Anisotropic Diffusion Stencils: From Simple Derivations over Stability Estimates to ResNet Implementations

Anisotropic diffusion processes with a diffusion tensor are important in image analysis, physics, and engineering. However, their numerical approximation has a strong impact on dissipative artefacts and deviations from rotation invariance. In this work, we study a large family of finite difference discretisations on a 3 x 3 stencil. We derive it by splitting 2-D anisotropic diffusion into four 1-D diffusions. The resulting stencil class involves one free parameter and covers a wide range of existing discretisations. It comprises the full stencil family of Weickert et al. (2013) and shows that their two parameters contain redundancy. Furthermore, we establish a bound on the spectral norm of the matrix corresponding to the stencil. This gives time step size limits that guarantee stability of an explicit scheme in the Euclidean norm. Our directional splitting also allows a very natural translation of the explicit scheme into ResNet blocks. Employing neural network libraries enables simple and highly efficient parallel implementations on GPUs

CNN-based Euler's Elastica Inpainting with Deep Energy and Deep Image Prior

Euler's elastica constitute an appealing variational image inpainting model. It minimises an energy that involves the total variation as well as the level line curvature. These components are transparent and make it attractive for shape completion tasks. However, its gradient flow is a singular, anisotropic, and nonlinear PDE of fourth order, which is numerically challenging: It is difficult to find efficient algorithms that offer sharp edges and good rotation invariance. As a remedy, we design the first neural algorithm that simulates inpainting with Euler's Elastica. We use the deep energy concept which employs the variational energy as neural network loss. Furthermore, we pair it with a deep image prior where the network architecture itself acts as a prior. This yields better inpaintings by steering the optimisation trajectory closer to the desired solution. Our results are qualitatively on par with state-of-the-art algorithms on elastica-based shape completion. They combine good rotation invariance with sharp edges. Moreover, we benefit from the high efficiency and effortless parallelisation within a neural framework. Our neural elastica approach only requires 3x3 central difference stencils. It is thus much simpler than other well-performing algorithms for elastica inpainting. Last but not least, it is unsupervised as it requires no ground truth training data.Comment: In Proceedings of the 10th European Workshop on Visual Information Processing, Lisbon, 202

Deep spatial and tonal data optimisation for homogeneous diffusion inpainting

Difusion-based inpainting can reconstruct missing image areas with high quality from sparse data, provided that their location and their values are well optimised. This is particularly useful for applications such as image compression, where the original image is known. Selecting the known data constitutes a challenging optimisation problem, that has so far been only investigated with model-based approaches. So far, these methods require a choice between either high quality or high speed since qualitatively convincing algorithms rely on many time-consuming inpaintings. We propose the frst neural network architecture that allows fast optimisation of pixel positions and pixel values for homogeneous difusion inpainting. During training, we combine two optimisation networks with a neural network-based surrogate solver for difusion inpainting. This novel concept allows us to perform backpropagation based on inpainting results that approximate the solution of the inpainting equation. Without the need for a single inpainting during test time, our deep optimisation accelerates data selection by more than four orders of magnitude compared to common model-based approaches. This provides real-time performance with high quality results

A demonstrator for the Micro-Vertex-Detector of the CBM experiment

CMOS sensors are the most promising candidates for the Micro-Vertex-Detector (MVD) of the CBM experiment at GSI, as they provide an unprecedented compromise between spatial resolution, low material budget, adequate radiation tolerance and readout speed. To study the integration of these sensors into a detector module, a so-called MVD-demonstrator has been developed. The demonstrator and its in-beam performance will be presented and discussed in this work

Connections Between Numerical Algorithms for PDEs and Neural Networks

We investigate numerous structural connections between numerical algorithms for partial differential equations (PDEs) and neural architectures. Our goal is to transfer the rich set of mathematical foundations from the world of PDEs to neural networks. Besides structural insights, we provide concrete examples and experimental evaluations of the resulting architectures. Using the example of generalised nonlinear diffusion in 1D, we consider explicit schemes, acceleration strategies thereof, implicit schemes, and multigrid approaches. We connect these concepts to residual networks, recurrent neural networks, and U-net architectures. Our findings inspire a symmetric residual network design with provable stability guarantees and justify the effectiveness of skip connections in neural networks from a numerical perspective. Moreover, we present U-net architectures that implement multigrid techniques for learning efficient solutions of partial differential equation models, and motivate uncommon design choices such as trainable nonmonotone activation functions. Experimental evaluations show that the proposed architectures save half of the trainable parameters and can thus outperform standard ones with the same model complexity. Our considerations serve as a basis for explaining the success of popular neural architectures and provide a blueprint for developing new mathematically well-founded neural building blocks

