arXiv research

Due to challenging applications such as collaborative filtering, the matrix completion problem has been widely studied in the past few years. Different approaches rely on different structure assumptions on the matrix in hand. Here, we focus on the completion of a (possibly) low-rank matrix with binary entries, the so-c…

New method for tensor completion using nonconvex dual total variation.

Suppose $S$ is a semispray on a manifold $M$. We know that the complete lift $S^c$ of $S$ is a semispray on $TM$ with the property that geodesics of $S^c$ correspond to Jacobi fields of $S$. In this note we generalize this result and show how geodesic variations of $k$-variables are related to geodesics of the $k$th it…

The stability and the index of complete one-sided minimal surfaces of certain three-dimensional Riemannian manifolds with positive scalar curvature are studied.

We derive a formula for the first variation of horizontal perimeter measure for $C^2$ hypersurfaces of completely general sub-Riemannian manifolds, allowing for the existence of characteristic points. For $C^2$ hypersurfaces in vertically rigid sub-Riemannian manifolds we also produce a second variation formula for var…

A complete solution to the multiplier version of the inverse problem of the calculus of variations is given for a class of hyperbolic systems of second-order partial differential equations in two independent variables. The necessary and sufficient algebraic and differential conditions for the existence of a variational…

A method to derive Lagrangians from field equations in metric-affine theories of gravity.

GLSKF improves tensor completion by capturing both global and local variations.

A complete error analysis of variational integrators is obtained, by blowing up the discrete variational principles, all of which have a singularity at zero time-step. Divisions by the time step lead to an order that is one less than observed in simulations, a deficit that is repaired with the help of a new past-future…

The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a W…

Proposes a new model for image restoration combining deep learning and total variation.

Geodesics become an essential element of the geometry of a semi-Riemannian manifold. In fact, their differences and similarities with the (positive definite) Riemannian case, constitute the first step to understand semi-Riemannian Geometry. The progress in the last two decades has become impressive, being especially re…

New method improves tensor completion by selectively preserving important elements.

A new particle algorithm improves mean-field variational inference.

Study shows how fast a specific matrix completion method works.

Since $n$-dimensional $λ$-hypersurfaces in the Euclidean space $\mathbb {R}^{n+1}$ are critical points of the weighted area functional for the weighted volume-preserving variations, in this paper, we study the rigidity properties of complete $λ$-hypersurfaces. We give a gap theorem of complete $λ$-hypersurfaces with po…

When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by the theory? This question is difficult to answer, because in general we do not kno…

This note is concerned with some essential properties (optimal isoperimetry, first variation, and monotonicity formula) of the so-called $[0,1)\niγ$-torsional rigidity $\mathcal{T}_{γ,\mathsf{g}}$ on a complete Riemannian two-manifold $(\mathbb M^2,\mathsf{g})$. Even in the special case of $\mathbb R^2$, major results …

The premorbid geometry of the mandible is of significant relevance in jaw reconstructive surgeries and occasionally unknown to the surgical team. In this paper, an optimization framework is introduced to train deep models for completion (reconstruction) of the missing segments of the bone based on the remaining healthy…

Bayesian neural networks ignore data in infinite units limit.

Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to posterior densities on model parameters. In this note, we review the main variants of …

We derive variational formulas for the total Q-prime curvature under the deformation of strictly pseudoconvex domains in a complex manifold. We also show that the total Q-prime curvature agrees with the renormalized volume of such domains with respect to the complete Einstein-Kähler metric. In the appendix, by Rod Gove…

A new method for filling in missing traffic data improves accuracy over existing techniques.

We present a variational formulation of electrodynamics using de Rham even and odd differential forms. Our formulation relies on a variational principle more complete than the Hamilton principle and thus leads to field equations with external sources and permits the derivation of the constitutive relations. We interpre…

We present a method for proving the existence of solutions to a class of one dimensional variational problems. The method is demonstrated by two examples of optimal interpolation problems which are motivated by engineering applications. In each case we prove that the variational problem satisfies the Palais-Smale condi…

We prove by variational means the existence of a complete, properly embedded, genus-one minimal surface in R^3 that is asymptotic to a helicoid at infinity. We also prove existence of surfaces that are asymptotic to a helicoid away from the helicoid's axis, but that have infinitely many handles arranged periodically al…

Music SketchNet generates missing measures in incomplete music pieces, guided by user input.

