The influence of Galactic aberration on precession parameters determined from VLBI observations

The influence of proper motions of sources due to Galactic aberration on precession models based on VLBI data is determined. Comparisons of the linear trends in the coordinates of the celestial pole obtained with and without taking into account Galactic aberration indicate that this effect can reach 20 $\mu$as per century, which is important for modern precession models. It is also shown that correcting for Galactic aberration influences the derived parameters of low-frequency nutation terms. It is therefore necessary to correct for Galactic aberration in the reduction of modern astrometric observations

Higher order approximation of isochrons

Phase reduction is a commonly used techinque for analyzing stable oscillators, particularly in studies concerning synchronization and phase lock of a network of oscillators. In a widely used numerical approach for obtaining phase reduction of a single oscillator, one needs to obtain the gradient of the phase function, which essentially provides a linear approximation of isochrons. In this paper, we extend the method for obtaining partial derivatives of the phase function to arbitrary order, providing higher order approximations of isochrons. In particular, our method in order 2 can be applied to the study of dynamics of a stable oscillator subjected to stochastic perturbations, a topic that will be discussed in a future paper. We use the Stuart-Landau oscillator to illustrate the method in order 2

Effect of physiological heart rate changes on left ventricular dimensions and mitral blood flow velocities in the normal fetus

M-mode echo recordings of the left ventricle (LV) and inflow LV Doppler velocimetry were performed in nine normal fetuses at a gestational age of 36–39 weeks. In each fetus ∼ 80 consecutive cardiac cycles were digitized. The duration of each cardiac cycle (T) and the corresponding end-diastolic (EDD), end-systolic (ESD) dimensions of LV or the peak velocity of early (E) and late atrial (A) mitral flow parameters was calculated. The role of sonographic parameters on current (Tn) and preceding (Tn − 1) cardiac cycles was assessed using linear regression. Significant dependency of ventricular EDD and transmitral A peak velocity upon Tn was demonstrated. We speculate that atrial systole has an important role to play in the beat-to-beat regulation of fetal stroke volume

Assessment of fetal left cardiac isovolumic relaxation time in appropriate and small-for-gestational-age fetuses

Left ventricular isovolumic relaxation time was studied in 22 appropriate-for-gestational-age fetuses (AGA, 26–40 wk) and 12 small-for-gestational-age fetuses (SGA, 29–37 wk). Left ventricular isovolumic relaxation time was determined from the interval between aortic valve closure and maximal left atrial dimension by M-mode, and from the interval between aortic valve closure artefact and onset of transmitral flow by pulsed Doppler. Mean left ventricular isovolumic relaxation time by M-mode (36 ± 6 ms) and by pulsed Doppler (49 ± 10 ms) were significantly different (p < 0.05) in AGA while this was not so in SGA (56 ± 10 ms vs. 60 ± 8 ms). A significant difference (p < 0.05) in mean left ventricular isovolumic relaxation time by M-mode existed between AGA (36 ± 6 ms) and SGA (56 ± 10 ms), whereas this was not so for pulsed Doppler (48 ± 10 ms vs. 60 ± 8 ms). Mean left ventricular isovolumic relaxation time by Doppler was significantly larger (mean difference 14 ± 8 ms; p < 0.05) than by M-mode in AGA. However, there was no difference in mean left ventricular isovolumic relaxation time between the two ultrasound modalities in SGA. These data suggest synchronization of mitral cusp separation and transmitral blood flow in the SGA fetus. We speculate that, in the SGA fetus, delayed left ventricular isovolumic relaxation time may reflect cardiac diastolic dysfunction

Evolution of squeezed states under the Fock-Darwin Hamiltonian

We develop a complete analytical description of the time evolution of squeezed states of a charged particle under the Fock-Darwin Hamiltonian and a time-dependent electric field. This result generalises a relation obtained by Infeld and Pleba\'nski for states of the one-dimensional harmonic oscillator. We relate the evolution of a state-vector subjected to squeezing to that of state which is not subjected to squeezing and for which the time-evolution under the simple harmonic oscillator dynamics is known (e.g. an eigenstate of the Hamiltonian). A corresponding relation is also established for the Wigner functions of the states, in view of their utility in the analysis of cold-ion experiments. In an appendix, we compute the response functions of the FD Hamiltonian to an external electric field, using the same techniques as in the main text

