When are Neural ODE Solutions Proper ODEs?

A key appeal of the recently proposed Neural Ordinary Differential Equation(ODE) framework is that it seems to provide a continuous-time extension of discrete residual neural networks. As we show herein, though, trained Neural ODE models actually depend on the specific numerical method used during training. If the trained model is supposed to be a flow generated from an ODE, it should be possible to choose another numerical solver with equal or smaller numerical error without loss of performance. We observe that if training relies on a solver with overly coarse discretization, then testing with another solver of equal or smaller numerical error results in a sharp drop in accuracy. In such cases, the combination of vector field and numerical method cannot be interpreted as a flow generated from an ODE, which arguably poses a fatal breakdown of the Neural ODE concept. We observe, however, that there exists a critical step size beyond which the training yields a valid ODE vector field. We propose a method that monitors the behavior of the ODE solver during training to adapt its step size, aiming to ensure a valid ODE without unnecessarily increasing computational cost. We verify this adaption algorithm on two common bench mark datasets as well as a synthetic dataset. Furthermore, we introduce a novel synthetic dataset in which the underlying ODE directly generates a classification task

Kosten der Erreichung von Umweltqualitätszielen in ausgewählten Regionen durch Umstellung auf Ökologischen Landbau im Vergleich zu anderen Agrarumweltmaßnahmen unter besonderer Berücksichtigung von Administrations- und Kontrollkosten

Der vorliegende Forschungsbericht untersucht für die Bundesrepublik Deutschland die Hypothese, dass der Ökologische Landbau aus Sicht der Transaktionskosten eine vorteilhafte Politikoption zur Erreichung agrarumweltpolitischer Ziele darstellt, da durch ihn einzelne Teilaspekte der umweltgerechten Bewirtschaftung gebündelt implementiert werden. Im Rahmen von insgesamt 74 Interviews (teilweise in Form von Fokusgruppen) und zwei regionalen Validierungsworkshops wurden die Aufwendungen, die im Zusammenhang mit der Administration und Kontrolle von Agrarumweltprogrammen auf Seiten des Staates und der Landwirte entstehen, für zwei Fallstudienregionen (Baden-Württemberg, Thüringen) ermittelt. Es wurde ein systematisches Konzept zur Erfassung von Transaktionskosten entwickelt, das die Charakteristika des Ökologischen Landbaus berücksichtigt. Es konnte festgestellt werden, dass die Transaktionskosten mit der Zahl der Maßnahmen je Betrieb ansteigen, vor allem dann, wenn es sich dabei um flächenspezifische Einzelmaßnahmen handelt, die auf die Fläche kumuliert werden können. Der Ökologische Landbau als gesamtbetriebliche Maßnahme ist aus der Sicht der Agrarverwaltung eine transaktionskostensparende Alternative. Auch andere betriebszweigbezogene Maßnahmen, wie z.B. der "kontrolliert-integrierte Ackerbau" in Thüringen, sind gegenüber Einzelmaßnahmen kostensparend. Aus der Sicht der Landwirte verliert der Ökologische Landbau seine Transaktionskostenvorteile, wenn die 100%-Kontrollen gegenüber den 5%-Kontrollen bei anderen Agrarumweltmaßnahmen und der höhere Vermarktungsaufwand berücksichtigt werden. Diesen Kosten stehen nur bei einigen Betrieben höhere Einnahmen durch höhere Produktpreise gegenüber. Wird der Ökologische Landbau als umweltpolitisches Instrument eingesetzt und ist eine gesonderte Vermarktung der Produkte zu höheren Preisen nicht möglich, stellt sich die Frage, ob eine 100%-Kontrolle notwendig und sinnvoll ist. Grundsätzlich gilt, dass eine hohe Akzeptanz der Agrarumweltprogramme nur mit einem Angebot an Maßnahmen zu erreichen ist, das die Präferenzen der Akteure vor Ort berücksichtigt

Ist der Ökologische Landbau ein transaktionskosteneffizientes Instrument zur Erreichung von Umweltqualitätszielen?

This paper presents the results of a transaction cost study on organic farming in the frame of the Federal Organic Farming Programme of Germany (Bundesprogramm Ökologischer Landbau). It investigates the hypothesis that organic farming represents a transaction cost reducing policy option to achieve agri-environmental objectives. It does so by comparing organic farming with a bundle of single measures that achieves nearly similar agri-environmental quality targets. In two case studies (Thuringia and Baden-Wuerttemberg), administration and control costs are measured from the state's and the farmers’ perspective. The study reveals that transaction costs increase with the number of single measures. From the viewpoint of agricultural administration, organic farming proved to be a policy option that saves transaction costs compared to single measures. For the farmers, organic farming loses its transaction cost advantages when the costs for 100-percent controls are taken into account, instead of 5-percent controls as practiced for other agri-environmental measures

