arXiv research

Consider a broken geodesics $α([0,l])$ on a compact Riemannian manifold $(M,g)$ with boundary of dimension $n\geq 3$. The broken geodesics are unions of two geodesics with the property that they have a common end point. Assume that for every broken geodesic $α([0,l])$ starting at and ending to the boundary $\partial M$…

Study geometric structure of Ricci shrinker ends without global curvature assumptions.

Research tackles unequal length time series for classification.

Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts by a noncontractible n-dimensional Peano cont…

Deep network solves maze path planning without training.

The Riemannian submersion $π: \text{SO}_0(1,n) \to \mathbb{H}^n$ is a principal bundle and its fiber at $π(e)$ is the imbedding of $\text{SO}(n)$ into $\text{SO}_0(1,n)$, where $e$ is the identity of both $\text{SO}_0(1,n)$ and $\text{SO}(n)$. In this study, we associate a curve, starting from the identity, in $\…

Applying neural-networks on Question Answering has gained increasing popularity in recent years. In this paper, I implemented a model with Bi-directional attention flow layer, connected with a Multi-layer LSTM encoder, connected with one start-index decoder and one conditioning end-index decoder. I introduce a new end-…

Let $S$ be a complete flat surface, such as the Euclidean plane. We obtain direct characterizations of the connected components of the space of all curves on $S$ which start and end at given points in given directions, and whose curvatures are constrained to lie in a given interval, in terms of all parameters involved.…

Model-free reinforcement learning (RL) requires a large number of trials to learn a good policy, especially in environments with sparse rewards. We explore a method to improve the sample efficiency when we have access to demonstrations. Our approach, Backplay, uses a single demonstration to construct a curriculum for a…

While the topology of the space of all smooth immersed curves on the $2$-sphere $\mathbb{S}^2$ that start and end at given points in given directions is well known, it is an open problem to understand the homotopy type of its subspaces consisting of the curves whose geodesic curvatures are constrained to a prescribed p…

Poor (even random) starting points for learning/training/optimization are common in machine learning. In many settings, the method of Robbins and Monro (online stochastic gradient descent) is known to be optimal for good starting points, but may not be optimal for poor starting points -- indeed, for poor starting point…

New bounds on shortest geodesic loops on a sphere.

For a Lattice crossing $L\left( m,n\right)$ we show which Catalan connection between $2\left( m+n\right)$ points on boundary of $m\times n$ rectangle $P$ can be realized as a Kauffman state and we give an explicit formula for the number of such Catalan connections. For the case of a Catalan connection with no arc sta…

FAB-COST improves cold-start recommendation accuracy with less data.

We survey some major contributions to Riemann's moduli space and Teichm{ü}ller space. Our report has a historical character, but the stress is on the chain of mathematical ideas. We start with the introduction of Riemann surfaces, and we end with the discovery of some of the basic structures of Riemann's moduli space a…

Let $S$ be a complete flat surface, such as the Euclidean plane. We determine the homeomorphism class of the space of all curves on $S$ which start and end at given points in given directions and whose curvatures are constrained to lie in a given open interval, in terms of all parameters involved. Any connected compone…

In the present work we investigate the multiscale nature of the correlations for high frequency data (1 minute) in different futures markets over a period of two years, starting on the 1st of January 2003 and ending on the 31st of December 2004. In particular, by using the concept of "local" Hurst exponent, we point ou…

Nonconvex optimization algorithms with random initialization have attracted increasing attention recently. It has been showed that many first-order methods always avoid saddle points with random starting points. In this paper, we answer a question: can the nonconvex heavy-ball algorithms with random initialization avoi…

Study precise rates of horizontal gap shrinkage on generic translation surfaces.

This is the second part of the investigation started in [Stationary solutions and asymptotic flatness I]. We prove here that Strongly Stationary ends having cubic volume growth are Weakly Asymptotically Flat. Combined with the results of the previous paper this shows that Strongly Stationary ends are Asymptotically Fla…

In what follows we give a quick tour through the field of minimal submanifolds, starting at the definition and the classical results and ending up with current areas of research.

We propose a simple but strong baseline for time series classification from scratch with deep neural networks. Our proposed baseline models are pure end-to-end without any heavy preprocessing on the raw data or feature crafting. The proposed Fully Convolutional Network (FCN) achieves premium performance to other state-…

Reweighted ALPS improves sampling from multimodal distributions using warm start points.

Bayesian optimization improves multi-start global optimization.

