The quadratic Wasserstein metric for inverse data matching. (arXiv:1911.06911v1 [math.NA])

This work characterizes, analytically and numerically, two major effects of the quadratic Wasserstein ($W_2$) distance as the measure of data discrepancy in computational solutions of inverse problems. First, we show, in the infinite-dimensional setup, that the $W_2$ distance has a smoothing effect on the inversion process, making it robust against high-frequency noise in the data…

Local minimizers with unbounded vorticity for the $2$d Ginzburg-Landau functional. (arXiv:1911.06914v1 [math.AP])

A central focus of Ginzburg-Landau theory is the understanding and characterization of vortex configurations. On a bounded domain $\Omega\subseteq \mathbb{R}^2,$ global minimizers, and critical states in general, of the corresponding energy functional have been studied thoroughly in the limit $\epsilon\to 0,$ where $\epsilon>0$ is the inverse of the Ginzburg-Landau parameter. The presence of an applied…

Regularity and asymptotic behavior of laminar flames in higher dimensions. (arXiv:1911.06916v1 [math.AP])

We study a parabolic free boundary problem, arising from a model for the propagation of equi-diffusional premixed flames with high activation energy. If an initial data is compactly supported, then the solution vanishes in a finite time, called the extinction time. In this paper, we give a quantitative estimate on the flatness of the free…

A Fully Stochastic Second-Order Trust Region Method. (arXiv:1911.06920v1 [math.OC])

A stochastic second-order trust region method is proposed, which can be viewed as a second-order extension of the trust-region-ish (TRish) algorithm proposed by Curtis et al. (INFORMS J. Optim. 1(3) 200-220, 2019). In each iteration, a search direction is computed by (approximately) solving a trust region subproblem defined by stochastic gradient and Hessian estimates. The…

Exploring Configurations for Multi-user Communication in Virtual Reality. (arXiv:1911.06877v1 [cs.HC])

Virtual Reality (VR) enables users to collaborate while exploring scenarios not realizable in the physical world. We propose CollabVR, a distributed multi-user collaboration environment, to explore how digital content improves expression and understanding of ideas among groups. To achieve this, we designed and examined three possible configurations for participants and shared manipulable objects. In configuration…

Separating Local & Shuffled Differential Privacy via Histograms. (arXiv:1911.06879v1 [cs.CR])

Recent work in differential privacy has highlighted the shuffled model as a promising avenue to compute accurate statistics while keeping raw data in users’ hands. We present a protocol in this model that estimates histograms with error independent of the domain size. This implies an arbitrarily large gap in sample complexity between the shuffled and…

Adaptive Leader-Follower Formation Control and Obstacle Avoidance via Deep Reinforcement Learning. (arXiv:1911.06882v1 [cs.RO])

We propose a deep reinforcement learning (DRL) methodology for the tracking, obstacle avoidance, and formation control of nonholonomic robots. By separating vision-based control into a perception module and a controller module, we can train a DRL agent without sophisticated physics or 3D modeling. In addition, the modular framework averts daunting retrains of an image-to-action end-to-end…

New Query Lower Bounds for Submodular Function MInimization. (arXiv:1911.06889v1 [cs.DS])

We consider submodular function minimization in the oracle model: given black-box access to a submodular set function $f:2^{[n]}\rightarrow \mathbb{R}$, find an element of $\arg\min_S \{f(S)\}$ using as few queries to $f(\cdot)$ as possible. State-of-the-art algorithms succeed with $\tilde{O}(n^2)$ queries [LeeSW15], yet the best-known lower bound has never been improved beyond $n$ [Harvey08]. We provide a…