Supersymmetry of a Nonstationary Pauli Equation

The supersymmetry of the electron in both the nonstationary magnetic and electric fields in a two-dimensional case is studied. The supercharges which are the integrals of motion and their algebra are established. Using the obtained algebra the solutions of nonstationary Pauli equation are generated.Comment: 12 pages, Late

Money for Nothing and Privacy for Free?

Privacy in the context of ubiquitous social computing systems has become a major concern for the society at large. As the number of online social computing systems that collect user data grows, this privacy threat is further exacerbated. There has been some work (both, recent and older) on addressing these privacy concerns. These approaches typically require extra computational resources, which might be beneficial where privacy is concerned, but when dealing with Green Computing and sustainability, this is not a great option. Spending more computation time results in spending more energy and more resources that make the software system less sustainable. Ideally, what we would like are techniques for designing software systems that address these privacy concerns but which are also sustainable - systems where privacy could be achieved "for free," i.e., without having to spend extra computational effort. In this paper, we describe how privacy can be achieved for free - an accidental and beneficial side effect of doing some existing computation - and what types of privacy threats it can mitigate. More precisely, we describe a "Privacy for Free" design pattern and show its feasibility, sustainability, and utility in building complex social computing systems

Space-Time Complexity in Hamiltonian Dynamics

New notions of the complexity function C(epsilon;t,s) and entropy function S(epsilon;t,s) are introduced to describe systems with nonzero or zero Lyapunov exponents or systems that exhibit strong intermittent behavior with ``flights'', trappings, weak mixing, etc. The important part of the new notions is the first appearance of epsilon-separation of initially close trajectories. The complexity function is similar to the propagator p(t0,x0;t,x) with a replacement of x by the natural lengths s of trajectories, and its introduction does not assume of the space-time independence in the process of evolution of the system. A special stress is done on the choice of variables and the replacement t by eta=ln(t), s by xi=ln(s) makes it possible to consider time-algebraic and space-algebraic complexity and some mixed cases. It is shown that for typical cases the entropy function S(epsilon;xi,eta) possesses invariants (alpha,beta) that describe the fractal dimensions of the space-time structures of trajectories. The invariants (alpha,beta) can be linked to the transport properties of the system, from one side, and to the Riemann invariants for simple waves, from the other side. This analog provides a new meaning for the transport exponent mu that can be considered as the speed of a Riemann wave in the log-phase space of the log-space-time variables. Some other applications of new notions are considered and numerical examples are presented.Comment: 27 pages, 6 figure

High resolution infrared absorption spectra, crystal field, and relaxation processes in CsCdBr_3:Pr^3+

High resolution low-temperature absorption spectra of 0.2% Pr^3+ doped CsCdBr_3 were measured in the spectral region 2000--7000 cm-1. Positions and widths of the crystal field levels within the 3H5, 3H4, 3F2, and 3F3 multiplets of the Pr^3+ main center have been determined. Hyperfine structure of several spectral lines has been found. Crystal field calculations were carried out in the framework of the semiphenomenological exchange charge model (ECM). Parameters of the ECM were determined by fitting to the measured total splittings of the 3H4 and 3H6 multiplets and to the observed in this work hyperfine splittings of the crystal field levels. One- and two-phonon relaxation rates were calculated using the phonon Green's functions of the perfect (CsCdBr_3) and locally perturbed (impurity dimer centers in CsCdBr_3:Pr^3+) crystal lattice. Comparison with the measured linewidths confirmed an essential redistribution of the phonon density of states in CsCdBr_3 crystals doped with rare-earth ions.Comment: 16 pages, 5 tables, 3 figure