Influence of the sunspot cycle on the Northern Hemisphere wintertime circulation from long upper-air data sets

Here we present a study of the 11 yr sunspot cycle's imprint on the Northern Hemisphere atmospheric circulation, using three recently developed gridded upper-air data sets that extend back to the early twentieth century. We find a robust response of the tropospheric late-wintertime circulation to the sunspot cycle, independent from the data set. This response is particularly significant over Europe, although results show that it is not directly related to a North Atlantic Oscillation (NAO) modulation; instead, it reveals a significant connection to the more meridional Eurasian pattern (EU). The magnitude of mean seasonal temperature changes over the European land areas locally exceeds 1 K in the lower troposphere over a sunspot cycle. We also analyse surface data to address the question whether the solar signal over Europe is temporally stable for a longer 250 yr period. The results increase our confidence in the existence of an influence of the 11 yr cycle on the European climate, but the signal is much weaker in the first half of the period compared to the second half. The last solar minimum (2005 to 2010), which was not included in our analysis, shows anomalies that are consistent with our statistical results for earlier solar minima.

Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviation with Gaussian process models

Several methods based on Kriging have recently been proposed for calculating a probability of failure involving costly-to-evaluate functions. A closely related problem is to estimate the set of inputs leading to a response exceeding a given threshold. Now, estimating such a level set—and not solely its volume—and quantifying uncertainties on it are not straightforward. Here we use notions from random set theory to obtain an estimate of the level set, together with a quantification of estimation uncertainty. We give explicit formulae in the Gaussian process set-up and provide a consistency result. We then illustrate how space-filling versus adaptive design strategies may sequentially reduce level set estimation uncertainty.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Holomorphic families of nonequivalent embeddings and of holomorphic group actions on affine space

We construct holomorphic families of proper holomorphic embeddings of \mathbb {C}^{k} into \mathbb {C}^{n} (0\textless k\textless n-1), so that for any two different parameters in the family, no holomorphic automorphism of \mathbb {C}^{n} can map the image of the corresponding two embeddings onto each other. As an application to the study of the group of holomorphic automorphisms of \mathbb {C}^{n}, we derive the existence of families of holomorphic \mathbb {C}^{*}-actions on \mathbb {C}^{n} (n\ge5) so that different actions in the family are not conjugate. This result is surprising in view of the long-standing holomorphic linearization problem, which, in particular, asked whether there would be more than one conjugacy class of \mathbb {C}^{*}-actions on \mathbb {C}^{n} (with prescribed linear part at a fixed point).

Infinite Transitivity on Affine Varieties

In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.

Blocking brain-derived neurotrophic factor inhibits injury-induced hyperexcitability of hippocampal CA3 neurons

Brain trauma can disrupt synaptic connections, and this in turn can prompt axons to sprout and form new connections. If these new axonal connections are aberrant, hyperexcitability can result. It has been shown that ablating tropomyosin-related kinase B (TrkB), a receptor for brain-derived neurotrophic factor (BDNF), can reduce axonal sprouting after hippocampal injury. However, it is unknown whether inhibiting BDNF-mediated axonal sprouting will reduce hyperexcitability. Given this, our purpose here was to determine whether pharmacologically blocking BDNF inhibits hyperexcitability after injury-induced axonal sprouting in the hippocampus. To induce injury, we made Schaffer collateral lesions in organotypic hippocampal slice cultures. As reported by others, we observed a 50% reduction in axonal sprouting in cultures treated with a BDNF blocker (TrkB-Fc) 14 days after injury. Furthermore, lesioned cultures treated with TrkB-Fc were less hyperexcitable than lesioned untreated cultures. Using electrophysiology, we observed a two-fold decrease in the number of CA3 neurons that showed bursting responses after lesion with TrkB-Fc treatment, whereas we found no change in intrinsic neuronal firing properties. Finally, evoked field excitatory postsynaptic potential recordings indicated an increase in network activity within area CA3 after lesion, which was prevented with chronic TrkB-Fc treatment. Taken together, our results demonstrate that blocking BDNF attenuates injury-induced hyperexcitability of hippocampal CA3 neurons. Axonal sprouting has been found in patients with post-traumatic epilepsy. Therefore, our data suggest that blocking the BDNF-TrkB signaling cascade shortly after injury may be a potential therapeutic target for the treatment of post-traumatic epilepsy.

Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

Automated 3D Lumbar Intervertebral Disc Segmentation from MRI Data Sets

This paper proposed an automated 3D lumbar intervertebral disc (IVD) segmentation strategy from MRI data. Starting from two user supplied landmarks, the geometrical parameters of all lumbar vertebral bodies and intervertebral discs are automatically extracted from a mid-sagittal slice using a graphical model based approach. After that, a three-dimensional (3D) variable-radius soft tube model of the lumbar spine column is built to guide the 3D disc segmentation. The disc segmentation is achieved as a multi-kernel diffeomorphic registration between a 3D template of the disc and the observed MRI data. Experiments on 15 patient data sets showed the robustness and the accuracy of the proposed algorithm.

Von Fuzzy-Sets zu Computing-with-Words

Dieser Artikel bietet einen Überblick über die Entwicklung und Zusammenhänge der einzelnen Elemente der Fuzzy-Logik, wovon Fuzzy-Set-Theorie die Grundlage bildet. Die Grundproblematik besteht in der Handhabung von linguistischen Informationen, die häufig durch Ungenauigkeit gekennzeichnet sind. Die verschiedenen technischen Anwendungen von Fuzzy-Logik bieten eine Möglichkeit, intelligentere Computersysteme zu konstruieren, die mit unpräzisen Informationen umgehen können. Solche Systeme sind Indizien für die Entstehung einer neuen Ära des Cognitive-Computing, di in diesemArtikel ebenfalls zur Sprache kommt. Für das bessere Verständnis wird der Artikel mit einem Beispiel aus der Meteorologie (d. h. Schnee in Adelboden) begleitet.

Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.