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We study the sequential empirical process indexed by general function classes and its smoothed set-indexed analogue. Sufficient conditions for asymptotic equicontinuity are provided for nonstationary arrays of time series. This yields…
Indoor localization systems often fuse inertial odometry with map information via hand-defined methods to reduce odometry drift, but such methods are sensitive to noise and struggle to generalize across odometry sources. To address the…
The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz-Sobolev spaces in $\mathbb R^n$. An improved embedding with an Orlicz-Lorentz target space, which is optimal in the broader class of all…
In this work we propose a graph-based learning framework to train models with provable robustness to adversarial perturbations. In contrast to regularization-based approaches, we formulate the adversarially robust learning problem as one of…
In this paper we will prove Hadamard-Stoker type theorems in the following ambient spaces: $\man ^n \times \r$, where $\man ^n $ is a $1/4-$pinched manifold, and certain Killing submersions, e.g., Berger spheres and Heisenberg spaces. That…
We study an abstract second order inclusion involving two nonlinear single-valued operators and a nonlinear multivalued term. Our goal is to establish the existence of solutions to the problem by applying numerical scheme based on time…
Starting from a recent a posteriori error estimator for the finite element solution of the wave equation with explicit time-stepping [Grote, Lakkis, Santos, 2024], we devise a space-time adaptive strategy which includes both time evolving…
Compressing word embeddings is important for deploying NLP models in memory-constrained settings. However, understanding what makes compressed embeddings perform well on downstream tasks is challenging---existing measures of compression…
Event suffix and remaining time prediction are sequence to sequence learning tasks. They have wide applications in different areas such as economics, digital health, business process management and IT infrastructure monitoring. Timestamped…
Performance optimization is an increasingly challenging but often repetitive task. While each platform has its quirks, the underlying code transformations rely on data movement and computational characteristics that recur across…
The purpose of this work is to build a framework that allows for an in-depth study of various generalisations to inhomogeneous space of models of Borodin-Ferrari, Dieker-Warren, Nordenstam, Warren-Windridge of interacting particles in…
We investigate stochastic averaging theory for locally Lipschitz discrete-time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete-time stochastic extremum seeking algorithms. Firstly, by…
We show the existence of a broad class of affine Markov processes in the cone of positive self-adjoint Hilbert-Schmidt operators. Such processes are well-suited as infinite dimensional stochastic volatility models. The class of processes we…
Given a point $A$ in the convex hull of a given adjoint orbit $\mathcal{O}(F)$ of a compact Lie group $G$, we give a polynomial time algorithm to compute the probability density supported on $\mathcal{O}(F)$ whose expectation is $A$ and…
Model Predictive Control (MPC) can be applied to safety-critical control problems, providing closed-loop safety and performance guarantees. Implementation of MPC controllers requires solving an optimization problem at every sampling…
In a Hilbert space $H$, in order to develop fast optimization methods, we analyze the asymptotic behavior, as time $t$ tends to infinity, of inertial continuous dynamics where the damping acts as a closed-loop control. The function $f: H…
Continuous-time models are a natural choice for irregular and asynchronous data. A central design choice is how to embed discrete observations into continuous time. Interpolation- and imputation-based embeddings reconstruct a continuous…
This paper examines the properties of flows around objects embedded within common envelopes in the simplified context of a "wind tunnel." We establish characteristic relationships between key common envelope flow parameters like the Mach…
We introduce LAWS (Learning from Actual Workloads Symbolically), a self-certifying inference caching architecture that builds a growing library of certified expert functions from deployment observations. Each expert covers a region of input…
Encoder-decoder recurrent neural network models (RNN Seq2Seq) have achieved great success in ubiquitous areas of computation and applications. It was shown to be successful in modeling data with both temporal and spatial dependencies for…