arXiv research

We show that complete uniform visibility manifolds of finite volume with sectional curvature $-1 \leq K \leq 0$ have positive simplicial volumes. This implies that their minimal volumes are non-zero.

Study ergodic properties of geodesic flows on specific manifolds without conjugate points.

The paper connects geodesic flows and limit sets on visibility manifolds.

A visible action on a complex manifold is a holomorphic action that admits a $J$-transversal totally real submanifold $S$. It is said to be strongly visible if there exists an orbit-preserving anti-holomorphic diffeomorphism $σ$ such that $σ|_S = \mathrm{id}$. In this paper, we prove that for any Hermitian symmetric sp…

The paper solves the Dirichlet problem at infinity and defines Poisson boundaries for certain manifolds.

Study on visibility properties of spiral sets in higher dimensions.

The study shows that the visible range from a point on harmonic manifolds follows an exponential distribution.

Study visibility properties of Kobayashi distance on unbounded domains.

Study equilibrium measures on manifolds without conjugate points with visibility covering.

Maps preserve distances in non-positively curved spaces.

Visible Lagrangians in Hitchin systems are studied for pillowcase covers.

A recent result of Bader, Gelander and Sauer shows that for manifolds of pinched negative curvature, the torsion part of the homology can be controlled by the volume. This is done by constructing an efficient simplicial model of the thick part, which also provides another proof of the analogous statement for the free p…

Asymptotically harmonic manifolds are simply connected complete Riemannian manifolds without conjugate points such that all horospheres have the same constant mean curvature $h$. In this article we present results for harmonic functions on rank one asymptotically harmonic manifolds $X$ with mild curvature boundedness c…

Characterizes visibility and geodesic loops in complex domains.

We show that the translation length of any parabolic isometry on a complete semi-uniformly visible CAT(0) space is always zero. As a consequence, we will classify the isometries on visible CAT(0) spaces in terms of translation lengths. We will also show that the moduli space $\mathbb{M}(S_{g,n})$ of surface $S_{g,n}$ o…

Recently, the visibility graph has been introduced as a novel view for analyzing time series, which maps it to a complex network. In this paper, we introduce new algorithm of visibility, "cross-visibility", which reveals the conjugation of two coupled time series. The correspondence between the two time series is mappe…

This article is devoted to the study of prime alternating +achiral knots. In the case of arborescent knots, we prove in +AAA Visibility Theorem 5.1, that the symmetry is visible on a certain projection (not necessarily minimal) and that it is realised by a homeomorphism of order 4. In the general case (arborescent or n…

Improved visibility forecasts using statistical post-processing.

The visibility transformation embeds data position into signature features for efficient pattern recognition.

The family of image visibility graphs (IVGs) have been recently introduced as simple algorithms by which scalar fields can be mapped into graphs. Here we explore the usefulness of such operator in the scenario of image processing and image classification. We demonstrate that the link architecture of the image visibilit…

In this paper we confirm a folklore conjecture which suggests that for a complete noncompact manifold $M$ of finite volume with sectional curvature $-1 \leq K \leq 0$, if the universal cover of $M$ is a visibility manifold, then the fundamental group of each end of $M$ is almost nilpotent.

We study relations of some classes of $k$-convex, $k$-visible bodies in Euclidean spaces. We introduce and study \textrm{circular projections} in normed linear spaces and classes of bodies related with families of such maps, in particular, \textrm{$k$-circular convex} and \textrm{$k$-circular visible} ones. Investigati…

Geodesic flows on compact manifolds without conjugate points are shown to have a unique measure of maximal entropy.

We show that the visible sector probability density function of the Riemann-Theta Boltzmann machine corresponds to a gaussian mixture model consisting of an infinite number of component multi-variate gaussians. The weights of the mixture are given by a discrete multi-variate gaussian over the hidden state space. This a…

Structural RBM reduces parameters for image denoising and classification.

Theorem A. Let $M^n$ denote a closed Riemannian manifold with nonpositive sectional curvature and let $\tilde M^n$ be the universal cover of $M^n$ with the lifted metric. Suppose that the universal cover $\tilde M^n$ contains no totally geodesic embedded Euclidean plane $\mathbb{R}^2$ (i.e., $M^n$ is a visibility manif…

Characterizes causal structure dominance for latent variables.

A complete Riemannian manifold without conjugate points is called asymptotically harmonic if the mean curvature of its horospheres is a universal constant. Examples of asymptotically harmonic manifolds include flat spaces and rank one locally symmetric spaces of noncompact type. In this paper we show that this list exh…

The investigations of financial markets from a complex network perspective have unveiled many phenomenological properties, in which the majority of these studies map the financial markets into one complex network. In this work, we investigate 30 world stock market indices through their visibility graphs by adopting the…

Enhanced visibility forecasts using CAMS data improve accuracy.

Sunshine trading theory predicts lower execution costs and liquidity provision through explicit preannouncements, but evidence is scarce in traditional markets.

Multi-view data are becoming common in real-world modeling tasks and many multi-view data clustering algorithms have thus been proposed. The existing algorithms usually focus on the cooperation of different views in the original space but neglect the influence of the hidden information among these different visible vie…

A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riema…

Uniform foliations with Reeb components on 3-manifolds.

Uniform K-stability ensures existence of special metrics on toric manifolds.

The paper solves a uniform Yau-Tian-Donaldson conjecture for toric manifolds.

Many users in online social networks are constantly trying to gain attention from their followers by broadcasting posts to them. These broadcasters are likely to gain greater attention if their posts can remain visible for a longer period of time among their followers' most recent feeds. Then when to post? In this pape…

Measuring the impact of scientific articles is important for evaluating the research output of individual scientists, academic institutions and journals. While citations are raw data for constructing impact measures, there exist biases and potential issues if factors affecting citation patterns are not properly account…

The probability density function for the visible sector of a Riemann-Theta Boltzmann machine can be taken conditional on a subset of the visible units. We derive that the corresponding conditional density function is given by a reparameterization of the Riemann-Theta Boltzmann machine modelling the original probability…

This paper studies periodic and free periodic knots in alternating projections.

VGRSI uses price visibility graphs to generate profitable trading signals.

We revisit Spakula's uniform K-homology, construct the external product for it and use this to deduce homotopy invariance of uniform K-homology. We define uniform K-theory and on manifolds of bounded geometry we give an interpretation of it via vector bundles of bounded geometry. We further construct a cap product with…

Uniformizes compact Sasakian manifolds into circle bundles.

Uniform waist inequalities proven for manifolds with Kazhdan groups in codimension two.

A Kronecker product model is the set of visible marginal probability distributions of an exponential family whose sufficient statistics matrix factorizes as a Kronecker product of two matrices, one for the visible variables and one for the hidden variables. We estimate the dimension of these models by the maximum rank …

New uniformity definition on noncompact manifolds without metrics.

Uniform K-homology theory applied to elliptic operators on manifolds with boundary.

The Tits alternative applies to groups acting on specific CAT(0) spaces.