361 research outputs found
Sturm-liouville problems and Hammerstein operators
It is shown that a generally complex-valued function of a real variable is a solution of a classical Sturm- Liouville eigenvalue problem if and only if a related twoparameter eigenvalue problem for a pair of integral operators, one of which is of Hammerstein type, admits a real solution belonging to a cone in a Krein space
Analysis of the first IPTA Mock Data Challenge by the EPTA timing data analysis working group
This is a summary of the methods we used to analyse the first IPTA Mock Data Challenge (MDC), and the obtained results. We have used a Bayesian analysis in the time domain, accelerated using the recently developed ABC-method which consists of a form of lossy linear data compression. The TOAs were first processed with Tempo2, where the design matrix was extracted for use in a subsequent Bayesian analysis. We used different noise models to analyse the datasets: no red noise, red noise the same for all pulsars, and individual red noise per pulsar. We sampled from the likelihood with four different samplers: "emcee", "t-walk", "Metropolis-Hastings", and "pyMultiNest". All but emcee agreed on the final result, with emcee failing due to artefacts of the high-dimensionality of the problem. An interesting issue we ran into was that the prior of all the 36 (red) noise amplitudes strongly affects the results. A flat prior in the noise amplitude biases the inferred GWB amplitude, whereas a flat prior in log-amplitude seems to work well. This issue is only apparent when using a noise model with individually modelled red noise for all pulsars. Our results for the blind challenges are in good agreement with the injected values. For the GWB amplitudes we found h_c = 1.03 +/- 0.11 [10^{-14}], h_c = 5.70 +/- 0.35 [10^{-14}], and h_c = 6.91 +/- 1.72 [10^{-15}], and for the GWB spectral index we found gamma = 4.28 +/- 0.20, gamma = 4.35 +/- 0.09, and gamma = 3.75 +/- 0.40. We note that for closed challenge 3 there was quite some covariance between the signal and the red noise: if we constrain the GWB spectral index to the usual choice of gamma = 13/3, we obtain the estimates: h_c = 10.0 +/- 0.64 [10^{-15}], h_c = 56.3 +/- 2.42 [10^{-15}], and h_c = 4.83 +/- 0.50 [10^{-15}], with one-sided 2 sigma upper-limits of: h_c <= 10.98 [10^{-15}], h_c <= 60.29 [10^{-15}], and h_c <= 5.65 [10^{-15}]
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
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
Sturm-Liouville operators on time scales
We establish the connection between Sturm-Liouville equations on time scales
and Sturm--Liouville equations with measure-valued coefficients. Based on this
connection we generalize several results for Sturm-Liouville equations on time
scales which have been obtained by various authors in the past.Comment: 12 page
The Local Nanohertz Gravitational-Wave Landscape From Supermassive Black Hole Binaries
Supermassive black hole binaries (SMBHBs) in the 10 million to 10 billion
range form in galaxy mergers, and live in galactic nuclei with large
and poorly constrained concentrations of gas and stars. There are currently no
observations of merging SMBHBs--- it is in fact possible that they stall at
their final parsec of separation and never merge. While LIGO has detected high
frequency GWs, SMBHBs emit GWs in the nanohertz to millihertz band. This is
inaccessible to ground-based interferometers, but possible with Pulsar Timing
Arrays (PTAs). Using data from local galaxies in the 2 Micron All-Sky Survey,
together with galaxy merger rates from Illustris, we find that there are on
average sources emitting GWs in the PTA band, and binaries
which will never merge. Local unresolved SMBHBs can contribute to GW background
anisotropy at a level of , and if the GW background can be
successfully isolated, GWs from at least one local SMBHB can be detected in 10
years.Comment: submitted to Nature Astronomy (reformatted for arXiv
Electro-clinical and neurodevelopmental outcome in six children with early diagnosis of tuberous sclerosis complex and role of the genetic background
Background: Seizures in individuals affected by tuberous sclerosis complex (TSC) commonly develop in the first year of life, are often preceded by a progressive deterioration of the electroencephalogram (EEG), and likely influence developmental outcome. Although early diagnosis of TSC has offered a tremendous opportunity to monitor affected patients before seizure onset, reports of the neurological manifestations of TSC in infants before seizure onset are still scarce. Here we describe early EEG activity, clinical and genetic data and developmental assessment in a group of TSC infants, with the aim of identifying possible prognostic factors for neurodevelopmental outcome. Methods: We report on six infants diagnosed with TSC pre-or perinatally, who underwent serial Video-EEG recordings during the first two years of life. EEGs were classified based on distribution and intensity of interictal epileptiform discharges, and Vigabatrin was introduced in case of ictal discharges. Psychomotor development, cognitive functioning and behavioral problems were assessed through standardized scales. Molecular testing included analysis for point mutations and deletions/duplications in TSC1 and TSC2. Results: EEG abnormalities appeared at a mean age of 4 months. Four of the six patients developed seizures. EEG abnormalities preceded the onset of clinical seizures in all of them. The two individuals with good seizure control showed normal development, while the other two exhibited psychomotor delays. The patients who did not develop seizures had normal development. A pathogenic variant in the TSC2 gene was detected in all patients but one. The one without a mutation identified did not develop seizures and showed normal neurodevelopment. Of note, the two patients presenting with the worst outcome (that is, poor seizure control and intellectual/behavioral disability) both carried pathogenic variants in the GAP domain of TSC2. Conclusion: Our report supports the importance of EEG monitoring before seizure onset in patients with TSC, and the correlation between prompt seizure control and positive neurodevelopmental outcome, regardless of seizure type. Our results also indicate a possible role of the genetic background in influencing the outcome
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
Observing the dynamics of super-massive black hole binaries with Pulsar Timing Arrays
Pulsar Timing Arrays are a prime tool to study unexplored astrophysical
regimes with gravitational waves. Here we show that the detection of
gravitational radiation from individually resolvable super-massive black hole
binary systems can yield direct information about the masses and spins of the
black holes, provided that the gravitational-wave induced timing fluctuations
both at the pulsar and at the Earth are detected. This in turn provides a map
of the non-linear dynamics of the gravitational field and a new avenue to
tackle open problems in astrophysics connected to the formation and evolution
of super-massive black holes. We discuss the potential, the challenges and the
limitations of these observations.Comment: 5 pages, 1 figur
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
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