Controlling Complex Langevin simulations of lattice models by boundary term analysis

One reason for the well known fact that the Complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit has been identified long ago: it is insufficient decay of the probability density either near infinity or near poles of the drift, leading to boundary terms that spoil the formal argument for correctness. To gain a deeper understanding of this phenomenon, in a previous paper we have studied the emergence of such boundary terms thoroughly in a simple model, where analytic results can be compared with numerics. Here we continue this type of analysis for more physically interesting models, focusing on the boundaries at infinity. We start with abelian and non-abelian one-plaquette models, then we proceed to a Polyakov chain model and finally to high density QCD (HDQCD) and the 3D XY model. We show that the direct estimation of the systematic error of the CL method using boundary terms is in principle possible.Comment: 17 pages, 11 figure

Regularization of Linear Ill-posed Problems by the Augmented Lagrangian Method and Variational Inequalities

We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a standard source condition. Using the method of variational inequalities, we extend these results in this paper to convergence rates of lower order, both for the case of an a priori parameter choice and an a posteriori choice based on Morozov's discrepancy principle. In addition, our approach allows the derivation of convergence rates with respect to distance measures different from the Bregman distance. As a particular application, we consider sparsity promoting regularization, where we derive a range of convergence rates with respect to the norm under the assumption of restricted injectivity in conjunction with generalized source conditions of H\"older type

Convergence rates in expectation for Tikhonov-type regularization of Inverse Problems with Poisson data

In this paper we study a Tikhonov-type method for ill-posed nonlinear operator equations \gdag = F( ag) where \gdag is an integrable, non-negative function. We assume that data are drawn from a Poisson process with density t\gdag where $t>0$ may be interpreted as an exposure time. Such problems occur in many photonic imaging applications including positron emission tomography, confocal fluorescence microscopy, astronomic observations, and phase retrieval problems in optics. Our approach uses a Kullback-Leibler-type data fidelity functional and allows for general convex penalty terms. We prove convergence rates of the expectation of the reconstruction error under a variational source condition as $t\to\infty$ both for an a priori and for a Lepski{\u\i}-type parameter choice rule

CANVAS: case report on a novel repeat expansion disorder with late-onset ataxia

This article presents the case of a 74-year-old female patient who first developed a progressive disease with sensory neuropathy, cerebellar ataxia and bilateral vestibulopathy at the age of 60 years. The family history was unremarkable. Magnetic resonance imaging (MRI) showed atrophy of the cerebellum predominantly in the vermis and atrophy of the spinal cord. The patient was given the syndromic diagnosis of cerebellar ataxia, neuropathy, vestibular areflexia syndrome (CANVAS). In 2019 the underlying genetic cause of CANVAS was discovered to be an intronic repeat expansion in the RFC1 gene with autosomal recessive inheritance. The patient exhibited the full clinical picture of CANVAS and was tested positive for this repeat expansion on both alleles. The CANVAS is a relatively frequent cause of late-onset hereditary ataxia (estimated prevalence 5‑13/100,000). In contrast to the present patient, the full clinical picture is not always present. Therefore, testing for the RFC1 gene expansion is recommended in the work-up of patients with otherwise unexplained late-onset sporadic ataxia. As intronic repeat expansions cannot be identified by next generation sequencing methods, specific testing is necessary

Plasma-borne indicators of inflammasome activity in Parkinson’s disease patients

Parkinson’s disease (PD) is a neurodegenerative disorder characterized by motor and non-motor symptoms and loss of dopaminergic neurons of the substantia nigra. Inflammation and cell death are recognized aspects of PD suggesting that strategies to monitor and modify these processes may improve the management of the disease. Inflammasomes are pro-inflammatory intracellular pattern recognition complexes that couple these processes. The NLRP3 inflammasome responds to sterile triggers to initiate pro-inflammatory processes characterized by maturation of inflammatory cytokines, cytoplasmic membrane pore formation, vesicular shedding, and if unresolved, pyroptotic cell death. Histologic analysis of tissues from PD patients and individuals with nigral cell loss but no diagnosis of PD identified elevated expression of inflammasome-related proteins and activation-related “speck” formation in degenerating mesencephalic tissues compared with controls. Based on previous reports of circulating inflammasome proteins in patients suffering from heritable syndromes caused by hyper-activation of the NLRP3 inflammasome, we evaluated PD patient plasma for evidence of inflammasome activity. Multiple circulating inflammasome proteins were detected almost exclusively in extracellular vesicles indicative of ongoing inflammasome activation and pyroptosis. Analysis of plasma obtained from a multi-center cohort identified elevated plasma-borne NLRP3 associated with PD status. Our findings are consistent with others indicating inflammasome activity in neurodegenerative disorders. Findings suggest mesencephalic inflammasome protein expression as a histopathologic marker of early-stage nigral degeneration and suggest plasma-borne inflammasome-related proteins as a potentially useful class of biomarkers for patient stratification and the detection and monitoring of inflammation in PD

Sparse Regularization with lql^q Penalty Term

We consider the stable approximation of sparse solutions to non-linear operator equations by means of Tikhonov regularization with a subquadratic penalty term. Imposing certain assumptions, which for a linear operator are equivalent to the standard range condition, we derive the usual convergence rate $O(\sqrt{\delta})$ of the regularized solutions in dependence of the noise level $\delta$. Particular emphasis lies on the case, where the true solution is known to have a sparse representation in a given basis. In this case, if the differential of the operator satisfies a certain injectivity condition, we can show that the actual convergence rate improves up to $O(\delta)$.Comment: 15 page

A combined first and second order variational approach for image reconstruction

In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a non-smooth second order regulariser. It combines convex functions of the total variation and the total variation of the first derivatives. In what follows, we prove existence and uniqueness of minimisers of the combined model and present the numerical solution of the corresponding discretised problem by employing the split Bregman method. The paper is furnished with applications of our model to image denoising, deblurring as well as image inpainting. The obtained numerical results are compared with results obtained from total generalised variation (TGV), infimal convolution and Euler's elastica, three other state of the art higher-order models. The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images -- a known disadvantage of the ROF model -- while being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure

Single hadron response measurement and calorimeter jet energy scale uncertainty with the ATLAS detector at the LHC

The uncertainty on the calorimeter energy response to jets of particles is derived for the ATLAS experiment at the Large Hadron Collider (LHC). First, the calorimeter response to single isolated charged hadrons is measured and compared to the Monte Carlo simulation using proton-proton collisions at centre-of-mass energies of sqrt(s) = 900 GeV and 7 TeV collected during 2009 and 2010. Then, using the decay of K_s and Lambda particles, the calorimeter response to specific types of particles (positively and negatively charged pions, protons, and anti-protons) is measured and compared to the Monte Carlo predictions. Finally, the jet energy scale uncertainty is determined by propagating the response uncertainty for single charged and neutral particles to jets. The response uncertainty is 2-5% for central isolated hadrons and 1-3% for the final calorimeter jet energy scale.Comment: 24 pages plus author list (36 pages total), 23 figures, 1 table, submitted to European Physical Journal

Standalone vertex finding in the ATLAS muon spectrometer

A dedicated reconstruction algorithm to find decay vertices in the ATLAS muon spectrometer is presented. The algorithm searches the region just upstream of or inside the muon spectrometer volume for multi-particle vertices that originate from the decay of particles with long decay paths. The performance of the algorithm is evaluated using both a sample of simulated Higgs boson events, in which the Higgs boson decays to long-lived neutral particles that in turn decay to bbar b final states, and pp collision data at √s = 7 TeV collected with the ATLAS detector at the LHC during 2011