Is There a Curse of Dimensionality for Contraction Fixed Points in the Worst Case?

This paper analyzes the complexity of the contraction fixed point problem: compute an ɛ-approximation to the fixed point V*Γ(V*) of a contraction mapping Γ that maps a Banach space Bd of continuous functions of d variables into itself. We focus on quasi linear contractions where Γ is a nonlinear functional of a finite number of conditional expectation operators. This class includes contractive Fredholm integral equations that arise in asset pricing applications and the contractive Bellman equation from dynamic programming. In the absence of further restrictions on the domain of Γ, the quasi linear fixed point problem is subject to the curse of dimensionality, i.e., in the worst case the minimal number of function evaluations and arithmetic operations required to compute an ε-approximation to a fixed point V*∈Bd increases exponentially in d. We show that the curse of dimensionality disappears if the domain of Γ has additional special structure. We identify a particular type of special structure for which the problem is strongly tractable even in the worst case, i.e., the number of function evaluations and arithmetic operations needed to compute an ɛ-approximation of V* is bounded by Cɛ−p where C and p are constants independent of d. We present examples of economic problems that have this type of special structure including a class of rational expectations asset pricing problems for which the optimal exponent p1 is nearly achieved

The first damselflies from the lowermost eocene of Denmark, with a description of a new subfamily (Odonata, Zygoptera: Dysagrionidae)

Eodysagrion mikkelseni gen. et sp. nov., type species of the new subfamily Eodysagrioninae, and the dysagrionine Primorilestes madseni sp. nov., the first thaumatoneurid damselflies from the lowermost Eocene of Denmark, are described. They confirm the presence of this American family in the Palaeogene of Western EuropeFacultad de Ciencias Naturales y Muse

Approaches for improving cutting processes and machine too in re-contouring

Re-contouring in the repair process of aircraft engine blades and vanes is a crucial task. Highest demands are made on the geometrical accuracy as well as on the machined surface of the part. Complexity rises even more due to the unique part characteristic originating from the operation and repair history. This requires well-designed processes and machine tool technologies. In this paper, approaches for coping with these challenges and improving the re-contouring process are described and discussed. This includes an advanced process simulation with its capabilities to accurately depict different material areas and predict process forces. Beyond, experimental investigations on workpiece-tooldeflection are presented. Finally, a machine tool prototype with a novel electromagnetic guiding system is introduced and the benefits of this technology in the field of repair are outlined.DFG/CRC/87

Impact of channelized flow on temperature distribution and fluid flow in restless calderas:Insight from Campi Flegrei caldera, Italy

Magmatic hydrothermal systems develop by the imposition of a magmatically derived heat flux upon a shallow groundwater system. As such their dynamics can be intermittently perturbed by changing conditions within the associated magmatic system. Understanding the nature of the coupling between the magmatic and groundwater systems is thus key to discriminating geophysical signals of magmatic unrest from purely hydrothermal ones.Using a series of numerical groundwater models run with TOUGH2, we simulate the coupled groundwater–magmatic system at Campi Flegrei caldera, with particular emphasis on the impact of permeability developed within local fault systems and the dynamics of the system during magmatic unrest. Simulation results suggest that faults can play an important role in controlling the dynamics of recharge and heat transport within the shallow hydrothermal reservoir. Results specifically highlight that contrasts in permeability between faults and surrounding rock impact local temperature gradients, with faults either acting as preferential routes for recharge or discharge of groundwater, depending on fault/caldera fill permeability contrast and the vertical extent of the fault. Simulations of magmatic unrest with a step-wise increase in basal heat flux suggest that periodic geophysical and chemical signals may stem from the interaction between the development of gas at depth and the recharge–discharge dynamics of the reservoir. These results highlight the potential for the dynamics of magmatic–hydrothermal systems to be significantly impacted by the presence and nature of local fault systems. Where dynamic groundwater systems are involved, it is thus important to understand the impact of such geological elements when interpreting monitoring data such as ground deformation, seismicity and gas emissions

