arXiv research

In this paper we consider planar sections and visual contours of co-dimension one affine immersions. The main theorem says that the third order Taylor expansion of the difference between the visual contour and planar section functions is exactly the cubic form. We also consider parameterizations on two dimensional affi…

New formulas for surface curvature when tangent vector points in asymptotic directions.

Defines surfaces with specific contour patterns.

We introduce an algorithm to locate contours of functions that are expensive to evaluate. The problem of locating contours arises in many applications, including classification, constrained optimization, and performance analysis of mechanical and dynamical systems (reliability, probability of failure, stability, etc.).…

A contour integral method recently proposed by Weideman [IMA J. Numer. Anal., to appear] for integrating semi-discrete advection-diffusion PDEs, is extended for application to some of the important equations of mathematical finance. Using estimates for the numerical range of the spatial operator, optimal contour parame…

Describing shapes by suitable measures in object segmentation, as proposed in [24], allows to combine the advantages of the representations as parametrized contours and indicator functions. The pseudo-Riemannian structure of optimal transport can be used to model shapes in ways similar as with contours, while the Kanto…

We study the geometry of the cuspidal edge $M$ in $\mathbb R^3$ derived from its contact with planes and lines (referred to as flat geometry). The contact of $M$ with planes is measured by the singularities of the height functions on $M$. We classify submersions on a model of $M$ by diffeomorphisms and recover the cont…

Investigate the local geometry of smooth surfaces in 4-space via contact with 2-planes and apparent contours.

We consider the quasiconformal dilatation of projective transformations of the real projective plane. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that are mapped to circles. We apply this result to analyze the dilatation of the circ…

Paper proposes a new Wasserstein distance for mixtures of radially contoured distributions.

We develop mask iterative hard thresholding algorithms (mask IHT and mask DORE) for sparse image reconstruction of objects with known contour. The measurements follow a noisy underdetermined linear model common in the compressive sampling literature. Assuming that the contour of the object that we wish to reconstruct i…

Machine learning models have been shown vulnerable to adversarial attacks launched by adversarial examples which are carefully crafted by attacker to defeat classifiers. Deep learning models cannot escape the attack either. Most of adversarial attack methods are focused on success rate or perturbations size, while we a…

Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can stabilize invariants characterizing these objects. We outline how so called contour fun…

A new method for analyzing shapes using FDA techniques.

The paper studies curves in surfaces using flow-spines and apparent contours.

The fundamental frequency (F0) contour of speech is a key aspect to represent speech prosody that finds use in speech and spoken language analysis such as voice conversion and speech synthesis as well as speaker and language identification. This work proposes new methods to estimate the F0 contour of speech using deep …

The contour map of estimation error of Expected Shortfall (ES) is constructed. It allows one to quantitatively determine the sample size (the length of the time series) required by the optimization under ES of large institutional portfolios for a given size of the portfolio, at a given confidence level and a given esti…

ICSGLD improves efficiency in posterior sampling for big data.

Separating overlapped nuclei is a major challenge in histopathology image analysis. Recently published approaches have achieved promising overall performance on public datasets; however, their performance in segmenting overlapped nuclei are limited. To address the issue, we propose the bending loss regularized network …

We present a new implementation of anisotropic mean curvature flow for contour recognition. Our procedure couples the mean curvature flow of planar closed smooth curves, with an external field from a potential of point-wise charges. This coupling constrains the motion when the curve matches a picture placed as backgrou…

The paper finds surfaces closest to being flat that span a given contour.

Completeness of the eigenfunctions of a quantum mechanical system is crucial for its probability interpretation. By using the method of contour integral we give properly normalized eigenfunctions for both discrete and continuum spectrum of the Morse potential, and explicitly prove the completeness relation. As an appli…

Any surface can be foliated into equipotential hypersurfaces of the level sets. A current result is that the contours are the progressing wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, as well as with a corresponding eikonal equation. The lev…

The progress of deep convolutional neural networks has been successfully exploited in various real-time computer vision tasks such as image classification and segmentation. Owing to the development of computational units, availability of digital datasets, and improved performance of deep learning models, fully automati…

Improved image learning using elliptically contoured tensor-variate distributions.

