Estimates for maximal functions associated to hypersurfaces in R3\Bbb R^3 with height h<2:h<2: Part II -- A geometric conjecture and its proof for generic 2-surfaces

In this article, we continue the study of $L^p$-boundedness of the maximal operator $\mathcal M_S$ associated to averages along isotropic dilates of a given, smooth hypersurface $S$ in 3-dimensional Euclidean space. We focus here on small surface-patches near a given point $x^0$ exhibiting singularities of type $\mathcal A$ in the sense of Arnol'd at this point; this is the situation which had yet been left open. Denoting by $p_c$ the minimal Lebesgue exponent such that $\mathcal M_S$ is $L^p$-bounded for $p>p_c,$ we are able to identify $p_c$ for all analytic surfaces of type $\mathcal A$ (with the exception of a small subclass), by means of quantities which can be determined from associated Newton polyhedra. Besides the well-known notion of height at $x^0,$ a new quantity, which we call the effective multiplicity, turns out to play a crucial role here. We also state a conjecture on how the critical exponent $p_c$ might be determined by means of a geometric measure theoretic condition, which measures in some way the order of contact of arbitrary ellipsoids with $S,$ even for hypersurfaces in arbitrary dimension, and show that this conjecture holds indeed true for all classes of 2-hypersurfaces $S$ for which we have gained an essentially complete understanding of $\mathcal M_S$ so far. Our results lead in particular to a proof of a conjecture by Iosevich-Sawyer-Seeger for arbitrary analytic 2-surfaces.Comment: 101 pages, 8 figure

Fish in the city

Aquaculture is the most recent addition to animal husbandry and it is the fastest growing food production industry. Its contribution to world food security in the 21st century is already significant and it is bound to continue to grow because demand for fish for human consumption is rapidly increasing whereas fish supplies from ocean fisheries are likely to decline. The rapid evolution of aquaculture involved a host of innovations of which many were based on R&D activities by public and private research organizations. Applied R&D tends to be the more effective the better focused it is on specific research problems or opportunities. Among the many possible aquaculture production systems on which aquaculture R&D might focus are recirculation aquaculture systems and in this paper we explore crucial aspects of the potential of urban recirculation aquaculture. Our exploration begins with a vision of recirculation aquaculture production plants located at the fringes of cities of converging economies. Such production systems are distinctly different from conventional urban aquaculture systems based on urban sewage. We scrutinize our vision from four perspectives: (i) the expected demand for aquaculture fish from urban consumers; (ii) cost competitiveness of fish produced at the fringes of cities as compared to fish produced in the rural hinterland; (iii) the potential for integration of urban recirculation aquaculture production into the modern food supply chains that are now emerging in converging economies, and (iv) the ecological footprint of aquaculture production compared to that of chicken production. Based on trends in the growth of urban populations world-wide and trends in demand for fish for food we estimate a total urban demand for aquaculture finfish between 11 and 51 million tons in 2025. We use von Thünen's location theory to provide support for the vision to locate recirculation aquaculture plants not within cities and not in their rural hinterland but on the fringes of cities. Moreover, we argue that tightly controlled recirculation aquaculture production would seem to be particularly well suited for being integrated into modern food supply chains. Finally, we compare the ecological footprint of recirculation aquaculture fish with that of industrially produced chicken and we find that the ecological balance depends on the source of energy used. We conclude our exploratory study with some thoughts on the implication for aquaculture R&D of the potential for recirculation aquaculture located on the fringes of cities in emerging economy countries. --

Prospects of a superradiant laser based on a thermal or guided beam of Sr-88

The prospects of superradiant lasing on the 7.5 kHz wide $^1$S$_0$-$^3$P$_1$ transition in $^{88}$Sr is explored by using numerical simulations of two systems based on realistic experimental numbers. One system uses the idea of demonstrating continuous superradiance in a simple, hot atom beam with high flux, and the other system is based on using ultra-cold atoms in a dipole guide. We find that the hot beam system achieves lasing above a flux of $2.5 \times 10^{12}$ atoms/s. It is capable of outputting hundreds of nW and suppressing cavity noise by a factor of 20-30. The second order Doppler shift causes a shift in the lasing frequency on the order of 500 Hz. For the cold atom beam we account for decoherence and thermal effects when using a repumping scheme for atoms confined in a dipole guide. We find that the output power is on the order of hundreds of pW, however the second order Doppler shift can be neglected, and cavity noise can be suppressed on the order of a factor 50-100. Additionally we show that both systems exhibit local insensitivity to fluctuations in atomic flux.Comment: 10 pages, 7 figure

On the commutability of homogenization and linearization in finite elasticity

We study non-convex elastic energy functionals associated to (spatially) periodic, frame indifferent energy densities with a single non-degenerate energy well at SO(n). Under the assumption that the energy density admits a quadratic Taylor expansion at identity, we prove that the Gamma-limits associated to homogenization and linearization commute. Moreover, we show that the homogenized energy density, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the quadratic term associated to the linearization of the initial energy density