Bayesian Numerical Integration with Neural Networks

Bayesian probabilistic numerical methods for numerical integration offer significant advantages over their non-Bayesian counterparts: they can encode prior information about the integrand, and can quantify uncertainty over estimates of an integral. However, the most popular algorithm in this class, Bayesian quadrature, is based on Gaussian process models and is therefore associated with a high computational cost. To improve scalability, we propose an alternative approach based on Bayesian neural networks which we call Bayesian Stein networks. The key ingredients are a neural network architecture based on Stein operators, and an approximation of the Bayesian posterior based on the Laplace approximation. We show that this leads to orders of magnitude speed-ups on the popular Genz functions benchmark, and on challenging problems arising in the Bayesian analysis of dynamical systems, and the prediction of energy production for a large-scale wind farm

Interdisciplinary Approaches to Deal with Alzheimer’s Disease : From Bench to Bedside: What Feasible Options Do Already Exist Today?

Alzheimer’s disease is one of the most common neurodegenerative diseases in the western population. The incidence of this disease increases with age. Rising life expectancy and the resulting increase in the ratio of elderly in the population are likely to exacerbate socioeconomic problems. Alzheimer’s disease is a multifactorial disease. In addition to amyloidogenic processing leading to plaques, and tau pathology, but also other molecular causes such as oxidative stress or inflammation play a crucial role. We summarize the molecular mechanisms leading to Alzheimer’s disease and which potential interventions are known to interfere with these mechanisms, focusing on nutritional approaches and physical activity but also the beneficial effects of cognition-oriented treatments with a focus on language and communication. Interestingly, recent findings also suggest a causal link between oral conditions, such as periodontitis or edentulism, and Alzheimer’s disease, raising the question of whether dental intervention in Alzheimer’s patients can be beneficial as well. Unfortunately, all previous single-domain interventions have been shown to have limited benefit to patients. However, the latest studies indicate that combining these efforts into multidomain approaches may have increased preventive or therapeutic potential. Therefore, as another emphasis in this review, we provide an overview of current literature dealing with studies combining the above-mentioned approaches and discuss potential advantages compared to monotherapies. Considering current literature and intervention options, we also propose a multidomain interdisciplinary approach for the treatment of Alzheimer’s disease patients that synergistically links the individual approaches. In conclusion, this review highlights the need to combine different approaches in an interdisciplinary manner, to address the future challenges of Alzheimer’s disease

Combining Slow and Fast: Complementary Filtering for Dynamics Learning

Modeling an unknown dynamical system is crucial in order to predict the future behavior of the system. A standard approach is training recurrent models on measurement data. While these models typically provide exact short-term predictions, accumulating errors yield deteriorated long-term behavior. In contrast, models with reliable long-term predictions can often be obtained, either by training a robust but less detailed model, or by leveraging physics-based simulations. In both cases, inaccuracies in the models yield a lack of short-time details. Thus, different models with contrastive properties on different time horizons are available. This observation immediately raises the question: Can we obtain predictions that combine the best of both worlds? Inspired by sensor fusion tasks, we interpret the problem in the frequency domain and leverage classical methods from signal processing, in particular complementary filters. This filtering technique combines two signals by applying a high-pass filter to one signal, and low-pass filtering the other. Essentially, the high-pass filter extracts high-frequencies, whereas the low-pass filter extracts low frequencies. Applying this concept to dynamics model learning enables the construction of models that yield accurate long- and short-term predictions. Here, we propose two methods, one being purely learning-based and the other one being a hybrid model that requires an additional physics-based simulator

Draft genome sequence of Bacillus anthracis BF-1, Isolated from Bavarian cattle

Antwerpen M, Proença DN, Rückert C, et al. Draft genome sequence of Bacillus anthracis BF-1, Isolated from Bavarian cattle. Journal of bacteriology. 2012;194(22):6360-6361.Bacillus anthracis BF-1 was isolated from a cow in Bavaria (Germany) that had succumbed to anthrax. Here, we report the draft genome sequence of this strain, which belongs to the European B2 subclade of B. anthracis. The closest phylogenetic neighbor of strain BF-1 is a strain isolated from cattle in France

Additional file 1: of BCL9L expression in pancreatic neoplasia with a focus on SPN: a possible explanation for the enigma of the benign neoplasia

Mean RNA expression Ratio derived from two independent experiments, normalized against GAPDH. (XLSX 12 kb

Draft Genome Sequence of Bacillus anthracis UR-1, Isolated from a German Heroin User

Rückert C, Licht K, Kalinowski J, et al. Draft Genome Sequence of Bacillus anthracis UR-1, Isolated from a German Heroin User. Journal of bacteriology. 2012;194(21):5997-5998.We report the draft genome sequence of Bacillus anthracis UR-1, isolated from a fatal case of injectional anthrax in a German heroin user. Analysis of the genome sequence of strain UR-1 may aid in describing phylogenetic relationships between virulent heroin-associated isolates of B. anthracis isolated in the United Kingdom, Germany, and other European countries