Fast and efficient motion planning algorithms are crucial for many state-of-the-art robotics applications such as self-driving cars. Existing motion planning methods become ineffective as their computational complexity increases exponentially with the dimensionality of the motion planning problem. To address this issue…

The aim of this paper is to associate a measure for certain sets of paths in the Euclidean plane $\mathbb{R}^2$ with fixed starting and ending points. Then, working on parameterized surfaces with a specific Riemannian metric, we define and calculate the integral of the length over the set of paths obtained as the image…

This survey starts with the historical landmarks leading to the study of principal configurations on surfaces, their structural stability and further generalizations. Here it is pointed out that in the work of Monge, 1796, are found elements of the qualitative theory of differential equations (QTDE), founded by Poincar…

Deep RNNs excel at capturing long-term dependencies in sequential data.

Let $S$ be a hyperbolic surface. We investigate the topology of the space of all curves on $S$ which start and end at given points in given directions, and whose curvatures are constrained to lie in a given interval $(κ_1,κ_2)$. Such a space falls into one of four qualitatively distinct classes, according to whet…

New method achieves optimal sample complexity without warm-start in bilevel optimization.

This work originates from a heart's images tracking which is to generate an apparent continuous motion, observable through intensity variation from one starting image to an ending one both supposed segmented. Given two images p0 and p1, we calculate an evolution process p(t, \cdot) which transports p0 to p1 by using th…

Researchers prove positive mass theorem for manifolds with arbitrary ends.

Deep structured-prediction energy-based models combine the expressive power of learned representations and the ability of embedding knowledge about the task at hand into the system. A common way to learn parameters of such models consists in a multistage procedure where different combinations of components are trained …

KZImputer improves time series data quality with adaptive imputation for short to medium-sized gaps.

Fix two points $x,\bar{x}\in S^2$ and two directions (without orientation) $η,\barη$ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost $J[γ]=\int_0^T g_{γ(t)}(\dotγ(t),\dotγ(t))+ K^2_{γ(t)}g_{γ(t)}(\dotγ(t),\dotγ(t)) ~dt$ along all smooth curves starting from $x…

"Ends of hyperbolic 3-manifolds should support canonical Wick Rotations, so they realize effective interactions of their ending globally hyperbolic spacetimes of constant curvature." We develop a consistent sector of WR-rescaling theory in 3D gravity, that, in particular, concretizes the above guess for many geometrica…

We develop an approach to Khovanov homology of knots via gauge theory (previous physics-based approches involved other descriptions of the relevant spaces of BPS states). The starting point is a system of D3-branes ending on an NS5-brane with a nonzero theta-angle. On the one hand, this system can be related to a Chern…

This paper is based on my talks (`Skein modules with a cubic skein relation: properties and speculations' and `Symplectic structure on colorings, Lagrangian tangles and its applications') given in Kyoto (RIMS), September 11 and September 18 respectively, 2001. The first three sections closely follow the talks: starting…

PinnerSage creates multi-modal user embeddings for better Pinterest recommendations.

For a compact Riemannian manifold with boundary, endowed with a magnetic potential $α$, we consider the problem of restoring the metric $g$ and the magnetic potential $α$ from the values of the Mañé action potential between boundary points and the associated linearized problem. We study simple magnetic systems. In this…

We consider a network in the Euclidean plane that consists of three distinct half-lines with common start points. From that network as initial condition, there exists a network that consists of three curves that all start at one point, where they form 120 degree angles, and expands homothetically under curve shortening…

Study on cut locus of submanifolds in Finsler geometry.

This paper, in which we develop ideas introduced in \cite{MR}, focuses on \emph{reduction methods} (basically, group actions or, more generally, simmetries) for the bienergy. This type of techniques enable us to produce examples of critical points of the bienergy by reducing the study of the relevant fourth order PDE's…

Framework for precise recall control in spatial conflation tasks.

The analysis of dollar inflation performed by the authors through the approximation of empirical data for 1913-2012 with a power-law function with an accelerating log-periodic oscillation superimposed over it has made it possible to detect a quasi-singularity point around the 17th of December, 2012. It is demonstrated …

Unified proof of end-point estimates for Radon transform on curved spaces.

Human communication takes many forms, including speech, text and instructional videos. It typically has an underlying structure, with a starting point, ending, and certain objective steps between them. In this paper, we consider instructional videos where there are tens of millions of them on the Internet. We propose a…

Optimal transport distances help impute missing data.