Distribution of diameters for Erd\"os-R\'enyi random graphs

We study the distribution of diameters d of Erd\"os-R\'enyi random graphs with average connectivity c. The diameter d is the maximum among all shortest distances between pairs of nodes in a graph and an important quantity for all dynamic processes taking place on graphs. Here we study the distribution P(d) numerically for various values of c, in the non-percolating and the percolating regime. Using large-deviations techniques, we are able to reach small probabilities like 10^{-100} which allow us to obtain the distribution over basically the full range of the support, for graphs up to N=1000 nodes. For values c<1, our results are in good agreement with analytical results, proving the reliability of our numerical approach. For c>1 the distribution is more complex and no complete analytical results are available. For this parameter range, P(d) exhibits an inflection point, which we found to be related to a structural change of the graphs. For all values of c, we determined the finite-size rate function Phi(d/N) and were able to extrapolate numerically to N->infinity, indicating that the large deviation principle holds.Comment: 9 figure

Differentially Private Empirical Risk Minimization with Sparsity-Inducing Norms

Differential privacy is concerned about the prediction quality while measuring the privacy impact on individuals whose information is contained in the data. We consider differentially private risk minimization problems with regularizers that induce structured sparsity. These regularizers are known to be convex but they are often non-differentiable. We analyze the standard differentially private algorithms, such as output perturbation, Frank-Wolfe and objective perturbation. Output perturbation is a differentially private algorithm that is known to perform well for minimizing risks that are strongly convex. Previous works have derived excess risk bounds that are independent of the dimensionality. In this paper, we assume a particular class of convex but non-smooth regularizers that induce structured sparsity and loss functions for generalized linear models. We also consider differentially private Frank-Wolfe algorithms to optimize the dual of the risk minimization problem. We derive excess risk bounds for both these algorithms. Both the bounds depend on the Gaussian width of the unit ball of the dual norm. We also show that objective perturbation of the risk minimization problems is equivalent to the output perturbation of a dual optimization problem. This is the first work that analyzes the dual optimization problems of risk minimization problems in the context of differential privacy

Laboratory colonisation and genetic bottlenecks in the tsetse fly Glossina pallidipes

Background The IAEA colony is the only one available for mass rearing of Glossina pallidipes, a vector of human and animal African trypanosomiasis in eastern Africa. This colony is the source for Sterile Insect Technique (SIT) programs in East Africa. The source population of this colony is unclear and its genetic diversity has not previously been evaluated and compared to field populations.&lt;p&gt;&lt;/p&gt; Methodology/Principal Findings We examined the genetic variation within and between the IAEA colony and its potential source populations in north Zimbabwe and the Kenya/Uganda border at 9 microsatellites loci to retrace the demographic history of the IAEA colony. We performed classical population genetics analyses and also combined historical and genetic data in a quantitative analysis using Approximate Bayesian Computation (ABC). There is no evidence of introgression from the north Zimbabwean population into the IAEA colony. Moreover, the ABC analyses revealed that the foundation and establishment of the colony was associated with a genetic bottleneck that has resulted in a loss of 35.7% of alleles and 54% of expected heterozygosity compared to its source population. Also, we show that tsetse control carried out in the 1990's is likely reduced the effective population size of the Kenya/Uganda border population.&lt;p&gt;&lt;/p&gt; Conclusions/Significance All the analyses indicate that the area of origin of the IAEA colony is the Kenya/Uganda border and that a genetic bottleneck was associated with the foundation and establishment of the colony. Genetic diversity associated with traits that are important for SIT may potentially have been lost during this genetic bottleneck which could lead to a suboptimal competitiveness of the colony males in the field. The genetic diversity of the colony is lower than that of field populations and so, studies using colony flies should be interpreted with caution when drawing general conclusions about G. pallidipes biology.&lt;p&gt;&lt;/p&gt

Quasi-invariance properties of a class of subordinators

We study absolute-continuity properties of a class of stochastic processes, including the gamma and the Dirichlet processes. We prove that the laws of a general class of non-linear transformations of such processes are locally equivalent to the law of the original process and we compute explicitly the associated Radon-Nikodym densities. This work unifies and generalizes to random non-linear transformations several previous results on quasi-invariance of gamma and Dirichlet processes

