arXiv research

New PAC-Bayes bounds for unbounded loss functions.

Note improves confidence bounds for random variables.

Paper develops estimators for unbounded density ratios with applications in error control.

We consider minimal graphs u(x,y)>0 over unbounded domains D (with u vanishing on the boundary of D). Assuming D contains a sector properly containing a halfplane, we obtain estimates on growth and provide examples illustrating a range of growth.

Efficiently estimates quantiles and maximum in unbounded datasets with differential privacy.

Extends Alexandrov's result to unbounded convex domains in hyperbolic 3-space.

Two new algorithms improve performance in adversarial bandits with unbounded losses.

Investigates RI strategies for life insurers with LRD mortality rates.

Unbounded convex domains have zero mean curvature on disconnected boundaries.

New algorithms adapt to both gradient norms and comparator norms in online learning.

The paper proves homotopy equivalences for spaces of unbounded Fredholm operators.

Golden L surface has unbounded bunching of saddle connections

We construct an unbounded representative for the shriek class associated to the embeddings of spheres into Euclidean space. We equip this unbounded Kasparov cycle with a connection and compute the unbounded Kasparov product with the Dirac operator on $\mathbb R^{n+1}$. We find that the resulting spectral triple for the…

This memoir presents a systematic study of the utility maximization problem of an investor in a constrained and unbounded financial market. Building upon the work of Hu et al. (2005) [Ann. Appl. Probab., 15, 1691--1712] in a bounded framework, we extend our analysis to the more challenging unbounded case. Our methodolo…

It is shown that the compactly supported identity component of the diffeomorphism group of the 2-dimensional punctured torus $\mathbb T^2_p$ is an unbounded group. It follows that the fragmentation norm of $\mathbb T^2_p$ is unbounded.

New inequalities for unbounded functions improve denoising score matching.

Study focal surfaces of wave fronts with unbounded curvatures.

Interaction graphs, such as those recording emails between individuals or transactions between institutions, tend to be sparse yet structured, and often grow in an unbounded manner. Such behavior can be well-captured by structured, nonparametric edge-exchangeable graphs. However, such exchangeable models necessarily ig…

Study shows unbounded Pontryagin numbers on curved manifolds.

Paper tackles online control of linear systems with unbounded noise.

We show that domains, that allow for convex functions with unbounded gradient at their boundary, are convex.

New approach finds solutions to games with unbounded controls.

The paper provides gradient estimates for Neumann semigroups on manifolds with boundary under unbounded curvature conditions.

New aggregation strategy handles unbounded losses with regret bounds.

Sequential tests for nonparametric hypotheses using supermartingales.

We study the barycentric straightening of simplices in irreducible symmetric spaces of non-compact type. We show that, for an n-dimensional symmetric space of rank r>1, the p-Jacobian has uniformly bounded norm, as soon as p is at least n-r+2. As a consequence, for a non-compact, connected, semisimple real Lie group G,…

Improved sampling from Gaussian distributions with privacy constraints.

Geometric model of unbounded sl3 laminations with tropical coordinates.

In this paper, we provided conditions for an entire constant mean curvature Killing graph lying inside a possible unbounded region to be necessarily a slice.

We show that any noncompact Riemann surface admits a complete Ricci flow g(t), t\in[0,\infty), which has unbounded curvature for all t\in[0,\infty).

In this paper, we investigate the problem of blow up and sharp upper bound estimates of the lifespan for the solutions to the semilinear wave equations, posed on asymptotically Euclidean manifolds. Here the metric is assumed to be exponential perturbation of the spherical symmetric, long range asymptotically Euclidean …

We construct a complete, embedded minimal surface in euclidean 3-space which has unbounded Gaussian curvature. It has infinite genus, infinitely many catenoidal type ends and one limit end.

In this paper, we derive Li-Yau inequality for unbounded Laplacian on complete weighted graphs with the assumption of the curvature-dimension inequality $CDE'(n,K)$, which can be regarded as a notion of curvature on graphs. Furthermore, we obtain some applications of Li-Yau inequality, including Harnack inequality, hea…

Study unbounded $\mathfrak{sl}_3$-laminations around punctures.

Metric WPD for pseudo-Anosov maps shows many unbounded quasi-morphisms.

Paper solves nonparametric contextual bandit with unbounded contexts.

New algorithms improve exploration in unbounded reward settings.

We consider the problem of minimizing the relative perimeter under a volume constraint in an unbounded convex body $C\subset \mathbb{R}^{n+1}$, without assuming any further regularity on the boundary of $C$. Motivated by an example of an unbounded convex body with null isoperimetric profile, we introduce the concept of…

Solves open problem on universally consistent online learning with unbounded losses.

We give an explicit formula for singular surfaces of revolution with prescribed unbounded mean curvature. Using it, we give conditions for singularities of that surfaces. Periodicity of that surface is also discussed.

Investigates optimal consumption and investment strategies in non-Markovian markets with unbounded parameters.

In infinite dimensional Heisenberg group, degenerate distances linked to unbounded curvature.

The CD equalities were introduced to imply the gradient estimate of laplace operator on graphs. This article is based on the unbounded Laplacians, and finally concludes some equivalent properties of the CD(K,$\infty$)and CD(K,n).

New algorithms for online learning without boundedness or Lipschitz loss assumptions.

We study ancient solutions of polynomial growth to both continuous-time and discrete-time heat equations on graphs with unbounded Laplacians. We generalize Colding and Minicozzi's theorem [CM19] on manifolds, and the result [Hua19] on graphs with normalized Laplacians to the setting of graphs with unbounded Laplacians:…

The paper solves the Dirichlet problem for minimal surfaces on unbounded helicoidal domains.

Study $L^2$-cohomology in unbounded geometry manifolds.

Study shows convergence rate for empirical minimizer of unbounded functions with fast growth.