Beyond inverse Ising model: structure of the analytical solution for a class of inverse problems

I consider the problem of deriving couplings of a statistical model from measured correlations, a task which generalizes the well-known inverse Ising problem. After reminding that such problem can be mapped on the one of expressing the entropy of a system as a function of its corresponding observables, I show the conditions under which this can be done without resorting to iterative algorithms. I find that inverse problems are local (the inverse Fisher information is sparse) whenever the corresponding models have a factorized form, and the entropy can be split in a sum of small cluster contributions. I illustrate these ideas through two examples (the Ising model on a tree and the one-dimensional periodic chain with arbitrary order interaction) and support the results with numerical simulations. The extension of these methods to more general scenarios is finally discussed.Comment: 15 pages, 6 figure

Reverse Engineering Gene Networks with ANN: Variability in Network Inference Algorithms

Motivation :Reconstructing the topology of a gene regulatory network is one of the key tasks in systems biology. Despite of the wide variety of proposed methods, very little work has been dedicated to the assessment of their stability properties. Here we present a methodical comparison of the performance of a novel method (RegnANN) for gene network inference based on multilayer perceptrons with three reference algorithms (ARACNE, CLR, KELLER), focussing our analysis on the prediction variability induced by both the network intrinsic structure and the available data. Results: The extensive evaluation on both synthetic data and a selection of gene modules of "Escherichia coli" indicates that all the algorithms suffer of instability and variability issues with regards to the reconstruction of the topology of the network. This instability makes objectively very hard the task of establishing which method performs best. Nevertheless, RegnANN shows MCC scores that compare very favorably with all the other inference methods tested. Availability: The software for the RegnANN inference algorithm is distributed under GPL3 and it is available at the corresponding author home page (http://mpba.fbk.eu/grimaldi/regnann-supmat

Detecting a stochastic gravitational wave background with the Laser Interferometer Space Antenna

The random superposition of many weak sources will produce a stochastic background of gravitational waves that may dominate the response of the LISA (Laser Interferometer Space Antenna) gravitational wave observatory. Unless something can be done to distinguish between a stochastic background and detector noise, the two will combine to form an effective noise floor for the detector. Two methods have been proposed to solve this problem. The first is to cross-correlate the output of two independent interferometers. The second is an ingenious scheme for monitoring the instrument noise by operating LISA as a Sagnac interferometer. Here we derive the optimal orbital alignment for cross-correlating a pair of LISA detectors, and provide the first analytic derivation of the Sagnac sensitivity curve.Comment: 9 pages, 11 figures. Significant changes to the noise estimate

Searches for Periodic Neutrino Emission from Binary Systems with 22 and 40 Strings of IceCube

Recent observations of GeV /TeV photon emission from several X-ray binaries have sparked a renewed interest in these objects as galactic particle accelerators. In spite of the available multi-wavelength data, their acceleration mechanisms are not determined, and the nature of the accelerated particles (hadrons or leptons) is unknown. While much evidence favors leptonic emission, it is very likely that a hadronic component is also accelerated in the jets of these binary systems. The observation of neutrino emission would be clear evidence for the presence of a hadronic component in the outflow of these sources. In this paper we look for periodic neutrino emission from binary systems. Such modulation, observed in the photon flux, would be caused by the geometry of these systems. The results of two searches are presented that differ in the treatment of the spectral shape and phase of the emission. The 'generic' search allows parameters to vary freely and best fit values, in a 'model-dependent' search, predictions are used to constrain these parameters. We use the IceCube data taken from May 31, 2007 to April 5, 2008 with its 22-string configuration, and from April 5, 2008 and May 20, 2009 with its 40-string configuration. For the generic search and the 40 string sample, we find that the most significant source in the catalog of 7 binary stars is Cygnus X-3 with a 1.8% probability after trials (2.10" sigma one-sided) of being produced by statistical fluctuations of the background. The model-dependent method tested a range of system geometries - the inclination and the massive star's disk size - for LS I+61 deg 303, no significant excess was found

Observation of Anisotropy in the Galactic Cosmic Ray Arrival Directions at 400 TEV With IceCube

In this paper we report the first observation in the Southern hemisphere of an energy dependence in the Galactic cosmic ray anisotropy up to a few hundred TeV. This measurement was performed using cosmic ray induced muons recorded by the partially deployed IceCube observatory between May 2009 and May 2010. The data include a total of 33x l0(epx 9) muon events with a median angular resolution of approx 3 degrees. A sky map of the relative intensity in arrival direction over the Southern celestial sky is presented for cosmic ray median energies of 20 and 400 Te V. The same large-scale anisotropy observed at median energies around 20 TeV is not present at 400 TeV. Instead, the high energy skymap shows a different anisotropy structure including a deficit with a post-trial significance of -6.30 sigma. This anisotropy reveals a new feature of the Galactic cosmic ray distribution, which must be incorporated into theories of the origin and propagation of cosmic rays

Searching for Soft Relativistic Jets in Core-Collapse Supernovae with the IceCube Optical Follow-up Program

