Predictability of band-limited, high-frequency, and mixed processes in the presence of ideal low-pass filters

Pathwise predictability of continuous time processes is studied in deterministic setting. We discuss uniform prediction in some weak sense with respect to certain classes of inputs. More precisely, we study possibility of approximation of convolution integrals over future time by integrals over past time. We found that all band-limited processes are predictable in this sense, as well as high-frequency processes with zero energy at low frequencies. It follows that a process of mixed type still can be predicted if an ideal low-pass filter exists for this process.Comment: 10 page

Actualización en el diagnóstico y terapéutica en hipertensión pulmonar arterial

Indexación: ScieloResumen: Pulmonary Arterial Hypertension includes a heterogeneous group of disorders with a common genetic, pathological and hemodinamyc origin. It is characterized by a high pulmonary artery pressure due to a primary vascular disease, as a consequence of genetic and environmental factors. The common pathway is a vascular imbalance towards vasoconstriction and proliferation inside the small vessels. According to the World Health Organization, 2003, Pulmonary Arterial Hypertension is classified as idiopathic, familiar or associated to connective tissue diseases, HIV, drugs, porto-pulmonary hypertension, congenital intracardiac shunts and others. The diagnosis is based in hemodynamics. Echocardiogram is a non invasive and right ventricular catheterization is an invasive diagnostic tool. Follow up is based on a clinical and functional assessment through functional class classification, dyspnea scores and 6-minute walking test. The prognosis is historically devastating but new therapies are changing the natural history of the disease. New treatments have demonstrated improvement in symptoms, hemodynamic profiles and survival. Intravenous, subcutaneous or inhaled prostanoids such as Epoprostenol, Treprostinil or Iloprost respectively have been approved for Pulmonary Arterial Hypertension treatment as well as oral endothelial receptor blockers. They are all considered first line treatments for arterial pulmonary hypertensive patients with even better benefits than lung transplantation. Phosphodiesterase inhibitors (Sildenafil), have been recently approved for the treatment of pulmonary arterial hypertension.http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0034-98872006000700015&nrm=is

Parameter estimation of coalescing supermassive black hole binaries with LISA

Laser Interferometer Space Antenna (LISA) will routinely observe coalescences of supermassive black hole (BH) binaries up to very high redshifts. LISA can measure mass parameters of such coalescences to a relative accuracy of $10^{-4}-10^{-6}$, for sources at a distance of 3 Gpc. The problem of parameter estimation of massive nonspinning binary black holes using post-Newtonian (PN) phasing formula is studied in the context of LISA. Specifically, the performance of the 3.5PN templates is contrasted against its 2PN counterpart using a waveform which is averaged over the LISA pattern functions. The improvement due to the higher order corrections to the phasing formula is examined by calculating the errors in the estimation of mass parameters at each order. The estimation of the mass parameters ${\cal M}$ and $\eta$ are significantly enhanced by using the 3.5PN waveform instead of the 2PN one. For an equal mass binary of $2\times10^6M_\odot$ at a luminosity distance of 3 Gpc, the improvement in chirp mass is $\sim 11$ and that of $\eta$ is $\sim 39$. Estimation of coalescence time $t_c$ worsens by 43%. The improvement is larger for the unequal mass binary mergers. These results are compared to the ones obtained using a non-pattern averaged waveform. The errors depend very much on the location and orientation of the source and general conclusions cannot be drawn without performing Monte Carlo simulations. Finally the effect of the choice of the lower frequency cut-off for LISA on the parameter estimation is studied.Comment: 12 pages, 5 figures (eps) significant revision, accepted for publication in Phys. Rev. D. Matches with the published versio

Caracterización clínica, funcional y hemodinámica de la población con hipertensión pulmonar arterial evaluada en el Instituto Nacional del Tórax

Pulmonary Arterial Hypertension is a rare, progressive and devastating disease with severe consequences in quality of life and survival. Aim: A clinical, functional and hemodynamic assessment of patients with pulmonary arterial hypertension and categorization according to severity. Material and methods: Prospective registry of patients with arterial pulmonary hypertension, hemodynamically defined. Clinical evaluation was performed using World Health Organization functional score (I to IV) and Borg dyspnea scale. Six minute walking test, echocardiography and right heart catheterization were used for functional and hemodynamic assessment. Intravenous Adenosine was used to assess vascular reactivity during the hemodynamic evaluation. Results: Twenty nine patients were included (25 women, age range 16-72 years). Pulmonary hypertension was idiopathic in 11, associated to connective tissue disease in seven, associated to congenital heart disease in nine and associated to chronic thromboembolism in two. The mean lapse of symptoms before assessment was 2.9 years and 100% had dyspnea (Borg 5.1). Functional class I, II, III and IV was observed in 0, 5, 21 and 3 patients respectively. Six minutes walking test was 378±113 m. Mean pulmonary pressure was 59.4±12.2 mmHg, cardiac index was 2.57±0.88 and pulmonary vascular resistance index: 1798.4±855 (dyne.sec)/cm5. Nine patients had a mean pulmonary arterial pressure >55 mmHg and a cardiac index <2.1, considered as bad prognosis criteria. Adenosine test was positive in 17%. Conclusions: This group of patients with Pulmonary Arterial Hypertension was mainly conformed by young females, with a moderate to severe disease.http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0034-98872006000500007&nrm=is

