Linearisable third order ordinary differential equations and generalised Sundman transformations

We calculate in detail the conditions which allow the most general third order ordinary differential equation to be linearised in X'''(T)=0 under the transformation X(T)=F(x,t), dT=G(x,t)dt. Further generalisations are considered.Comment: 33 page

A catalogue of the Chandra Deep Field South with multi-colour classification and photometric redshifts from COMBO-17

We present the COMBO-17 object catalogue of the Chandra Deep Field South for public use, covering a field which is 31.5' x 30' in size. This catalogue lists astrometry, photometry in 17 passbands from 350 to 930 nm, and ground-based morphological data for 63,501 objects. The catalogue also contains multi-colour classification into the categories 'Star', 'Galaxy' and 'Quasar' as well as photometric redshifts. We include restframe luminosities in Johnson, SDSS and Bessell passbands and estimated errors. The redshifts are most reliable at R<24, where the sample contains approximately 100 quasars, 1000 stars and 10000 galaxies. We use nearly 1000 spectroscopically identified objects in conjunction with detailed simulations to characterize the performance of COMBO-17. We show that the selection of quasars, more generally type-1 AGN, is nearly complete and minimally contaminated at z=[0.5,5] for luminosities above M_B=-21.7. Their photometric redshifts are accurate to roughly 5000 km/sec. Galaxy redshifts are accurate to 1% in dz/(1+z) at R<21. They degrade in quality for progressively fainter galaxies, reaching accuracies of 2% for galaxies with R~222 and of 10% for galaxies with R>24. The selection of stars is complete to R~23, and deeper for M stars. We also present an updated discussion of our classification technique with maps of survey completeness, and discuss possible failures of the statistical classification in the faint regime at R>24.Comment: submitted to Astronomy & Astrophysics, public data set available at http://www.mpia.de/COMBO/combo_index.htm

Do antibiotics interfere with the efficacy of oral contraceptives?

Among antibiotics, only rifampin has been demonstrated to interfere with the effectiveness of oral contraceptives (OCs) (strength of recommendation [SOR]: C, limited case series). There is little convincing evidence to show a systematic interaction between other antibiotics and oral contraceptive steroids (SOR: B, based on systematic reviews, case reports, and pharmacologic studies). However, current studies may not have separately evaluated the minority of women whose metabolism of contraceptive steroids makes them more vulnerable to OC failure. Given the significant consequences of unintended pregnancy, some experts recommend a conservative approach, including patient education and backup forms of birth control (SOR: C, expert opinion)

Spectral Dependence of Polarized Radiation due to Spatial Correlations

We study the polarization of light emitted by spatially correlated sources. We show that in general polarization acquires nontrivial spectral dependence due to spatial correlations. The spectral dependence is found to be absent only for a special class of sources where the correlation length scales as the wavelength of light. We further study the cross correlations between two spatially distinct points that are generated due to propagation. It is found that such cross correlation leads to sufficiently strong spectral dependence of polarization which can be measured experimentally.Comment: 5 pages, 4 figure

Speed of synchronization in complex networks of neural oscillators Analytic results based on Random Matrix Theory

We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is determined by multiple operators, for which standard analysis is not suitable. We describe a general non-standard solution to the multi-operator problem. Subsequently, we derive a class of rise functions for which all stability operators become degenerate and standard eigenvalue analysis becomes a suitable tool. Interestingly, this class is found to consist of networks of leaky integrate and fire neurons. For random networks of inhibitory integrate-and-fire neurons, we then develop an analytical approach, based on the theory of random matrices, to precisely determine the eigenvalue distribution. This yields the asymptotic relaxation time for perturbations to the synchronous state which provides the characteristic time scale on which neurons can coordinate their activity in such networks. For networks with finite in-degree, i.e. finite number of presynaptic inputs per neuron, we find a speed limit to coordinating spiking activity: Even with arbitrarily strong interaction strengths neurons cannot synchronize faster than at a certain maximal speed determined by the typical in-degree.Comment: 17 pages, 12 figures, submitted to Chao

Pore Stabilization in Cohesive Granular Systems

Cohesive powders tend to form porous aggregates which can be compacted by applying an external pressure. This process is modelled using the Contact Dynamics method supplemented with a cohesion law and rolling friction. Starting with ballistic deposits of varying density, we investigate how the porosity of the compacted sample depends on the cohesion strength and the friction coefficients. This allows to explain different pore stabilization mechanisms. The final porosity depends on the cohesion force scaled by the external pressure and on the lateral distance between branches of the ballistic deposit r_capt. Even if cohesion is switched off, pores can be stabilized by Coulomb friction alone. This effect is weak for round particles, as long as the friction coefficient is smaller than 1. However, for nonspherical particles the effect is much stronger.Comment: 10 pages, 15 figure