Effects of endothelin on hemodynamics, prostaglandins, blood coagulation and renal function

Effects of endothelin on hemodynamics, prostaglandins, blood coagulation and renal function. The interaction of the endogenous vasoconstrictors endothelin (ET), angiotensin II (Ang II) and catecholamines with the kallikrein-kinin-, prostaglandin and renin-aldosterone systems in the pathogenesis of acute renal failure (ARF) is still to be defined. In 18 anesthesized pigs the influence of i.v. bolus applications of ET (2 µg/kg), Ang II (10 µg/kg) and norepinephrine (NE; 20 µg/kg) on hemodynamics, plasmatic coagulation and fibrinolysis system, prostaglandins and renal function was studied. ET induced a biphasic change in blood pressure, starting with an initial short-lasting reduction followed by a long-lasting elevation of systolic and diastolic blood pressure. Endothelin bolus resulted in a significant increase of 6-keto-PGF1α, PGE2 and TXB2 plasma levels (P < 0.05 against preinjection values), whereas prostaglandins remained unchanged in the Ang II and NE groups. There was a distinct correlation between the plasma ET and 6-keto-PGF1α levels (r = 0.82). In contrast to Ang II or NE, ET induced a shortening of the activated partial thromboplastin time (aPTT) and increase of antithrombin III levels (ATIII), fibrin monomers (FM), prekallikrein (PKK) and factor VIII activity at the beginning. Finally a pronounced decrease of ATIII, FM and PKK occurred, indicating a consumptive coagulopathy. At the end of the experiment, elevated plasma renin activity and pCO2, significantly decreased creatinine clearance, blood pH, pO2, base excess, HCO3-, oxygen saturation (P < 0.01), a distinct glomerular proteinuria, and a final anuria were observated. These results reveal that ET activates the plasmatic coagulation system and induces an ARF accompanied by impairment of pulmonary function. Its coagulation activating and renal vasoconstrictive effects may be important pathophysiological factors, especially when the counteractive release of vasodilatator and antiaggregatory prostacyclin or NO is impaired

Advanced Nanophotonics: Silicon-Organic Hybrid Technology

Integrated photonic devices have gained increasing research interests. Especially silicon photonics have become very attractive for various optical applications. Using silicon-on-insulator as a material platform provides the ability to fabricate photonic devices with electronic devices on a single chip. Driven by substantial research investments, the integration of photonic devices on silicon-on-insulator substrates has reached a degree of maturity that already permits industrial adoption. However, silicon has the disadvantage of linear electro-optical effects, and, therefore, advanced modulation formats are difficult to realize when using silicon-based high-speed modulators. Hence, a new approach was proposed: the silicon-organic hybrid technology. This technology is a viable extension of the silicon-on-insulator material system for efficient high-speed modulation. We herewith present our theoretical and experimental investigations of the silicon-organic hybrid slot-waveguide ring resonator. The advanced device design is described in detail, which allows using both, the efficient silicon-on-insulator strip-waveguides and the silicon-organic hybrid slot-waveguides in single ring resonator. For the first time, we report the transmission spectra of such a resonator covered with an electro-optical polymer.Integrierte photonische Bauelemente werden in der Forschung immer bedeutender. Besonders die Siliziumphotonik ist für verschiedene optische Anwendungen sehr attraktiv. Die Verwendung von Silizium-auf-Isolator-Materialsystemen bietet die Möglichkeit, photonische Bauelemente mit elektronischen Geräten auf einem einzelnen Chip zu entwickeln. Durch erhebliche Forschungsinvestitionen hat die photonische Integration auf Silizium-auf-Isolator-Substraten einen Reifegrad, der bereits Industriemaßstäben genügt. Jedoch hat Silizium keinen linearen elektrooptischen Effekt und damit sind moderne Modulationsformate nur schwierig zu realisieren. Daher wird seit eingen Jahren ein neuer Ansatz, die Silizium-Organik Hybridtechnologie, verfolgt. Diese Technologie ist eine tragfähige Ausdehnung des Silizium-auf-Isolator-Materialsystems für eine effiziente Hochgeschwindigkeitsmodulation und optische Signalverarbeitung. In diesem Artikel präsentieren wir unsere theoretischen und experimentellen Untersuchungen zu einem Silizium-Organik Hybrid Ringresonator. Das Design und die Herstellung des neuartigen nanophotonischen Bauelements werden im Detail beschrieben. Der demonstrierte Ringresonator kombiniert die Vorteile zweier verschiedener Wellenleiterarten in einem einzelnen Ring, dem verlustarmen Kanal-Wellenleiter und dem Silizium-organischen Hybridschlitzwellenleiter. Wir demonstrieren erstmals ein Transmissionsspektrum eines solchen Ringresonators, der mit einem elektro-optischen Polymer beschichtet ist