Towards many colors in FISH on 3D-preserved interphase nuclei

The article reviews the existing methods of multicolor FISH on nuclear targets, first of all, interphase chromosomes. FISH proper and image acquisition are considered as two related components of a single process. We discuss (1) M-FISH (combinatorial labeling + deconvolution + widefield microscopy); (2) multicolor labeling + SIM (structured illumination microscopy); (3) the standard approach to multicolor FISH + CLSM (confocal laser scanning microscopy; one fluorochrome - one color channel); (4) combinatorial labeling + CLSM; (5) non-combinatorial labeling + CLSM + linear unmixing. Two related issues, deconvolution of images acquired with CLSM and correction of data for chromatic Z-shift, are also discussed. All methods are illustrated with practical examples. Finally, several rules of thumb helping to choose an optimal labeling + microscopy combination for the planned experiment are suggested. Copyright (c) 2006 S. Karger AG, Basel

Management of Urban Stormwater at Block-Level (MUST-B): A New Approach for Potential Analysis of Decentralized Stormwater Management Systems

Cities worldwide are facing problems to mitigate the impact of urban stormwater runoff caused by the increasing occurrence of heavy rainfall events and urban re-densification. This study presents a new approach for estimating the potential of the Management of Urban STormwater at Block-level (MUST-B) by decentralized blue-green infrastructures here called low-impact developments (LIDs) for already existing urban environments. The MUST-B method was applied to a study area in the northern part of the City of Leipzig, Germany. The Study areas was divided into blocks smallest functional units and considering two different soil permeability and three different rainfall events, seven scenarios have been developed: current situation, surface infiltration, swale infiltration, trench infiltration, trough-trench infiltration, and three different combinations of extensive roof greening, trough-trench infiltration, and shaft infiltration. The LIDs have been simulated and their maximum retention/infiltration potential and the required area have been estimated together with a cost calculation. The results showed that even stormwater of a 100 year rainfall event can be fully retained and infiltrated within the blocks on a soil with low permeability (kf = 10−6 m/s). The cost and the required area for the LIDs differed depending on the scenario and responded to the soil permeability and rainfall events. It is shown that the MUST-B method allows a simple down- and up-scaling process for different urban settings and facilitates decision making for implementing decentralized blue-green-infrastructure that retain, store, and infiltrate stormwater at block level

Universal spectral form factor for chaotic dynamics

We consider the semiclassical limit of the spectral form factor $K(\tau)$ of fully chaotic dynamics. Starting from the Gutzwiller type double sum over classical periodic orbits we set out to recover the universal behavior predicted by random-matrix theory, both for dynamics with and without time reversal invariance. For times smaller than half the Heisenberg time $T_H\propto \hbar^{-f+1}$, we extend the previously known $\tau$-expansion to include the cubic term. Beyond confirming random-matrix behavior of individual spectra, the virtue of that extension is that the ``diagrammatic rules'' come in sight which determine the families of orbit pairs responsible for all orders of the $\tau$-expansion.Comment: 4 pages, 1 figur

The Cilialyzer - A freely available open-source software for the analysis of mucociliary activity in respiratory cells.

BACKGROUND AND OBJECTIVE Primary ciliary dyskinesia (PCD) is a rare genetic disorder causing a defective ciliary structure, which predominantly leads to an impaired mucociliary clearance and associated airway disease. As there is currently no single diagnostic gold standard test, PCD is diagnosed by a combination of several methods comprising genetic testing and the examination of the ciliary structure and function. Among the approved diagnostic methods, only high-speed video microscopy (HSVM) allows to directly observe the ciliary motion and therefore, to directly assess ciliary function. In the present work, we present our recently developed freely available open-source software - termed "Cilialyzer", which has been specifically designed to support and facilitate the analysis of the mucociliary activity in respiratory epithelial cells captured by high-speed video microscopy. METHODS In its current state, the Cilialyzer software enables clinical PCD analysts to load, preprocess and replay recorded image sequences as well as videos with a feature-rich replaying module facilitating the commonly performed qualitative visual assessment of ciliary function (including the assessment of the ciliary beat pattern). The image processing methods made accessible through an intuitive user interface allow clinical specialists to comfortably compute the ciliary beating frequency (CBF), the activity map and the "frequency correlation length" - an observable getting newly introduced. Furthermore, the Cilialyzer contains a simple-to-use particle tracking interface to determine the mucociliary transport speed. RESULTS Cilialyzer is fully written in the Python programming language and freely available under the terms of the MIT license. The proper functioning of the computational analysis methods constituting the Cilialyzer software is demonstrated by using simulated and representative sample data from clinical practice. Additionally, the software was used to analyze high-speed videos showing samples obtained from healthy controls and genetically confirmed PCD cases (DNAI1 and DNAH11 mutations) to show its clinical applicability. CONCLUSIONS Cilialyzer serves as a useful clinical tool for PCD analysts and provides new quantitative information awaiting to be clinically evaluated using cohorts of PCD. As Cilialyzer is freely available under the terms of a permissive open-source license, it serves as a ground frame for further development of computational methods aiming at the quantification and automation of the analysis of mucociliary activity captured by HSVM