Construction of optimal spectral methods in phase retrieval

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Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem. Spectral algorithms ...

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

The increasing complexity of transformer models in artificial intelligence expands their computational costs, memory usage, and energy consumption. Hardware acceleration tackles the ensuing challenges by designing processors and accelerators tailored for t ...

In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...

Situational awareness strategies are essential for the reliable and secure operation of the electric power grid which represents critical infrastructure in modern society. With the rise of converter-interfaced renewable generation and the consequent shift ...

Materials for high -temperature environments are actively being investigated for deployment in aerospace and nuclear applications. This study uses computational approaches to unravel the crystallography and thermodynamics of a promising class of refractory ...

The desire and ability to place AI-enabled applications on the edge has grown significantly in recent years. However, the compute-, area-, and power-constrained nature of edge devices are stressed by the needs of the AI-enabled applications, due to a gener ...

We generalize and provide a linear algebra-based perspective on a finite element (FE) ho-mogenization scheme, pioneered by Schneider et al. (2017)[1] and Leuschner and Fritzen (2018)[2]. The efficiency of the scheme is based on a preconditioned, well-scale ...

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

Sylvester matrix equations are ubiquitous in scientific computing. However, few solution techniques exist for their generalized multiterm version, as they now arise in an increasingly large number of applications. In this work, we consider algebraic parame ...

In this thesis we study how physical principles imposed on the S-matrix, such as Lorentz invariance, unitarity, crossing symmetry and analyticity constrain quantum field theories at the nonperturbative level. We start with a pedagogical introduction to the ...

Modern data management systems aim to provide both cutting-edge functionality and hardware efficiency. With the advent of AI-driven data processing and the post-Moore Law era, traditional memory-bound scale-up data management operations face scalability ch ...

We present a nonperturbative recipe for directly computing the S-matrix in strongly-coupled QFTs. The method makes use of spectral data obtained in a Hamiltonian framework and can be applied to a wide range of theories, including potentially QCD. We demons ...

A new model is proposed for the consolidation of hybrid textiles, in which air entrapment and dissolution are considered. One of the key parameters is tow permeability, which is described by the analytical model of Gebart and validated at very high fibre v ...

State-of-the-art Artificial Intelligence (AI) algorithms, such as graph neural networks and recommendation systems, require floating-point computation of very large matrix multiplications over sparse data. Their execution in resource-constrained scenarios, ...

Single-photon 3D cameras can record the time-of-arrival of billions of photons per second with picosecond accuracy. One common approach to summarize the photon data stream is to build a per-pixel timestamp histogram, resulting in a 3D histogram tensor that ...

In this paper, we study the rank-one convex hull of a differential inclusion associated to entropy solutions of a hyperbolic system of conservation laws. This was introduced in [B. Kirchheim, S. Muller and V. S(sic)ver & aacute;k, Studying Nonlinear PDE by ...

We expand Hilbert series technologies in effective field theory for the inclusion of massive particles, enabling, among other things, the enumeration of operator bases for non-linearly realized gauge theories. We find that the Higgs mechanism is manifest a ...

The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Funct ...

Construction of optimal spectral methods in phase retrieval

Chattez avec Graph Search

The Power of Two Matrices in Spectral Algorithms for Community Recovery

Spectral Estimators for High-Dimensional Matrix Inference

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Accelerator-driven Data Arrangement to Minimize Transformers Run-time on Multi-core Architectures

Randomized low-rank approximation and its applications

Functional-Basis Analysis of Non-Stationary Signals in Modern Power Grids: Theory and Implementation in Embedded Systems

First-principles thermodynamics of precipitation in aluminum-containing refractory alloys

Exploring High-Performance and Energy-Efficient Architectures for Edge AI-Enabled Applications

An optimal preconditioned FFT-accelerated finite element solver for homogenization

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

Preconditioning techniques for generalized Sylvester matrix equations

Nonperturbative aspects of scattering amplitudes

Post-Moore's Law Fusion: High-Bandwidth Memory, Accelerators, and Native Half-Precision Processing for CPU-Local Analytics

Towards a nonperturbative construction of the S-matrix

A model for the consolidation of hybrid textiles considering air entrapment, dissolution and diffusion

A 16-bit Floating-Point Near-SRAM Architecture for Low-power Sparse Matrix-Vector Multiplication

Learned Compressive Representations for Single-Photon 3D Imaging

T-5 configurations and hyperbolic systems

Hilbert series, the Higgs mechanism, and HEFT

Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics