Trade-offs between retroactivity and noise in connected transcriptional components

At the interconnection of two gene transcriptional components in a biomolecular network, the noise in the downstream component can be reduced by increasing its gene copy number. However, this method of reducing noise increases the load applied to the upstream system, called retroactivity, thereby causing a perturbation in the upstream system. In this work, we quantify the error in the system trajectories caused by perturbations due to retroactivity and noise, and analyze the trade-off between these two perturbations. We model the system as a set of nonlinear chemical Langevin equations and quantify the trade-off by employing contraction theory for stochastic systems.National Science Foundation (U.S.). Division of Computing and Communication Foundations (Award 1058127)United States. Air Force Office of Scientific Research (Award FA9550-12-1-0129

Comparison of Gravitational Wave Detector Network Sky Localization Approximations

Gravitational waves emitted during compact binary coalescences are a promising source for gravitational-wave detector networks. The accuracy with which the location of the source on the sky can be inferred from gravitational wave data is a limiting factor for several potential scientific goals of gravitational-wave astronomy, including multi-messenger observations. Various methods have been used to estimate the ability of a proposed network to localize sources. Here we compare two techniques for predicting the uncertainty of sky localization -- timing triangulation and the Fisher information matrix approximations -- with Bayesian inference on the full, coherent data set. We find that timing triangulation alone tends to over-estimate the uncertainty in sky localization by a median factor of $4$ for a set of signals from non-spinning compact object binaries ranging up to a total mass of $20 M_\odot$, and the over-estimation increases with the mass of the system. We find that average predictions can be brought to better agreement by the inclusion of phase consistency information in timing-triangulation techniques. However, even after corrections, these techniques can yield significantly different results to the full analysis on specific mock signals. Thus, while the approximate techniques may be useful in providing rapid, large scale estimates of network localization capability, the fully coherent Bayesian analysis gives more robust results for individual signals, particularly in the presence of detector noise.Comment: 11 pages, 7 Figure

The Effect of the LISA Response Function on Observations of Monochromatic Sources

The Laser Interferometer Space Antenna (LISA) is expected to provide the largest observational sample of binary systems of faint sub-solar mass compact objects, in particular white-dwarfs, whose radiation is monochromatic over most of the LISA observational window. Current astrophysical estimates suggest that the instrument will be able to resolve about 10000 such systems, with a large fraction of them at frequencies above 3 mHz, where the wavelength of gravitational waves becomes comparable to or shorter than the LISA arm-length. This affects the structure of the so-called LISA transfer function which cannot be treated as constant in this frequency range: it introduces characteristic phase and amplitude modulations that depend on the source location in the sky and the emission frequency. Here we investigate the effect of the LISA transfer function on detection and parameter estimation for monochromatic sources. For signal detection we show that filters constructed by approximating the transfer function as a constant (long wavelength approximation) introduce a negligible loss of signal-to-noise ratio -- the fitting factor always exceeds 0.97 -- for f below 10mHz, therefore in a frequency range where one would actually expect the approximation to fail. For parameter estimation, we conclude that in the range 3mHz to 30mHz the errors associated with parameter measurements differ from about 5% up to a factor of 10 (depending on the actual source parameters and emission frequency) with respect to those computed using the long wavelength approximation.Comment: replacement version with typos correcte

The conserved immunoglobulin domain controls the subcellular localization of the homophilic adhesion receptor protein-tyrosine phosphatase mu

The receptor protein-tyrosine phosphatase mu (PTPmu) is a homophilic adhesion protein thought to regulate cell-cell adhesion in the vascular endothelium through dephosphorylation of cell junction proteins. In subconfluent cell cultures, PTPmu resides in an intracellular membrane pool; however, as culture density increases and cell contacts form, the phosphatase localizes to sites of cell-cell contact, and its expression level increases. These characteristics of PTPmu, which are consistent with a role in cell-cell adhesion, suggest that control of subcellular localization is an important mechanism to regulate the function of this phosphatase. To gain a better understanding of how PTPmu is regulated, we examined the importance of the conserved immunoglobulin domain, containing the homophilic binding site, in control of the localization of the enzyme. Deletion of the immunoglobulin domain impaired localization of PTPmu to the cell-cell contacts in endothelial and epithelial cells. In addition, deletion of the immunoglobulin domain affected the distribution of PTPmu in subconfluent endothelial cells when homophilic binding to another PTPmu molecule on an apposing cell was not possible, resulting in an accumulation of the mutant phosphatase at the cell surface with a concentration at the cell periphery in the region occupied by focal adhesions. This aberrant localization correlated with reduced survival and alterations in normal focal adhesion and cytoskeleton morphology. This study therefore illustrates the critical role of the immunoglobulin domain in regulation of the localization of PTPmu and the importance of such control for the maintenance of normal cell physiology

Eccentric double white dwarfs as LISA sources in globular clusters

We consider the formation of double white dwarfs (DWDs) through dynamical interactions in globular clusters. Such interactions can give rise to eccentric DWDs, in contrast to the exclusively circular population expected to form in the Galactic disk. We show that for a 5-year Laser Interferometer Space Antenna (LISA) mission and distances as far as the Large Magellanic Cloud, multiple harmonics from eccentric DWDs can be detected at a signal-to-noise ratio higher than 8 for at least a handful of eccentric DWDs, given their formation rate and typical lifetimes estimated from current cluster simulations. Consequently the association of eccentricity with stellar-mass LISA sources does not uniquely involve neutron stars, as is usually assumed. Due to the difficulty of detecting (eccentric) DWDs with present and planned electromagnetic observatories, LISA could provide unique dynamical identifications of these systems in globular clusters.Comment: Published in ApJ 665, L5

Model reduction for a class of singularly perturbed stochastic differential equations

A class of singularly perturbed stochastic differential equations (SDE) with linear drift and nonlinear diffusion terms is considered. We prove that, on a finite time interval, the trajectories of the slow variables can be well approximated by those of a system with reduced dimension as the singular perturbation parameter becomes small. In particular, we show that when this parameter becomes small the first and second moments of the reduced system's variables closely approximate the first and second moments, respectively, of the slow variables of the singularly perturbed system. Chemical Langevin equations describing the stochastic dynamics of molecular systems with linear propensity functions including both fast and slow reactions fall within the class of SDEs considered here. We therefore illustrate the goodness of our approximation on a simulation example modeling a well known biomolecular system with fast and slow processes.United States. Air Force Office of Scientific Research (Grant FA9550-14-1-0060)National Institute of General Medical Sciences (U.S.) (Grant P50 GMO9879

A rapid assay for tyrosinase activity

A rapid assay for tyrosinase activit

LISA data analysis: The monochromatic binary detection and initial guess problems

We consider the detection and initial guess problems for the LISA gravitational wave detector. The detection problem is the problem of how to determine if there is a signal present in instrumental data and how to identify it. Because of the Doppler and plane-precession spreading of the spectral power of the LISA signal, the usual power spectrum approach to detection will have difficulty identifying sources. A better method must be found. The initial guess problem involves how to generate {\it a priori} values for the parameters of a parameter-estimation problem that are close enough to the final values for a linear least-squares estimator to converge to the correct result. A useful approach to simultaneously solving the detection and initial guess problems for LISA is to divide the sky into many pixels and to demodulate the Doppler spreading for each set of pixel coordinates. The demodulated power spectra may then be searched for spectral features. We demonstrate that the procedure works well as a first step in the search for gravitational waves from monochromatic binaries.Comment: 8 pages, 8 figure

A data analysis library for gravitational wave detection

One of the main goals of Pulsar Timing Arrays (PTAs) is the direct detection of gravitational waves (GWs). A first detection will be a major leap for astronomy and substantial effort is currently going into timing as many pulsars as possible, with the highest possible accuracy. As part of the individual PTA projects, several groups are developing data analysis methods for the final stage of a gravitational-waves search pipeline: the analysis of the timing residuals. Here we report the progress of on-going work to develop, within a Bayesian framework, a comprehensive and user friendly analysis library to search for gravitational waves in PTA data

Solar Atmospheric Oscillations and the Chromospheric Magnetic Topology

We investigate the oscillatory properties of the quiet solar chromosphere in relation to the underlying photosphere, with particular regard to the effects of the magnetic topology. We perform a Fourier analysis on a sequence of line-of-sight velocities measured simultaneously in a photospheric (Fe I 709.0 nm) and a chromospheric line (Ca II 854.2 nm). The velocities were obtained from full spectroscopic data acquired at high spatial resolution with the Interferometric BIdimensional Spectrometer (IBIS). The field of view encompasses a full supergranular cell, allowing us to discriminate between areas with different magnetic characteristics. We show that waves with frequencies above the acoustic cut-off propagate from the photosphere to upper layers only in restricted areas of the quiet Sun. A large fraction of the quiet chromosphere is in fact occupied by ``magnetic shadows'', surrounding network regions, that we identify as originating from fibril-like structures observed in the core intensity of the Ca II line. We show that a large fraction of the chromospheric acoustic power at frequencies below the acoustic cut-off, residing in the proximity of the magnetic network elements, directly propagates from the underlying photosphere. This supports recent results arguing that network magnetic elements can channel low-frequency photospheric oscillations into the chromosphere, thus providing a way to input mechanical energy in the upper layers.Comment: 4 pages, 3 figure, A&A Letters in pres