Effect of a Physical Phase Plate on Contrast Transfer in an Aberration-Corrected Transmission Electron Microscope

In this theoretical study we analyze contrast transfer of weak-phase objects in a transmission electron microscope, which is equipped with an aberration corrector (Cs-corrector) in the imaging lens system and a physical phase plate in the back focal plane of the objective lens. For a phase shift of pi/2 between scattered and unscattered electrons induced by a physical phase plate, the sine-type phase contrast transfer function is converted into a cosine-type function. Optimal imaging conditions could theoretically be achieved if the phase shifts caused by the objective lens defocus and lens aberrations would be equal zero. In reality this situation is difficult to realize because of residual aberrations and varying, non-zero local defocus values, which in general result from an uneven sample surface topography. We explore the conditions - i.e. range of Cs-values and defocus - for most favourable contrast transfer as a function of the information limit, which is only limited by the effect of partial coherence of the electron wave in Cs-corrected transmission electron microscopes. Under high-resolution operation conditions we find that a physical phase plate improves strongly low- and medium-resolution object contrast, while improving tolerance to defocus and Cs-variations, compared to a microscope without a phase plate

Fast parallel algorithms for a broad class of nonlinear variational diffusion approaches

Variational segmentation and nonlinear diffusion approaches have been very active research areas in the fields of image processing and computer vision during the last years. In the present paper, we review recent advances in the development of efficient numerical algorithms for these approaches. The performance of parallel implement at ions of these algorithms on general-purpose hardware is assessed. A mathematically clear connection between variational models and nonlinear diffusion filters is presented that allows to interpret one approach as an approximation of the other, and vice versa. Numerical results confirm that, depending on the parametrization, this approximation can be made quite accurate. Our results provide a perspective for uniform implement at ions of both nonlinear variational models and diffusion filters on parallel architectures

Modification of the carbide microstructure by N- and S-functionalization of the support in MoxC/CNT catalysts

A series of catalysts based on molybdenum carbide nanoparticles supported on carbon were prepared by carburization of an oxidic Mo precursor impregnated on differently treated multi-walled carbon nanotubes (CNTs) and reference carbons, respectively. The effects of surface defects and decoration of the support with heteroatoms (O, N, and S), as analyzed by IR and Raman spectroscopy as well as by TPD, were investigated. The catalysts were characterized by XRD, N2 physisorption, and electron microscopy. The catalytic performance in steam reforming of methanol was used as a probe to indicate changes in the catalyst surface during catalytic action. The surface chemistry of the carbon supports influences the process of carburization and the nature of resulting supported MoxC (nano) particles. This includes crystal phase composition (α- and β-MoxC) and crystallite as well as particle diameter. However, if the surface decoration of the support is limited to oxygen groups, these differences are not reflected in the catalytic action, which is almost identical for oxygen functionalized carriers. A significant modification of the catalytic performance can only be achieved by surface modification of a CNT support with S- or N-containing functionalities, which causes changes in the lattice constant of the resulting carbide compared to reference systems. These changes are sensitivily reflected in activity and CO2/CH4 product ratio in steam reforming of methanol

Computing Topology Preservation of RBF Transformations for Landmark-Based Image Registration

In image registration, a proper transformation should be topology preserving. Especially for landmark-based image registration, if the displacement of one landmark is larger enough than those of neighbourhood landmarks, topology violation will be occurred. This paper aim to analyse the topology preservation of some Radial Basis Functions (RBFs) which are used to model deformations in image registration. Mat\'{e}rn functions are quite common in the statistic literature (see, e.g. \cite{Matern86,Stein99}). In this paper, we use them to solve the landmark-based image registration problem. We present the topology preservation properties of RBFs in one landmark and four landmarks model respectively. Numerical results of three kinds of Mat\'{e}rn transformations are compared with results of Gaussian, Wendland's, and Wu's functions

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

Calcium sensor kinase activates potassium uptake systems in gland cells of Venus flytraps

The Darwin plant Dionaea muscipula is able to grow on mineral-poor soil, because it gains essential nutrients from captured animal prey. Given that no nutrients remain in the trap when it opens after the consumption of an animal meal, we here asked the question of how Dionaea sequesters prey-derived potassium. We show that prey capture triggers expression of a K+ uptake system in the Venus flytrap. In search of K+ transporters endowed with adequate properties for this role, we screened a Dionaea expressed sequence tag (EST) database and identified DmKT1 and DmHAK5 as candidates. On insect and touch hormone stimulation, the number of transcripts of these transporters increased in flytraps. After cRNA injection of K+-transporter genes into Xenopus oocytes, however, both putative K+ transporters remained silent. Assuming that calcium sensor kinases are regulating Arabidopsis K+ transporter 1 (AKT1), we coexpressed the putative K+ transporters with a large set of kinases and identified the CBL9-CIPK23 pair as the major activating complex for both transporters in Dionaea K+ uptake. DmKT1 was found to be a K+-selective channel of voltage-dependent high capacity and low affinity, whereas DmHAK5 was identified as the first, to our knowledge, proton-driven, high-affinity potassium transporter with weak selectivity. When the Venus flytrap is processing its prey, the gland cell membrane potential is maintained around -120 mV, and the apoplast is acidified to pH 3. These conditions in the green stomach formed by the closed flytrap allow DmKT1 and DmHAK5 to acquire prey-derived K+, reducing its concentration from millimolar levels down to trace levels

Necessary conditions for variational regularization schemes

We study variational regularization methods in a general framework, more precisely those methods that use a discrepancy and a regularization functional. While several sets of sufficient conditions are known to obtain a regularization method, we start with an investigation of the converse question: How could necessary conditions for a variational method to provide a regularization method look like? To this end, we formalize the notion of a variational scheme and start with comparison of three different instances of variational methods. Then we focus on the data space model and investigate the role and interplay of the topological structure, the convergence notion and the discrepancy functional. Especially, we deduce necessary conditions for the discrepancy functional to fulfill usual continuity assumptions. The results are applied to discrepancy functionals given by Bregman distances and especially to the Kullback-Leibler divergence.Comment: To appear in Inverse Problem

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

Parkinson's disease biomarkers: perspective from the NINDS Parkinson's Disease Biomarkers Program

Biomarkers for Parkinson's disease (PD) diagnosis, prognostication and clinical trial cohort selection are an urgent need. While many promising markers have been discovered through the National Institute of Neurological Disorders and Stroke Parkinson's Disease Biomarker Program (PDBP) and other mechanisms, no single PD marker or set of markers are ready for clinical use. Here we discuss the current state of biomarker discovery for platforms relevant to PDBP. We discuss the role of the PDBP in PD biomarker identification and present guidelines to facilitate their development. These guidelines include: harmonizing procedures for biofluid acquisition and clinical assessments, replication of the most promising biomarkers, support and encouragement of publications that report negative findings, longitudinal follow-up of current cohorts including the PDBP, testing of wearable technologies to capture readouts between study visits and development of recently diagnosed (de novo) cohorts to foster identification of the earliest markers of disease onset

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