Inspiralling compact binaries in quasi-elliptical orbits: The complete third post-Newtonian energy flux

The instantaneous contributions to the 3PN gravitational wave luminosity from the inspiral phase of a binary system of compact objects moving in a quasi elliptical orbit is computed using the multipolar post-Minkowskian wave generation formalism. The necessary inputs for this calculation include the 3PN accurate mass quadrupole moment for general orbits and the mass octupole and current quadrupole moments at 2PN. Using the recently obtained 3PN quasi-Keplerian representation of elliptical orbits the flux is averaged over the binary's orbit. Supplementing this by the important hereditary contributions arising from tails, tails-of-tails and tails squared terms calculated in a previous paper, the complete 3PN energy flux is obtained. The final result presented in this paper would be needed for the construction of ready-to-use templates for binaries moving on non-circular orbits, a plausible class of sources not only for the space based detectors like LISA but also for the ground based ones.Comment: 40 pages. Minor changes in text throughout. Minor typos in Eqs. (3.3b), (7.7f), (8.19d) and (8.20) corrected. Matches the published versio

Universal analytic properties of noise. Introducing the J-Matrix formalism

We propose a new method in the spectral analysis of noisy time-series data for damped oscillators. From the Jacobi three terms recursive relation for the denominators of the Pad\'e Approximations built on the well-known Z-transform of an infinite time-series, we build an Hilbert space operator, a J-Operator, where each bound state (inside the unit circle in the complex plane) is simply associated to one damped oscillator while the continuous spectrum of the J-Operator, which lies on the unit circle itself, is shown to represent the noise. Signal and noise are thus clearly separated in the complex plane. For a finite time series of length 2N, the J-operator is replaced by a finite order J-Matrix J_N, having N eigenvalues which are time reversal covariant. Different classes of input noise, such as blank (white and uniform), Gaussian and pink, are discussed in detail, the J-Matrix formalism allowing us to efficiently calculate hundreds of poles of the Z-transform. Evidence of a universal behaviour in the final statistical distribution of the associated poles and zeros of the Z-transform is shown. In particular the poles and zeros tend, when the length of the time series goes to infinity, to a uniform angular distribution on the unit circle. Therefore at finite order, the roots of unity in the complex plane appear to be noise attractors. We show that the Z-transform presents the exceptional feature of allowing lossless undersampling and how to make use of this property. A few basic examples are given to suggest the power of the proposed method.Comment: 14 pages, 8 figure

Parametrized tests of post-Newtonian theory using Advanced LIGO and Einstein Telescope

General relativity has very specific predictions for the gravitational waveforms from inspiralling compact binaries obtained using the post-Newtonian (PN) approximation. We investigate the extent to which the measurement of the PN coefficients, possible with the second generation gravitationalwave detectors such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and the third generation gravitational-wave detectors such as the Einstein Telescope (ET), could be used to test post-Newtonian theory and to put bounds on a subclass of parametrized-post-Einstein theories which differ from general relativity in a parametrized sense. We demonstrate this possibility by employing the best inspiralling waveform model for nonspinning compact binaries which is 3.5PN accurate in phase and 3PN in amplitude. Within the class of theories considered, Advanced LIGO can test the theory at 1.5PN and thus the leading tail term. Future observations of stellar mass black hole binaries by ET can test the consistency between the various PN coefficients in the gravitational-wave phasing over the mass range of 11-44 Msun. The choice of the lower frequency cut off is important for testing post-Newtonian theory using the ET. The bias in the test arising from the assumption of nonspinning binaries is indicated.Comment: 18 pages, 11 figures, Matches with the published versio

Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects

The Fisher-matrix formalism is used routinely in the literature on gravitational-wave detection to characterize the parameter-estimation performance of gravitational-wave measurements, given parametrized models of the waveforms, and assuming detector noise of known colored Gaussian distribution. Unfortunately, the Fisher matrix can be a poor predictor of the amount of information obtained from typical observations, especially for waveforms with several parameters and relatively low expected signal-to-noise ratios (SNR), or for waveforms depending weakly on one or more parameters, when their priors are not taken into proper consideration. In this paper I discuss these pitfalls; show how they occur, even for relatively strong signals, with a commonly used template family for binary-inspiral waveforms; and describe practical recipes to recognize them and cope with them. Specifically, I answer the following questions: (i) What is the significance of (quasi-)singular Fisher matrices, and how must we deal with them? (ii) When is it necessary to take into account prior probability distributions for the source parameters? (iii) When is the signal-to-noise ratio high enough to believe the Fisher-matrix result? In addition, I provide general expressions for the higher-order, beyond--Fisher-matrix terms in the 1/SNR expansions for the expected parameter accuracies.Comment: 24 pages, 3 figures, previously known as "A User Manual for the Fisher Information Matrix"; final, corrected PRD versio

Gravitational radiation in d>4 from effective field theory

Some years ago, a new powerful technique, known as the Classical Effective Field Theory, was proposed to describe classical phenomena in gravitational systems. Here we show how this approach can be useful to investigate theoretically important issues, such as gravitational radiation in any spacetime dimension. In particular, we derive for the first time the Einstein-Infeld-Hoffman Lagrangian and we compute Einstein's quadrupole formula for any number of flat spacetime dimensions.Comment: 32 pages, 10 figures. v2: Factor in eq. (3.11) fixed. References adde