In this short note we prove that, in dimension three, flat metrics are the only complete metrics with non-negative scalar curvature which are critical for the $σ_{2}$-curvature functional.

We give a variation of McShane's identity, which describes the cusp shape of a hyperbolic 2-bridge link in terms of the complex translation lengths of simple loops on the bridge sphere. We also explicitly determine the set of end invariants of $SL(2,\mathbb{C})$-characters of the once-punctured torus corresponding to t…

We investigate variations of Brieskorn lattices over non-compact parameter spaces, and discuss the corresponding limit objects on the boundary divisor. We study the associated variation of twistors and the corresponding limit mixed twistor structures. We construct a compact classifying space for regular singular Briesk…

We calculate the first and the second variation formula for the sub-Riemannian area in three dimensional pseudo-hermitian manifolds. We consider general variations that can move the singular set of a C^2 surface and non-singular variation for C_H^2 surfaces. These formulas enable us to construct a stability operator fo…

The paper finds local minimizers for obstacle avoidance on curved spaces.

SRTC model for background/foreground separation with missing pixels.

This paper presents a multi-dimensional computational method to predict the spatial variation data inside and across multiple dies of a wafer. This technique is based on tensor computation. A tensor is a high-dimensional generalization of a matrix or a vector. By exploiting the hidden low-rank property of a high-dimens…

The PAC-Bayesian approach is a powerful set of techniques to derive non- asymptotic risk bounds for random estimators. The corresponding optimal distribution of estimators, usually called the Gibbs posterior, is unfortunately intractable. One may sample from it using Markov chain Monte Carlo, but this is often too slow…

DGPs with variational inference suffer from SNR issues that degrade gradient estimates, leading to unreliable training.

Study improves posterior inference in neural processes with limited data.

In this paper, we introduce a definition of $λ$-hypersurfaces of weighted volume-preserving mean curvature flow in Euclidean space. We prove that $λ$-hypersurfaces are critical points of the weighted area functional for the weighted volume-preserving variations. Furthermore, we classify complete $λ$-hypersurfaces with …

Inferring air quality from a limited number of observations is an essential task for monitoring and controlling air pollution. Existing inference methods typically use low spatial resolution data collected by fixed monitoring stations and infer the concentration of air pollutants using additional types of data, e.g., m…

In this paper we complete the proof of the existence of multiple solutions (and, in particular, non minimal ones), to the epsilon-Dirichlet problem obtained as a variational problem for the SU(2)-epsilon-Yang Mills functional. This is equivalent to proving the existence of multiple solutions to the Dirichlet problem fo…

Minimal annuli constructed in PSL2 via variational method.

The paper simplifies conditions for optimal paths on manifolds avoiding obstacles.

In order to apply variational methods to the action functional for geodesics of a stationary spacetime, some hypotheses, useful to obtain classical Palais-Smale condition, are commonly used: pseudo-coercivity, bounds on certain coefficients of the metric, etc. We prove that these technical assumptions admit a natural i…

The main result is the identification of the orthogonal complement of the subalgebra of conformal vector field inside the algebra of all vector fields of a compact flat 2-manifold. As a fundamental tool, the complete Hodge decomposition for manifold with boundary is used. The identification allows the derivation of gov…

New model reconstructs flow from sparse data with uncertainty quantification.

We extend the classification of Robert Bryant of Willmore spheres in $S^3$ to variational branched Willmore spheres $S^3$ and show that they are inverse stereographic projections of complete minimal surfaces with finite total curvature in $\mathbb{R}^3$ and vanishing flux. We also obtain a classification of variational…

We give an explicit formula for the second variation of the logarithm of the Selberg zeta function, $Z(s)$, on Teichmüller space. We then use this formula to determine the asymptotic behavior as $\text{Re} (s) \to \infty$ of the second variation. As a consequence, for $m \in \mathbb{N}$, we obtain the complete expansio…

VPR improves posterior uncertainty quantification by combining VI and predictive resampling.