Control of cellular automata

We study the problem of master-slave synchronization and control of totalistic cellular automata (CA) by putting a fraction of sites of the slave equal to those of the master and finding the distance between both as a function of this fraction. We present three control strategies that exploit local information about the CA, mainly, the number of nonzero Boolean derivatives. When no local information is used, we speak of synchronization. We find the critical properties of control and discuss the best control strategy compared with synchronization

Orthogonal polynomials of discrete variable and Lie algebras of complex size matrices

We give a uniform interpretation of the classical continuous Chebyshev's and Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie algebra gl(N), where N is any complex number. One can similarly interpret Chebyshev's and Hahn's q-polynomials and introduce orthogonal polynomials corresponding to Lie superlagebras. We also describe the real forms of gl(N), quasi-finite modules over gl(N), and conditions for unitarity of the quasi-finite modules. Analogs of tensors over gl(N) are also introduced.Comment: 25 pages, LaTe

Gravitational wave astronomy with the SKA

On a time scale of years to decades, gravitational wave (GW) astronomy will become a reality. Low frequency (nanoHz) GWs are detectable through long-term timing observations of the most stable pulsars. Radio observatories worldwide are currently carrying out observing programmes to detect GWs, with data sets being shared through the International Pulsar Timing Array project. One of the most likely sources of low frequency GWs are supermassive black hole binaries (SMBHBs), detectable as a background due to a large number of binaries, or as continuous or burst emission from individual sources. No GW signal has yet been detected, but stringent constraints are already being placed on galaxy evolution models. The SKA will bring this research to fruition. In this chapter, we describe how timing observations using SKA1 will contribute to detecting GWs, or can confirm a detection if a first signal already has been identified when SKA1 commences observations. We describe how SKA observations will identify the source(s) of a GW signal, search for anisotropies in the background, improve models of galaxy evolution, test theories of gravity, and characterise the early inspiral phase of a SMBHB system. We describe the impact of the large number of millisecond pulsars to be discovered by the SKA; and the observing cadence, observation durations, and instrumentation required to reach the necessary sensitivity. We describe the noise processes that will influence the achievable precision with the SKA. We assume a long-term timing programme using the SKA1-MID array and consider the implications of modifications to the current design. We describe the possible benefits from observations using SKA1-LOW. Finally, we describe GW detection prospects with SKA1 and SKA2, and end with a description of the expectations of GW astronomy.Comment: 19 pages, 3 figures, to be published in: "Advancing Astrophysics with the Square Kilometre Array", Proceedings of Science, PoS(AASKA14)03

Standardization of Preclinical PET/CT Imaging to Improve Quantitative Accuracy, Precision, and Reproducibility: A Multicenter Study

Preclinical PET/CT is a well-established noninvasive imaging tool for studying disease development/progression and the development of novel radiotracers and pharmaceuticals for clinical applications. Despite this pivotal role, standardization of preclinical PET/CT protocols, including CT absorbed dose guidelines, is essentially nonexistent. This study (1) quantitatively assesses the variability of current preclinical PET/CT acquisition and reconstruction protocols routinely used across multiple centers and scanners; and (2) proposes acquisition and reconstruction PET/CT protocols for standardization of multicenter data, optimized for routine scanning in the preclinical PET/CT laboratory. Methods: Five different commercial preclinical PET/CT scanners in Europe and the United States were enrolled. Seven different PET/CT phantoms were used for evaluating biases on default/general scanner protocols, followed by developing standardized protocols. PET, CT, and absorbed dose biases were assessed. Results: Site default CT protocols were the following: greatest extracted Hounsfield units (HU) were 133 HU for water and −967 HU for air; significant differences in all tissue equivalent material (TEM) groups were measured. The average CT absorbed doses for mouse and rat were 72 mGy and 40 mGy, respectively. Standardized CT protocol were the following: greatest extracted HU were −77 HU for water and −990 HU for air; TEM precision improved with a reduction in variability for each tissue group. The average CT absorbed dose for mouse and rat decreased to 37 mGy and 24 mGy, respectively. Site default PET protocols were the following: uniformity was substandard in one scanner, recovery coefficients (RCs) were either over- or underestimated (maximum of 43%), standard uptake values (SUVs) were biased by a maximum of 44%. Standardized PET protocols were the following: scanner with substandard uniformity improved by 36%, RC variability decreased by 13% points, and SUV accuracy improved to 10%. Conclusion: Data revealed important quantitative biases in preclinical PET/CT and absorbed doses with default protocols. Standardized protocols showed improvements in measured PET/CT accuracy and precision with reduced CT absorbed dose across sites. Adhering to standardized protocols generates reproducible and consistent preclinical imaging datasets, thus augmenting translation of research findings to the clinic

