Optimally Packed Chains of Bulges in Multishift QR Algorithms

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For a high-dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in terms of both computational cost and numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g., to the ge ...

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 ...

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 ...

Genes implicated in translation control have been associated with autism spectrum disorders (ASDs). However, some important genetic causes of autism, including the 16p11.2 microdeletion, bear no obvious connection to translation. Here, we use proteomics, g ...

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...

The locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm is a popular approach for computing a few smallest eigenvalues and the corresponding eigenvectors of a large Hermitian positive definite matrix A. In this work, we propose a mix ...

Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by using kernel me ...

Unsupervised Domain Adaptation Regression (DAR) aims to bridge the domain gap between a labeled source dataset and an unlabelled target dataset for regression problems. Recent works mostly focus on learning a deep feature encoder by minimizing the discrepa ...

Cell-sized giant unilamellar vesicles (GUVs) are an ideal tool for understanding lipid membrane structure and properties. Label-free spatiotemporal images of their membrane potential and structure would greatly aid the quantitative understanding of membran ...

Dense image-based prediction methods have advanced tremendously in recent years. Their remarkable development has been possible due to the ample availability of real-world imagery. While these methods work well on photographs, their abilities do not genera ...

Non-noble metal catalysts (NNMCs) hold the potential to replace the expensive Pt-based materials currently used to speed up the oxygen reduction reaction (ORR) in proton exchange membrane fuel cell (PEMFC) cathodes, but they feature poor durability that in ...

Polymer brushes have been theoretically described, their behavior under diverse conditions has been modeled, and their preparation via surface-initiated polymerizations (SIPs) has been progressively refined. However, despite three decades of research endea ...

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

The Schur decomposition of a square matrix A is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following task: Compute a (m ...

This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for performing low-rank up ...

Cell-free biology is increasingly utilized for engineering biological systems, incorporating novel functionality, and circumventing many of the complications associated with cells. The central dogma describes the information flow in biology consisting of t ...

The characterization of open quantum systems is a central and recurring problem for the development of quantum technologies. For time-independent systems, an (often unique) steady state describes the average physics once all the transient processes have fa ...

The activation of memory T cells is a very rapid and concerted cellular response that requires coordination between cellular processes in different compartments and on different time scales. In this study, we use ribosome profiling and deep RNA sequencing ...

This thesis focuses on non-parametric covariance estimation for random surfaces, i.e.~functional data on a two-dimensional domain. Non-parametric covariance estimation lies at the heart of functional data analysis, and considerations of statistical and com ...

Crossing properties of soil saturation, defined as the duration and excursion of soil saturation below and above certain thresholds, are key variables to ecosystem functioning and evolution by primarily influencing the plant and soil microbes physiological ...

Optimally Packed Chains of Bulges in Multishift QR Algorithms

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The autism susceptibility kinase, TAOK2, phosphorylates eEF2 and modulates translation

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DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

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