Kernel Matching Pursuit for Large Datasets

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We study the glass transition by exploring a broad class of kinetic rules that can significantly modify the normal dynamics of supercooled liquids while maintaining thermal equilibrium. Beyond the usual dynamics of liquids, this class includes dynamics in ...

We study the statistical mechanics and the equilibrium dynamics of a system of classical Heisenberg spins with frustrated interactions on a d -dimensional simple hypercubic lattice, in the limit of infinite dimensionality d -> infinity . In the analysis we ...

This paper explores data assimilation methods in the context of Bayesian Calibration for fuel performance models. It compares deterministic and stochastic approaches, concentrating on the Generalized Linear Least Squares (GLLS) method and stochastic techni ...

We introduce an algorithm to reconstruct a mesh from discrete samples of a shape's Signed Distance Function (SDF). A simple geometric reinterpretation of the SDF lets us formulate the problem through a point cloud, from which a surface can be extracted wit ...

The optimal pricing of goods, especially when they are new and the innovating firm is a monopolist, must proceed without precise knowledge of the demand curve. This paper provides a pricing method with a relative robustness guarantee by maximizing a perfor ...

In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating the solution as a linear combination of a small number of basis vectors with r ...

A kernel method for estimating a probability density function from an independent and identically distributed sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined b ...

Given a hyperelliptic hyperbolic surface S of genus g >= 2, we find bounds on the lengths of homologically independent loops on S. As a consequence, we show that for any lambda is an element of (0, 1) there exists a constant N(lambda) such that every such ...

In this thesis, we give new approximation algorithms for some NP-hard problems arising in resource allocation and network design. As a resource allocation problem, we study the Santa Claus problem (also known as the MaxMin Fair Allocation problem) in which ...

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for time-dependent n ...

We generalize the class vectors found in neural networks to linear subspaces (i.e., points in the Grassmann manifold) and show that the Grassmann Class Representation (GCR) enables simultaneous improvement in accuracy and feature transferability. In GCR, e ...

An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n. Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed ...

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

We address multi-robot safe mission planning in uncertain dynamic environments. This problem arises in several applications including safety-critical exploration, surveillance, and emergency rescue missions. Computation of a multi-robot optimal control pol ...

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

Collaborative learning algorithms, such as distributed SGD (or D-SGD), are prone to faulty machines that may deviate from their prescribed algorithm because of software or hardware bugs, poisoned data or malicious behaviors. While many solutions have been ...

In this thesis we present and analyze approximation algorithms for three different clustering problems. The formulations of these problems are motivated by fairness and explainability considerations, two issues that have recently received attention in the ...

The advent of comprehensive synaptic wiring diagrams of large neural circuits has created the field of connectomics and given rise to a number of open research questions. One such question is whether it is possible to reconstruct the information stored in ...

Background: Although digital mobility outcomes (DMOs) can be readily calculated from real-world data collected with wearable devices and ad-hoc algorithms, technical validation is still required. The aim of this paper is to comparatively assess and validat ...

This paper proposes a method for the construction of quadratic serendipity element (QSE) shape functions on planar convex and concave polygons. Existing approaches for constructing QSE shape functions are linear combinations of the pair-wise products of ge ...

Kernel Matching Pursuit for Large Datasets

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Testing Theories of the Glass Transition with the Same Liquid but Many Kinetic Rules

Frustrated magnets in the limit of infinite dimensions: Dynamics and disorder-free glass transition

Comparison of Bayesian Model Calibration Techniques for Future Application to Fuel Performance Behavior Models

Reach For the Arcs: Reconstructing Surfaces from SDFs via Tangent Points

Monopoly Pricing with Unknown Demand

Dynamical Low-Rank Approximation for Stochastic Differential Equations

Density estimation in RKHS with application to Korobov spaces in high dimensions

Short homology bases for hyperelliptic hyperbolic surfaces

Approximation Algorithms for Allocation and Network Design

Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems

Get the Best of Both Worlds: Improving Accuracy and Transferability by Grassmann Class Representation

Results on Sparse Integer Programming and Geometric Independent Sets

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Multi-robot task allocation for safe planning against stochastic hazard dynamics

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Robust Collaborative Learning with Linear Gradient Overhead

Fairness and Explainability in Clustering Problems

Bayesian reconstruction of memories stored in neural networks from their connectivity

Assessing real-world gait with digital technology? Validation, insights and recommendations from the Mobilise-D consortium

Quadratic serendipity element shape functions on general planar polygons