Almost sure functional central limit theorems for multiparameter stochastic processes

We present almost sure central limit theorems for stochastic processes whose time parameter ranges over the d-dimensional unit cube. Our purpose here is to generalize the classic functional central limit theorem of Prokhorov (1956) for such processes. We prove multidimensional analogues of Glivenko-Cantelli type theorems.Ми подаємо майже певнi центральнi граничнi теореми для стохастичних процесiв з часовим параметром, що змiнюється у α-вимiрному одиничному кубi. Нашою метою є узагальнення класичної функцiональної центральної граничної теореми Прохорова (1956) для таких процесiв. Ми доводимо багатовимiрнi аналоги теореми типу Глiвенко-Кантелi

Network Analysis of Differential Expression for the Identification of Disease-Causing Genes

Genetic studies (in particular linkage and association studies) identify chromosomal regions involved in a disease or phenotype of interest, but those regions often contain many candidate genes, only a few of which can be followed-up for biological validation. Recently, computational methods to identify (prioritize) the most promising candidates within a region have been proposed, but they are usually not applicable to cases where little is known about the phenotype (no or few confirmed disease genes, fragmentary understanding of the biological cascades involved). We seek to overcome this limitation by replacing knowledge about the biological process by experimental data on differential gene expression between affected and healthy individuals. Considering the problem from the perspective of a gene/protein network, we assess a candidate gene by considering the level of differential expression in its neighborhood under the assumption that strong candidates will tend to be surrounded by differentially expressed neighbors. We define a notion of soft neighborhood where each gene is given a contributing weight, which decreases with the distance from the candidate gene on the protein network. To account for multiple paths between genes, we define the distance using the Laplacian exponential diffusion kernel. We score candidates by aggregating the differential expression of neighbors weighted as a function of distance. Through a randomization procedure, we rank candidates by p-values. We illustrate our approach on four monogenic diseases and successfully prioritize the known disease causing genes

Adult Cardiac Progenitor Cell Aggregates Exhibit Survival Benefit Both In Vitro and In Vivo

Background: A major hurdle in the use of exogenous stems cells for therapeutic regeneration of injured myocardium remains the poor survival of implanted cells. To date, the delivery of stem cells into myocardium has largely focused on implantation of cell suspensions. Methodology and Principal Findings: We hypothesize that delivering progenitor cells in an aggregate form would serve to mimic the endogenous state with proper cell-cell contact, and may aid the survival of implanted cells. Microwell methodologies allow for the culture of homogenous 3D cell aggregates, thereby allowing cell-cell contact. In this study, we find that the culture of cardiac progenitor cells in a 3D cell aggregate augments cell survival and protects against cellular toxins and stressors, including hydrogen peroxide and anoxia/reoxygenation induced cell death. Moreover, using a murine model of cardiac ischemia-reperfusion injury, we find that delivery of cardiac progenitor cells in the form of 3D aggregates improved in vivo survival of implanted cells. Conclusion: Collectively, our data support the notion that growth in 3D cellular systems and maintenance of cell-cell contact improves exogenous cell survival following delivery into myocardium. These approaches may serve as a strategy to improve cardiovascular cell-based therapies

First LIGO search for gravitational wave bursts from cosmic (super)strings

We report on a matched-filter search for gravitational wave bursts from cosmic string cusps using LIGO data from the fourth science run (S4) which took place in February and March 2005. No gravitational waves were detected in 14.9 days of data from times when all three LIGO detectors were operating. We interpret the result in terms of a frequentist upper limit on the rate of gravitational wave bursts and use the limits on the rate to constrain the parameter space (string tension, reconnection probability, and loop sizes) of cosmic string models.Comment: 11 pages, 3 figures. Replaced with version submitted to PR

All-sky LIGO Search for Periodic Gravitational Waves in the Early S5 Data

We report on an all-sky search with the LIGO detectors for periodic gravitational waves in the frequency range 50--1100 Hz and with the frequency's time derivative in the range -5.0E-9 Hz/s to zero. Data from the first eight months of the fifth LIGO science run (S5) have been used in this search, which is based on a semi-coherent method (PowerFlux) of summing strain power. Observing no evidence of periodic gravitational radiation, we report 95% confidence-level upper limits on radiation emitted by any unknown isolated rotating neutron stars within the search range. Strain limits below 1.E-24 are obtained over a 200-Hz band, and the sensitivity improvement over previous searches increases the spatial volume sampled by an average factor of about 100 over the entire search band. For a neutron star with nominal equatorial ellipticity of 1.0E-6, the search is sensitive to distances as great as 500 pc--a range that could encompass many undiscovered neutron stars, albeit only a tiny fraction of which would likely be rotating fast enough to be accessible to LIGO. This ellipticity is at the upper range thought to be sustainable by conventional neutron stars and well below the maximum sustainable by a strange quark star.Comment: 6 pages, 1 figur