Context. Transient neutrino sources such as Gamma-Ray Bursts (GRBs) and Supernovae (SNe) are hypothesized to emit bursts of high-energy neutrinos on a time-scale of < or approx.100 s. While GRB neutrinos would be produced in high relativistic jets, core-collapse SNe might host soft-relativistic jets, which become stalled in the outer layers of the progenitor star leading to an efficient production of high-energy neutrinos. Aims. To increase the sensitivity to these neutrinos and identify their sources, a low-threshold optical follow-up program for neutrino multiplets detected with the IceCube observatory has been implemented. Methods. If a neutrino multiplet, i.e. two or more neutrinos from the same direction within 100 s, is found by IceCube a trigger is sent to the Robotic Optical Transient Search Experiment, ROTSE. The 4 ROTSE telescopes immediately start an observation program of the corresponding region of the sky in order to detect an optical counterpart to the neutrino events. Results. No statistically significant excess in the rate of neutrino multiplets has been observed and furthermore no coincidence with an optical counterpart was found. Conclusions. The search allows, for the first time, to set stringent limits on current models predicting a high-energy neutrino flux from soft relativistic hadronic jets in core-collapse SNe. We conclude that a sub-population of SNe with typical Lorentz boost factor and jet energy of 10 and 3 x 10(exp 51) erg, respectively, does not exceed 4:2% at 90% confidence

Direct constraint on the distance of y2 Velorum from AMBER/VLTI observations

In this work, we present the first AMBER observations, of the Wolf-Rayet and O (WR+O) star binary system y2 Velorum. The AMBER instrument was used with the telescopes UT2, UT3, and UT4 on baselines ranging from 46m to 85m. It delivered spectrally dispersed visibilities, as well as differential and closure phases, with a resolution R = 1500 in the spectral band 1.95-2.17 micron. We interpret these data in the context of a binary system with unresolved components, neglecting in a first approximation the wind-wind collision zone flux contribution. We show that the AMBER observables result primarily from the contribution of the individual components of the WR+O binary system. We discuss several interpretations of the residuals, and speculate on the detection of an additional continuum component, originating from the free-free emission associated with the wind-wind collision zone (WWCZ), and contributing at most to the observed K-band flux at the 5% level. The expected absolute separation and position angle at the time of observations were 5.1&plusmn;0.9mas and 66&plusmn;15&deg; respectively. However, we infer a separation of 3.62+0.11-0.30 mas and a position angle of 73+9-11&deg;. Our analysis thus implies that the binary system lies at a distance of 368+38-13 pc, in agreement with recent spectrophotometric estimates, but significantly larger than the Hipparcos value of 258+41-31 pc

Increasing the Depth of Current Understanding: Sensitivity Testing of Deep-Sea Larval Dispersal Models for Ecologists

Larval dispersal is an important ecological process of great interest to conservation and the establishment of marine protected areas. Increasing numbers of studies are turning to biophysical models to simulate dispersal patterns, including in the deep-sea, but for many ecologists unassisted by a physical oceanographer, a model can present as a black box. Sensitivity testing offers a means to test the models' abilities and limitations and is a starting point for all modelling efforts. The aim of this study is to illustrate a sensitivity testing process for the unassisted ecologist, through a deep-sea case study example, and demonstrate how sensitivity testing can be used to determine optimal model settings, assess model adequacy, and inform ecological interpretation of model outputs. Five input parameters are tested (timestep of particle simulator (TS), horizontal (HS) and vertical separation (VS) of release points, release frequency (RF), and temporal range (TR) of simulations) using a commonly employed pairing of models. The procedures used are relevant to all marine larval dispersal models. It is shown how the results of these tests can inform the future set up and interpretation of ecological studies in this area. For example, an optimal arrangement of release locations spanning a release area could be deduced; the increased depth range spanned in deep-sea studies may necessitate the stratification of dispersal simulations with different numbers of release locations at different depths; no fewer than 52 releases per year should be used unless biologically informed; three years of simulations chosen based on climatic extremes may provide results with 90% similarity to five years of simulation; and this model setup is not appropriate for simulating rare dispersal events. A step-by-step process, summarising advice on the sensitivity testing procedure, is provided to inform all future unassisted ecologists looking to run a larval dispersal simulation

All-Particle Cosmic Ray Energy Spectrum Measured with 26 Icetop Stations

We report on a measurement of the cosmic ray energy spectrum with the IceTop air shower array, thesurface component of the IceCube Neutrino Observatory at the South Pole. The data used in this analysiswere taken between June and October, 2007, with 26 surface stations operational at that time, corresponding to about one third of the final array. The fiducial area used in this analysis was 0.122 square kilometers.The analysis investigated the energy spectrum from 1 to 100 PeV measured for three different zenithangle ranges between 0 and 46. Because of the isotropy of cosmic rays in this energy range the spectrafrom all zenith angle intervals have to agree. The cosmic-ray energy spectrum was determined under differentassumptions on the primary mass composition. Good agreement of spectra in the three zenithangle ranges was found for the assumption of pure proton and a simple two-component model. Forzenith angles theta less than 30 deg., where the mass dependence is smallest, the knee in the cosmic ray energy spectrumwas observed at about 4 PeV, with a spectral index above the knee of about -3.1. Moreover, an indicationof a flattening of the spectrum above 22 PeV was observed