The noise properties of 42 millisecond pulsars from the European Pulsar Timing Array and their impact on gravitational wave searches

The sensitivity of Pulsar Timing Arrays to gravitational waves depends on the noise present in the individual pulsar timing data. Noise may be either intrinsic or extrinsic to the pulsar. Intrinsic sources of noise will include rotational instabilities, for example. Extrinsic sources of noise include contributions from physical processes which are not sufficiently well modelled, for example, dispersion and scattering effects, analysis errors and instrumental instabilities. We present the results from a noise analysis for 42 millisecond pulsars (MSPs) observed with the European Pulsar Timing Array. For characterising the low-frequency, stochastic and achromatic noise component, or "timing noise", we employ two methods, based on Bayesian and frequentist statistics. For 25 MSPs, we achieve statistically significant measurements of their timing noise parameters and find that the two methods give consistent results. For the remaining 17 MSPs, we place upper limits on the timing noise amplitude at the 95% confidence level. We additionally place an upper limit on the contribution to the pulsar noise budget from errors in the reference terrestrial time standards (below 1%), and we find evidence for a noise component which is present only in the data of one of the four used telescopes. Finally, we estimate that the timing noise of individual pulsars reduces the sensitivity of this data set to an isotropic, stochastic GW background by a factor of >9.1 and by a factor of >2.3 for continuous GWs from resolvable, inspiralling supermassive black-hole binaries with circular orbits.Comment: Accepted for publication by the Monthly Notices of the Royal Astronomical Societ

A functional model, eigenvalues, and finite singular critical points for indefinite Sturm-Liouville operators

Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach to the problem is given via a functional model for indefinite Sturm-Liouville operators. Algebraic multiplicities of eigenvalues are obtained. Also, operators with finite singular critical points are considered.Comment: 38 pages, Proposition 2.2 and its proof corrected, Remarks 2.5, 3.4, and 3.12 extended, details added in subsections 2.3 and 4.2, section 6 rearranged, typos corrected, references adde

Abnormal cognition, sleep, EEG and brain metabolism in a novel knock-in Alzheimer mouse, PLB1

Peer reviewedPublisher PD

The NANOGrav 11-Year Data Set: Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries

Observations indicate that nearly all galaxies contain supermassive black holes (SMBHs) at their centers. When galaxies merge, their component black holes form SMBH binaries (SMBHBs), which emit low-frequency gravitational waves (GWs) that can be detected by pulsar timing arrays (PTAs). We have searched the recently-released North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 11-year data set for GWs from individual SMBHBs in circular orbits. As we did not find strong evidence for GWs in our data, we placed 95\% upper limits on the strength of GWs from such sources as a function of GW frequency and sky location. We placed a sky-averaged upper limit on the GW strain of $h_0 < 7.3(3) \times 10^{-15}$ at $f_\mathrm{gw}= 8$ nHz. We also developed a technique to determine the significance of a particular signal in each pulsar using ``dropout' parameters as a way of identifying spurious signals in measurements from individual pulsars. We used our upper limits on the GW strain to place lower limits on the distances to individual SMBHBs. At the most-sensitive sky location, we ruled out SMBHBs emitting GWs with $f_\mathrm{gw}= 8$ nHz within 120 Mpc for $\mathcal{M} = 10^9 \, M_\odot$, and within 5.5 Gpc for $\mathcal{M} = 10^{10} \, M_\odot$. We also determined that there are no SMBHBs with $\mathcal{M} > 1.6 \times 10^9 \, M_\odot$ emitting GWs in the Virgo Cluster. Finally, we estimated the number of potentially detectable sources given our current strain upper limits based on galaxies in Two Micron All-Sky Survey (2MASS) and merger rates from the Illustris cosmological simulation project. Only 34 out of 75,000 realizations of the local Universe contained a detectable source, from which we concluded it was unsurprising that we did not detect any individual sources given our current sensitivity to GWs.Comment: 10 pages, 11 figures. Accepted by Astrophysical Journal. Please send any comments/questions to S. J. Vigeland ([email protected]

