Fourier, Gauss, Fraunhofer, Porod and the Shape from Moments Problem

We show how the Fourier transform of a shape in any number of dimensions can be simplified using Gauss's law and evaluated explicitly for polygons in two dimensions, polyhedra three dimensions, etc. We also show how this combination of Fourier and Gauss can be related to numerous classical problems in physics and mathematics. Examples include Fraunhofer diffraction patterns, Porods law, Hopfs Umlaufsatz, the isoperimetric inequality and Didos problem. We also use this approach to provide an alternative derivation of Davis's extension of the Motzkin-Schoenberg formula to polygons in the complex plane.Comment: 21 pages, no figure

Optical Spectroscopy of IRAS 02091+6333

We present a detailed spectroscopic investigation, spanning four winters, of the asymptotic giant branch (AGB) star IRAS 02091+6333. Zijlstra & Weinberger (2002) found a giant wall of dust around this star and modelled this unique phenomenon. However their work suffered from the quality of the optical investigations of the central object. Our spectroscopic investigation allowed us to define the spectral type and the interstellar foreground extinction more precisely. Accurate multi band photometry was carried out. This provides us with the possibility to derive the physical parameters of the system. The measurements presented here suggest a weak irregular photometric variability of the target, while there is no evidence of a spectroscopic variability over the last four years.Comment: 5 pages, Latex, 3 tables, 4 figures, Astron. & Astrophys. - in pres

Stability for Borell-Brascamp-Lieb inequalities

We study stability issues for the so-called Borell-Brascamp-Lieb inequalities, proving that when near equality is realized, the involved functions must be $L^1$-close to be $p$-concave and to coincide up to homotheties of their graphs.Comment: to appear in GAFA Seminar Note

Affine and toric hyperplane arrangements

We extend the Billera-Ehrenborg-Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements. For arrangements on the torus, we also generalize Zaslavsky's fundamental results on the number of regions.Comment: 32 pages, 4 figure

DEAR project: Lunar dust surface interactions, risk and removal investigations

The DEAR project (Dusty Environment Application Research) investigates the interaction between lunar regolith and surfaces and components relevant for lunar exploration. Based on the TUBS regolith simulant which is representative in chemistry, size and shape properties to Moon soils to study the regolith transport, adhesion and strategies for cleaning. The regolith simulant will be applied to thermal, structural, optical sensor, sealing and other astronautic systems, providing input for requirements, justification and verification. The key applications are split in human space flight regolith investigations, wrinkled surface with random movement and hardware surfaces, flat material defined movement. The paper provides an overview of the DEAR project including a discussion of the first results, in particular vibration, shock and micro-vibration on regolith bearing surfaces. The investigation shall enable better understand the regolith layers interaction and the release mechanism, as well as potential cross contamination and cleaning strategies. The research is complemented by simulation of the regolith motion as parameter surface plasma interactions. The project is funded and supported by the European Space Agency (ESA). DEAR specifically addresses the development and testing of lunar dust removal strategies on optics, mechanisms and human space flight hardware (e.g., space suits). As the Moons regolith is known to be highly abrasive, electrically chargeable, and potentially chemically reactive, lunar dust might reduce the performance of hardware, such as cameras, thermal control surfaces and solar cells. The dust can cause malfunction on seals for on/off mechanisms or space suits. Of particular interest are risk assessment, avoidance, and cleaning techniques such as the use of electric fields to remove lunar dust from surfaces. Representative dust (e.g., regolith analogues of interesting landing sites) will be used in a dedicated test setup to evaluate risks and effects of lunar dust. We describe designs and methods developed by the DEAR consortium to deal with the regolith-related issues, in particular an electrode design to deflect regolith particles, cleaning of astronautical systems with CO2, design of a robotic arm for the testing within the DEAR chamber, regolith removal via shock, and regolith interaction with cleanroom textile

Orientations, lattice polytopes, and group arrangements II: Modular and integral flow Polynomials of graphs

