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In this thesis, we study two distinct problems.
The first problem consists of studying the linear system of partial differential equations which consists of taking a k-form, and applying the exterior derivative 'd' to it and add the wedge product with a 1- ...
It is known that in many functions of banded, and more generally, sparse Hermitian positive definite matrices, the entries exhibit a rapid decay away from the sparsity pattern. This is in particular true for the inverse, and based on results for the invers ...
Functional connectomes (FCs) containing pairwise estimations of functional couplings between pairs of brain regions are commonly represented by correlation matrices. As symmetric positive definite matrices, FCs can be transformed via tangent space projecti ...
We consider the problem of decomposing monotone Boolean functions into majority-of-three operations, with a particular focus on decomposing the majority-n function. When targeting monotone Boolean functions, Shannon's expansion can be expressed by a single ...
Perturbations to an ecosystem's steady state can trigger transient responses of great ecological relevance. Asymptotic stability determines whether a generic perturbation will fade out in the long run, but falls short of characterizing the dynamics imme ...
A new family of organometallic p-cymene ruthenium(II) and osmium(II) complexes conjugated to ethacrynic acid, a glutathione transferase (GST) inhibitor, is reported. The ethacrynic acid moiety (either one or two) is tethered to the arene ruthenium(II) and ...
The development of a sequential copper-catalyzed oxy-alkynylation/intramolecular [4+2] cycloaddition of allenes and arenes was investigated at first. This one-pot protocol allowed the construction of complex polycylic architectures with high efficiency fro ...
This paper is concerned with the eigenvalue decay of the solution to operator Lyapunov equations with right-hand sides of finite rank. We show that the kth (generalized) eigenvalue decays exponentially in root k, provided that the involved operator A gener ...
Enzymes are biocatalysts widely used in a large number of industrial biotech processes as they offer clear advantages over their chemical counterparts. Indeed, enzymes often show high substrate selectivity along with elevated turnover rates. Enzymatic cata ...
This paper presents an algorithm and its implementation in the software package NCSOStools for finding sums of Hermitian squares and commutators decompositions for polynomials in noncommuting variables. The algorithm is based on noncommutative analogs of t ...