First-line antihypertensive treatment in patients with pre-diabetes: Rationale, design and baseline results of the ADaPT investigation

<p>Abstract</p> <p>Background</p> <p>Recent clinical trials reported conflicting results on the reduction of new-onset diabetes using RAS blocking agents. Therefore the role of these agents in preventing diabetes is still not well defined. Ramipril is an ACE inhibitor (ACEi), that has been shown to reduce cardiovascular events in high risk patients and post-hoc analyses of the HOPE trial have provided evidence for its beneficial action in the prevention of diabetes.</p> <p>Methods</p> <p>The ADaPT investigation ("ACE inhibitor-based versus diuretic-based antihypertensive primary treatment in patients with pre-diabetes") is a 4-year open, prospective, parallel group phase IV study. It compares an antihypertensive treatment regimen based on ramipril versus a treatment based on diuretics or betablockers. The primary evaluation criterion is the first manifestation of type 2 diabetes. The study is conducted in primary care to allow the broadest possible application of its results. The present article provides an outline of the rationale, the design and baseline characteristics of AdaPT and compares these to previous studies including ASCOT-BLPA, VALUE and DREAM.</p> <p>Results</p> <p>Until March 2006 a total of 2,015 patients in 150 general practices (general physicians and internists) throughout Germany were enrolled. The average age of patients enrolled was 67.1 ± 10.3 years, with 47% being male and a BMI of 29.9 ± 5.0 kg/m². Dyslipidemia was present in 56.5%. 37.8% reported a family history of diabetes, 57.8% were previously diagnosed with hypertension (usually long standing). The HbA1c value at baseline was 5.6 %. Compared to the DREAM study patients were older, had more frequently hypertension and patients with cardiovascular disease were not excluded.</p> <p>Conclusion</p> <p>Comparing the ADaPT design and baseline data to previous randomized controlled trial it can be acknowledged that AdaPT included patients with a high risk for diabetes development. Results are expected to be available in 2010. Data will be highly valuable for clinical practice due to the observational study design.</p

Ramipril-based versus diuretic-based antihypertensive primary treatment in patients with pre-diabetes (ADaPT) study

<p>Abstract</p> <p>Background</p> <p>Previous randomized controlled trials demonstrated a protective effect of renin angiotensin system blocking agents for the development of type-2 diabetes in patients with pre-diabetes. However, there are no real-world data available to illustrate the relevance for clinical practice.</p> <p>Methods</p> <p>Open, prospective, parallel group study comparing patients with an ACE inhibitor versus a diuretic based treatment. The principal aim was to document the first manifestation of type-2 diabetes in either group.</p> <p>Results</p> <p>A total of 2,011 patients were enrolled (mean age 69.1 ± 10.3 years; 51.6% female). 1,507 patients were available for the per-protocol analysis (1,029 ramipril, 478 diuretic group). New-onset diabetes was less frequent in the ramipril than in the diuretic group over 4 years. Differences were statistically different at a median duration of 3 years (24.4% vs 29.5%; p < 0.05). Both treatments were equally effective in reducing BP (14.7 ± 18.0/8.5 ± 8.2 mmHg and 12.7 ± 18.1/7.0 ± 8.3 mmHg) at the 4 year follow-up (p < 0.001 vs. baseline; p = n.s. between groups). In 38.6% and 39.7% of patients BP was below 130/80 mmHg (median time-to-target 3 months). There was a significant reduction of cardiovascular morbidity and mortality in favour of ramipril (p = 0.033). No significant differences were found for a change in HbA1c as well as for fasting blood glucose levels during follow-up. The rate of adverse events was higher in diuretic treated patients (SAE 15.4 vs. 12.4%; p < 0.05; AE 26.6 vs. 25.6%; p = n.s).</p> <p>Conclusions</p> <p>Ramipril treatment is preferable over diuretic based treatment regimens for the treatment of hypertension in pre-diabetic patients, because new-onset diabetes is delayed.</p