Stacked Search for Gravitational Waves from the 2006 SGR 1900+14 Storm

We present the results of a LIGO search for short-duration gravitational waves (GWs) associated with the 2006 March 29 SGR 1900+14 storm. A new search method is used, "stacking'' the GW data around the times of individual soft-gamma bursts in the storm to enhance sensitivity for models in which multiple bursts are accompanied by GW emission. We assume that variation in the time difference between burst electromagnetic emission and potential burst GW emission is small relative to the GW signal duration, and we time-align GW excess power time-frequency tilings containing individual burst triggers to their corresponding electromagnetic emissions. We use two GW emission models in our search: a fluence-weighted model and a flat (unweighted) model for the most electromagnetically energetic bursts. We find no evidence of GWs associated with either model. Model-dependent GW strain, isotropic GW emission energy E_GW, and \gamma = E_GW / E_EM upper limits are estimated using a variety of assumed waveforms. The stacking method allows us to set the most stringent model-dependent limits on transient GW strain published to date. We find E_GW upper limit estimates (at a nominal distance of 10 kpc) of between 2x10^45 erg and 6x10^50 erg depending on waveform type. These limits are an order of magnitude lower than upper limits published previously for this storm and overlap with the range of electromagnetic energies emitted in SGR giant flares.Comment: 7 pages, 3 figure

Search for Gravitational Waves from Low Mass Compact Binary Coalescence in LIGO's Sixth Science Run and Virgo's Science Runs 2 and 3

We report on a search for gravitational waves from coalescing compact binaries using LIGO and Virgo observations between July 7, 2009 and October 20, 2010. We searched for signals from binaries with total mass between 2 and 25 solar masses; this includes binary neutron stars, binary black holes, and binaries consisting of a black hole and neutron star. The detectors were sensitive to systems up to 40 Mpc distant for binary neutron stars, and further for higher mass systems. No gravitational-wave signals were detected. We report upper limits on the rate of compact binary coalescence as a function of total mass, including the results from previous LIGO and Virgo observations. The cumulative 90%-confidence rate upper limits of the binary coalescence of binary neutron star, neutron star- black hole and binary black hole systems are 1.3 x 10^{-4}, 3.1 x 10^{-5} and 6.4 x 10^{-6} Mpc^{-3}yr^{-1}, respectively. These upper limits are up to a factor 1.4 lower than previously derived limits. We also report on results from a blind injection challenge.Comment: 11 pages, 5 figures. For a repository of data used in the publication, go to: . Also see the announcement for this paper on ligo.org at: <http://www.ligo.org/science/Publication-S6CBCLowMass/index.php

Quantum state preparation and macroscopic entanglement in gravitational-wave detectors

Long-baseline laser-interferometer gravitational-wave detectors are operating at a factor of 10 (in amplitude) above the standard quantum limit (SQL) within a broad frequency band. Such a low classical noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150 Hz and an occupation number of 200. This result, along with the prospect for further improvements, heralds the new possibility of experimentally probing macroscopic quantum mechanics (MQM) - quantum mechanical behavior of objects in the realm of everyday experience - using gravitational-wave detectors. In this paper, we provide the mathematical foundation for the first step of a MQM experiment: the preparation of a macroscopic test mass into a nearly minimum-Heisenberg-limited Gaussian quantum state, which is possible if the interferometer's classical noise beats the SQL in a broad frequency band. Our formalism, based on Wiener filtering, allows a straightforward conversion from the classical noise budget of a laser interferometer, in terms of noise spectra, into the strategy for quantum state preparation, and the quality of the prepared state. Using this formalism, we consider how Gaussian entanglement can be built among two macroscopic test masses, and the performance of the planned Advanced LIGO interferometers in quantum-state preparation

Search for Gravitational Wave Bursts from Soft Gamma Repeaters

We present the results of a LIGO search for short-duration gravitational waves (GWs) associated with Soft Gamma Repeater (SGR) bursts. This is the first search sensitive to neutron star f-modes, usually considered the most efficient GW emitting modes. We find no evidence of GWs associated with any SGR burst in a sample consisting of the 27 Dec. 2004 giant flare from SGR 1806-20 and 190 lesser events from SGR 1806-20 and SGR 1900+14 which occurred during the first year of LIGO's fifth science run. GW strain upper limits and model-dependent GW emission energy upper limits are estimated for individual bursts using a variety of simulated waveforms. The unprecedented sensitivity of the detectors allows us to set the most stringent limits on transient GW amplitudes published to date. We find upper limit estimates on the model-dependent isotropic GW emission energies (at a nominal distance of 10 kpc) between 3x10^45 and 9x10^52 erg depending on waveform type, detector antenna factors and noise characteristics at the time of the burst. These upper limits are within the theoretically predicted range of some SGR models.Comment: 6 pages, 1 Postscript figur