Line-robust statistics for continuous gravitational waves: safety in the case of unequal detector sensitivities

The multi-detector F-statistic is close to optimal for detecting continuous gravitational waves (CWs) in Gaussian noise. However, it is susceptible to false alarms from instrumental artefacts, for example quasi-monochromatic disturbances ('lines'), which resemble a CW signal more than Gaussian noise. In a recent paper [Keitel et al 2014, PRD 89 064023], a Bayesian model selection approach was used to derive line-robust detection statistics for CW signals, generalising both the F-statistic and the F-statistic consistency veto technique and yielding improved performance in line-affected data. Here we investigate a generalisation of the assumptions made in that paper: if a CW analysis uses data from two or more detectors with very different sensitivities, the line-robust statistics could be less effective. We investigate the boundaries within which they are still safe to use, in comparison with the F-statistic. Tests using synthetic draws show that the optimally-tuned version of the original line-robust statistic remains safe in most cases of practical interest. We also explore a simple idea on further improving the detection power and safety of these statistics, which we however find to be of limited practical use.Comment: 21 pages, 11 figures, updated to match published versio

Energy of Magnetic Vortices in Rotating Superconductor

We carry out a systematic analytic investigation of stationary and cylindrically symmetric vortex configurations for simple models representing an incompressible non-relativistic superconductor in a rigidly rotating background. It is shown that although the magnetic and kinetic contributions to the energy per unit length of such a vortex are separately modified by the background angular velocity, its effect on the total energy per unit length cancels out. For a type II superconductor threaded by a parallel array of such vortices, this result implies that the relevant macroscopic magnetic field strength H will not be equal to the large scale average of the local magnetic induction B (as has previously been suggested) but instead that H will simply be equal to the external London field that characterizes the value of B outside the vortices.Comment: 8 pages, uses RevTeX, submitted to Phys.Rev.

Optimal rates of decay for operator semigroups on Hilbert spaces

We investigate rates of decay for $C_0$-semigroups on Hilbert spaces under assumptions on the resolvent growth of the semigroup generator. Our main results show that one obtains the best possible estimate on the rate of decay, that is to say an upper bound which is also known to be a lower bound, under a comparatively mild assumption on the growth behaviour. This extends several statements obtained by Batty, Chill and Tomilov (J. Eur. Math. Soc., vol. 18(4), pp. 853-929, 2016). In fact, for a large class of semigroups our condition is not only sufficient but also necessary for this optimal estimate to hold. Even without this assumption we obtain a new quantified asymptotic result which in many cases of interest gives a sharper estimate for the rate of decay than was previously available, and for semigroups of normal operators we are able to describe the asymptotic behaviour exactly. We illustrate the strength of our theoretical results by using them to obtain sharp estimates on the rate of energy decay for a wave equation subject to viscoelastic damping at the boundary.Comment: 25 pages. To appear in Advances in Mathematic

An F-statistic based multi-detector veto for detector artifacts in continuous-wave gravitational wave data

Continuous gravitational waves (CW) are expected from spinning neutron stars with non-axisymmetric deformations. A network of interferometric detectors (LIGO, Virgo and GEO600) is looking for these signals. They are predicted to be very weak and retrievable only by integration over long observation times. One of the standard methods of CW data analysis is the multi-detector F-statistic. In a typical search, the F-statistic is computed over a range in frequency, spin-down and sky position, and the candidates with highest F values are kept for further analysis. However, this detection statistic is susceptible to a class of noise artifacts, strong monochromatic lines in a single detector. By assuming an extended noise model - standard Gaussian noise plus single-detector lines - we can use a Bayesian odds ratio to derive a generalized detection statistic, the line veto (LV-) statistic. In the absence of lines, it behaves similarly to the F-statistic, but it is more robust against line artifacts. In the past, ad-hoc post-processing vetoes have been implemented in searches to remove these artifacts. Here we provide a systematic framework to develop and benchmark this class of vetoes. We present our results from testing this LV-statistic on simulated data.Comment: 2 pages, 1 figure, to be published in Proceedings of Statistical Challenges in Modern Astronomy V, Springer 201

Identification of control targets in Boolean molecular network models via computational algebra

Motivation: Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system. Experimentally, node manipulation requires technology to completely repress or fully activate a particular gene product while edge manipulations only require a drug that inactivates the interaction between two gene products. Results: This paper presents a method for the identification of potential intervention targets in Boolean molecular network models using algebraic techniques. The approach exploits an algebraic representation of Boolean networks to encode the control candidates in the network wiring diagram as the solutions of a system of polynomials equations, and then uses computational algebra techniques to find such controllers. The control methods in this paper are validated through the identification of combinatorial interventions in the signaling pathways of previously reported control targets in two well studied systems, a p53-mdm2 network and a blood T cell lymphocyte granular leukemia survival signaling network.Comment: 12 pages, 4 figures, 2 table

The Republican Right since 1945

In 1981, a Right Wing Republican at long last resided in the White House, presiding over what may prove to be the most fundamental restructuring of American political life since the days of Franklin D. Roosevelt. Fortunately, The Republican Right since 1945 now provides us with the necessary historical understanding of conservative Republicans. David Reinhard\u27s dispassionate yet lively book recounts the Republican Right\u27s political struggles from the death of FDR in 1945 to the inauguration of Ronald Reagan. Younger readers will discover that Right Wing Republicans are older than Ronald Reagan or Barry Goldwater and that some conservative Republicans once feared the overextension of American power abroad and the rise of the garrison state at home. Those old enough to remember when the Republican Right was called the Old Guard will rediscover the events and personalities of those earlier years, thanks to Reinhard’s use of more than thirty five manuscript collections and the most recent historical writing. Not content to let this history end where traditional manuscript sources run thin, Reinhard has brought the story of the Republican Right Wing forward to President Ronald Reagan\u27s inauguration, placing Right Wing Republican reaction to the Johnson and the Nixon-Ford years within the context of the earlier period and chronicling the electoral triumph of Ronald Reagan and the Republican Right. Students of the past and observers of the present will appreciate Reinhard\u27s treatment of the always-troubled Nixon-Republican Right association; challenger Ronald Reagan\u27s battle against President Gerald Ford in 1976; the decline of GOP moderation; and the rise of the New Right-Moral Majority forces and their relationship to the now ascendant Republican Right. Reinhard illuminates the conservative Republican past and thereby makes the current political scene more understandable. Thoroughly researched and brilliantly written, The Republican Right since 1945 will fascinate scholars and general readers alike. A graduate of Albright College, David W. Reinhard holds a doctorate from Pennsylvania State University. He was the American Historical Association\u27s National Congressional Fellow in 1981-82 and currently works on Capitol Hill.https://uknowledge.uky.edu/upk_political_science_american_politics/1023/thumbnail.jp