arXiv research

Narrow neural networks have unbounded decision regions.

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…

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.

In this paper we consider the problem of minimizing the relative perimeter under a volume constraint in the interior of a conically bounded convex set, i.e., an unbounded convex body admitting an \emph{exterior} asymptotic cone. Results concerning existence of isoperimetric regions, the behavior of the isoperimetric pr…

We call a Delta Diagram any diagram of a knot or link whose regions (including the unbounded one) have 3, 4, or 5 sides. We prove that any knot or link admits a delta diagram. We define and estimate combinatorial link invariants stemming from this definition.

We show that in dimension 4 and above, the lifespan of Ricci flows depends on the relative smallness of the Ricci curvature compared to the Riemann curvature on the initial manifold. We can generalize this lifespan estimate to the local Ricci flow, using which we prove the short-time existence of Ricci flow solutions o…

Rectangular Bounding Process (RBP) improves partitioning efficiency in multi-dimensional spaces.

Many engineering problems require identifying feasible domains under implicit constraints. One example is finding acceptable car body styling designs based on constraints like aesthetics and functionality. Current active-learning based methods learn feasible domains for bounded input spaces. However, we usually lack pr…

The paper constructs ancient solutions to curvature flows in bounded and unbounded regions.

We show that if an asymptotically flat manifold with horizon boundary admits a global static potential, then the static potential must be zero on the boundary. We also show that if an asymptotically flat manifold with horizon boundary admits an unbounded static potential in the exterior region, then the manifold must c…

New RL policy for unbounded state space with stability guarantee.

Paper proves existence of isometric immersions for negatively curved surfaces with unbounded second fundamental form.

A theorem connects integral of second-order derivatives to function rise.

In this article we investigate the restrictions imposed by the dominant energy condition (DEC) on the topology and conformal type of \textsl{possibly non-compact} marginally outer-trapped surfaces (thus extending Hawking's classical theorem on the topology of black holes). We first prove that an unbounded, stable margi…

Estimates CDF over complex regions using normalizing flows.

Model predicts growth competition on curved surfaces.

Given a warped product space $\mathbb{R} \times_{f} N$ with logarithmically convex warping function $f$, we prove a relative isoperimetric inequality for regions bounded between a subset of a vertical fiber and its image under an almost everywhere differentiable mapping in the horizontal direction. In particular, given…

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

Constructs unbounded Kasparov product for sphere embeddings into Euclidean space.

Unbounded convex domains have zero mean curvature on disconnected boundaries.

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

Analyzes packing of circles in bounded and unbounded planes using mathematical formulas.

Golden L surface has unbounded bunching of saddle connections

Bayesian interpretation explains double descent in deep learning models.

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…

New inequalities for unbounded functions improve denoising score matching.

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.

Study focal surfaces of wave fronts with unbounded curvatures.

Study ancient solutions on graphs with unbounded Laplacians, generalizing previous results.

Study optimal stopping for variable annuity contracts with discontinuous rewards.

Study shows unbounded Pontryagin numbers on curved manifolds.

Paper tackles online control of linear systems with unbounded noise.

Study solves wealth maximization problem with unbounded mean and volatility.

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.

Gradient estimates for unbounded graph Laplacians under Bakry-Emery curvature.

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.

Global existence of Yamabe flow on non-compact manifolds with unbounded initial curvature.

Unbounded output networks improve classification performance.

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 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…

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.

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

Paper solves nonparametric contextual bandit with unbounded contexts.