Multi-Messenger Gravitational Wave Searches with Pulsar Timing Arrays: Application to 3C66B Using the NANOGrav 11-year Data Set

When galaxies merge, the supermassive black holes in their centers may form binaries and, during the process of merger, emit low-frequency gravitational radiation in the process. In this paper we consider the galaxy 3C66B, which was used as the target of the first multi-messenger search for gravitational waves. Due to the observed periodicities present in the photometric and astrometric data of the source of the source, it has been theorized to contain a supermassive black hole binary. Its apparent 1.05-year orbital period would place the gravitational wave emission directly in the pulsar timing band. Since the first pulsar timing array study of 3C66B, revised models of the source have been published, and timing array sensitivities and techniques have improved dramatically. With these advances, we further constrain the chirp mass of the potential supermassive black hole binary in 3C66B to less than $(1.65\pm0.02) \times 10^9~{M_\odot}$ using data from the NANOGrav 11-year data set. This upper limit provides a factor of 1.6 improvement over previous limits, and a factor of 4.3 over the first search done. Nevertheless, the most recent orbital model for the source is still consistent with our limit from pulsar timing array data. In addition, we are able to quantify the improvement made by the inclusion of source properties gleaned from electromagnetic data to `blind' pulsar timing array searches. With these methods, it is apparent that it is not necessary to obtain exact a priori knowledge of the period of a binary to gain meaningful astrophysical inferences.Comment: 14 pages, 6 figures. Accepted by Ap

Gravitational Waves From Known Pulsars: Results From The Initial Detector Era

We present the results of searches for gravitational waves from a large selection of pulsars using data from the most recent science runs (S6, VSR2 and VSR4) of the initial generation of interferometric gravitational wave detectors LIGO (Laser Interferometric Gravitational-wave Observatory) and Virgo. We do not see evidence for gravitational wave emission from any of the targeted sources but produce upper limits on the emission amplitude. We highlight the results from seven young pulsars with large spin-down luminosities. We reach within a factor of five of the canonical spin-down limit for all seven of these, whilst for the Crab and Vela pulsars we further surpass their spin-down limits. We present new or updated limits for 172 other pulsars (including both young and millisecond pulsars). Now that the detectors are undergoing major upgrades, and, for completeness, we bring together all of the most up-to-date results from all pulsars searched for during the operations of the first-generation LIGO, Virgo and GEO600 detectors. This gives a total of 195 pulsars including the most recent results described in this paper.United States National Science FoundationScience and Technology Facilities Council of the United KingdomMax-Planck-SocietyState of Niedersachsen/GermanyAustralian Research CouncilInternational Science Linkages program of the Commonwealth of AustraliaCouncil of Scientific and Industrial Research of IndiaIstituto Nazionale di Fisica Nucleare of ItalySpanish Ministerio de Economia y CompetitividadConselleria d'Economia Hisenda i Innovacio of the Govern de les Illes BalearsNetherlands Organisation for Scientific ResearchPolish Ministry of Science and Higher EducationFOCUS Programme of Foundation for Polish ScienceRoyal SocietyScottish Funding CouncilScottish Universities Physics AllianceNational Aeronautics and Space AdministrationOTKA of HungaryLyon Institute of Origins (LIO)National Research Foundation of KoreaIndustry CanadaProvince of Ontario through the Ministry of Economic Development and InnovationNational Science and Engineering Research Council CanadaCarnegie TrustLeverhulme TrustDavid and Lucile Packard FoundationResearch CorporationAlfred P. Sloan FoundationAstronom