Monetary Policy Committees: meetings and outcomes

Monetary Policy Committees differ in the way the interest rate proposal is prepared and presented in the policy meeting. In this paper we show analytically how different arrangements could affect the voting behaviour of individual MPC members and therefore policy outcomes. We then apply our results to the Bank of England and the Federal Reserve. A general finding is that when MPC members are not too diverse in terms of expertise and experience, policy discussions should not be based on pre- prepared policy options. Instead, interest rate proposals should arise endogenously as a majority of views expressed by the members, as is the case at the Bank of England and appears to be the case in the FOMC under Chairman Bernanke. JEL Classification: E58, D71, D78Bank of England, Federal Open Market Committee, monetary policy committee, voting

Ion optics for high power 50-cm-diam ion thrusters

The process used at the NASA-Lewis to fabricate 30 and 50-cm-diameter ion optics is described. The ion extraction capabilities of the 30 and 50-cm diameter ion optics were evaluated on divergent field and ring-cusp discharge chambers and compared. Perveance was found to be sensitive to the effects of the type and power of the discharge chamber and to the accelerator electrode hole diameter. Levels of up to 0.64 N and 20 kW for thrust and input power, respectively, were demonstrated with the divergent-field discharge chamber. Thruster efficiencies and specific impulse values up to 79 percent and 5000 sec., respectively, were achieved with the ring-cusp discharge chamber

Improved and Quality-assessed Emission and Absorption Line measurements in Sloan Digital Sky Survey galaxies

We present a new database of absorption and emission-line measurements based on the entire spectral atlas from the Sloan Digital Sky Survey (SDSS) 7th data release of galaxies within a redshift of 0.2. Our work makes use of the publicly available penalized pixel-fitting(pPXF) and gas and absorption line fitting (gandalf) IDL codes, aiming to improve the existing measurements for stellar kinematics, the strength of various absorption-line features, and the flux and width of the emissions from different species of ionised gas. Our fit to the stellar continuum uses both standard stellar population models and empirical templates obtained by combining a large number of stellar spectra in order to fit a subsample of high-quality SDSS spectra for quiescent galaxies. Furthermore, our fit to the nebular spectrum includes an exhaustive list of both recombination and forbidden lines. Foreground Galactic extinction is implicitly treated in our models, whereas reddening in the SDSS galaxies is included in the form of a simple dust screen component affecting the entire spectrum that is accompanied by a second reddening component affecting only the ionised gas emission. In order to check for systematic departures, we provide a quality assessment for our fit to the SDSS spectra in our sample. This quality assessment also allows the identification of objects with either problematic data or peculiar features. For example, based on the quality assessment, approximately 1% of the SDSS spectra classified as "galaxies" by the SDSS pipeline do in fact require additional broad lines to be matched, even though they do not show a strong continuum from an active nucleus, as do the SDSS objects classified as "quasars". Finally, we provide new spectral templates for galaxies of different Hubble types, obtained by combining the results of our spectral fit for a subsample of 452 morphologically selected objects.Comment: Accepted for publication in ApJS. 23 pages, 14 figures, 4 tables. A version with high-resolution figures is available at http://gem.yonsei.ac.kr/~ksoh/ossy/arXiv/Oh_11_OSSY.pd

SCOPe: Structural Classification of Proteins--extended, integrating SCOP and ASTRAL data and classification of new structures.

Structural Classification of Proteins-extended (SCOPe, http://scop.berkeley.edu) is a database of protein structural relationships that extends the SCOP database. SCOP is a manually curated ordering of domains from the majority of proteins of known structure in a hierarchy according to structural and evolutionary relationships. Development of the SCOP 1.x series concluded with SCOP 1.75. The ASTRAL compendium provides several databases and tools to aid in the analysis of the protein structures classified in SCOP, particularly through the use of their sequences. SCOPe extends version 1.75 of the SCOP database, using automated curation methods to classify many structures released since SCOP 1.75. We have rigorously benchmarked our automated methods to ensure that they are as accurate as manual curation, though there are many proteins to which our methods cannot be applied. SCOPe is also partially manually curated to correct some errors in SCOP. SCOPe aims to be backward compatible with SCOP, providing the same parseable files and a history of changes between all stable SCOP and SCOPe releases. SCOPe also incorporates and updates the ASTRAL database. The latest release of SCOPe, 2.03, contains 59 514 Protein Data Bank (PDB) entries, increasing the number of structures classified in SCOP by 55% and including more than 65% of the protein structures in the PDB