arXiv research

Unbounded convex domains have zero mean curvature on disconnected boundaries.

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.

New method estimates volatility for Lévy processes with unbounded jumps efficiently.

We prove a version of Gromov's compactness theorem for pseudo-holomorphic curves which holds locally in the target symplectic manifold. This result applies to sequences of curves with an unbounded number of free boundary components, and in families of degenerating target manifolds which have unbounded geometry (e.g. no…

We show that the identity component of the group of diffeomorphisms of a closed oriented surface of positive genus admits many unbounded quasi-morphisms. As a corollary, we also deduce that this group is not uniformly perfect and its fragmentation norm is unbounded, answering a question of Burago--Ivanov--Polterovich. …

New method estimates volatility for processes with jumps of unbounded variation.

Study of Gordian graphs' behavior at infinity for various local moves.

New algorithm tackles multiclass transductive online learning with unbounded labels.

Private learning of Gaussian Mixture Models without boundedness assumptions.

The study finds infinite knot exteriors with meridional surfaces of any genus and boundary components.

Let $X$ be a geodesic metric space with $H_1(X)$ uniformly generated. If $X$ has asymptotic dimension one then $X$ is quasi-isometric to an unbounded tree. As a corollary, we show that the asymptotic dimension of the curve graph of a compact, oriented surface with genus $g \ge 2$ and one boundary component is at least …

Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this paper, we provide a novel framework to obtain uniform deviation bounds for loss…

We show that for neural network functions that have width less or equal to the input dimension all connected components of decision regions are unbounded. The result holds for continuous and strictly monotonic activation functions as well as for the ReLU activation function. This complements recent results on approxima…

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

It it known that the set of L-space surgeries on a nontrivial L-space knot is always bounded from below. However, already for two-component torus links the set of L-space surgeries might be unbounded from below. For algebraic two-component links we provide three complete characterizations for the boundedness from below…

In this paper we study some global properties of static potentials on asymptotically flat $3$-manifolds $(M,g)$ in the nonvacuum setting. Heuristically, a static potential $f$ represents the (signed) length along $M$ of an irrotational timelike Killing vector field, which can degenerate on surfaces corresponding to the…

We define an integer-valued non-degenerate bi-invariant metric (the discriminant metric) on the universal cover of the identity component of the contactomorphism group of any contact manifold. This metric has a very simple geometric definition, based on the notion of discriminant points of contactomorphisms. Using gene…

In this paper we prove a general and sharp Asymptotic Theorem for minimal surfaces in $H^2\times R$. As a consequence, we prove that there is no properly immersed minimal surface whose asymptotic boundary $C$ is a Jordan curve homologous to zero in the asymptotic boundary of $H^2\times R,$ say $\partial_\infty H^2\tim…

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

The value function of an optimal stopping problem for jump diffusions is known to be a generalized solution of a variational inequality. Assuming that the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the Lévy measure, this paper shows that the value function of this op…

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…

Study focal surfaces of wave fronts with unbounded curvatures.

In this paper we study the affine geometric structure of the graph of a polynomial $f \in \mathbb{R} [x,y]$. We provide certain criteria to determine when the parabolic curve is compact and when the unbounded component of its complement is hyperbolic or elliptic. We analyse the extension to the real projective plane of…

Maximal concentration bounds for stochastic approximation with heavy-tailed noise.

Study shows unbounded Pontryagin numbers on curved manifolds.

Defines spectral selectors on lens spaces for contactomorphisms.

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.

We study singular stochastic control of a two dimensional stochastic differential equation, where the first component is linear with random and unbounded coefficients. We derive existence of an optimal relaxed control and necessary conditions for optimality in the form of a mixed relaxed-singular maximum principle in a…

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.

Improved sampling from Gaussian distributions with privacy constraints.

New PAC-Bayes bounds for unbounded loss functions.

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).

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.