arXiv research

Improved DP optimization for nonconvex, nonsmooth objectives with reduced sample complexity.

First-order method solves stochastic bilevel optimization with linear constraints.

Optimizes nonconvex optimization by converting it to static regret minimization.

Estimator calculates surface curvature from point cloud samples.

New tools for constructing fixed point sets in digital topology.

While Multiple Instance (MI) data are point patterns -- sets or multi-sets of unordered points -- appropriate statistical point pattern models have not been used in MI learning. This article proposes a framework for model-based MI learning using point process theory. Likelihood functions for point pattern data derived …

Study on connection points on double regular polygons, providing coordinates and proving non-connection points.

New families of translation surfaces with multiple oblivious points discovered.

This paper reverses a construction by merging boundary critical points into an interior one.

A new model for point processes without intensity function trade-offs.

PINNACLE optimizes point selection for PINNs, improving accuracy.

The minimal number of critical points is studied for smooth functions on closed manifolds.

Convergence to a saddle point for convex-concave functions has been studied for decades, while recent years has seen a surge of interest in non-convex (zero-sum) smooth games, motivated by their recent wide applications. It remains an intriguing research challenge how local optimal points are defined and which algorith…

Investigates point spectra of vector fields and their properties.

We revisit an example of a semi-Riemannian geodesic that was discussed by Musso, Pejsachowicz and Portaluri in 2007 to show that not every conjugate point is a bifurcation point. We point out a mistake in their argument, showing that on this geodesic actually every conjugate point is a bifurcation point. Finally, we pr…

Hard to approximate critical points for simple nonconvex functions.

Algorithm finds periodic points on Veech surfaces.

Estimating boundaries from point clouds with improved accuracy and rigorous error estimates.

The paper classifies circle actions on 6D manifolds with isolated fixed points.

PoPPy is a Point Process toolbox based on PyTorch, which achieves flexible designing and efficient learning of point process models. It can be used for interpretable sequential data modeling and analysis, e.g., Granger causality analysis of multi-variate point processes, point process-based simulation and prediction of…

The paper models user-advertiser interactions using point processes.

A limit point p of a discrete group of Mobius transformations acting on S^n is called a concentration point if for any sufficiently small connected open neighborhood U of p, the set of translates of U contains a local basis for the topology of S^n at p. For the case of Fuchsian groups (n = 1), every concentration point…

The paper develops methods to create private synthetic spatial point patterns.

Self-focal points on ellipsoids of dimension 3 or higher are rare.

We construct non-trapping asymptotically hyperbolic manifolds with boundary conjugate points but no interior conjugate points.

The paper introduces a method to probabilistically select inducing points in sparse Gaussian processes.

Groups with special properties always have fixed points.

The paper proves $\Gamma$-convergence of discrete tangent-point energies to continuous energies and ropelength, with applications to biarc curves.

The study confirms a conjecture about critical points of smooth functions.

New method upsamples sparse, non-uniform point clouds more accurately.

Characterizes Lebesgue points using nearest neighbor methods.

We give a explicit computation of the pointed harmonic volumes of hyperelliptic curves with Weierstrass base points, which are paraphrased into a combinatorial formula.

We propose to explain the predictions of a deep neural network, by pointing to the set of what we call representer points in the training set, for a given test point prediction. Specifically, we show that we can decompose the pre-activation prediction of a neural network into a linear combination of activations of trai…

In recent decades, the use of 3D point clouds has been widespread in computer industry. The development of techniques in analyzing point clouds is increasingly important. In particular, mapping of point clouds has been a challenging problem. In this paper, we develop a discrete analogue of the Teichmüller extremal mapp…

Estimates geodesics on surfaces without conjugate points.

The main result is a direct proof of the implication $(LVKF_{k,3})\Rightarrow( LT_{3k-1,3})$ below. Consider the following statements: ($LVKF_{1,3}$) From any 11 points in $\mathbb{R}^{3}$ one can choose 3 pairwise disjoint triples whose convex hulls have a common point. ($LVKF_{k,3}$) From any $6k + 5$ points in $ \m…

Study shows periodic points of Prym eigenforms in specific genera.

Periodic points are points on Veech surfaces, whose orbit under the group of affine diffeomorphisms is finite. We characterise those points as being torsion points if the Veech surfaces is suitably mapped to its Jacobian or an appropriate factor thereof. For a primitive Veech surface in genus two we show that the only …

The wide adoption of DNNs has given birth to unrelenting computing requirements, forcing datacenter operators to adopt domain-specific accelerators to train them. These accelerators typically employ densely packed full precision floating-point arithmetic to maximize performance per area. Ongoing research efforts seek t…

Study finds central points of double heptagon surface are not connection points.

Quantized neural networks can represent all fixed-point functions under certain conditions.

Study circle actions on unitary manifolds with discrete fixed points.

Study on choosing points on cubic curves, answering some questions about their flexibility.

Study circle actions on manifolds with 3 fixed points, finding dimension constraints and unique structures.

Unified framework detects changes in complex system models.

Fold singular points play important roles in the theory of maximal surfaces. For example, if a maximal surface admits fold singular points, it can be extended to a timelike minimal surface analytically. Moreover, there is a duality between conelike singular points and folds. In this paper, we investigate fold singular …

Study behavior of curvatures near singular points of frontals.

Research shows quadratic growth in derivative maxima for certain interval diffeos with parabolic fixed points.