We study modular and integral flow polynomials of graphs by means of subgroup arrangements and lattice polytopes. We introduce an Eulerian equivalence relation on orientations, flow arrangements, and flow polytopes; and we apply the theory of Ehrhart polynomials to obtain properties of modular and integral flow polynomials. The emphasis is on the geometrical treatment through subgroup arrangements and Ehrhart polynomials. Such viewpoint leads to a reciprocity law on the modular flow polynomial, which gives rise to an interpretation on the values of the modular flow polynomial at negative integers and answers a question by Beck and Zaslavsky.Regal Entertainment Group (Competitive Earmarked Research Grants 600703)Regal Entertainment Group (Competitive Earmarked Research Grants 600506)Regal Entertainment Group (Competitive Earmarked Research Grants 600608

Key Physiological Parameters Dictate Triggering of Activity-Dependent Bulk Endocytosis in Hippocampal Synapses

To maintain neurotransmission in central neurons, several mechanisms are employed to retrieve synaptically exocytosed membrane. The two major modes of synaptic vesicle (SV) retrieval are clathrin-mediated endocytosis and activity-dependent bulk endocytosis (ADBE). ADBE is the dominant SV retrieval mode during intense stimulation, however the precise physiological conditions that trigger this mode are not resolved. To determine these parameters we manipulated rat hippocampal neurons using a wide spectrum of stimuli by varying both the pattern and duration of stimulation. Using live-cell fluorescence imaging and electron microscopy approaches, we established that stimulation frequency, rather than the stimulation load, was critical in the triggering of ADBE. Thus two hundred action potentials, when delivered at high frequency, were sufficient to induce near maximal bulk formation. Furthermore we observed a strong correlation between SV pool size and ability to perform ADBE. We also identified that inhibitory nerve terminals were more likely to utilize ADBE and had a larger SV recycling pool. Thus ADBE in hippocampal synaptic terminals is tightly coupled to stimulation frequency and is more likely to occur in terminals with large SV pools. These results implicate ADBE as a key modulator of both hippocampal neurotransmission and plasticity

Amyloid Precursor Protein Is Trafficked and Secreted via Synaptic Vesicles

A large body of evidence has implicated amyloid precursor protein (APP) and its proteolytic derivatives as key players in the physiological context of neuronal synaptogenesis and synapse maintenance, as well as in the pathology of Alzheimer's Disease (AD). Although APP processing and release are known to occur in response to neuronal stimulation, the exact mechanism by which APP reaches the neuronal surface is unclear. We now demonstrate that a small but relevant number of synaptic vesicles contain APP, which can be released during neuronal activity, and most likely represent the major exocytic pathway of APP. This novel finding leads us to propose a revised model of presynaptic APP trafficking that reconciles existing knowledge on APP with our present understanding of vesicular release and recycling

Synapse Clusters Are Preferentially Formed by Synapses with Large Recycling Pool Sizes

Synapses are distributed heterogeneously in neural networks. The relationship between the spatial arrangement of synapses and an individual synapse's structural and functional features remains to be elucidated. Here, we examined the influence of the number of adjacent synapses on individual synaptic recycling pool sizes. When measuring the discharge of the styryl dye FM1–43 from electrically stimulated synapses in rat hippocampal tissue cultures, a strong positive correlation between the number of neighbouring synapses and recycling vesicle pool sizes was observed. Accordingly, vesicle-rich synapses were found to preferentially reside next to neighbours with large recycling pool sizes. Although these synapses with large recycling pool sizes were rare, they were densely arranged and thus exhibited a high amount of release per volume. To consolidate these findings, functional terminals were marked by live-cell antibody staining with anti-synaptotagmin-1-cypHer or overexpression of synaptopHluorin. Analysis of synapse distributions in these systems confirmed the results obtained with FM 1–43. Our findings support the idea that clustering of synapses with large recycling pool sizes is a distinct developmental feature of newly formed neural networks and may contribute to functional plasticity