A data-driven iteratively regularized Landweber iteration

We derive and analyse a new variant of the iteratively regularized Landweber iteration, for solving linear and nonlinear ill-posed inverse problems. The method takes into account training data, which are used to estimate the interior of a black box, which is used to define the iteration process. We prove convergence and stability for the scheme in infinite dimensional Hilbert spaces. These theoretical results are complemented by several numerical experiments for solving linear inverse problems for the Radon transform and a nonlinear inverse problem for Schlieren tomography

Incorporating History and Deviations in Forward--Backward Splitting

We propose a variation of the forward--backward splitting method for solving structured monotone inclusions. Our method integrates past iterates and two deviation vectors into the update equations. These deviation vectors bring flexibility to the algorithm and can be chosen arbitrarily as long as they together satisfy a norm condition. We present special cases where the deviation vectors, selected as predetermined linear combinations of previous iterates, always meet the norm condition. Notably, we introduce an algorithm employing a scalar parameter to interpolate between the conventional forward--backward splitting scheme and an accelerated O(1/n^2)-convergent forward--backward method that encompasses both the accelerated proximal point method and the Halpern iteration as special cases. The existing methods correspond to the two extremes of the allowed scalar parameter range. By choosing the interpolation scalar near the midpoint of the permissible range, our algorithm significantly outperforms these previously known methods when addressing a basic monotone inclusion problem stemming from minimax optimization

Taming Tin(IV) Polyazides

The first charge-neutral Lewis base adducts of tin(IV) tetraazide, [Sn(N3)4(bpy)], [Sn(N3)4(phen)] and [Sn(N3)4(py)2], and the salt bis{bis(triphenylphosphine)iminium} hexa(azido)stannate [(PPN)2Sn(N3)6] (bpy = 2,2′-bipyridine; phen = 1,10-phenanthroline; py = pyridine; PPN = N(PPh3)2) have been prepared using covalent or ionic azide-transfer reagents and ligand-exchange reactions. The azides were isolated on the 0.3 to 1 g scale and characterized by IR and NMR spectroscopies, microanalytical and thermal methods and their molecular structures determined by single-crystal XRD. All complexes have a distorted octahedral Sn[N]6 coordination geometry and possess greater thermal stability than their Si and Ge homologues. The nitrogen content of the adducts of up to 44 % exceed any SnIV compound known hitherto

Automatisierte Fehlerdetektierung in der Halbleiter-Waferproduktion mittels maschinellen Lernens

Die vorliegende wissenschaftliche Arbeit beschäftigt sich mit der Anwendung von maschinellem Lernen auf einen Waferdatensatz. Nach einer Einführung in Wafer und deren Defektbildung sowie einer Erklärung der Grundlagen des maschinellen Lernens und insbesondere des überwachten Lernens mit Hilfe von einem Convolutional Neural Network (CNN), wird der Datensatz analysiert, und es werden die verschiedenen Waferdefekte beschrieben. Der Datensatz wird für das maschinelle Lernen verwendet, und sowohl das CNN als auch dasWavelet Scattering Transformation (WST )-Modell erreichen eine hohe Genauigkeit von 96% bzw. 97%. Besonders hervorgehoben wird die höhere durchschnittliche Genauigkeit des WST -Modell im Vergleich zu den Ergebnissen des Papers, aus dem der Datensatz stammt

Automated tight Lyapunov analysis for first-order methods

We present a methodology for establishing the existence of quadratic Lyapunov inequalities for a wide range of first-order methods used to solve convex optimization problems. In particular, we consider i) classes of optimization problems of finite-sum form with (possibly strongly) convex and possibly smooth functional components, ii) first-order methods that can be written as a linear system on state-space form in feedback interconnection with the subdifferentials of the functional components of the objective function, and iii) quadratic Lyapunov inequalities that can be used to draw convergence conclusions. We provide a necessary and sufficient condition for the existence of a quadratic Lyapunov inequality that amounts to solving a small-sized semidefinite program. We showcase our methodology on several first-order methods that fit the framework. Most notably, our methodology allows us to significantly extend the region of parameter choices that allow for duality gap convergence in the Chambolle-Pock method when the linear operator is the identity mapping

Circuit Analysis using Monotone+Skew Splitting

It is shown that the behavior of an $m$-port circuit of maximal monotone elements can be expressed as a zero of the sum of a maximal monotone operator containing the circuit elements, and a structured skew-symmetric linear operator representing the interconnection structure, together with a linear output transformation. The Condat-V\~u algorithm solves inclusion problems of this form, and may be used to solve for the periodic steady-state behavior, given a periodic excitation at each port, using an iteration in the space of periodic trajectories.Comment: Submitted to the 2023 European Control Conferenc

Acremolin, a stable natural product with an antiaromatic 1H-azirine moiety? A structural reorientation

Recently, acremolin (4), a novel modified base, was isolated from a marine-derived fungus and claimed to possess a structure with a 1H-azirine moiety. It is shown now that the reported NMR data are not compatible with this antiaromatic heterocycle, which should be an extremely unstable compound. An isomeric, substituted N2,3-ethenoguanine is presented as a plausible alternative structure of acremolin that is consistent with all spectroscopic data. Thus, 1H-azirines keep their classification as very short-lived intermediates