Image inpainting based on coherence transport with adapted distance functions

We discuss an extension of our method Image Inpainting Based on Coherence Transport. For the latter method the pixels of the inpainting domain have to be serialized into an ordered list. Up till now, to induce the serialization we have used the distance to boundary map. But there are inpainting problems where the distance to boundary serialization causes unsatisfactory inpainting results. In the present work we demonstrate cases where we can resolve the difficulties by employing other distance functions which better suit the problem at hand

A well-posedness framework for inpainting based on coherence transport

Image inpainting is the process of touching-up damaged or unwanted portions of a picture and is an important task in image processing. For this purpose Bornemann and März [J. Math. Imaging Vis. , 28 (2007), pp. 259– 278] introduced a very efficient method called Image Inpainting Based on Coherence Transport which fills the missing region by advecting the image information along integral curves of a coherence vector field from the boundary towards the interior of the hole. The mathematical model behind this method is a first-order functional advection PDE posed on a compact domain with all inflow boundary. We show that this problem is well-posed under certain conditions

Calculus on surfaces with general closest point functions

The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface differentials of a surface function can be replaced with Cartesian differentials of its closest point extension, i.e., its composition with a closest point function. We introduce a general class of these closest point functions (a subset of differentiable retractions), show that these are exactly the functions necessary to satisfy the above idea, and give a geometric characterization this class. Finally, we construct some closest point functions and demonstrate their effectiveness numerically on surface PDEs

An embedding technique for the solution of reaction-fiffusion equations on algebraic surfaces with isolated singularities

In this paper we construct a parametrization-free embedding technique for numerically evolving reaction-diffusion PDEs defined on algebraic curves that possess an isolated singularity. In our approach, we first desingularize the curve by appealing to techniques from algebraic geometry.\ud We create a family of smooth curves in higher dimensional space that correspond to the original curve by projection. Following this, we pose the analogous reaction-diffusion PDE on each member of this family and show that the solutions (their projection onto the original domain) approximate the solution of the original problem. Finally, we compute these approximants numerically by applying the Closest Point Method which is an embedding technique for solving PDEs on smooth surfaces of arbitrary dimension or codimension, and is thus suitable for our situation. In addition, we discuss the potential to generalize the techniques presented for higher-dimensional surfaces with multiple singularities

The Secret ‘After Life’ of Foraminifera: Big Things Out of Small

Calcareous and siliceous microorganisms are common components of mudrocks, and can be important in terms of stratigraphy and environmental interpretation. In addition, such microorganisms can have a significant ‘after life’, through post-mortem alteration, and represent a potential source of additional information about the diagenetic and deformation history of the rock unit. Some examples of the latter are illustrated in this study from foraminifera within a Cretaceous black shale of Colombia. This includes foraminifera tests acting as understudied repositories of authigenic calcite cement, and of elements such as Ba, Zn, Fe and S through the formation of baryte, sphalerite and iron sulphides (pyrite, marcasite). Such repositories, within the body chambers of foraminiferal tests, can provide important windows into the diagenetic processes within mudstones. If calcite cement is not recognised or separated from biogenic calcite, the depositional calcite budget can be easily overestimated, skewing the application of mudrock classification schemes, and affecting environmental interpretation including that of productivity. The elements Ba, Zn and Fe (often in ratio with Al) are commonly utilised as geochemical proxies of environmental parameters (productivity, bottom water redox conditions, etc.). Therefore, the presence of significant amounts of baryte, sphalerite and pyrite-marcasite (within foraminifera) should be noted and their origins (source and timing) investigated based on their spatial relationships before making environmental deductions based on geochemical analysis alone. Additionally, commonly observed marginal shell damage of many of the observed foraminifera is reported. We interpret this damage, for the first time, as an indicator of lateral dissolution, brought about by horizontal foreshortening during orogenesis. This is also supported by the occurrence of microscale anastomosing horizontal to inclined baryte-filled fractures within the mudstone matrix