In this paper we present a new method for motion tracking of tumors in liver ultrasound image sequences. Our algorithm has two main steps. In the first step, we apply mean shift algorithm with multiple features to estimate the center of the target in each frame. Target in the first frame is defined using an ellipse. Ed…

Optimizes learning Hilbert-Schmidt operators between Sobolev spaces.

The contour maps of the error of historical resp. parametric estimates for large random portfolios optimized under the risk measure Expected Shortfall (ES) are constructed. Similar maps for the sensitivity of the portfolio weights to small changes in the returns as well as the VaR of the ES-optimized portfolio are also…

Study on Gaussian random fields' singularities on manifolds.

The paper tightens bounds on distances between Reeb graphs.

Quaternion-Kaehler four-manifolds, or equivalently anti-self-dual Einstein manifolds, are locally determined by one scalar function subject to Przanowski's equation. Using twistorial methods we construct a Lax Pair for Przanowski's equation, confirming its integrability. The Lee form of a compatible local complex struc…

We present an approach for polarimetric Synthetic Aperture Radar (SAR) image region boundary detection based on the use of B-Spline active contours and a new model for polarimetric SAR data: the GHP distribution. In order to detect the boundary of a region, initial B-Spline curves are specified, either automatically or…

It is proposed a new code for contours of plane images. This code was applied for optical character recognition of printed and handwritten characters. One can apply it to recognition of any visual images.

Wilson loops in ${\cal N}=4$ supersymmetric Yang-Mills theory correspond at strong coupling to extremal surfaces in $AdS_5$. We study a class of extremal surfaces known as special Legendrian submanifolds. The "hemisphere" corresponding to the circular Wilson loop is an example of a special Legendrian submanifold, and w…

We consider a complex Plateau problem for strongly pseudoconvex contours in non Kähler manifolds. A positive solution in the case of manifolds carrying a pluriclosed Hermitian metric forms is given. For the general case we propose a conjecture.

New method improves combinatorial optimization by overcoming inefficient sampling.

We determine the precise bifurcation diagrams of the apparent contours of generic crosscaps, which contain the information of bifurcations with respect to the images of the singular sets of crosscaps: crosscap points and double point curves. Especially, three different kinds of equivalences play key roles.

Motivated by the idea of turbomachinery active subspace performance maps, this paper studies dimension reduction in turbomachinery 3D CFD simulations. First, we show that these subspaces exist across different blades---under the same parametrization---largely independent of their Mach number or Reynolds number. This is…

Computer simulators are nowadays widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modeling, and manufacturing. One fundamental issue in the study of computer simulators is known as experimental design, that is, how to select the input settings where the compu…

A new algorithm flattens multi-modal distributions for better deep learning.

Entropy-based GP adaptive design improves failure probability estimation.

We explore a connection between the Finslerian area functional and well-investigated Cartan functionals to prove new Bernstein theorems, uniqueness and removability results for Finsler-minimal graphs, as well as enclosure theorems and isoperimetric inequalities for minimal immersions in Finsler spaces. In addition, we …

The paper reinterprets a quantum invariant using state integrals and contour integrals.

PFs and iPFs learn principal manifolds for efficient density estimation.

The segmentation of the left ventricle (LV) from CINE MRI images is essential to infer important clinical parameters. Typically, machine learning algorithms for automated LV segmentation use annotated contours from only two cardiac phases, diastole, and systole. In this work, we present an analysis work-flow for fully-…

New method uses contours of segmented images for X-ray classification.

Semi-analytical approach for optimal wealth management contributions.

We study the soliton flow on the domain of a twistorial harmonic morphism between Riemannian manifolds of dimensions four and three. Assuming real-analyticity, we prove that, for the Gibbons-Hawking construction, any soliton flow is uniquely determined by its restriction to any local section of the corresponding harmon…