iteration of GGVF may lead the false contours or the existing noise and finally the snake could not reach the true boundary. In this paper, the new vector field analysis for breast tumor US image segmentation is proposed. The GGVF vector field will be derived from the edge map of the original image. The algorithm analyzes the GGVF vectors in terms of the entropy of the angle of vectors in the corresponding window. The windows will be vertically and horizontally flipped, then the entropy will be evaluated again. Next, the ratio of the entropy before and after flip will be determined to be the classifier of the boundary and non-boundary. The algorithm has been tested on the real US breast tumor images with a set of ground truth images hand-drawn by radiologists. The proposed algorithm is compared with conventional edge detectors such as Sobel and Canny operator. The numerical experiments show that the proposed techniques lead to a better segmentation accuracy with the reference to the conventional edge detection.

We present a new globally smooth parameterization method for the triangulated surfaces of arbitrary topology. Given two orthogonal piecewise linear vector fields defined over the input mesh (typically the estimated principal curvature directions), our method computes two piecewise linear periodic functions, aligned with the input vector fields, by minimizing an objective function. The bivariate function they define is a smooth parameterization almost everywhere on the surface, except in the vicinity of singular vertices, edges, and triangles, where the derivatives of the parameterization vanish. We extract a quadrilateral chart layout from the parameterization function and propose an automatic procedure to detect the singularities, and fix them by splitting and reparameterizing the containing charts. Our method can construct both quasiconformal (angle preserving) and quasi-isometric (angle and area preserving) parameterizations. The more restrictive class of quasi-isometric parameterizations is constructed at the expense of introducing more singularities. The constructed parameterizations can be used for a variety of geometry processing applications. Since we can align the parameterization with the principal curvature directions, our result is particularly suitable for surface fitting and remeshing.