Insights into the Electronic Structure of a U(IV) Amido and U(V) Imido Complex

Reaction of the N-heterocylic carbene ligand $^{i}$PrIm (L$^{1}$) and lithium bis(trimethylsilyl)amide (TMSA) as a base with UCl$_{4}$ resulted in U(IV) and U(V) complexes. Uranium\u27s +V oxidation state in (HL$^{1}$)$_{2}$[U(V)(TMSI)Cl$_{5}$] (TMSI=trimethylsilylimido) (2) was confirmed by HERFD-XANES measurements. Solid state characterization by SC-XRD and geometry optimisation of [U(IV)(L$^{1}$)$_{2}$(TMSA)Cl$_{3}$] (1) indicated a silylamido ligand mediated inverse trans influence (ITI). The ITI was examined regarding different metal oxidation states and was compared to transition metal analogues by theoretical calculations

Measuring lung mechanics of expiratory tidal breathing with non-invasive breath occlusion

Background and objective: Lung mechanics measurements provide clinically useful information about disease progression and lung health. Currently, there are no commonly practiced methods to non-invasively measure both resistive and elastic lung mechanics during tidal breathing, preventing the important information provided by lung mechanics from being utilised. This study presents a novel method to easily assess lung mechanics of spontaneously breathing subjects using a dynamic elastance, single-compartment lung model. Methods: A spirometer with a built-in shutter was used to occlude expiration during tidal breathing, creating exponentially decaying flow when the shutter re-opened. The lung mechanics measured were respiratory system elastance and resistance, separated from the exponentially decaying flow, and interrupter resistance calculated at shutter closure. Progressively increasing resistance was added to the spirometer mouthpiece to simulate upper airway obstruction. The lung mechanics of 17 healthy subjects were successfully measured through spirometry. Results: N = 17 (8 female, 9 male) healthy subjects were recruited. Measured decay rates ranged from 5 to 42/s, subjects with large variation of decay rates showed higher muscular breathing effort. Lung elastance measurements ranged from 3.9 to 21.2 cmH -2 2 O/L, with no clear trend between change in elastance and added resistance. Resistance calculated from decay rate and elastance ranged from 0.15 to 1.95 cmH -2 2 Os/L. These very small resistance values are due to the airflow measured originating from low-resistance areas in the centre of airways. Occlusion resistance measurements were as expected for healthy subjects, and increased as expected as resistance was added. Conclusions: This test was able to identify reasonable dynamic lung elastance and occlusion resistance values, providing new insight into expiratory breathing effort. Clinically, this lung function test could impact current practice. It does not require high levels of cooperation from the subject, allowing a wider cohort of patients to be assessed more easily. Additionally, this test can be simply implemented in a small standalone device, or with standard lung function testing equipment

Unmet needs in the diagnosis and treatment of dyslipidemia in the primary care setting in Germany

Objectives and methods: DETECT is a cross-sectional study of 55,518 unselected consecutive patients in 3188 representative primary care offices in Germany. In a random subset of 7519 patients, an extensive standardized laboratory program was undertaken. The study investigated the prevalence of cardiovascular disease, known risk factors (such as diabetes, hypertension and dyslipidemia and their co-morbid manifestation), as well as treatment patterns. The present analysis of the DETECT laboratory dataset focused on the prevalence and treatment of dyslipidemia in primary medical care in Germany. Coronary artery disease (CAD), risk categories and LDL-C target achievement rates were determined in the subset of 6815 patients according to the National Cholesterol Education Program (NCEP) ATP III Guidelines. Results: Of all patients, 54.3% had dyslipidemia. Only 54.4% of the NCEP-classified dyslipidemic patients were diagnosed as ‘dyslipidemic’ by their physicians. Only 27% of all dyslipidemic patients (and 40.7% of the recognized dyslipidemic patients) were treated with lipid-lowering medications, and 11.1% of all dyslipidemic patients (41.4% of the patients treated with lipid-lowering drugs) achieved their LDL-C treatment goals. In conclusion, 80.3% of patients in the sample with dyslipidemia went undiagnosed, un-treated or under-treated

The role of red yeast rice (RYR) supplementation in plasma cholesterol control: a review and expert opinion

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