Flank instability on Mount Etna: radon, radar interferometry and geodetic data from the south-western boundary of the unstable sector

Understanding Etnean flank instability is hampered by uncertainties over its western boundary. Accordingly, we combine soil radon emission, InSAR and EDM data to study the Ragalna fault system (RFS) on the SW flank of the volcano. Valuable synergy developed between our differing techniques, producing consistent results and serving as a model for other studies of partly obscured active faults. The RFS, limited in its surface expression, is revealed as a complex interlinked structure ~14 km long that extends from the edifice base towards the area of summit rifting, possibly linking north-eastwards to the Pernicana fault system (PFS) to define the unstable sector. Short-term deformation rates on the RFS from InSAR data reach ~7 mm a-1 in the satellite line of sight on the upslope segment and ~5 mm a-1 on the prominent central segment. While combining this with EDM data confirms the central segment of the RFS as a dextral transtensive structure, with strike-slip and dip-slip components of ~3.4 and ~3.7 mm a-1 respectively. We measured thoron (220Rn, half-life 56 secs) as well as radon and, probably because of its limited diffusion range, this appears a more sensitive but previously unexploited isotope for pinpointing active near-surface faults. Contrasting activity of the PFS and RFS reinforces proposals that the instability they bound is divided into at least three sub-sectors by intervening faults, while, in section, fault-associated basal detachments also form a nested pattern. Complex temporal and spatial movement interactions are expected between these structural components of the unstable sector

The diversity of Odonata and their endophytic ovipositions from the Upper Oligocene Fossillagerstätte of Rott (Rhineland, Germany

A commented list of fossil Odonata from the Oligocene outcrop of Rott is given, together with descriptions of new traces of oviposition in plant tissues, very similar to ichnotaxa already known from the early Eocene Laguna del Hunco floras of Patagonia. The joint presences of odonatan larvae and traces of oviposition demonstrate the autochthony of these insects in the palaeolake of Rott, confirming the existence of a diverse and abundant aquatic entomofauna, a situation strikingly different to that in the contemporaneous Oligocene palaeolake of Céreste (France).Museo de La Plat

Evolution of helicity in NOAA 10923 over three consecutive solar rotations

We have studied the evolution of magnetic helicity and chirality in an active region over three consecutive solar rotations. The region when it first appeared was named NOAA10923 and in subsequent rotations it was numbered NOAA 10930, 10935 and 10941. We compare the chirality of these regions at photospheric, chromospheric and coronal heights. The observations used for photospheric and chromospheric heights are taken from Solar Vector Magnetograph (SVM) and H_alpha imaging telescope of Udaipur Solar Observatory (USO), respectively. We discuss the chirality of the sunspots and associated H_alpha filaments in these regions. We find that the twistedness of superpenumbral filaments is maintained in the photospheric transverse field vectors also. We also compare the chirality at photospheric and chromospheric heights with the chirality of the associated coronal loops, as observed from the HINODE X-Ray Telescope.Comment: 8 pages, 4 figure

Learning to Extract Motion from Videos in Convolutional Neural Networks

This paper shows how to extract dense optical flow from videos with a convolutional neural network (CNN). The proposed model constitutes a potential building block for deeper architectures to allow using motion without resorting to an external algorithm, \eg for recognition in videos. We derive our network architecture from signal processing principles to provide desired invariances to image contrast, phase and texture. We constrain weights within the network to enforce strict rotation invariance and substantially reduce the number of parameters to learn. We demonstrate end-to-end training on only 8 sequences of the Middlebury dataset, orders of magnitude less than competing CNN-based motion estimation methods, and obtain comparable performance to classical methods on the Middlebury benchmark. Importantly, our method outputs a distributed representation of motion that allows representing multiple, transparent motions, and dynamic textures. Our contributions on network design and rotation invariance offer insights nonspecific to motion estimation