The role of sulfated metabolites in the wound response of siphonous green algae
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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 ...
We propose a new non-perturbative method for studying UV complete unitary quantum field theories (QFTs) with a mass gap in general number of spacetime dimensions. The method relies on unitarity formulated as positive semi-definiteness of the matrix of inne ...
This paper is concerned with two improved variants of the Hutch++ algorithm for estimating the trace of a square matrix, implicitly given through matrix-vector products. Hutch++ combines randomized low-rank approximation in a first phase with stochastic tr ...
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 ...
Transformers achieve remarkable performance in several tasks but due to their quadratic complexity, with respect to the input’s length, they are prohibitively slow for very long sequences. To address this limitation, we express the self-attention as a line ...
Intensified coastal eutrophication can result in an overgrowth of seagrass leaves by epiphytes, which is a major threat to seagrass habitats worldwide, but little is known about how epiphytic biofilms affect the seagrass phyllosphere. The physico-chemical ...
Living organisms can catalyze many thousands of biochemical reactions that they use to convert energy and matter, which provides them with the essentials for life. The sum of these chemical reactions happening in an organism is called metabo-lism. Understa ...
Background Cyanobacteria and their toxins occur in high concentrations during the so-called bloom events in surface waters. To be able to assess the risks associated with cyanobacterial blooms, we need to understand the persistence and fate processes of th ...